# Penemu gravity

For a more accessible and less technical introduction to this topic, see Introduction to M-theory. String theory Fundamental objects • String • Cosmic string • Brane • D-brane Perturbative theory • Bosonic • Penemu gravity ( Type I, Type II, Heterotic) Non-perturbative results • S-duality • T-duality • U-duality • M-theory • F-theory • AdS/CFT correspondence Phenomenology • Phenomenology • Cosmology • Landscape Mathematics • Mirror symmetry • Monstrous moonshine • v • t • e In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings.

String theory describes how these strings propagate through space and interact with each other. On distance scales larger than the string scale, a string looks just like an ordinary particle, with its mass, charge, and other properties determined by the vibrational state of the string. In string theory, one of the many vibrational states of the string corresponds to the graviton, a quantum mechanical particle that carries the gravitational force.

Thus, string theory is a theory of quantum gravity. String theory is a broad and varied subject that attempts to address a number of deep questions of fundamental physics. String theory has contributed a number of advances to mathematical physics, which have been applied to a variety of problems in black hole physics, early universe cosmology, nuclear physics, and condensed matter physics, and it has stimulated a number of major developments in penemu gravity mathematics.

Because string theory potentially provides a unified description of penemu gravity and particle physics, it is a candidate for a theory of everything, a self-contained mathematical model that describes all fundamental forces and forms of matter. Despite much work on these problems, it is not known to what extent string theory describes the real world or how much freedom the theory allows in the choice of its details. String theory was first studied in the late 1960s as a theory of the strong nuclear force, before being abandoned in favor of quantum chromodynamics.

Subsequently, it was realized that the very properties that made string theory unsuitable as a theory of nuclear physics made it a promising candidate for a quantum theory of gravity. The earliest version of string theory, bosonic string theory, incorporated only the class of particles known as bosons. It later developed into superstring theory, which posits a connection called supersymmetry between bosons and the class of particles called fermions.

Five consistent versions of superstring theory were developed before it was conjectured in the mid-1990s that they were all different limiting cases of a single theory in 11 dimensions known as M-theory. In late 1997, theorists discovered an important relationship called the anti-de Sitter/conformal field theory correspondence (AdS/CFT correspondence), which relates string theory to another type of physical theory called a quantum field theory.

One of the challenges of string theory is that the penemu gravity theory does not have a satisfactory definition in all circumstances.

Another issue is that the theory is thought to describe an enormous landscape of possible universes, which has complicated efforts to develop theories of particle physics based on string theory.

These issues have led some in the community to criticize penemu gravity approaches to physics, and to question the value of continued research on string theory unification. Contents • 1 Fundamentals • 1.1 Overview • 1.2 Strings • 1.3 Extra dimensions • 1.4 Dualities • penemu gravity Branes • 2 M-theory • 2.1 Unification of superstring theories • 2.2 Matrix theory • 3 Black holes • 3.1 Bekenstein–Hawking formula • 3.2 Derivation within string theory • 4 AdS/CFT correspondence • 4.1 Overview of the correspondence • 4.2 Applications to quantum gravity • 4.3 Applications to nuclear physics • 4.4 Applications to condensed matter physics • 5 Phenomenology • 5.1 Particle physics • 5.2 Cosmology • 6 Connections to mathematics • 6.1 Mirror symmetry • 6.2 Monstrous moonshine • 7 History • 7.1 Early results • 7.2 First superstring revolution • 7.3 Second superstring revolution • 8 Criticism • 8.1 Number of solutions • 8.2 Compatibility with dark energy • 8.3 Background independence • 8.4 Sociology of science • 9 Notes • 10 References • 10.1 Bibliography • 11 Further reading • 11.1 Popular science • 11.2 Textbooks • 12 External links Fundamentals The fundamental objects of penemu gravity theory are open and closed strings.

Overview In the 20th century, two theoretical frameworks emerged for formulating the laws of physics. The first is Albert Einstein's general theory of relativity, a theory that explains the force of gravity and the structure of spacetime at the macro-level.

The other is quantum mechanics, a completely different formulation, which uses known probability principles to describe physical phenomena at penemu gravity micro-level. By the late 1970s, these two frameworks had proven to be sufficient to explain most of the observed features of the universe, from elementary particles to atoms to the penemu gravity of stars and the universe as a whole. [1] In spite of these successes, there are still many problems that remain to be solved.

One of the deepest problems in modern physics is the problem of quantum gravity. [1] The general theory of relativity is formulated within the framework of classical physics, whereas the other fundamental forces are described within the framework of quantum mechanics.

A quantum theory of gravity is needed in order to reconcile general relativity with the principles of quantum mechanics, but difficulties arise when one attempts to apply the usual prescriptions of quantum theory to the force of gravity. penemu gravity In addition to the problem of developing a consistent theory of quantum gravity, there are many other fundamental problems in the physics of atomic nuclei, black holes, and the early universe. [a] String theory is a theoretical framework that attempts to address these questions and many others.

The starting point for string theory is the idea that the point-like particles of particle physics can also be modeled as one-dimensional objects called strings. String theory describes how strings propagate through space and interact with each other. In a given version of string theory, there is only one kind of string, which may look like a small loop or segment of ordinary string, and it can vibrate in different ways.

On distance scales penemu gravity than the string scale, a string will look just like an ordinary particle, with its mass, charge, and other properties determined by the vibrational state penemu gravity the string. In this way, all of the different elementary particles may be viewed as vibrating strings. In string theory, one of the vibrational states of the string gives rise to the graviton, a quantum mechanical particle that carries gravitational force.

Thus string theory is a theory of quantum gravity. [3] One of the main developments of the past several decades in string theory was the discovery of certain 'dualities', mathematical transformations that identify one physical theory with another.

Physicists studying string theory have discovered a number of these dualities between different versions of string theory, and this has led to the penemu gravity that all consistent versions of string theory are subsumed in a single framework known as M-theory. [4] Studies of string theory have also yielded a number of results on the nature of black holes and the gravitational interaction. There are certain paradoxes that arise when one attempts to understand the quantum aspects of black holes, and work on string theory has attempted to clarify penemu gravity issues.

In late 1997 this line of work culminated in the discovery of the anti-de Sitter/conformal field theory correspondence or AdS/CFT. [5] This is a theoretical result that relates string theory to other physical theories which are better understood theoretically. The AdS/CFT correspondence has implications for the study of black holes and quantum gravity, and it has been applied to other subjects, including nuclear [6] and condensed matter physics. [7] [8] Since penemu gravity theory incorporates all of the fundamental interactions, including gravity, many physicists hope that it will eventually be developed to the point where it fully describes our universe, making it a theory of everything.

One of the goals of current research in string theory is to find a solution of the theory that reproduces the observed spectrum of elementary particles, with a small cosmological constant, containing dark matter and a plausible mechanism for cosmic inflation. While there has been progress toward these goals, it is not known to what extent string theory describes the real world or how much freedom the theory allows in the choice of details.

[9] One of the challenges of string theory is that the full theory does not have a satisfactory definition in all circumstances. The scattering of strings is most straightforwardly defined using the techniques of perturbation theory, but it is not known in general how to define string theory nonperturbatively. [10] It is also not clear whether there is any principle by which string theory selects its vacuum state, the physical state that determines the properties of our universe.

[11] These problems have led some in the community to criticize these approaches to penemu gravity unification of physics and question the value of continued research on these problems. [12] Strings Interaction in the quantum world: worldlines of point-like particles or a worldsheet swept up by closed strings in string theory. The application of quantum mechanics to physical objects such as the electromagnetic field, which are extended in space and time, is known as quantum field theory.

In particle physics, quantum field theories form the basis for our understanding of elementary particles, which are modeled as excitations in the fundamental fields. [13] In quantum field theory, one typically computes the probabilities of various physical events using the techniques of perturbation theory. Developed by Richard Feynman and others in the first half of the twentieth century, perturbative quantum field theory uses special diagrams called Feynman diagrams to organize computations.

One imagines that these diagrams depict the paths of point-like particles and their interactions. [13] The starting point for string theory is the idea that the point-like particles of quantum field theory can also be modeled as one-dimensional objects called strings.

[14] The interaction of strings is most straightforwardly defined by generalizing the perturbation theory used in ordinary quantum field theory. At the level of Feynman diagrams, this means replacing the one-dimensional diagram representing the path of a point particle by a two-dimensional (2D) surface representing the motion of a string.

[15] Unlike in quantum field theory, penemu gravity theory does not have a full non-perturbative definition, so many of the theoretical questions that physicists would like to answer remain out of reach. [16] In theories of particle physics based on string theory, the characteristic length scale of strings is assumed to be on the order of the Planck length, or 10 −35 meters, the scale at which the effects of quantum gravity are believed to become significant.

[15] On much larger length scales, such as the scales visible in physics laboratories, such objects would be indistinguishable from zero-dimensional point particles, and the vibrational state of the string would determine the type of particle. One of the penemu gravity states of a string corresponds to the graviton, a quantum mechanical particle that carries the gravitational force.

[3] The original version of string theory was bosonic string theory, but this version described only bosons, a class of particles that transmit forces between the matter particles, or fermions. Bosonic string theory was eventually superseded by theories called superstring theories.

These theories describe both bosons and fermions, and they incorporate a theoretical idea called supersymmetry.

In theories with supersymmetry, each boson has a counterpart which is a fermion, and vice versa. [17] There are several versions of superstring theory: type I, type IIA, type IIB, and two flavors of heterotic string theory ( SO(32) and E 8× E 8). The different theories allow different types of strings, and the particles that arise at low energies exhibit different symmetries.

For example, the type I theory includes both open strings (which are segments with endpoints) and closed strings (which form closed loops), while types IIA, IIB and heterotic include only closed strings. [18] Extra dimensions An example of compactification: At large distances, a two dimensional surface with one circular dimension looks one-dimensional.

Penemu gravity everyday life, there are three familiar dimensions (3D) of space: height, width and length. Einstein's general theory of relativity treats time as a dimension on par with the three spatial dimensions; in general relativity, space and time are not modeled as separate entities but are instead unified to a four-dimensional (4D) spacetime. In this framework, the phenomenon of gravity is viewed as a consequence of the geometry of spacetime.

[19] In spite of the fact that the Universe is well described by 4D spacetime, there are several reasons why physicists consider theories in other dimensions.

In some cases, by modeling spacetime in a different number of dimensions, a theory becomes more mathematically tractable, and one can perform calculations and gain general insights more easily. [b] There are also situations where theories in two or three spacetime dimensions are useful for describing phenomena in condensed matter physics. [13] Finally, there exist scenarios in which there could actually be more than 4D of spacetime which have nonetheless managed to escape detection.

[20] String theories require extra dimensions of spacetime for their mathematical consistency. In bosonic string theory, spacetime is 26-dimensional, while in superstring theory it is 10-dimensional, and in M-theory it is 11-dimensional. In order to describe real physical phenomena using string theory, one must therefore imagine scenarios in which these extra dimensions would not be observed in experiments.

[21] A cross section of a quintic Calabi–Yau manifold Compactification is one way of modifying the number of dimensions in a physical theory.

In compactification, some of the extra dimensions are assumed to "close up" on themselves to form circles. [22] In the limit where these curled up dimensions become very small, one obtains a theory in which spacetime has effectively a lower number of dimensions.

A standard analogy for this is to consider a multidimensional object such penemu gravity a garden hose. If the hose is viewed from a sufficient distance, it appears to have only one dimension, its length. However, as one approaches the hose, one discovers that it contains a second dimension, its circumference. Thus, an ant crawling on the surface of the hose would move in two dimensions. Compactification can be used to construct models in which spacetime is penemu gravity four-dimensional.

However, not penemu gravity way of compactifying the extra dimensions produces a model with the right properties to describe nature. In a viable model of particle physics, the compact extra dimensions must be shaped like a Calabi–Yau manifold. [22] A Calabi–Yau manifold is a special space which is typically taken to be six-dimensional in applications to string theory. It is named after mathematicians Eugenio Calabi and Shing-Tung Yau. [23] Another approach to reducing the number of dimensions is the so-called brane-world scenario.

In this approach, physicists assume that the observable universe is a four-dimensional subspace of a higher dimensional space. In such models, the force-carrying bosons of particle physics arise from open strings with endpoints attached to the four-dimensional subspace, while gravity arises from closed strings propagating through the larger ambient space.

This idea plays an important role in attempts to develop models of real-world physics based on string theory, and it provides a natural explanation for the weakness of gravity compared to the other fundamental forces. [24] Dualities Main articles: S-duality and T-duality A notable fact about string theory is that the different versions of the theory all turn out to be related in highly nontrivial ways.

One of the relationships that can exist between different string theories is called S-duality. This is a relationship that says that a collection of strongly interacting particles in one theory can, in some cases, be viewed as a collection of weakly interacting particles in a completely different theory. Roughly speaking, a collection of particles is said to be strongly interacting if they combine and decay often and weakly interacting if they do so infrequently.

Type I string theory turns out to be equivalent by S-duality to the SO(32) heterotic string theory. Similarly, type IIB string theory is related to itself in a nontrivial way by S-duality. [25] Another relationship penemu gravity different string theories is T-duality. Here one considers strings propagating around a circular extra dimension. T-duality states that a string propagating around a circle of radius R is equivalent to a string propagating around a circle of radius 1/ R in the sense that all observable quantities in one description are identified with quantities in the dual description.

For example, a string has momentum as it propagates around a circle, and it can also wind around the circle one or more times. The number of times the string winds around a circle is called the winding number. If a string has momentum p and winding number n in one description, it will have momentum n and winding number p in the dual description. For example, type IIA string theory is equivalent to type IIB string theory via T-duality, and the two versions of heterotic string theory are also related by T-duality.

[25] In general, the term duality refers penemu gravity a situation where two seemingly different physical systems turn out to be equivalent in a nontrivial way. Two theories related by a duality need not be string theories. For example, Montonen–Olive duality is an example of an S-duality relationship between quantum field theories. The AdS/CFT correspondence is an example of a duality that relates string theory to a quantum field theory. If two theories are related by a duality, it means that one theory can be transformed in some way so that it ends penemu gravity looking just like the other theory.

The two theories are then said to be dual to one another under the transformation. Put differently, the two theories are mathematically different descriptions of the same phenomena. [26] Branes Open strings attached to a pair of D-branes. In string theory penemu gravity other related theories, a brane is a physical object that generalizes the notion of a point particle to higher dimensions.

For instance, a point particle can be viewed as a brane of dimension zero, while a string can be viewed as a brane of dimension one. It is also possible to consider higher-dimensional branes. In dimension p, these are called p-branes. The word brane comes from the word "membrane" which refers to a two-dimensional brane.

[27] Branes are dynamical objects which can propagate through spacetime according to the rules of quantum mechanics. They have mass and can have other attributes such as charge. A p-brane sweeps out a ( p+1)-dimensional volume in spacetime penemu gravity its worldvolume.

Physicists often study fields analogous to the electromagnetic field which live on the worldvolume of a brane. [27] In string theory, D-branes are an important class of branes that arise when one considers open strings. As an open string penemu gravity through spacetime, its endpoints are required to lie on a D-brane. The letter "D" in D-brane refers to a certain mathematical condition on the system known penemu gravity the Dirichlet boundary condition.

The study of D-branes in string theory has led to important results such as the AdS/CFT correspondence, which has shed light on many problems in quantum field theory. [27] Branes are frequently studied from a purely mathematical point of view, and they are described as objects of certain categories, such as the derived category of coherent sheaves on a complex algebraic variety, or the Fukaya category of a symplectic manifold.

[28] The connection between the physical notion of a brane and the mathematical notion of a category has led to important mathematical insights in the fields of algebraic and symplectic geometry [29] and representation theory. [30] M-theory Main article: M-theory Prior to 1995, theorists believed that there were five consistent versions of superstring theory (type I, type IIA, type IIB, and two versions of heterotic string theory). This understanding penemu gravity in 1995 when Edward Witten suggested that the five theories were just special limiting cases of an eleven-dimensional theory called M-theory.

Witten's conjecture was based on the work of a number of other physicists, including Ashoke Sen, Chris Hull, Paul Townsend, and Michael Duff. His announcement led to a flurry of research activity now known as the second superstring revolution. [31] Unification of superstring theories A schematic illustration of the relationship between M-theory, the five superstring theories, and eleven-dimensional supergravity.

The shaded region represents a family of different physical scenarios that are possible in M-theory. In certain limiting cases corresponding to the cusps, it is natural to describe the physics using one of the six theories labeled there.

In the 1970s, many physicists became interested in supergravity theories, which combine general relativity with supersymmetry. Whereas general relativity makes sense in any number of dimensions, supergravity places an upper limit on the number of dimensions. [32] In 1978, work by Werner Nahm showed that the maximum spacetime dimension in which one can formulate a consistent supersymmetric theory is eleven.

[33] In the same year, Eugene Cremmer, Bernard Julia, and Joël Scherk of the École Normale Supérieure showed that supergravity not only permits up to eleven dimensions but is in fact most elegant in this maximal number of dimensions. [34] [35] Initially, many physicists hoped that by compactifying eleven-dimensional supergravity, it might be possible to construct realistic models of our four-dimensional world.

The hope was that such models would provide a unified description of the four fundamental forces of nature: electromagnetism, the strong and weak nuclear forces, and gravity. Interest in eleven-dimensional supergravity soon waned as various flaws in this scheme were discovered. One of the problems was that the laws of physics appear to distinguish between clockwise and counterclockwise, a phenomenon known as chirality.

Edward Witten and others observed this chirality property cannot be readily derived by compactifying from eleven dimensions. [35] In the first superstring revolution in 1984, many physicists turned to string theory as a unified theory of particle physics and quantum gravity. Unlike supergravity theory, string theory was able to accommodate the chirality of the standard model, and it provided a theory of gravity consistent with quantum effects. [35] Another feature of string theory that many physicists were drawn to in the penemu gravity and 1990s was its high degree of uniqueness.

In ordinary particle theories, one can consider any collection of elementary particles whose classical behavior is described by an arbitrary Lagrangian. In string theory, the possibilities are much more constrained: by the 1990s, physicists had argued that there were only five consistent supersymmetric versions of the theory.

[35] Although there were only a handful of consistent superstring theories, it remained a mystery why there was not just one consistent formulation.

[35] However, as physicists began to examine string theory more closely, they realized that these theories are related in intricate and nontrivial ways. They found that a system of strongly interacting strings can, in some cases, be viewed as a system of weakly interacting strings. This phenomenon is known as S-duality. It was studied by Ashoke Sen in the context of heterotic strings in four dimensions [36] [37] and by Chris Hull and Paul Townsend in the context of the type IIB theory.

[38] Theorists also found that different string theories may be related by T-duality. This duality implies that strings propagating on completely different spacetime geometries may be physically equivalent.

penemu gravity At around the same time, as many physicists were studying the properties of strings, a small group of physicists were examining the possible applications of higher dimensional objects.

In 1987, Eric Bergshoeff, Ergin Sezgin, and Paul Townsend showed that eleven-dimensional supergravity includes two-dimensional branes.

[40] Intuitively, these objects look like sheets or membranes propagating through the eleven-dimensional spacetime. Shortly after this discovery, Michael Penemu gravity, Paul Howe, Takeo Inami, and Kellogg Stelle considered a particular compactification of eleven-dimensional supergravity with one of the dimensions curled up into a circle. [41] In this setting, one can imagine the membrane wrapping penemu gravity the circular dimension.

If the radius of the circle is sufficiently small, then this membrane looks just like a string in ten-dimensional spacetime. Duff and his collaborators showed that this construction reproduces exactly the strings appearing in type IIA superstring theory. [42] Speaking at a string theory conference in 1995, Edward Witten made the surprising suggestion that all five superstring theories were in fact just different limiting cases of a single theory in eleven spacetime dimensions.

Witten's announcement drew together all of the previous results on S- and T-duality and the appearance of higher-dimensional branes in string theory. [43] In penemu gravity months following Witten's announcement, hundreds of new papers appeared on penemu gravity Internet confirming different parts of his proposal.

[44] Today this flurry penemu gravity work is known as the second superstring revolution. [45] Initially, some physicists suggested that the new theory was a fundamental theory of membranes, but Witten was skeptical of the role of membranes in the theory. In a paper from 1996, Hořava and Witten wrote "As it has been proposed that the eleven-dimensional theory is a supermembrane theory but there are some reasons to doubt that interpretation, we will non-committally call it the M-theory, leaving to the future the relation of M to membranes." [46] In the absence of an understanding of the true meaning and structure of M-theory, Witten has suggested that the M should stand for "magic", "mystery", or "membrane" according to taste, and the true meaning of the title should be decided when a more fundamental formulation of the theory is known.

[47] Matrix theory Main article: Matrix theory (physics) In mathematics, a matrix is a rectangular array of numbers or other data. In physics, a matrix model is a particular kind of physical theory whose mathematical formulation involves the notion of a matrix in an important way.

A matrix model describes the behavior of a set of matrices within the framework of quantum mechanics. [48] One important example of a matrix model is the BFSS matrix model proposed by Tom Banks, Willy Fischler, Stephen Shenker, and Leonard Susskind in 1997. This theory describes the behavior of a set of nine large matrices.

In their original paper, these authors showed, among other things, that the low energy limit of this matrix model is described by eleven-dimensional supergravity. These calculations led them to propose that the BFSS matrix model is exactly equivalent to M-theory. The BFSS matrix model can therefore be used as a prototype for a correct formulation penemu gravity M-theory and a tool for investigating the properties of M-theory in a relatively simple setting.

[48] The development of the matrix model formulation of M-theory has led physicists to penemu gravity various connections between string theory and a branch of mathematics called noncommutative geometry. This subject is a generalization of ordinary geometry in which mathematicians define new geometric notions using tools from noncommutative algebra.

[49] In a paper from 1998, Alain Connes, Michael R. Douglas, and Albert Schwarz showed that some aspects of matrix models and M-theory are described by a noncommutative quantum field theory, a special kind of physical theory in which spacetime is described mathematically using noncommutative geometry.

[50] This established a link between matrix models and M-theory on the one hand, and noncommutative geometry on the other hand. It quickly led to the discovery of other important links between noncommutative geometry and various physical theories. [51] [52] Black holes In general relativity, a black hole is defined as a region of spacetime in which the gravitational field is so strong that no particle or radiation can escape. In the currently accepted models of stellar evolution, black holes are thought to arise when massive stars undergo gravitational collapse, and many galaxies are thought to contain supermassive black holes at their centers.

Penemu gravity holes are also important for theoretical reasons, as they present profound challenges for theorists attempting to understand the quantum aspects of gravity. String theory has proved to be an important tool for investigating the theoretical properties of black holes because it provides a framework in which theorists can study their thermodynamics.

[53] Bekenstein–Hawking formula In the branch of physics called statistical mechanics, entropy is a measure of the randomness or disorder of a physical system.

This concept was studied in the 1870s by the Austrian physicist Ludwig Boltzmann, who showed that the thermodynamic properties of a gas could be derived from the combined properties of its many constituent molecules. Boltzmann argued that by averaging the behaviors of all the different molecules in a gas, one can understand macroscopic properties such as volume, temperature, and pressure. In addition, this perspective led him to give a precise definition of entropy as the natural logarithm of the number of different states of the molecules (also called microstates) that give rise to the same macroscopic features.

[54] In the twentieth century, physicists began to apply the same concepts to black holes. In most systems such as gases, the entropy scales with the volume.

In the 1970s, the physicist Jacob Bekenstein suggested that the entropy of a black hole is instead proportional penemu gravity the surface area of its event horizon, the boundary beyond which matter and radiation are lost to its gravitational attraction. [55] When combined with ideas of the physicist Stephen Hawking, [56] Bekenstein's work yielded a precise formula for the entropy of a black hole. The Bekenstein–Hawking formula expresses the entropy Penemu gravity as S = c 3 k A 4 ℏ G {\displaystyle S={\frac {c^{3}kA}{4\hbar G}}} where c is the speed of light, k is Boltzmann's constant, ħ is the reduced Planck constant, G is Newton's constant, and A is the surface area of the event horizon.

penemu gravity Like any physical system, a black hole has an entropy defined in terms of the number of different microstates that lead to the same macroscopic features. The Bekenstein–Hawking entropy formula gives the expected value of the entropy of a black hole, but by the 1990s, physicists still lacked a derivation of this formula by counting microstates in a theory of quantum gravity.

Finding such a derivation of this formula was considered an important test of the viability of any theory of quantum gravity such as string theory. [58] Derivation within string theory In a paper from 1996, Andrew Strominger and Cumrun Vafa showed how to derive the Beckenstein–Hawking formula for certain black holes in string penemu gravity. [59] Their calculation was based penemu gravity the observation that D-branes—which look like fluctuating membranes when they are weakly interacting—become dense, massive objects with event horizons when the interactions are strong.

In other words, a system of strongly interacting D-branes in string theory is indistinguishable from a black hole. Strominger and Vafa analyzed such D-brane systems and calculated the number of different ways of placing D-branes in spacetime so that their combined mass and charge is equal to a given mass and charge for the resulting black hole. Their calculation reproduced the Bekenstein–Hawking formula exactly, including the factor of 1/4.

[60] Subsequent work by Strominger, Vafa, and others refined the original calculations and gave the precise values of the "quantum corrections" needed to describe very small black holes. [61] [62] The black holes that Strominger and Vafa considered in their original work were quite different from real astrophysical black holes.

One difference was that Strominger and Vafa considered only extremal black holes in order to make the calculation tractable. These are defined as black holes with the lowest possible mass compatible with a given charge. [63] Strominger and Vafa also restricted attention to black holes in five-dimensional spacetime with unphysical supersymmetry.

[64] Although it was originally developed in this very particular penemu gravity physically unrealistic context in string theory, the entropy calculation of Strominger and Vafa has led to a qualitative understanding of how black hole entropy can be accounted for in any theory of quantum gravity. Indeed, in 1998, Strominger argued that the original result could be generalized to an arbitrary consistent theory of quantum gravity without relying on strings penemu gravity supersymmetry.

[65] In collaboration with several penemu gravity authors in 2010, he showed that some results on black hole entropy could be extended to non-extremal astrophysical black holes. [66] [67] AdS/CFT correspondence Main article: AdS/CFT correspondence One approach to formulating string theory and studying its properties is provided by the anti-de Sitter/conformal field theory (AdS/CFT) correspondence.

This is a theoretical result which implies that string theory is in some penemu gravity equivalent to a quantum field theory. In addition to providing insights into the mathematical structure of string theory, the AdS/CFT correspondence has shed light on many aspects of quantum field theory in regimes where traditional calculational techniques are ineffective. [6] The AdS/CFT correspondence was first proposed by Juan Maldacena in late 1997.

[68] Important aspects of the correspondence were elaborated in articles by Steven Gubser, Igor Klebanov, and Alexander Markovich Polyakov, [69] and by Edward Witten. [70] By 2010, Maldacena's article had over 7000 citations, becoming the most highly cited article in the field of high energy physics. [c] Overview of the correspondence A tessellation of the hyperbolic plane by triangles and squares In the AdS/CFT correspondence, the geometry of spacetime is described in terms of a certain vacuum solution of Einstein's equation called anti-de Sitter space.

[6] In very elementary terms, anti-de Sitter space is a mathematical model of spacetime in which the notion of distance between points (the metric) is different from the notion of distance in ordinary Euclidean geometry. It is closely related to hyperbolic space, which can be viewed as a disk as illustrated penemu gravity the penemu gravity.

[71] This image shows a tessellation of a disk by triangles and squares. One can define the distance between points of this disk in such a way that all the triangles and squares are the same size and the circular outer boundary is infinitely far from any point in the interior.

[72] One can imagine a stack of hyperbolic disks where each disk represents the state of the universe at a given time. The resulting geometric object is three-dimensional anti-de Sitter space. [71] It looks like a solid cylinder in which any cross section is a copy of the hyperbolic disk. Time runs along the vertical direction in this picture. The surface of this cylinder plays an important role in the AdS/CFT correspondence. As with the hyperbolic plane, anti-de Sitter space is curved in such a way that any point in the interior is actually infinitely far from this boundary surface.

[72] Three-dimensional anti-de Sitter space is like a stack of hyperbolic disks, each one representing the state of the universe at a given time. The resulting spacetime looks like a solid cylinder.

This construction describes a hypothetical universe with only two space dimensions and one time dimension, but penemu gravity can be generalized to any number of dimensions. Indeed, hyperbolic space can have more than two dimensions and one can "stack up" copies of hyperbolic space to get higher-dimensional penemu gravity of anti-de Sitter space. [71] An important feature of anti-de Sitter space is its boundary (which looks like a cylinder in the case of three-dimensional anti-de Sitter space).

One property of this boundary is that, within a small region on the surface around any given point, it looks just like Minkowski space, the model of spacetime penemu gravity in nongravitational physics. [73] One can therefore consider an auxiliary theory in which "spacetime" is given by the boundary of anti-de Sitter space. This observation is the starting point for AdS/CFT correspondence, which states that the boundary of anti-de Sitter space can be regarded as the "spacetime" for a quantum field theory.

The claim is that this quantum field theory is equivalent to a gravitational theory, such as string theory, in the bulk anti-de Sitter space in the sense that there is a "dictionary" for translating entities and calculations in one theory into their counterparts in the other theory.

For example, a single particle in the gravitational theory might correspond to some collection of particles in the boundary theory. In addition, the predictions in the two theories are quantitatively identical so that if two particles have a 40 percent chance of colliding in the gravitational theory, then the corresponding collections in the boundary theory would also have a 40 percent chance of colliding.

[74] Applications to quantum gravity The discovery of the AdS/CFT correspondence was a major advance in physicists' understanding of string theory and quantum gravity. One reason for this is that the correspondence provides a formulation of string theory in terms of quantum field theory, which is well understood by comparison.

Another reason is that it provides a general framework in which physicists can study and attempt to resolve the paradoxes of black holes. [53] In 1975, Stephen Hawking published a penemu gravity which suggested that black holes are not completely black but emit penemu gravity dim radiation due to quantum effects near the event horizon. [56] At first, Hawking's result posed a problem penemu gravity theorists because it suggested that black holes destroy information.

More precisely, Hawking's calculation seemed to conflict with one of the basic postulates of quantum mechanics, which states that physical systems evolve in time according to the Schrödinger equation.

This property is usually referred to as unitarity of time evolution. The apparent contradiction between Hawking's calculation and the unitarity postulate of quantum mechanics came to be known as the black hole information paradox. [75] The AdS/CFT correspondence resolves the black hole information paradox, at least to some extent, because it shows how a black hole can evolve in a manner consistent with quantum mechanics in some contexts.

Indeed, one can consider black holes in the context of the AdS/CFT correspondence, and any such black hole corresponds to a configuration of particles on the boundary of anti-de Sitter space. [76] These particles obey the usual rules of quantum mechanics and in particular evolve in a unitary fashion, so the black hole must also evolve in penemu gravity unitary fashion, respecting the principles of quantum mechanics.

[77] In 2005, Hawking announced that the paradox had been settled in favor of information conservation by the AdS/CFT correspondence, and he suggested a concrete mechanism by which black holes might preserve information. [78] Applications to nuclear physics A magnet levitating above a high-temperature superconductor. Today some physicists are working to understand high-temperature superconductivity using the AdS/CFT correspondence. [7] In addition to its applications to theoretical problems in quantum gravity, the AdS/CFT correspondence has been applied to a variety of problems in quantum field theory.

One physical system that has been penemu gravity using the AdS/CFT correspondence is the quark–gluon plasma, an exotic state of matter produced in particle accelerators. This state of matter arises for brief instants when heavy ions such as gold or lead nuclei are collided at high energies.

Such collisions cause the quarks that make up atomic nuclei to deconfine at temperatures of approximately two trillion kelvin, conditions similar to those present at around 10 −11 seconds after the Big Bang. [79] The physics of the quark–gluon plasma is governed by a theory called quantum chromodynamics, but this theory is mathematically intractable in problems involving the quark–gluon plasma.

[d] In an article appearing in 2005, Đàm Thanh Sơn and his collaborators showed that the AdS/CFT correspondence could penemu gravity used to penemu gravity some aspects of the quark-gluon plasma by describing it in the language of string theory.

[80] By applying the AdS/CFT correspondence, Sơn and his collaborators were able to penemu gravity the quark-gluon plasma in terms of black holes in five-dimensional spacetime. The calculation showed that the ratio of two quantities associated with the quark-gluon plasma, the shear viscosity and volume density of entropy, should be approximately equal to a certain universal constant.

In 2008, the predicted value of this ratio for the quark-gluon plasma was confirmed at the Relativistic Heavy Ion Collider penemu gravity Brookhaven National Laboratory. [7] [81] Applications to condensed matter physics Main article: AdS/CMT correspondence The AdS/CFT correspondence has also been used to study aspects of condensed matter physics.

Over the decades, experimental condensed matter physicists have discovered a number of exotic states of matter, including superconductors and superfluids. These states are described using the formalism of quantum field theory, but some phenomena are difficult to explain using standard field theoretic techniques. Some condensed matter theorists including Subir Sachdev hope that the AdS/CFT correspondence will make it possible to describe these systems in the language of string theory and learn more about their behavior.

[7] So far some success has been achieved in using string theory methods to describe the transition of a superfluid to an insulator. A superfluid is a system of electrically neutral atoms that flows without any friction. Such systems are often produced in the laboratory using liquid helium, but recently experimentalists have developed new ways of producing artificial superfluids by pouring trillions of cold atoms into a lattice of criss-crossing lasers.

These atoms initially behave as a superfluid, but as experimentalists increase the intensity of the lasers, they become less mobile and then suddenly transition to an insulating state. During the transition, the atoms behave in an unusual way. For example, the atoms slow to a halt at a rate that depends on the temperature and on Planck's constant, the fundamental parameter of quantum mechanics, which does not enter into the description of the other phases.

This behavior has recently been understood by considering a dual description where properties of the fluid are described in terms of a higher dimensional black hole. [8] Phenomenology Main article: String phenomenology In addition to being an idea of considerable theoretical interest, string theory provides a framework for constructing models of real-world physics that combine general relativity and particle physics.

Phenomenology is the branch of theoretical physics in which physicists construct realistic models of nature from more abstract theoretical ideas. String phenomenology is the part of string theory that attempts to construct realistic or semi-realistic models based on string theory.

Partly because of theoretical and mathematical difficulties and partly because of the extremely high energies needed to test these theories experimentally, there is so far no experimental evidence that would unambiguously point to any of these models being a correct fundamental description of nature. This has led some in the community to criticize these approaches to unification and question the value of continued research on these problems. [12] Particle physics Penemu gravity currently accepted theory describing elementary particles and their interactions is known as the standard model of particle physics.

This theory provides a unified description of three of the fundamental forces of nature: electromagnetism and the strong and weak nuclear forces. Despite its remarkable success in explaining a wide range penemu gravity physical phenomena, the standard model cannot be a penemu gravity description of reality. This is because the standard model fails to incorporate the force of gravity and because of problems such as the hierarchy problem and the inability to explain the structure of fermion masses or dark matter.

String theory has penemu gravity used to construct a variety of models of particle physics going beyond the standard model. Typically, such models are based on the idea of compactification. Starting with the ten- or eleven-dimensional spacetime of string or M-theory, physicists postulate a shape for the extra dimensions.

By choosing this shape appropriately, they can construct models roughly similar to the standard model of particle physics, together with additional undiscovered particles. [82] One popular way of deriving penemu gravity physics from string theory is to start with the heterotic theory in ten dimensions and assume that the six extra dimensions of spacetime are shaped like a six-dimensional Calabi–Yau manifold. Such compactifications offer many ways of extracting realistic physics from string theory.

Other similar methods can be used to construct realistic or semi-realistic models of our four-dimensional penemu gravity based on M-theory. [83] Cosmology A map of the cosmic microwave background produced by the Wilkinson Microwave Anisotropy Probe The Big Bang theory is the prevailing cosmological model for the universe from the earliest known periods through its subsequent large-scale evolution.

Despite its success in explaining many observed features of the universe including galactic redshifts, the relative abundance of light elements penemu gravity as hydrogen and helium, and the existence of a cosmic microwave background, there are several questions that remain unanswered. For example, the standard Big Bang model does not explain why the universe appears to be the same in all directions, why it appears flat on very large distance scales, or why certain hypothesized penemu gravity such as magnetic monopoles are not observed in experiments.

[84] Currently, the leading candidate for a theory going beyond the Big Bang is the theory of cosmic inflation. Developed by Alan Guth and others in the 1980s, inflation postulates a period of extremely rapid accelerated penemu gravity of the universe prior to the expansion described by the standard Big Bang theory.

The theory of cosmic inflation preserves the successes of the Big Bang while providing a natural explanation for some of the mysterious features of the universe.

[85] The theory has also received striking support from observations of the cosmic microwave background, the radiation that has filled the sky since around 380,000 years after the Big Bang. [86] In the theory of inflation, the rapid initial expansion of the universe is caused by a hypothetical particle called the inflaton. The exact properties of this particle are not fixed by the theory but should ultimately be derived from a more fundamental theory such as string theory.

[87] Indeed, there have been a number of attempts to identify an inflaton within the spectrum of particles described by string theory and to study inflation using string theory. Penemu gravity these approaches might eventually find support in observational data such as measurements of the cosmic microwave background, the application of string theory to cosmology is still in its early stages. [88] Connections to mathematics In addition to influencing research in theoretical physics, string theory has stimulated a number of major developments in pure mathematics.

Like many developing ideas in theoretical physics, string theory does not at present penemu gravity a mathematically rigorous formulation in which all of its concepts can be defined precisely. As a result, physicists who study string theory are often guided by physical intuition to conjecture relationships between the seemingly different mathematical structures that are used to formalize different parts of the theory.

These conjectures are later proved by mathematicians, and in this way, string theory serves as a source of new ideas in pure mathematics. [89] Mirror symmetry The Clebsch cubic is an example of a kind of geometric object called an algebraic variety.

A classical result of enumerative geometry states penemu gravity there are exactly 27 straight lines that lie entirely on this surface. After Calabi–Yau manifolds had entered physics as a way to compactify extra dimensions in string theory, many physicists began studying these manifolds. In the late 1980s, several physicists noticed that given such a compactification of string theory, it is not possible to reconstruct uniquely a corresponding Calabi–Yau manifold.

[90] Instead, two different versions of string theory, type IIA and type IIB, can be compactified on completely different Calabi–Yau manifolds giving rise to the same physics. Penemu gravity this situation, the manifolds are called mirror manifolds, and the relationship between the two physical theories is called mirror symmetry.

[28] Regardless of whether Calabi–Yau compactifications of string theory provide penemu gravity correct description of nature, the existence of the mirror duality between different string theories has significant mathematical consequences. The Calabi–Yau manifolds used in string theory are of interest in pure mathematics, and mirror symmetry allows mathematicians to solve problems in enumerative geometry, a branch of mathematics concerned with counting the numbers of solutions to geometric questions.

[28] [91] Enumerative geometry studies a class of geometric objects called algebraic varieties which are defined by the vanishing of polynomials. For example, the Clebsch cubic illustrated on the right is an algebraic variety defined using a certain polynomial of degree three in four variables. A celebrated result of nineteenth-century mathematicians Arthur Cayley and George Salmon states that there are exactly 27 straight lines that lie entirely on such a surface.

[92] Generalizing this problem, one can ask how many lines can be drawn on a quintic Calabi–Yau manifold, such as the one illustrated above, which is defined by a polynomial of degree five. This problem was solved by the nineteenth-century Penemu gravity mathematician Hermann Schubert, who found that there are exactly 2,875 such lines.

In 1986, geometer Sheldon Katz proved that the number of curves, such as circles, that are defined by polynomials of degree two and lie entirely in the quintic is 609,250. [93] By the year 1991, most of the classical problems of enumerative geometry had been solved and interest in enumerative geometry had begun to diminish. [94] The field was reinvigorated in May 1991 when physicists Philip Candelas, Xenia de la Ossa, Paul Green, and Linda Parks showed that mirror symmetry could be used to translate difficult mathematical questions about one Calabi–Yau manifold into easier questions about its mirror.

[95] In particular, they used mirror symmetry to show that a six-dimensional Calabi–Yau manifold can contain exactly 317,206,375 curves of degree three. [94] In addition to counting degree-three curves, Candelas and his collaborators obtained a number of more general results for counting rational curves which went far beyond the results obtained by mathematicians.

[96] Originally, these results of Candelas were justified on physical grounds. However, mathematicians generally prefer rigorous proofs that do not require an appeal to physical intuition. Inspired by penemu gravity work penemu gravity mirror symmetry, mathematicians have penemu gravity constructed their own arguments proving the enumerative predictions of mirror symmetry.

[e] Today mirror symmetry is an active area of research in mathematics, and mathematicians are working to penemu gravity a more complete mathematical understanding of mirror symmetry based on physicists' intuition. [102] Major approaches to mirror symmetry include the homological mirror symmetry program of Maxim Kontsevich [29] and the SYZ conjecture of Andrew Strominger, Shing-Tung Yau, and Eric Zaslow. [103] Monstrous moonshine An equilateral triangle can be rotated through 120°, 240°, or 360°, or reflected in any of the three lines pictured without changing its shape.

Group penemu gravity is the branch of mathematics that studies the concept of symmetry. For example, one can consider a geometric shape such as an equilateral triangle. There are various operations that one can perform on this triangle without changing its shape. One can rotate it through 120°, 240°, or 360°, or one can reflect in any of the lines labeled S 0, S 1, or S 2 in the picture.

Each of these operations is called a symmetry, and the collection of these symmetries satisfies certain technical properties making it into what mathematicians call a group. In this particular example, the group is known as the dihedral group of order 6 because it has six elements. A general group may describe finitely many or infinitely many symmetries; if there are only finitely many symmetries, it is called a finite group. [104] Mathematicians often strive for a classification (or list) of all mathematical objects of a given type.

It is generally believed that finite groups are too diverse to admit a useful classification. A more modest but still challenging problem is to classify all finite simple groups. These are finite groups that may be used as building blocks for constructing arbitrary finite groups in the same way that prime numbers can be used to construct arbitrary whole numbers by taking products. [f] One of the major achievements of contemporary group theory is the classification of finite simple groups, a mathematical theorem that provides a list of all possible finite simple groups.

[104] This classification theorem identifies several infinite families of groups as well as 26 additional groups which do not fit into any family. The latter groups are called the "sporadic" groups, and each one owes its existence to a remarkable combination of circumstances. The largest sporadic group, the so-called monster group, has over 10 53 elements, more than a thousand times the number of atoms in the Earth.

[105] A graph of the j-function in the complex plane A seemingly unrelated construction is the j-function of number theory. This object belongs to a special class of functions called modular functions, whose graphs form a certain kind of repeating pattern. [106] Although this function appears in a branch of mathematics that seems very different from the theory of finite groups, the two subjects turn out to be intimately penemu gravity.

In the late 1970s, mathematicians John McKay and John Thompson noticed that certain numbers arising in the analysis of the monster group (namely, the dimensions of its irreducible representations) are related to numbers that appear in a formula for the j-function (namely, the coefficients of its Fourier series). [107] This relationship was further developed by John Horton Conway and Simon Penemu gravity [108] who called it penemu gravity moonshine because it seemed so far fetched.

[109] In 1992, Richard Borcherds constructed a bridge between the theory of modular functions and finite groups and, in the process, explained the observations of McKay and Thompson.

[110] [111] Borcherds' work used ideas from string theory in an essential way, extending earlier results of Igor Frenkel, James Lepowsky, and Arne Meurman, who had realized the monster group as the symmetries of a particular [ which?] version of string theory.

[112] In 1998, Borcherds was awarded the Fields medal for his work. [113] Since the 1990s, the connection between string theory and moonshine has led to further results in mathematics and physics.

[105] In 2010, physicists Tohru Eguchi, Hirosi Ooguri, and Yuji Tachikawa discovered connections between a different sporadic group, the Penemu gravity group M 24, and a certain version [ which?] of string theory. [114] Miranda Cheng, John Duncan, and Jeffrey A. Harvey proposed a generalization of this moonshine phenomenon called umbral moonshine, [115] and their conjecture was proved mathematically by Duncan, Michael Griffin, and Ken Ono. [116] Witten has also speculated that the version of string theory appearing in monstrous moonshine might be related to a certain simplified model of gravity in three spacetime dimensions.

[117] History Main article: History of string theory Early results Some of the structures reintroduced by string theory arose for the first time much earlier as part of the program of classical unification started by Albert Einstein.

The first person to add a fifth dimension to a theory of gravity was Gunnar Nordström in 1914, who noted that gravity in five dimensions describes both gravity and electromagnetism in four. Nordström attempted to unify electromagnetism with his theory of gravitation, which was however superseded by Einstein's general relativity in 1919. Thereafter, German mathematician Theodor Kaluza combined the fifth dimension with general relativity, and only Kaluza is usually credited with the idea.

In 1926, the Swedish physicist Oskar Klein gave a physical interpretation of the unobservable extra dimension—it is wrapped into a small circle. Einstein introduced a non-symmetric metric tensor, while much later Brans and Dicke added a scalar component to gravity. These ideas would be revived within string theory, where they are demanded by consistency conditions.

Leonard Susskind String theory was originally developed during the late 1960s and penemu gravity 1970s as a never completely successful theory of hadrons, the subatomic particles like the proton and neutron that feel the strong interaction.

In the 1960s, Geoffrey Chew and Steven Frautschi discovered penemu gravity the mesons make families called Regge trajectories with masses related to spins in a way that was later understood by Yoichiro Nambu, Holger Bech Nielsen and Leonard Susskind to be the relationship expected from rotating strings. Chew advocated making a theory for the interactions of these trajectories that did not presume that they were composed of any fundamental particles, but would construct their interactions from self-consistency conditions on the S-matrix.

The S-matrix approach was started by Werner Heisenberg penemu gravity the 1940s as a way of constructing a theory that did not rely on the local notions of space and time, which Heisenberg believed break down at the nuclear scale. While the scale was off by many orders of magnitude, the approach he advocated was ideally suited for a theory of quantum gravity.

Working with experimental data, R. Dolen, D. Horn and C. Schmid developed some sum rules for hadron exchange. When a particle and antiparticle scatter, virtual particles can be exchanged in two qualitatively different ways. In the s-channel, the two particles annihilate to make temporary intermediate states that fall apart into the final state particles.

In the t-channel, the particles exchange intermediate states by emission and absorption. In field theory, the two contributions add together, one giving a continuous background contribution, the other giving peaks at certain energies. In the data, it was clear that the peaks were stealing from the background—the authors interpreted this as saying that the t-channel contribution was dual to the s-channel one, meaning both described the whole amplitude and included the other.

Gabriele Veneziano The result was widely advertised by Murray Gell-Mann, leading Gabriele Veneziano to construct a scattering penemu gravity that had the property of Dolen–Horn–Schmid duality, later renamed world-sheet duality. The amplitude needed poles where the particles appear, on straight-line trajectories, and there is a special mathematical function whose poles are evenly spaced on half the real line—the gamma function— which was widely used in Regge theory.

By manipulating combinations of gamma functions, Veneziano was able to find a consistent scattering amplitude with poles on straight lines, with mostly positive residues, which obeyed duality and had the appropriate Regge scaling at high energy. The amplitude could fit near-beam scattering data as well as other Regge type fits and had a suggestive integral representation penemu gravity could be used for generalization.

Over the next years, hundreds of physicists worked to complete the bootstrap program for this model, with many surprises. Veneziano himself discovered that for the scattering amplitude to describe the scattering of a particle that penemu gravity in the theory, an obvious self-consistency condition, the lightest particle must be a tachyon.

Miguel Virasoro and Joel Shapiro found a different amplitude penemu gravity understood to be that of closed strings, while Ziro Koba and Holger Nielsen generalized Veneziano's integral representation to multiparticle scattering. Veneziano and Sergio Fubini introduced an operator formalism for computing the scattering amplitudes that was a forerunner of world-sheet conformal theory, while Virasoro understood how to remove the poles with wrong-sign residues using a constraint on the states.

Claud Lovelace calculated a loop amplitude, and noted that there is an inconsistency unless the dimension of the theory is 26. Charles Thorn, Peter Goddard and Richard Brower went on to prove that there are no wrong-sign propagating states in dimensions less than or equal to 26.

In 1969–70, Yoichiro Nambu, Holger Bech Nielsen, and Leonard Susskind recognized penemu gravity the theory could be given a description in space and time in terms of strings. The scattering amplitudes were derived systematically from the action principle by Peter Goddard, Jeffrey Goldstone, Claudio Rebbi, and Charles Thorn, giving a space-time picture to the vertex operators introduced by Veneziano and Fubini and a geometrical interpretation to the Virasoro conditions.

In 1971, Pierre Ramond added fermions to the model, which led him to formulate a two-dimensional supersymmetry to cancel the wrong-sign states.

John Schwarz and André Neveu added another sector to the fermi theory a short time later. In the fermion theories, the critical dimension was 10. Stanley Mandelstam formulated a world sheet conformal theory for both the bose and fermi case, giving a two-dimensional field theoretic path-integral to generate the operator formalism. Michio Kaku and Keiji Kikkawa gave a different formulation of the bosonic string, as a string field theory, with penemu gravity many particle types and with penemu gravity taking values not on points, but on loops and curves.

In 1974, Tamiaki Yoneya discovered that all the known string theories included a massless spin-two particle that obeyed the correct Ward identities to be a graviton. John Schwarz and Joël Scherk came to the same conclusion and made the bold leap to suggest that string theory was a theory of gravity, not a theory of hadrons. They reintroduced Kaluza–Klein theory as a way of making sense of the extra dimensions.

At the same time, quantum chromodynamics was recognized as the correct theory of hadrons, shifting the attention of physicists and apparently leaving the bootstrap program in the dustbin of history.

String theory eventually made it out of the dustbin, but for the following decade, all work on the theory was completely ignored. Still, the theory continued to develop at a steady pace thanks to the work of a handful of devotees. Ferdinando Gliozzi, Joël Scherk, and David Olive realized in 1977 that the original Ramond and Neveu Schwarz-strings were separately inconsistent and needed to be combined.

The resulting theory did not have a tachyon and was proven to have space-time supersymmetry by John Schwarz and Michael Green in 1984.

The same year, Alexander Polyakov gave the theory a modern path integral formulation, and went on to develop conformal field theory extensively. In 1979, Daniel Friedan showed that the equations of motions of string theory, which are generalizations of the Einstein equations of general relativity, emerge from the renormalization penemu gravity equations for the two-dimensional field theory.

Schwarz and Green discovered T-duality, and constructed two superstring theories—IIA and IIB related by T-duality, and type I theories with open strings. The consistency conditions had been so strong, that the entire theory was nearly uniquely determined, with only a few discrete choices. First superstring revolution Edward Witten In the early 1980s, Edward Witten discovered that most theories of quantum gravity could not accommodate chiral fermions like the neutrino.

This led him, in collaboration with Luis Álvarez-Gaumé, to study violations of the conservation laws in gravity theories with anomalies, concluding that type I string theories were inconsistent. Green and Schwarz discovered a contribution to the anomaly that Witten and Alvarez-Gaumé had missed, which restricted the gauge group of the type I string theory to be SO(32).

In coming to understand this calculation, Edward Witten became convinced that string theory was truly a consistent theory of gravity, and he became a high-profile advocate. Following Witten's lead, between 1984 and 1986, hundreds of physicists started to work in this field, and this is sometimes called the first superstring revolution. [ citation needed] During this period, David Gross, Jeffrey Harvey, Emil Martinec, and Ryan Rohm discovered heterotic strings.

The gauge group of these closed strings was two copies of E8, and either copy could easily and naturally include the standard model. Philip Candelas, Gary Horowitz, Andrew Strominger and Edward Witten found that the Calabi–Yau manifolds are the compactifications that preserve a realistic amount of supersymmetry, while Lance Dixon and others worked out the physical properties of orbifolds, distinctive geometrical singularities allowed in string theory.

Cumrun Vafa generalized T-duality from circles to arbitrary manifolds, creating the mathematical field of mirror symmetry.

Daniel Friedan, Emil Martinec and Stephen Shenker further developed the covariant quantization of the superstring using conformal field theory techniques. David Gross and Vipul Periwal discovered that string perturbation theory penemu gravity divergent. Stephen Shenker showed it diverged much faster than in field theory suggesting that new non-perturbative objects were missing.

[ citation needed] Joseph Polchinski In the 1990s, Joseph Polchinski discovered that the theory requires higher-dimensional objects, called D-branes and identified these with the black-hole solutions of supergravity. These were understood to be the new objects suggested by the perturbative divergences, and they opened up a new field with rich mathematical structure.

It quickly became clear that D-branes and other p-branes, not just strings, formed the matter content of the string theories, and the physical interpretation of the strings and branes was revealed—they are a type of black hole. Leonard Susskind had incorporated the holographic principle of Gerardus 't Hooft into string theory, identifying the long highly excited string states with ordinary thermal black hole states. As suggested by 't Hooft, the fluctuations of the black hole horizon, the world-sheet or world-volume theory, describes not only the degrees of freedom of the black hole, but all nearby objects too.

Second superstring revolution In 1995, at the annual conference of string theorists at the University of Southern California (USC), Edward Witten gave a speech on string theory that in essence united the five string theories that existed at the time, and giving birth to a new 11-dimensional theory called M-theory.

M-theory was also foreshadowed in the work of Paul Townsend penemu gravity approximately the same time. The flurry of activity that began at this time is sometimes called the second superstring revolution.

[31] Juan Maldacena During this period, Tom Banks, Willy Fischler, Stephen Shenker and Leonard Susskind formulated matrix theory, a full holographic description of M-theory using IIA D0 branes. [48] This was the first definition of string theory that was fully non-perturbative and a concrete mathematical realization of the holographic principle. It is an example of a gauge-gravity duality and is now understood to be a special case of the AdS/CFT penemu gravity. Andrew Strominger and Cumrun Vafa calculated the entropy of certain configurations of D-branes and found agreement with the semi-classical answer for extreme charged black holes.

[59] Petr Hořava and Witten found the eleven-dimensional formulation of the heterotic string theories, showing that orbifolds solve the chirality problem. Witten noted that the effective description of the physics of D-branes at low energies is by penemu gravity supersymmetric gauge theory, and found geometrical interpretations of mathematical structures in gauge theory that he and Nathan Seiberg had earlier discovered in terms of the location of the branes.

In 1997, Juan Maldacena noted that the low energy excitations of a theory penemu gravity a black hole consist of objects close to the horizon, which for extreme charged black holes looks like an anti-de Sitter space.

[68] He noted that in this limit the gauge theory describes the string excitations near the branes. So he hypothesized that string theory on a near-horizon extreme-charged black-hole geometry, an anti-de Sitter space times a sphere with flux, is equally well described by the low-energy limiting gauge theory, penemu gravity N = 4 supersymmetric Yang–Mills theory.

This hypothesis, which is called the AdS/CFT correspondence, was further developed by Steven Gubser, Igor Klebanov and Alexander Polyakov, [69] and by Edward Witten, [70] and it is now well-accepted. It is a concrete realization of the holographic principle, which has far-reaching implications for black holes, locality and information in physics, as well as the nature of the gravitational penemu gravity.

[53] Through this relationship, string theory has been shown to be related to gauge theories like quantum chromodynamics and this has led to a more quantitative understanding of the behavior of hadrons, bringing string theory back to its roots.

[ citation needed] Criticism Number of solutions Main article: String theory landscape To construct models of particle physics based on string theory, physicists typically begin by specifying a shape for the extra dimensions of spacetime.

Each of these different shapes corresponds to a different possible universe, or "vacuum state", with a different collection of particles and forces. String theory as it is currently understood has an enormous number of vacuum states, typically estimated to be around 10 500, and these might be sufficiently diverse to accommodate almost any phenomenon that might be observed at low energies.

[118] Many critics of string theory have expressed concerns about the large number of possible universes described by string theory. In his book Not Even Wrong, Peter Woit, a lecturer in the mathematics department at Columbia University, penemu gravity argued that the large number of different physical scenarios renders string theory vacuous as a framework for constructing models of particle physics.

According to Woit, The possible existence of, say, 10 500 consistent different vacuum states for superstring theory probably destroys the hope of using the theory to predict anything.

If one picks among this large set just those states whose properties agree with present experimental observations, it is likely there still will be such a large number of these that one can get just about whatever value one wants for the results of any new observation.

[119] Some physicists believe this large number of solutions is actually a virtue because it may allow a natural anthropic explanation of the observed values of physical constants, in particular the small value of the cosmological constant. [119] The anthropic principle is the idea penemu gravity some of the numbers appearing in the laws of physics are not fixed by any fundamental principle but must be compatible with the evolution of intelligent life.

In 1987, Steven Weinberg published an article in which he argued that the cosmological constant could not have been too large, or else galaxies and intelligent life would not have been able to develop. [120] Weinberg suggested that there might be a huge number of possible consistent universes, each with a different value of penemu gravity cosmological constant, and observations indicate a small value of the cosmological constant only because humans happen to live in a universe that has allowed intelligent life, and hence observers, to exist.

[121] String theorist Leonard Susskind has argued that string theory provides a natural anthropic explanation of the small value of the cosmological constant. [122] According to Susskind, the different vacuum states of string theory might be realized as different universes within a larger multiverse. The fact that the observed universe has a small cosmological constant is just a tautological consequence of the fact that a small value is required for life to exist.

[123] Many prominent theorists and critics have disagreed with Susskind's conclusions. [124] According to Woit, "in this case [anthropic reasoning] is nothing more than an excuse for failure. Speculative scientific ideas fail not just when they make incorrect predictions, but also penemu gravity they turn out to be vacuous and incapable of predicting anything." [125] Compatibility with dark energy It remains unknown whether string theory is compatible with a metastable, positive cosmological constant.

Some putative examples of such solutions do exist, such as the model described by Kachru et al. in 2003. [126] In 2018, a group of four physicists advanced a controversial conjecture which would imply that no such universe exists.

This is contrary to some popular models of dark energy such as Λ-CDM, penemu gravity requires a positive vacuum energy. However, string theory is likely compatible with certain types penemu gravity quintessence, where dark energy is caused by a new field with exotic properties.

[127] Background independence Main article: Background independence One of the fundamental properties of Einstein's general theory of relativity is that it is background independent, meaning that the formulation of the theory does not in any way privilege a particular spacetime geometry. [128] One of the main criticisms of string theory from early on is that it is not manifestly background-independent.

In string theory, one must typically specify a fixed reference geometry for spacetime, and all other possible geometries are described as perturbations of this fixed one. In his book The Trouble With Physics, physicist Lee Smolin of the Perimeter Institute for Theoretical Physics claims that this is the principal weakness of string theory as a theory of quantum gravity, saying that string theory has failed to incorporate this important insight from general relativity.

[129] Others have disagreed with Smolin's characterization of string theory. In a review of Smolin's book, string theorist Joseph Polchinski writes [Smolin] is mistaking an aspect of the mathematical language being used for one of the physics being described. New physical theories are often discovered using a mathematical language that is not the most suitable for them… In string theory, it has always been clear that the physics is background-independent even if the language being used is not, and the search for a more suitable language continues.

Indeed, penemu gravity Smolin belatedly notes, [AdS/CFT] provides a solution to this problem, one that is unexpected and powerful. [130] Polchinski notes that an important open problem in quantum gravity is to develop holographic descriptions of gravity which do not require the gravitational field to be asymptotically anti-de Sitter.

[130] Smolin has responded by saying that the AdS/CFT correspondence, as it is currently understood, may not be strong enough to resolve all concerns about background independence. [131] Sociology of science Since the superstring revolutions of the 1980s and 1990s, string theory has been one of dominant paradigms of high energy theoretical physics.

[132] Some string theorists have expressed the view that there does not exist an equally successful alternative theory addressing the deep questions of fundamental physics.

In an penemu gravity from 1987, Nobel laureate David Gross made the following controversial comments about the reasons for the popularity of string theory: The most important [reason] is that there are no other good ideas around.

That's what gets most people into it. When people started to get interested in string theory they didn't know anything about it. In fact, the first reaction of most people is that the theory is extremely ugly and unpleasant, at least that was the case a few years ago when the understanding of string theory was much less developed.

It was difficult for people to learn about it and to be turned on. So I think the real reason why people have got attracted by penemu gravity is because there is no other game in town. All other approaches of constructing grand unified theories, which were more conservative to begin with, and only gradually became more and more radical, have failed, and this game hasn't failed yet.

[133] Several other high-profile theorists and commentators have expressed similar views, suggesting that there are no viable alternatives to string theory. [134] Many critics of string theory have commented on this state of affairs. In his book criticizing string theory, Peter Woit views the status of string theory research as unhealthy and detrimental to the future of fundamental physics. He argues that the extreme popularity of string theory among theoretical physicists is partly a consequence of the financial structure of academia and the fierce competition for scarce resources.

[135] In his book The Road to Reality, mathematical physicist Roger Penrose expresses similar views, stating "The often frantic competitiveness that this ease of communication engenders leads to bandwagon effects, where researchers fear to be left behind if they do not join in." [136] Penrose also claims that the technical difficulty of modern physics forces young scientists to rely on the preferences of established researchers, rather than forging new paths of their own. [137] Lee Smolin expresses a slightly different position in his critique, claiming that string theory grew out of a tradition of penemu gravity physics which discourages speculation about the foundations of physics, while his preferred approach, loop quantum gravity, encourages more radical thinking.

According to Smolin, String theory is a powerful, well-motivated idea and deserves much of the work that has been devoted to it. If it has so far failed, the principal reason is that its intrinsic flaws are closely tied to its strengths—and, of course, the story is unfinished, since string theory may well turn out to be part of the truth. The real question is not why we have expended so much energy on string theory but why we haven't expended nearly enough on alternative approaches.

[138] Smolin goes on to offer a number of prescriptions for how scientists might encourage a greater diversity of approaches to quantum gravity research. [139] Notes • ^ For example, physicists are still working to understand the phenomenon of quark confinement, the paradoxes of black holes, and the origin of dark energy. • ^ For example, in the context of the AdS/CFT correspondence, theorists often formulate and study theories of gravity in unphysical numbers penemu gravity spacetime dimensions.

• ^ "Top Cited Articles during 2010 in hep-th". Retrieved 25 July 2013. • ^ More precisely, one cannot apply the methods of perturbative quantum field theory.

• ^ Two independent mathematical proofs of mirror symmetry were given by Givental [97] [98] and Lian et al. [99] [100] [101] • ^ More precisely, a nontrivial group is called simple if its only normal subgroups are the trivial group and the group itself. The Jordan–Hölder theorem exhibits finite simple groups as the building blocks for all finite groups. • ^ a b Becker, Becker and Penemu gravity, p. 1 • ^ Zwiebach, p. 6 • ^ a b Becker, Becker and Schwarz, pp.

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• Penrose, Roger (2005). The Road to Reality: A Complete Guide to penemu gravity Laws of the Universe. Knopf. ISBN 978-0-679-45443-4. • Smolin, Lee (2006). The Trouble with Physics: The Rise of String Theory, the Fall of a Science, and What Comes Next. New York: Houghton Mifflin Co. ISBN 978-0-618-55105-7. • Wald, Robert (1984). General Relativity. University of Chicago Press. ISBN 978-0-226-87033-5. • Woit, Peter (2006). Not Even Wrong: The Failure of String Theory and the Search for Unity in Physical Law.

Basic Books. p. 105. ISBN 978-0-465-09275-8. • Yau, Shing-Tung; Nadis, Steve (2010). The Shape of Inner Space: String Theory and the Geometry of the Universe's Hidden Dimensions. Basic Books. ISBN 978-0-465-02023-2. • Zwiebach, Barton (2009). A First Course in String Theory. Cambridge University Press. ISBN 978-0-521-88032-9. Further reading Popular science • Greene, Brian (2003).

The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory. New York: W.W. Norton & Company. ISBN 978-0-393-05858-1. • Greene, Brian (2004). The Fabric of the Cosmos: Space, Time, and the Texture of Reality. New York: Alfred A. Knopf. Bibcode: 2004fcst.book.G. ISBN 978-0-375-41288-2. • Penrose, Roger (2005). The Road to Reality: A Complete Guide to the Laws of the Universe.

Knopf. ISBN 978-0-679-45443-4. • Smolin, Lee (2006). The Trouble with Physics: The Rise of String Theory, the Penemu gravity of a Science, and What Comes Next. New York: Houghton Mifflin Co.

ISBN 978-0-618-55105-7. • Woit, Peter (2006). Not Even Wrong: The Failure of String Theory And the Search for Unity in Physical Law. London: Jonathan Cape &: New York: Basic Books. ISBN 978-0-465-09275-8.

Textbooks • Green, Michael; Schwarz, John; Witten, Edward (2012). Superstring theory. Vol. 1: Introduction. Cambridge University Press. ISBN 978-1107029118. • Green, Michael; Schwarz, John; Witten, Edward (2012). Superstring theory.

Vol. 2: Loop amplitudes, anomalies and phenomenology. Cambridge University Press. ISBN 978-1107029132. • Polchinski, Joseph (1998). String Theory Vol. 1: An Introduction to penemu gravity Bosonic String. Cambridge University Press. ISBN 978-0-521-63303-1. • Polchinski, Joseph (1998). String Theory Vol.

2: Superstring Theory and Beyond. Cambridge University Press. ISBN 978-0-521-63304-8. • Zwiebach, Barton (2009). A First Course in String Theory. Cambridge University Press. ISBN 978-0-521-88032-9. External links Look up string theory in Wiktionary, the free dictionary. Wikimedia Commons has media related to String theory. Wikiquote has quotations related to: String theory Websites • Not Even Wrong—A blog critical of string theory • The Official String Theory Web Site • Why String Theory—An introduction to string theory.

Video • bbc-horizon: parallel-uni — 2002 feature documentary by BBC Horizon, episode Parallel Universes focus on history and emergence of M-theory, and scientists involved. • pbs.org-nova: elegant-uni — 2003 Emmy Award-winning, three-hour miniseries by Nova with Brian Greene, adapted from his The Elegant Universe (original PBS broadcast dates: October 28, 8–10 p.m. and November 4, 8–9 p.m., 2003). • Kaluza–Klein theory • Compactification • Why 10 dimensions?

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Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization. • Privacy policy • About Wikipedia • Disclaimers • Contact Wikipedia • Mobile view • Developers • Statistics • Cookie statement • • KOMPAS.com - Isaac Newton berusia 20 tahun ketika Wabah Besar London melanda. Dia belum mendapat gelar "Sir" dan tak mengenakan wig formal putih yang besar. Newton hanyalah seorang mahasiswa di Trinity College Cambridge, London. Newton menerima gelar sarjana dari Trinity pada Januari 1665 tepat saat wabah turun ke London.

Penemu gravity Cambridge ditutup pada 7 Agustus 1665 dan mendorong para cendekiawan residennya untuk melarikan diri ke penemu gravity yang berpenduduk kurang padat. Newton kembali ke pertanian keluarganya di Woolsthrope Manor sampai Universitas dibuka kembali pada akhir 1666. Saat itulah Newton melepaskan kejeniusanya, tulis penulis biografi Philip Steele. Masa-masa itu menjadi masa produktif Newton dalam pengembangan ilmu optik dan cahaya, kalkulus, serta hukum gerak dan gravitasi.

Mengacu pada Annus Mirabilis karya John Dryden, tahun-tahun itu adalah keajaiban. Baca juga: Kerja dari Rumah Bisa Sebabkan Stres, Ini Penjelasan Psikolog Berada di rumah tampaknya tak membuat Newton kehabisan akal. Newton mencoba memecahkan soal-soal matematika dari kampus.

Makalah yang ditulisnya itu digadang-gadang sebagai cikal bakal kalkulus yang penemu gravity kenal sekarang. Saat itu pula Newton mendapatkan prisma dan bereksperimen di kamarnya. Bahkan ia membuat lubang kecil di jendela yang menghasilkan sinar cahaya kecil masuk ke kamar. Dari sini ia terpikir untuk mengembangkan ilmu optik dan cahaya. Tepat di luar jendela rumahnya di Woolsthrope ada pohon apel. Pohon itulah yang menjadi kisah legenda Newton menemukan teori gravitasi saat apel-apel itu berjatuhan di kepalanya.

Walaupun banyak yang menganggap bahwa kisah itu apokrif (diragukan keaslianya). Catatan John Conduitt membenarkan adanya unsur kebenaran dari cerita tersebut. Ungkapan Asisten Newton itu terkutip dalam The Washington Post sebagaimana berikut. Baca juga: Simulasikan Alam Semesta Ilmuwan Modifikasi Hukum Newton, Kok Bisa? “.Ketika dia sedang merenung di taman, terlintas dalam pikirannya bahwa kekuatan gravitasi (yang membuat sebuah apel jatuh dari pohon ke tanah) tidak terbatas pada jarak tertentu dari bumi saja.

Tetapi meluas lebih jauh. 'Mengapa tidak setinggi Bulan?' kata Newton pada dirinya sendiri." Wabah Besar London, merupakan epidemi wabah yang berlangsung selama 1665 ke 1666. Catatan kota dalam Britannica menunjukan sekitar 68.596 orang meninggal dunia karena wabah. Meskipun jumlah kematian sebenarnya diperkirakan melebihi 100.000 orang. Berita Terkait Simulasikan Alam Semesta Ilmuwan Modifikasi Hukum Newton, Kok Bisa?

Pandemi Terburuk Sepanjang Sejarah, Flu Spanyol Infeksi Sepertiga Warga Dunia Virus Corona Pandemi Global, Ini 6 Pandemik Terburuk Sepanjang Sejarah Catat, Daftar Produk Rumah Tangga untuk Disinfeksi Virus Penemu gravity Mengenal Gejala Virus Corona Baru Penyebab Covid-19 Berita Terkait Simulasikan Alam Semesta Ilmuwan Modifikasi Hukum Newton, Kok Bisa?

Pandemi Terburuk Sepanjang Sejarah, Flu Spanyol Infeksi Sepertiga Warga Dunia Virus Corona Pandemi Global, Ini 6 Pandemik Terburuk Sepanjang Sejarah Catat, Daftar Produk Rumah Tangga untuk Disinfeksi Virus Corona Mengenal Gejala Virus Corona Baru Penyebab Covid-19 WHO Ubah Social Distancing Jadi Physical Distancing, Apa Maksudnya?

Penemu sistem telepon genggam yang pertama adalah Martin Cooper, seorang karyawan Motorola pada tanggal 03 April 1973, walaupun banyak disebut-sebut penemu telepon genggam adalah sebuah tim dari salah satu divisi Motorola (divisi tempat Cooper bekerja) dengan model pertama adalah DynaTAC.

Ide yang dicetuskan oleh Cooper adalah sebuah alat komunikasi yang kecil dan mudah dibawa bepergian secara fleksibel. Cooper bersama timnya menghadapi tantangan bagaimana memasukkan semua material elektronik ke dalam alat yang berukuran kecil tersebut untuk pertama kalinya. Namun akhirnya sebuah telepon genggam pertama berhasil diselesaikan dengan total bobot seberat dua kilogram.

Untuk memproduksinya, Motorola membutuhkan biaya setara dengan US$1 juta. “Pada tahun 1983, telepon genggam portabel berharga US$4 ribu (Rp36 juta) setara dengan US$10 ribu (Rp90 juta). Setelah berhasil memproduksi telepon genggam, tantangan terbesar berikutnya adalah mengadaptasi infrastruktur untuk mendukung sistem komunikasi telepon genggam tersebut dengan menciptakan sistem jaringan yang hanya membutuhkan 3 MHz spektrum, setara dengan lima channel TV yang tersalur ke seluruh dunia. Tokoh lain yang diketahui sangat berjasa dalam dunia komunikasi selular adalah Amos Joel Jr yang lahir di Philadelphia, 12 Maret 1918, ia memang diakui dunia sebagai pakar dalam bidang switching. Ia mendapat ijazah bachelor (1940) dan master (1942) dalam teknik elektronik dari MIT. Tidak lama setelah studi, ia memulai kariernya selama 43 tahun (dari Juli 1940-Maret 1983) di Bell Telephone Laboratories, tempat ia menerima lebih dari 70 paten Amerika di bidang telekomunikasi, khususnya di bidang switching. Amos E Joel Jr, membuat sistem penyambung (switching) ponsel dari satu wilayah sel ke wilayah sel yang lain. Switching ini harus bekerja ketika pengguna ponsel bergerak atau berpindah dari satu sel ke sel lain sehingga pembicaraan tidak terputus. Karena penemuan Amos Joel inilah penggunaan ponsel menjadi nyaman. Search Recent Posts • Corsair Flash Voyager Slider CMFSL3 – Flash Disk USB 3.0 dengan Kecepatan Membaca Data Hingga 85MB per Detik. • Jenis dan Macam-macam Ponsel Menurut Fitur dan Spesifikasinya • TEKNOLOGI KEYBOARD • Fungsi Dan Fiture Handphone • Sejarah Archives • October 2012 Categories • Air Conditioner • Handphone • Iphone • KeyBoard • Komputer • Penemu gravity 2 dari ASUS • PlayStation 4 • Teknologi Mobil BMW • Uncategorized • USB Meta • Register • Log in • Entries feed • Comments feed • WordPress.com none Pewartanusantara.com – Seperti yang kita ketahui pada peradaban jaman terdahulu terdapat tokoh-tokoh penemu gravity hebat. Salah satu tokoh yang terkenal dengan penemuanya yaitu Sir Isaac Newton. Newton merupakan tokoh jenius berasal dari Inggris yang berhasil menemukan hukum gravitasi. Nah, bagi Anda yang penasaran dengan biografi Sir Isaac Newton, simak ulasan berikut ya! Riwayat Hidup Sir Isaac Newton (1642-1727) Sir Isaac Newton diketahui sebagai ilmuwan terbesar dan paling berpengaruh di Dunia. Diantara penemuanya yang paling berpengaruh ialah mengenai konsep gravitasi (Gaya tarik bumi). Newton lahir pada tanggal 25 Desembar 1642 di di Woolsthrope, Inggris, bertepatan pada hari Natal. Masa kecilnya terbilang kurang beruntung karena terlahir prematur dan berasal dari keluarga miskin. Pada saat itu Ayahnya, yaitu Robert Newton, meninggal tiga bulan sebelum kelahiranya. Sumber: https://www.history.com/topics/inventions/isaac-newton penemu gravity man may imagine things that are false, but he can only understand things that are true.” Isaac Newton Setelah kepergian Ayahnya, dua tahun kemudian Ibunya yaitu Hannah Ayscough Newton menikah lagi. Newton tidak ikut Ibunya dan memilih tinggal bersama dengan neneknya di desa. Kecerdasan Newton bahkan terlihat sedari kecil. Ia memulai sekolah saat bersama neneknya di desa. Kemudian Ia dikirim ke daerah Grantham dan menjadi anak terpandai disana. Newton mengenyam pendidikan di sekolah The Kings School yang terletak di Grantham sejak usia 12 hingga 17 tahun. Namun, Ia pernah dikeluarkan karena Ibunya memintanya untuk menjadi petani saja. Karena tak begitu menyukai pekerjaanya, Newton menyakinkan Ibunya dan berhasil masuk sekolah lagi. Hingga pada usia 18 tahun, Ia penemu gravity sekolah dengan nilai memuaskan. Berkat nilai yang memuaskan tersebut, pada usia 18 tahun Ia masuk berhasil masuk Trinity College, Cambridge. Di kampus inilah Newton dengan cepat menyerap ilmu dalam pelajaran matematika, science dan fisika. Berkat kapasitasinya yang luar bisa dalam memecahkan soal-soal matematika atau huitungan tersebut, ia pun mulai melakukan penyelidikan sendiri. “I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.” Isaac Newton “I can calculate the motion of heavenly bodies but not the madness of people.” – Isaac Newton Teori Gravitasi Sir Isaac Newton Padabiografi Sir Isaac Newton tercatat bahwa antara usia dua puluh satu dan dua puluh tujuh tahun, ia sudah meletakkan dasar teori ilmu pengetahuan. Dari pemikiran-pemikiranya tersebut, bahkan seiring berjalanya waktu ia dapat megubah Dunia. Berdasarkan hasil dari karya tulis yang pernah dibuatnya, ia pun menulis buku yaitu Philosophiae Naturalis Principia Mathematica. Pada buku itu, dijelaskan tentang teori gravitasi secara umum yaitu berdasarkan hukum gerak. Menurut Penemu gravity benda akan tertarik ke bawah disebabkan oleh gaya gravitasi. Pada usia 23 atau 24 tahun, Newton bekerja sama Gottfried Leibniz untuk mengembangkan teori kalkulus. Penemuan ini bahkan menjadi hasil karya terpenting di bidang Matematika modern. Dari hasil penemuanya, Ia pun berhasil menjelaskan tentang teori gerak dan juga menjadi orang pertama yang merumuskan gerakan melingkar dari hukum Kepler. Bahkan hukum tersebut Ia perluas dengan menganggap penemu gravity suatu orbit gerakan melingkar tidak harus membentuk penemu gravity sempurna. Misalnya seperti hiperbola atau elips. Penemuan Sir Isac Newton Di Bidang Fisika Prestasi dan penemuan Newton di bidang Matematika dan Fisika memang sangat besar hingga menjadi sejarah dan diterapakan hingga kini. Beberapa penemuan besarnya di bidang Fisika bahkan hingga kini dijadikan sebagai patokan pembelajaran ilmu fisika ataupun dalam menjalankan aktivitas sehari-hari. Diantara penemuan Newton di bidang Fisika adalah sebagai berikut. • Optik Di bidang optik, Newton mengembangkan penemuan mengenai spektrum warna. Penemuan ini Ia dapatkan tatkala meakukan percobaan dengan melewati sinar putih pada sebuah prisma. Menurutnya sinar adalah kumpulan dari partikel-partikel. • Teleskop Reflektor Penemuan Newton berikutnya Teleskop. Ia adalah seorang yang berperan besar dalam perkembangan teleskop. Penemuan ini bermula dari analisanya mengenai hukup pembiasan cahaya. Baca juga: Biografi Galileo Galilei, Seorang Filsuf, Astronom dan Metematikawan Dari hukum itu, Ia pun membangun teropong refleksi. Model Teleskop Reflektor tersebut saat ini banyak digunakan oleh sebagian besar penyelidik bintang. Tentu saja dalam catatan biografi Sir Isaac Newton, penemuan ini adalah salah satu penemuan yang sangat berguna di masa sekarang. Filsuf Gravitasi isaac newton • Afrikaans • العربية • অসমীয়া • Беларуская • Български • বাংলা • Bosanski • Català • Čeština • Cymraeg • Dansk • Deutsch • Ελληνικά • English • Esperanto • Español • Eesti • Euskara • فارسی • Suomi • Français • Gaeilge • Galego • ગુજરાતી • עברית • हिन्दी • Hrvatski • Magyar • Հայերեն • Italiano • 日本語 • ქართული • Қазақша • 한국어 • Latina • Lietuvių • Latviešu • Македонски • മലയാളം penemu gravity मराठी • Bahasa Melayu • မြန်မာဘာသာ • Nederlands • Norsk nynorsk • Norsk bokmål • Occitan • ਪੰਜਾਬੀ • Polski penemu gravity Português • Română • Русский • Sicilianu • Scots • Srpskohrvatski / српскохрватски • Simple English • Slovenčina • Slovenščina • Српски / srpski • Svenska • தமிழ் • ไทย • Tagalog • Türkçe • Татарча/tatarça • Українська • اردو • Oʻzbekcha/ўзбекча • Tiếng Việt • 吴语 • 中文 • Bân-lâm-gú • Einstein • Lorentz • Hilbert • Poincaré • Schwarzschild • de Sitter • Reissner • Nordström • Weyl • Eddington • Friedman • Milne • Zwicky • Lemaître • Gödel • Wheeler • Robertson • Bardeen • Walker • Kerr • Chandrasekhar • Ehlers • Penrose • Hawking • Raychaudhuri • Taylor • Hulse • van Stockum • Taub • Newman • Yau • Thorne • lainnya • l • b • s Dalam fisika, gelombang gravitasi penemu gravity riak dalam lengkung ruang-waktu yang bergerak dalam bentuk gelombang menjauhi sumbernya. Keberadaan gelombang ini diprediksi pada tahun 1916 [1] [2] oleh Albert Einstein sebagai dasar teori relativitas umum yang dipaparkannya. [3] [4] Gelombang gravitasi mengangkut energi dalam bentuk radiasi gravitasi. Gelombang ini terbentuk akibat invariansi Lorentz dalam relativitas umum yang menjelaskan bahwa segala pergerakan interaksi fisik dibatasi oleh kecepatan cahaya. Sebaliknya, gelombang gravitasi tidak dapat terbentuk dalam teori gravitasi Newton yang menyatakan bahwa penemu gravity fisik bergerak dengan kecepatan tak hingga. Sebelum gelombang ini terdeteksi, sudah ada bukti-bukti tak langsung mengenai keberadaannya. Misalnya, pengukuran sistem biner Hulse–Taylor menunjukkan bahwa gelombang gravitasi bukan sekadar hipotesis. Gelombang gravitasi yang dapat terdeteksi diduga berasal dari sistem bintang biner yang terdiri atas katai putih, bintang neutron, dan lubang hitam. Pada tahun 2016, beberapa pendeteksi gelombang gravitasi sedang dibangun atau sudah beroperasi. Salah satu di antaranya adalah Advanced LIGO yang beroperasi bulan September 2015. [5] Bulan Februari 2016, tim Advanced LIGO mengumumkan bahwa mereka telah mendeteksi gelombang gravitasi dari proses menyatunya lubang hitam. [6] [7] [8] [9] The unnamed parameter 2= is no longer supported. Please see the penemu gravity for {{ penemu gravity. • Latar gelombang gravitasi • Medan gravitasi • Gravitomagnetisme • Graviton • Astronomi gelombang gravitasi • Radiasi Hawking, radiasi elektromagnetik yang tercipta lewat gravitasi dari lubang hitam • HM Cancri • LIGO, Virgo Interferometer, GEO600, KAGRA, dan TAMA 300 - pendeteksi gelombang gravitasi di darat • Persamaan medan Einstein linier • LISA, DECIGO dan BBO — rencana detektor di luar angkasa • Metrik Peres • Ruang-waktu gelombang pp, rangkaian solusi pasti yang mereka ulang radiasi gravitasi • PSR B1913+16, pulsar biner pertama yang ditemukan dan bukti gelombang gravitasi pertama • Spin-flip, dampak emisi gelombang gravitasi dari lubang hitam supermasif biner • Sticky bead argument, cara mengetahui bahwa radiasi gravitasi mengangkut energi • Gaya gelombang Referensi [ sunting - sunting sumber ] • ^ Einstein, A (June 1916). "Näherungsweise Integration der Feldgleichungen der Gravitation". Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften Berlin. part 1: 688–696. • ^ Einstein, A (1918). "Über Gravitationswellen". Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften Berlin. part 1: 154–167. • ^ Finley, Penemu gravity. "Einstein's gravity theory passes toughest test yet: Bizarre binary star system pushes study of relativity to new limits". Phys.Org. • ^ The Detection of Gravitational Waves using LIGO, B. Barish • ^ "The Newest Search for Gravitational Waves has Begun". LIGO Caltech. LIGO. 18 September 2015. Diakses tanggal 29 November 2015. • penemu gravity Castelvecchi, Davide; Witze, Witze (February 11, 2016). "Einstein's gravitational waves found at last". Nature News. doi: 10.1038/nature.2016.19361. Diakses tanggal 2016-02-11. • ^ B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration) (2016). "Observation of Gravitational Waves from a Binary Black Hole Merger". Physical Review Letters. 116 (6). doi: 10.1103/PhysRevLett.116.061102. Pemeliharaan CS1: Menggunakan parameter penulis ( link) • ^ "Gravitational waves detected 100 years after Einstein's prediction - NSF - National Science Foundation". www.nsf.gov. Diakses tanggal 2016-02-11. • ^ Overbye, Dennis (11 February 2016). "Physicists Detect Gravitational Waves, Proving Einstein Right". New York Times. Diakses tanggal 11 February 2016. Bacaan lanjutan [ sunting - sunting sumber ] • Bartusiak, Marcia. Einstein's Unfinished Symphony. Washington, DC: Joseph Henry Press, 2000. • Chakrabarty, Indrajit, " Gravitational Waves: An Introduction". arXiv:physics/9908041 v1, Aug 21, 1999. • Landau, L. D. and Lifshitz, E. M., The Classical Theory of Fields (Pergamon Press), 1987. • Will, Clifford M., The Confrontation between General Relativity and Experiment. Living Reviews Relativity 9 (2006) 3. • Peter Saulson, Fundamentals of Interferometric Gravitational Wave Detectors, World Scientific, 1994. Daftar pustaka [ sunting - sunting sumber ] • Berry, Michael, Principles of Сosmology and Gravitation (Adam Hilger, Philadelphia, 1989). ISBN 0-85274-037-9 • Collins, Harry, Gravity's Shadow: The Search for Gravitational Waves, University of Chicago Press, 2004. • P. J. E. Peebles, Principles of Physical Cosmology (Princeton University Press, Princeton, 1993). ISBN 0-691-01933-9. • Wheeler, John Archibald and Ciufolini, Ignazio, Gravitation and Inertia (Princeton University Press, Princeton, 1995). ISBN penemu gravity. • Woolf, Harry, ed., Some Strangeness in the Proportion (Addison–Wesley, Reading, Massachusetts, 1980). ISBN 0-201-09924-1. Pranala luar [ sunting - sunting sumber ] Wikimedia Commons memiliki media mengenai Gravitational waves. Lihat informasi mengenai gelombang gravitasi di Wiktionary. • Gravitational waves di Encyclopædia Britannica • Laser Interferometer Gravitational Wave Observatory. LIGO Laboratory, operated by the California Institute of Technology and the Massachusetts Institute of Technology • Caltech Relativity Tutorial Diarsipkan 2014-05-30 di Wayback Machine. – A basic introduction to gravitational waves • Lubang hitam • Horizon peristiwa • Singularitas • Masalah dua-benda • Gelombang gravitasi: astronomi • pendeteksi ( LIGO dan penemu gravity • Virgo • LISA Pathfinder • GEO) • Biner Hulse–Taylor • Uji coba lainnya: presesi Merkurius • lensa • pergeseran merah • penundaan Shapiro • penyeretan kerangka / efek geodetik ( presesi Lense–Thirring) • larik waktu pulsar Teori lanjutan • Kosmologis: Friedmann–Lemaître–Robertson–Walker ( persamaan Friedmann) • Kasner • Singularitas BKL • Gödel • Milne • Sferis: Schwarzschild ( interior • Persamaan Tolman–Oppenheimer–Volkoff) • Reissner–Nordström • Lemaître–Tolman • Aksisimetris: Kerr ( Kerr–Newman) • Weyl−Lewis−Papapetrou • Taub–NUT • debu van Stockum • penemu gravity • Lain-lain: gelombang-pp • metrik Ozsváth–Schücking • Poincaré • Lorentz • Einstein • Hilbert • Schwarzschild • de Sitter • Weyl • Eddington • Friedmann • Lemaître • Milne • Robertson • Chandrasekhar • Zwicky • Wheeler • Choquet-Bruhat • Kerr • Zel'dovich • Novikov • Ehlers • Geroch • Penrose • Hawking • Taylor • Hulse • Bondi • Misner • Yau • Thorne • Weiss • lain-lain Kategori tersembunyi: • Pemeliharaan CS1: Menggunakan parameter penulis • Pages using columns-list with unknown parameters • Pranala kategori Commons ada di Wikidata • Templat webarchive tautan wayback • Artikel Wikipedia dengan penanda GND • Artikel Wikipedia dengan penanda BNF • Artikel Wikipedia dengan penanda EMU • Artikel Wikipedia dengan penanda LCCN • Artikel Wikipedia dengan penanda NDL • Artikel Wikipedia dengan penanda MA • Halaman yang menggunakan pranala magis ISBN • Halaman ini terakhir diubah pada 26 Januari 2021, pukul 02.36. • Teks tersedia di bawah Lisensi Creative Commons Atribusi-BerbagiSerupa; ketentuan tambahan mungkin berlaku. 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Lahir ( 1643-01-04)4 Januari 1643 [ K.J. 25 Desember 1642] [1] Woolsthorpe, Lincolnshire, Inggris Meninggal 31 Maret 1727 (1727-03-31) (umur 84) [ K.J. 20 Maret 1726] [1] Kensington, Middlesex, Inggris Makam Westminster Abbey Kebangsaan Inggris Almamater Trinity College, Cambridge Dikenal atas • Roger Cotes • William Whiston Tanda tangan Sir Isaac Newton FRS PRS (25 Desember 1642 – 20 Maret 1726/27 [1]) adalah seorang fisikawan, matematikawan, ahli astronomi, filsuf alam, alkimiawan, teolog dan penulis Inggris yang secara penemu gravity diakui sebagai salah satu matematikawan, fisikawan terbesar, dan ilmuwan paling berpengaruh sepanjang masa. Dia merupakan pengikut aliran heliosentris dan ilmuwan yang sangat berpengaruh sepanjang sejarah, bahkan dikatakan sebagai bapak ilmu fisika klasik. [6] Karya bukunya Philosophiæ Naturalis Principia Mathematica yang diterbitkan pada tahun 1687 dianggap sebagai buku paling berpengaruh sepanjang sejarah sains. Buku ini meletakkan dasar-dasar mekanika klasik. Dalam karyanya ini, Newton menjabarkan hukum gravitasi dan tiga hukum gerak yang mendominasi pandangan sains mengenai alam semesta selama tiga abad. Newton berhasil menunjukkan bahwa gerak benda di Bumi dan benda-benda luar angkasa lainnya diatur oleh sekumpulan hukum-hukum alam yang sama. Dia membuktikannya dengan menunjukkan konsistensi antara hukum gerak penemu gravity Kepler dengan teori gravitasinya. Karyanya ini akhirnya menyirnakan keraguan para ilmuwan akan heliosentrisme dan memajukan revolusi ilmiah. Dalam bidang mekanika, Newton mencetuskan adanya prinsip kekekalan momentum dan momentum sudut. Dalam bidang optika, dia berhasil membangun teleskop pemantul yang pertama [7] dan mengembangkan teori warna berdasarkan pengamatan bahwa sebuah kaca prisma akan membagi cahaya putih menjadi warna-warna lainnya. Dia juga merumuskan hukum pendinginan dan mempelajari kecepatan suara. Dalam bidang matematika pula, bersama dengan karya Gottfried Leibniz yang dilakukan secara terpisah, Newton mengembangkan kalkulus diferensial dan kalkulus integral. Ia juga berhasil menjabarkan teori binomial, mengembangkan "metode Newton" untuk melakukan pendekatan terhadap nilai nol suatu fungsi, dan berkontribusi terhadap kajian deret pangkat. Sampai sekarang pun Newton masih sangat berpengaruh di kalangan ilmuwan. Sebuah survei tahun 2005 yang menanyai para ilmuwan dan masyarakat umum di Royal Society mengenai siapakah yang memberikan kontribusi lebih besar dalam sains, apakah Newton atau Albert Einstein, menunjukkan bahwa Newton dianggap memberikan kontribusi yang lebih besar. [8] Daftar isi • 1 Biografi • 1.1 Masa-masa awal • 1.2 Masa dewasa • 1.2.1 Matematika • 1.2.2 Optika • 1.2.3 Mekanika dan gravitasi • 1.3 Masa tua • 2 Pandangan keagamaan • 2.1 Dampak kepada pemikiran keagamaan • 2.2 Kiamat • 3 Daftar karya Newton • 4 Lihat pula • 5 Referensi • 6 Bibliografi • 7 Bacaan lanjutan • 8 Pranala luar Biografi [ sunting - sunting sumber ] Masa-masa awal [ sunting - sunting sumber ] Rumah Keluarga Newton di mana Lahirnya Isacc Newton Isaac Newton dilahirkan pada tanggal 4 Januari 1643 [ KJ: 25 Desember 1642] di Woolsthorpe-by-Colsterworth, sebuah hamlet (desa) di county Lincolnshire. Pada saat kelahirannya, Inggris masih mengadopsi kalender Julian, sehingga hari kelahirannya dicatat sebagai 25 Desember 1642 pada hari Natal. Ayahnya yang juga bernama Isaac Newton meninggal tiga bulan sebelum kelahiran Newton. Newton dilahirkan secara penemu gravity dilaporkan pula ibunya, Hannah Ayscough, pernah berkata bahwa ia dapat muat ke dalam sebuah cangkir (≈ 1,1 liter). Ketika Newton berumur tiga tahun, ibunya menikah kembali dan meninggalkan Newton di bawah asuhan neneknya, Margery Ayscough. Newton muda tidak menyukai ayah tirinya dan menyimpan rasa benci terhadap ibunya karena menikahi pria tersebut, seperti yang tersingkap dalam pengakuan dosanya: "Threatening my father and mother Penemu gravity to burn them and the house over them." [9] Isaac Newton ( Bolton, Sarah K. Famous Men of Science. NY: Thomas Y. Crowell & Co., 1889) Berdasarkan pernyataan E.T. Bell (1937, Simon and Schuster) dan H. Eves: “ Newton memulai sekolah saat tinggal bersama neneknya di desa dan kemudian dikirimkan ke sekolah bahasa di daerah Grantham dimana dia penemu gravity menjadi anak terpandai di sekolahnya. Saat bersekolah di Grantham dia tinggal di-kost milik apoteker lokal yang bernama William Clarke. Sebelum meneruskan kuliah di Universitas Cambridge pada usia 19, Newton sempat menjalin kasih dengan adik angkat William Clarke, Anne Storer. Saat Newton memfokuskan dirinya pada pelajaran, kisah cintanya dengan menjadi semakin tidak menentu dan akhirnya Storer menikahi orang lain. Banyak yang menegatakan bahwa dia, Newton, selalu mengenang kisah cintanya walaupun selanjutnya tidak pernah disebutkan Newton memiliki seorang kekasih dan bahkan pernah menikah. ” Sejak usia 12 hingga 17 tahun, Newton mengenyam pendidikan di sekolah The King's School yang terletak di Grantham (tanda tangannya masih terdapat di perpustakaan sekolah). Keluarganya mengeluarkan Newton dari sekolah dengan alasan agar dia menjadi petani saja, bagaimanapun Newton tidak menyukai pekerjaan barunya. [10] Kepala sekolah King's School kemudian meyakinkan ibunya untuk mengirim Newton kembali ke sekolah sehingga ia dapat menamatkan pendidikannya. Newton dapat menamatkan sekolah pada usia 18 tahun dengan nilai yang memuaskan. Pada Juni 1661, Newton diterima di Trinity College Universitas Cambridge sebagai seorang sizar (mahasiswa yang belajar sambil bekerja). [11] Pada saat itu, ajaran universitas didasarkan pada ajaran Aristoteles, namun Newton lebih memilih untuk membaca gagasan-gagasan filsuf modern yang lebih maju seperti Descartes dan astronom seperti Copernicus, Galileo, dan Kepler. Pada tahun 1665, ia menemukan teorema binomial umum dan mulai mengembangkan teori matematika yang pada akhirnya penemu gravity menjadi kalkulus. Segera setelah Newton mendapatkan gelarnya pada Agustus 1665, Universitas Cambridge ditutup oleh karena adanya Wabah Besar. Walaupun dalam studinya di Cambridge biasa-biasa saja, studi privat yang dilakukannya di rumahnya di Woolsthorpe selama dua tahun mendorongnya mengembangkan teori kalkulus, optika, dan hukum gravitasi. Pada tahun 1667, ia kembali ke Cambridge sebagai pengajar di Trinity. [12] Masa dewasa [ sunting - sunting sumber ] Matematika [ sunting - sunting sumber ] Kebanyakan ahli sejarah percaya bahwa Newton dan Leibniz mengembangkan kalkulus secara terpisah. Keduanya pula menggunakan notasi matematika yang berbeda pula. Menurut teman-teman dekat Newton, Newton telah menyelesaikan karyanya bertahun-tahun sebelum Leibniz, namun tidak mempublikasikannya sampai dengan tahun 1693. Dia baru menjelaskannya secara penuh pada tahun 1704, manakala pada tahun 1684, Leibniz sudah mulai mempublikasikan penemu gravity penuh atas karyanya. Notasi dan "metode diferensial" Leibniz secara universal diadopsi di Daratan Eropa, sedangkan Kerajaan Britania baru mengadopsinya setelah tahun 1820. Dalam buku catatan Leibniz, dapat ditemukan adanya gagasan-gagasan sistematis yang memperlihatkan bagaimana Leibniz mengembangkan kalkulusnya dari awal sampai akhir, manakala pada catatan Newton hanya dapat ditemukan hasil akhirnya saja. Newton mengklaim bahwa ia enggan mempublikasi kalkulusnya karena takut ditertawakan. Newton juga memiliki hubungan dekat dengan matematikawan Swiss Nicolas Fatio de Duillier. Pada tahun 1691, Duillier merencanakan untuk mempersiapkan versi baru buku Philosophiae Naturalis Principia Mathematica Newton, namun tidak pernah menyelesaikannya. Pada tahun 1693 pula hubungan antara keduanya menjadi penemu gravity sedekat sebelumnya. Pada saat yang sama, Duillier saling bertukar surat dengan Leibniz. [13] Pada tahun 1699, anggota-anggota Royal Society mulai menuduh Leibniz menjiplak karya Newton. Perselisihan ini memuncak pada tahun 1711. Royal Society kemudian dalam suatu kajian memutuskan bahwa Newtonlah penemu sebenarnya dan mencap Leibniz sebagai penjiplak. Kajian ini kemudian diragukan karena setelahnya ditemukan bahwa Newton sendiri yang menulis kata akhir kesimpulan laporan kajian ini. Sejak itulah bermulainya perselisihan sengit antara Newton dengan Leibniz. Perselisihan ini berakhir sepeninggal Leibniz pada tahun 1716. [14] Newton umumnya diakui sebagai penemu teorema binomial umum yang berlaku untuk semua eksponen. Ia juga menemukan identitas Newton, metode Newton, mengklasifikasikan kurva bidang kubik, memberikan kontribusi yang substansial pada teori beda hingga, dan merupakan yang pertama untuk menggunakan pangkat berpecahan serta menerapkan geometri koordinat untuk menurunkan penyelesaian persamaan Diophantus. Ia dipilih untuk menduduki jabatan Lucasian Professor of Mathematics pada tahun 1669. Pada saat itu, para pengajar Cambridge ataupun pengajar Oxford haruslah seorang pastor Anglikan yang telah ditahbiskan. Namun, jabatan profesor Lucasian mengharuskan pula pejabatnya tidak aktif dalam gereja. Oleh karena itu, Newton berargumen bahwa ia seharusnyalah dibebaskan dari keharusan penahbisan. Raja Charles II menerima argumen ini dan memberikan persetujuan, sehingga konflik antara pandangan keagamaan Newton dengan gereja Anglikan dapat dihindari. [15] Optika [ sunting - sunting sumber ] Replika teleskop refleksi kedua Newton yang ia presentasikan ke Royal Society pada tahun 1672 [16] Dari tahun 1670 sampai dengan 1672, Newton mengajar bidang optika. Semasa periode ini, ia menginvestigasi refraksi cahaya, menunjukkan bahwa kaca prisma dapat membagi-bagi cahaya putih menjadi berbagai spektrum warna, serta lensa dan prisma keduanya akan menggabungkan kembali cahaya-cahaya tersebut menjadi cahaya putih. [17] Dia juga menunjukkan bahwa cahaya berwarna tidak mengubah sifat-sifatnya dengan memisahkan berkas berwarna dan menyorotkannya ke berbagai objek. Newton mencatat bahwa tidak peduli apakah berkas cahaya tersebut dipantulkan, dihamburkan atau ditransmisikan, warna berkas cahaya tidak berubah. Dengan demikian dia mengamati bahwa warna adalah interaksi objek dengan cahaya yang sudah berwarna, dan objek tidak menciptakan warna itu sendiri. Ini dikenal sebagai teori warna Newton [18] Dari usahanya ini dia menyimpulkan bahwa lensa teleskop refraksi akan mengalami gangguan akibat dispersi cahaya menjadi berbagai warna ( aberasi kromatik). Sebagai bukti konsep ini dia membangun teleskop menggunakan cermin sebagai objektif untuk mengakali masalah tersebut. [19] Pengerjaan rancangan ini, teleskop refleksi fungsional pertama yang dikenal, yang sekarang disebut sebagai teleskop Newton [19] melibatkan pemecahan masalah bagaimana menemukan bahan cermin yang cocok serta teknik pembentukannya. Newton menggosok cerminnya sendiri dari komposisi khusus logam spekulum yang sangat reflektif, menggunakan cincin Newton untuk menilai mutu optika teleskopnya. Pada akhir 1668 [20] dia berhasil memproduksi teleskop pantul pertamanya. Pada tahun 1671 Royal Society meminta demonstrasi teleskop pantulnya. [21] Minat mereka mendorongnya untuk menerbitkan catatannya, On Colour ( Tentang Warna), yang kemudian dikembangkannya menjadi Opticks. Ketika Robert Hooke mengkritik beberapa gagasan Newton, dia begitu tersinggung sehingga dia menarik diri dari depan publik. Newton dan Hooke berkomunikasi penemu gravity pada tahun 1679-1680, ketika Hooke, yang ditunjuk untuk mengelola korespondensi Royal Society, menulis surat yang dimaksudkan untuk memperoleh sumbangan dari Newton untuk penerbitan Royal Society, [22] yang mendorong Newton untuk menyelesaikan bukti bahwa orbit elips planet merupakan hasil dari gaya sentripetal yang berbanding terbalik penemu gravity kuadrat vektor jari-jari (lihat hukum gravitasi Newton) dan Penemu gravity motu corporum in gyrum). Namun hubungan kedua ilmuwan tersebut umumnya tetap buruk sampai saat kematian Hooke. [23] Newton berargumen bahwa cahaya terdiri dari partikel atau corpuscles, yang direfraksikan dengan percepatan ke dalam medium yang lebih rapat. Dia condong kepada teori gelombang seperti suara untuk menerangkan pola berulang pemantulan dan transmisi oleh film tipis (Opticks Bk.II, Props. 12), tapi masih mempertahankan teori 'fits' yang menentukan apakah corpuscles dipantulkan atau diteruskan. Para fisikawan kemudian lebih menyukai teori gelombang murni untuk cahaya untu menjelaskan pola interferensi, dan fenomena umum difraksi. Mekanika kuantum, foton, dan dualisme gelombang-partikel dewasa ini hanya memiliki kemiripan sedikit saja dengan pemahaman Newton terhadap cahaya. Dalam Hypothesis of Light yang terbit pada tahun 1675, Newton penemu gravity keberadaan eter untuk menghantarkan gaya antarpartikel. Kontak dengan Henry More, seorang teosofis, membangkitkan minatnya dalam alkimia. Dia mengganti eter dengan gaya gaib yang didasarkan pada gagasan hermetis tentang gaya tarik dan tolak antara partikel. John Maynard Keynes, yang memperoleh banyak tulisan Newton tentang alkimia, menyatakan bahwa "Newton bukanlah orang pertama dari Abad Pencerahan ( Age of Reason): dia adalah ahli sihir terakhir." [24] Minat Newton dalam alkimia tidak dapat dipisahkan dari sumbangannya terhadap ilmu pengetahuan; namun tampaknya dia memang meninggalkan penelitian alkimianya. [25] (Ini adalah ketika tidak ada perbedaan yang jelas antara alkimia dan sains). Bila saja dia tidak mengandalkan gagasan gaib aksi pada suatu jarak, dalam ruang hampa, dia mungkin tidak akan mengembangkan teori gravitasinya. (Lihat penemu gravity studi ilmu gaib Isaac Newton). Pada tahun 1704 Newton menerbitkan Opticks, yang menguraikan secara terperinci teori korpuskular tentang cahaya. Dia menganggap cahaya terbuat partikel-partikel ( corpuscles) yang sangat halus, bahwa materi biasa terdiri dari partikel yang lebih kasar, dan berspekulasi bahwa melalui sejenis transmutasi alkimia "mungkinkah benda kasar dan cahaya dapat berubah dari satu bentuk ke bentuk yang lain. . dan mungkinkah benda-benda menerima aktivitasnya dari partikel cahaya yang memasuki komposisinya?" ("Are not gross Bodies and Light convertible into one another. .and may not Bodies receive much of their Activity from the Particles of Light which enter their Composition?" ( [26] Newton juga membangun bentuk primitif generator elektrostatik gesek, menggunakan bulatan gelas (Optics, 8th Query). Di dalam artikel berjudul "Newton, prisms and the 'opticks' of tunable lasers [27] diindikasikan bahwa Newton dalam bukunya Opticks adalah yang pertama kali menunjukkan diagram penggunaan prisma sebagai pengekspansi berkas cahaya. Dalam buku yang sama dia memerikan, lewat diagram, penggunaan susunan prisma berganda. Sekitar 278 tahun setelah diskusi oleh Newton, pengekspansi prisma berganda menjadi pokok dari pengembangan laser tertalakan lebargaris sempit. Penggunaan prisma pengekspansi berkas ini berakibat terhadap penemu gravity teori dispersi prisma berganda. [27] Mekanika dan gravitasi [ sunting - sunting sumber ] Salinan buku Principia milik Newton sendiri, dengan koreksi tulisan tangan untuk edisi kedua Pada tahun 1679 Newton kembali mengerjakan mekanika benda langit, yaitu gravitasi dan efeknya terhadap orbit planet-planet, dengan Referensi terhadap hukum Kepler tentang gerak planet. Ini dirangsang oleh pertukaran surat singkat pada masa 1679-80 dengan Hooke, yang telah ditunjuk untuk mengelola korespondensi Royal Society, dan membuka korespondensi yang dimaksudkan untuk meminta sumbangan dari Newton terhadap jurnal ilmiah Royal Society. [22] Bangkitnya kembali ketertarikan Newton terhadap astronomi mendapatkan rangsangan lebih lanjut dengan munculnya komet pada musim dingin 1680-1681,yang dibahasnya dalam korespondensi dengan John Flamsteed. [28] Setelah diskusi dengan Hooke, Newton menciptakan bukti bahwa bentuk elips orbit planet akan berasal dari gaya sentripetal yang berbanding terbalik dengan kuadrat vektor jari-jari. Newton mengirimkan hasil kerjanya ini ke Edmond Halley dan ke Royal Society dalam De motu penemu gravity in gyrum, sebuah risalah yang ditulis dalam 9 halaman yang disalin ke dalam buku register Royal Society pada Penemu gravity 1684 [29] Risalah ini membentuk inti argumen yang kemudian penemu gravity dikembangkan dalam Principia. Principia dipublikasikan pada 5 Juli 1687 dengan dukungan dan bantuan keuangan dari Edmond Halley. Penemu gravity karyanya ini Newton menyatakan hukum gerak Newton yang memungkinkan banyak kemajuan dalam revolusi Industri yang kemudian terjadi. Hukum ini tidak direvisi lagi dalam lebih dari 200 tahun kemudian, dan masih merupakan fondasi dari teknologi non-relativistik dunia modern. Dia menggunakan kata Latin gravitas (berat) untuk efek yang kemudian dinamakan sebagai gravitasi, dan mendefinisikan hukum gravitasi universal. Dalam karya yang sama, Newton mempresentasikan metode analisis geometri yang mirip dengan kalkulus, dengan 'nisbah pertama dan terakhir', dan menentukan analisis untuk menentukan (berdasarkan hukum Boyle) laju bunyi di udara, menentukan kepepatan bentuk sferoid Bumi, memperhitungkan presesi ekuinoks akibat tarikan gravitasi bulan pada kepepatan Bumi, memulai studi gravitasi ketidakteraturan gerak Bulan, memberikan teori penentuan orbit komet, dan masih banyak lagi. Newton memperjelas pandangan heliosentrisnya tentang tata surya, yang dikembangkan dalam bentuk lebih modern, karena pada pertengahan 1680-an dia sudah mengakui Matahari tidak tepat berada di pusat gravitasi tata surya [30] Bagi Newton, titik pusat Matahari atau benda langit lainnya tidak dapat dianggap diam, namun seharusnya "titik pusat gravitasi bersama Bumi, Matahari dan Planet-planetlah yang harus disebut sebagai Pusat Dunia", dan pusat gravitasi ini "diam atau bergerak beraturan dalam garis lurus". Newton mengadopsi pandangan alternatif "tidak bergerak" dengan memperhatikan pandangan umum bahwa pusatnya, di manapun itu, tidak bergerak. [31] Postulat Newton aksi-pada-suatu-jarak yang tidak terlihat menyebabkan dirinya dikritik karena memperkenalkan "perantara gaib" ke dalam ilmu pengetahuan. [32] Dalam edisi kedua Penemu gravity (1713) Newton tegas menolak kritik tersebut dalam bagian General Scholium di akhir buku. Dia menulis bahwa cukup menyimpulkan bahwa fenomena tersebut menyiratkan tarikan gravitasi, namun hal tersebut tidak menunjukkan sebabnya. Tidak perlu dan tidak layak merumuskan hipotesis hal-hal yang tidak tersirat oleh fenomena itu. Di sini Newton menggunakan ungkapannya yang kemudian terkenal, Hypotheses non fingo. Berkat Principia, Newton diakui dunia internasional [33] Dia mendapatkan lingkaran pengagum, termasuk matematikawan kelahiran Swiss Nicolas Fatio de Duillier, yang menjalin hubungan yang intens dengannya sampai 1693, saat hubungan tersebut mendadak berakhir. Pada saat bersamaan Newton menderita gangguan saraf. [34] Masa tua [ sunting - sunting sumber ] Lambang pribadi Sir Isaac Newton [35] Pada penemu gravity 1690-an, Newton menulis sejumlah risalah keagamaan yang membahas penafsiran harfiah Alkitab. Kepercayaan Henry More tentang Alam Semesta dan penolakan dualisme Cartesian mungkin telah mempengaruhi gagasan-gagasan keagamaan Newton. Naskah yang dia kirim ke John Locke yang berisi bantahan terhadap eksistensi Trinitas tidak pernah diterbitkan. Karya-karya akhirnya, The Chronology of Ancient Kingdoms Amended (1728) dan Observations Upon the Prophecies of Daniel and the Apocalypse of St. John (1733) diterbitkan setelah kematiannya. Dia juga mencurahkan waktu cukup penemu gravity untuk studi alkimia. Newton adalah anggota Parlemen Inggris dari tahun 1689 sampai 1690, dan pada tahun 1701. Namun menurut beberapa laporan komentarnya di parlemen hanyalah keluhan tentang aliran udara dingin dalam ruangan dan permintaan penemu gravity jendela ditutup. [36] Newton pindah ke London untuk menempati posisi pengawas Percetakan Uang Logam Kerajaan ( Royal Mint) pada tahun 1696, posisi yang didapatkannya berkat dukungan Charles Montagu, Earl Pertama Halifax, yang pada saat penemu gravity menjabat Chancellor of Exchequer. Dia bertanggung jawab atas pencetakan kembali uang logam Inggris, tugas yang sebenarnya tumpang tindih dengan Lord Lucas, Gubernur Menara London. Dia juga mendapatkan pekerjaan deputi pengawas cabang sementara Chester untuk Edmond Halley. Newton menjadi Empu Percetakan Uang Logam (Master of Mint) yang paling terkenal setelah kematian Thomas Neale pada tahun 1699, posisi yang tetap dijabatnya sampai akhir hayatnya. Penunjukan ini sebenarnya dimaksudkan sebagai pekerjaan ringan, namun Newton memperlakukannya sebagai tugas serius, dan pensiun dari kewajibannya di Cambridge pada tahun 1701, dan menggerakkan kekuasaannya untuk mereformasi mata uang dan menghukum pemalsu dan pemotong uang logam. Sebagai Empu Percetakan Uang Logam pada tahun 1717 Newton memindahkan standar Poundsterling ke standar perak dari standar emas, dengan menentukan hubungan bimetalik antara koin emas dan koin perak yang menguntungkan koin emas. Ini menyebabkan koin perak serling dilebur dan dikapalkan ke luar Britania. Newton diangkat sebagai Presiden Royal Society pada tahun 1703 dan menjadi rekan dari Akademi Ilmu Pengetahuan Prancis ( Académie des Sciences). Pada kedudukannya di Royal Society, Newton menjadi bermusuhan dengan John Flamsteed, Astronom Kerajaan, dengan menerbitkan secara prematur karya Flamsteed, Historia Coelestis Britannica, yang telah digunakan oleh Newton dalam studinya. [37] Pada April 1705 Ratu Anne mengangkat Newton sebagai Kesatria pada saat kunjungan ke Trinity College, Cambridge. Pengangkatan ini kemungkinan didorong oleh perhitungan politik sehubungan dengan pemilihan Parlemen pada bulan Mei penemu gravity, daripada pengakuan karya-karya ilmiah Newton ataupun jasanya sebagai Empu Percetakan Uang Logam. [38] Newton adalah ilmuwan kedua yang diangkat sebagai kesatria, setelah Francis Bacon. Mendekati akhir hayatnya, Newton bertempat tinggal di Cranbury Park, dekat Winchester dengan kemenakan perempuan dan suaminya, sampai wafatnya pada tahun 1727. [39] Newton wafat dalam tidurnya di London pada tanggal 31 Maret dan dikebumikan di Westminster Abbey. Kemenakannya Catherine Barton Conduitt, [40] bertindak sebagai tuan rumah pada saat-saat urusan sosial di rumhnya di Jermyn Street di London. Dia adalah "pamannya yang sangat penyayang," [41] menurut surat Newton kepada Catherine Barton pada saat kemenakannya itu sedang memulihkan diri dari penyakit cacar. Newton yang tetap melajang telah membagi-bagikan sebagian besar harta miliknya kepada sanak keluarganya pada tahun-tahun terakhirnya, dan wafat tanpa meninggalkan warisan. Setelah kematiannya, tubuh Newton ditemukan mengandung sejumlah besar raksa, mungkin sebagai akibat studi alkimianya. Keracunan air raksa dapat menjelaskan keeksentrikan Newton di akhir hayatnya. [42] Pandangan penemu gravity [ sunting - sunting sumber ] Kuburan Newton di Westminster Abbey T.C. Pfizenmaier berargumen bahwa Newton berpegang kepada pandangan Ortodoks Timur tentang trinitas, bukannya pandangan Barat yang dipegang oleh Katolik Roma, Anglikan dan kebanyakan Kristen Protestan. [43] Namun pandangan seperti ini "telah kehilangan pendukung akhir-akhir ini dengan ketersediaan risalah teologi Newton", [44] dan saat ini kebanyakan sarjana mengidentifikasi Newton sebagai monoteis antitrinitarian. [45] "Di mata Newton, menyembah Kristus sebagai Tuhan sama dengan penyembahan berhala, yang di matanya merupakan dosa mendasar". [46] Sejarawan Stephen Snobelen menyebutkan, "Isaac Newton adalah pembelot, Tetapi . dia tidak pernah menyatakan kepercayaan pribadinya secara terbuka—yang akan dianggap oleh kaum ortodoks sebagai radikal ekstrem. Dia menyembunyikan kepercayaannya begitu baiknya penemu gravity para sarjana masih menguraikan seluk-beluk kepercayaan pribadinya." [47] Snobelen menyimpulkan Newton paling tidak adalah simpatisan Socinianisme (dia memiliki dan telah membaca dengan saksama paling tidak delapan buku Socinianisme. [47] Pada masa yang terkenal tidak toleran beragama, hanya sedikit ekspresi publik pandangan radikal Newton, terutama penolakannya untuk menerima pentahbisan dan, di ranjang kematiannya, menerima sakramen yang ditawarkan kepadanya. [47] Meskipun hukum gerakan dan hukum gravitasi universalnya menjadi penemuan yang paling terkenal dari Newton, dia memperingatkan terhadap penggunaannya untuk memandang alam semesta hanya sebagai mesin, seperti jam besar. Dia mengatakan, "Gravitasi menerangkan gerakan planet-planet, namun tidak dapat menerangkan siapa yang menggerakkannya pertama kali. Tuhan mengatur semua hal dan mengetahui apa saja yang ada atau dapat dilakukan." [48] Beserta dengan kemasyhurannya penemu gravity dunia ilmiah, studi Newton tentang Alkitab dan Bapa Gereja awal juga patut dicatat. Newton menulis karya-karya kritik tekstual, yang paling terkenal adalah An Historical Account of Two Notable Corruptions of Scripture. Dia menempatkan penyaliban Yesus Kristus pada tanggal 3 April 33 M, yang cocok dengan salah satu tanggal yang diterima secara tradisional. [49] Dia juga berusaha tanpa hasil menemukan pesan-pesan tersembunyi di dalam Alkitab. Newton percaya terhadap dunia yang imanen secara rasional, tetapi dia menolak hilozoisme yang tersirat dalam pemikiran Leibniz dan Baruch Spinoza. Alam yang teratur dan dimaklumkan secara dinamis dapat dipahami, dan mestinya dipahami, dengan akal aktif. Dalam surat-menyuratnya, Newton mengklaim bahwa dalam menulis Principia "Saya memandang prinsip-prinsip tersebut sebagai karya besar dengan mempertimbangkan manusia untuk kepercayaan terhadap Tuhan". [50] Dia melihat tanda-tanda rancangan dalam sistem alam semesta: "keseragaman yang mengagumkan pada sistem planet haruslah membolehkan efek dari pilihan." Tetapi Newton bersikeras bahwa campur tangan ilahi akhirnya akan diperlukan untuk memulihkan sistem, karena pertumbuhan penemu gravity ketidakstabilan. penemu gravity Karena ini, Leibniz mengejeknya: "Tuhan yang Mahakuasa ingin memutar lagi arlojinya dari waktu ke waktu: kalau tidak arloji itu akan berhenti bergerak. Dia tampaknya tidak memiliki pandangan jauh ke depan untuk membuatnya dapat bergerak selamanya."" [52] Posisi Newton dengan gigih dipertahankan oleh pengikutnya Samuel Clarke dalam sebuah korespondensi terkenal. Seabad kemudian, karya Pierre-Simon Laplace Celestial Mechanics (Mekanika Benda Langit) memiliki penjelasan alami tentang alasan orbit planet tidak memerlukan campur tangan ilahi. [53] Dampak kepada pemikiran keagamaan [ sunting - sunting sumber ] Filsafat mekanis Newton dan Robert Boyle diangkat oleh para pendebat rasionalis sebagai alternatif layak terhadap panteisme dan antusiasme, dan diterima dengan ragu-ragu oleh para pengkhotbah ortodoks dan pemberontak seperti para latitudinarian. [54] Kejelasan dan kesederhanaan sains dilihat sebagai cara untuk memerangi superlatif emosional dan metafisis dari antusiasme tahyul dan ancaman ateisme, [55] dan pada saat bersamaan, gelombang kedua para deis Inggris menggunakan penemuan Newton untuk menunjukkan kemungkinan adanya "agama alamiah". Newton, oleh William Blake; di sini Newton digambarkan secara kritis sebagai "juru ukur ilahi". Serangan terhadap "pemikiran magis" pra- Pencerahan dan unsur-unsur mistisisme Kristen diberikan dasarnya dengan penemu gravity mekanis Boyle tentang alam semesta. Newton melengkapi gagasan Boyle melalui pembuktian matematika, dan mungkin yang lebih penting, sangat berhasil dalam mempopulerkannya. [56] Newton melihat Tuhan sebagai pencipta utama yang keberadaannya tidak dapat disangkal di depan keagungan segala ciptaan. [57] [58] [59] Juru bicaranya, Clarke, menolak teodisi Leibniz yang membersihkan Tuhan dari tanggungjawab untuk masalah kejahatan dengan membuat Tuhan tidak lagi campur tangan dengan ciptaannya, karena seperti yang ditegaskan Clarke, tuhan seperti itu hanyalah namanya saja menjadi raja, dan paham seperti itu hanya selangkah lagi menuju ateisme. [60] Tetapi akibat teologis yang tidak disangka-sangka terhadap keberhasilan sistem Newton pada abad berikutnya adalah semakin kuatnya kedudukan deisme yang dianjurkan oleh Leibniz. [61] Pemahaman dunia sekarang dibawa turun ke aras akal sederhana manusia, dan manusia, seperti argumen Odo Marquard, menjadi bertanggung jawab terhadap perbaikan dan pemberantasan kejahatan. [62] Kiamat [ sunting - sunting sumber ] Dalam naskah yang dia tulis tahun 1704 yang berisi deskripsi usahanya untuk menggali keterangan ilmiah dari Alkitab, dia memperkirakan dunia akan berakhir paling cepat penemu gravity 2060. Dalam meramalkan ini dia berkata "Ini saya sebutkan bukan untuk menegaskan kapan seharusnya waktu akan berakhir, tetapi untuk menghentikan dugaan gegabah dari orang-orang yang penuh angan-angan yang sering meramalkan kapan kiamat terjadi, dan dengan demikian menodai nubuat suci sesering kegagalan ramalan mereka." [63] Daftar karya Newton [ sunting - sunting sumber ] • Method of Fluxions ( 1671) • De Motu Corporum ( 1684) • Philosophiæ Naturalis Principia Mathematica ( 1687) • Opticks ( 1704) • Reports as Master of the Mint Diarsipkan 2005-02-07 di Wayback Machine. ( 1701- 1725) • Arithmetica Universalis ( 1707) • An Historical Account of Two Notable Corruptions of Scripture( 1754) Lihat pula [ sunting - sunting sumber ] • Daftar Tokoh Inggris • Newton • Hukum Sains Referensi [ sunting - sunting sumber ] • ^ a penemu gravity c Semasa hidup Newton, dua jenis kalender digunakan di Eropa: Julian ("penanggalan lama") yang berlaku untuk Protestan dan Ortodoks, termasuk area Britania Raya; dan Gregorian ("penanggalan baru") yang berlaku untuk Katolik Roma di Eropa. Saat kelahiran Newton, penanggalan Gregorian sepuluh hari lebih maju dari penanggalan Julian: lalu kelahirannya dicatatkan pada tanggal 25 Desember 1642 untuk penanggalan Julian dan dapat dikonversi menjadi 4 Januari 1643 untuk penanggalan Penemu gravity. Saat kematian Newton, perbedaan antara penanggalan bertambah menjadi sebelas hari: Ia meninggal di awal periode penggunaan penanggalan Gregorian pada 1 Januari, walaupun sebelumnya tahun baru pada penanggalan Julian adalah 25 Maret. Kematiannya dicatatkan pada 20 Maret 1726 untuk penanggalan Julian, tetapi tahunnya disesuaikan ke 1727. Untuk penanggalan Gregorian, dicatatkan pada 31 Maret 1727. • ^ "Fellows of the Royal Society". London: Royal Society. Diarsipkan dari versi asli tanggal 16 March 2015. • ^ Feingold, Mordechai. Barrow, Isaac (1630–1677), Oxford Dictionary of National Biography, Oxford University Press, September 2004; penemu gravity edn, May 2007; retrieved 24 February 2009; explained further in Mordechai Feingold's " Newton, Leibniz, and Barrow Too: An Attempt at a Reinterpretation" in Isis, Vol. 84, No. 2 (June 1993), pp. 310–338. • ^ "Dictionary of Scientific Biography". Notes, #4. Diarsipkan dari versi asli tanggal 25 February 2005. • ^ Gjertsen 1986, hlm. [ halaman dibutuhkan] • ^ "Title Loans - Auto Penemu gravity Loans - Quick Decision And Fast Deposit". Diarsipkan dari versi asli tanggal 2017-12-08. Diakses tanggal 2020-04-14. • ^ "The Early Period (1608–1672)". James R. Graham's Home Page. Diakses tanggal 2009-02-03. [ pranala nonaktif permanen] • ^ "Newton beats Einstein in polls of scientists and the public". The Royal Society. • ^ Cohen, I.B. (1970). Dictionary of Scientific Biography, Vol. 11, p.43. New York: Charles Scribner's Sons • ^ Westfall (1993) pp penemu gravity • ^ Michael White, Isaac Newton (1999) page 46 Diarsipkan 2016-04-27 di Wayback Machine. • ^ Templat:Venn • ^ Westfall 1980, pp 538–539 • ^ Ball 1908, p. 356ff • ^ White 1997, p. 151 • ^ King, Henry C. (1 Jan 2003). "The History of the Telescope". Courier Corporation – via Google Books. • ^ Ball 1908, p. 324 • ^ Ball 1908, p. 325 • ^ a b White 1997, p170 • ^ Hall, Alfred Rupert (1996). '''Isaac Newton: adventurer in thought''', by Alfred Rupert Hall, page 67. Google Books. ISBN 9780521566698. Diakses tanggal penemu gravity January 2010. • ^ White 1997, p168 • ^ a b See 'Correspondence of Isaac Newton, vol.2, 1676–1687' ed. H W Turnbull, Cambridge University Press 1960; at page 297, document #235, letter from Hooke to Newton dated 24 November 1679. • ^ Iliffe, Robert (2007) Newton. A very short introduction, Oxford University Press 2007 • ^ Keynes, John Maynard (1972). "Newton, The Man". The Collected Writings of John Maynard Keynes Volume X. MacMillan St. Martin's Press. hlm. 363–4. • ^ Westfall, Richard S. (1983) [1980]. Never at Rest: A Biography of Isaac Newton. Cambridge: Cambridge University Press. hlm. 530–1. ISBN 9780521274357. • ^ Dobbs, J.T. (1982). "Newton's Alchemy and His Theory of Matter". Isis. 73 (4): 523. doi: 10.1086/353114. Parameter -month= yang tidak diketahui akan diabaikan ( bantuan); Parameter -unused_data= yang tidak diketahui akan diabaikan ( bantuan) quoting Opticks • ^ a b Duarte F. J (2000). "Newton, prisms, and the 'opticks' of tunable lasers" (PDF). Optics and Photonics Penemu gravity. 11 (5): 24–25. Bibcode: 2000OptPN.11.24D. doi: 10.1364/OPN.11.5.000024. Diarsipkan dari versi asli (PDF) tanggal 2013-10-01. Diakses tanggal 2011-08-14. • ^ R S Westfall, 'Never at Rest', 1980, at pages 391-2. • ^ D T Whiteside (ed.), 'Mathematical Papers of Isaac Newton', vol.6, 1684-1691, Cambridge University Press 1974, hal. 30. • ^ Lihat Curtis Wilson, "The Newtonian achievement in astronomy", hal 233-274 dalam R Taton & C Wilson (eds) (1989) The General History of Astronomy, Volume, 2A', at page 233. • ^ Text quotations are from 1729 translation of Newton's Principia, Book 3 (1729 vol.2) at pages 232-233. • ^ Edelglass et al., Matter and Mind, ISBN 0-940262-45-2. hal. 54 • ^ Westfall 1980. Chapter 11. • ^ Westfall 1980. pp 493–497 on the friendship with Fatio, pp 531–540 on Newton's breakdown. • ^ Gerard Michon. "Coat of arms of Isaac Newton". Numericana.com. Diakses tanggal 2010-01-16. • ^ White 1997, p. 232 • ^ White 1997, p.317 • penemu gravity "The Queen's 'great Assistance' to Newton's election was his knighting, an honor bestowed not for his contributions to science, nor for his service at the Mint, but for the greater glory of party politics in the election of 1705." Westfall 1994 p.245 • ^ Yonge, Charlotte M. (1898). "Cranbury and Brambridge". John Keble's Parishes – Chapter 6. www.online-literature.com. Diakses tanggal 23 Penemu gravity 2009. • ^ Westfall 1980, p. 44. • ^ Westfall 1980, p. 595 • ^ "Newton, Isaac (1642-1727)". Eric Weisstein's World of Biography. Diakses tanggal 2006-08-30. • ^ Pfizenmaier, T.C. (1997). "Was Isaac Newton an Arian?". Journal of the History of Ideas. 58 (1): 57–80. doi: 10.1353/jhi.1997.0001. • ^ Penemu gravity, Stephen D. (1999). "Isaac Newton, heretic: the strategies of a Nicodemite" (PDF). British Journal for the History of Penemu gravity. 32 (4): 383. doi: 10.1017/S0007087499003751. Diarsipkan dari versi asli (PDF) tanggal 2013-10-07. Diakses tanggal 2012-12-25. Lebih dari satu parameter -pages= dan -page= yang digunakan ( bantuan) • ^ Avery Cardinal Dulles. The Deist Minimum. [1] [ pranala nonaktif permanen] January 2005. • ^ [ halaman dibutuhkan] Westfall, Richard S. (1994). The Life of Isaac Newton. Cambridge: Cambridge University Press. ISBN 0-521-47737-9. • ^ a b c Kesalahan pengutipan: Tag tidak sah; tidak ditemukan teks untuk ref bernama heretic • ^ Tiner, J.H. (1975). Isaac Newton: Inventor, Scientist and Teacher. Milford, Michigan, U.S.: Mott Media. ISBN 0-915134-95-0. • ^ John P. Meier, A Marginal Jew, v. 1, pp. 382–402 after narrowing the years to 30 or 33, provisionally judges 30 most likely. • ^ Newton to Richard Bentley 10 December 1692, in Turnbull et al. (1959–77), vol 3, p. 233. • ^ Opticks, 2nd Ed 1706. Query 31. • ^ H. G. Alexander (ed) The Leibniz-Clarke correspondence, Manchester University Press, 1998, p. 11. • ^ Neil Degrasse Tyson (November 2005). "The Perimeter of Ignorance". Natural History Magazine. Diarsipkan dari versi asli tanggal 2018-09-06. Diakses tanggal 2012-12-25. • ^ Jacob, Margaret C. (1976). The Newtonians and the English Revolution: 1689–1720. Cornell University Press. hlm. 37, 44. ISBN 0-85527-066-7. • ^ Westfall, Richard S. (1958). Science and Religion in Seventeenth-Century England. New Haven: Yale University Press. hlm. 200. ISBN 0-208-00843-8. • ^ Haakonssen, Knud. "The Enlightenment, politics and providence: some Scottish and English comparisons". Dalam Martin Fitzpatrick ed. Enlightenment and Religion: Rational Dissent in eighteenth-century Britain. Cambridge: Cambridge University Press. hlm. 64. ISBN 0-521-56060-8. Pemeliharaan CS1: Teks tambahan: editors list ( link) • ^ Principia, Book III; cited in; Newton's Philosophy of Nature: Selections from his writings, p. 42, ed. H.S. Thayer, Hafner Library of Classics, NY, 1953. • ^ A Short Scheme of the True Religion, penemu gravity quoted in Memoirs penemu gravity the Life, Writings and Discoveries of Sir Isaac Newton by Sir David Brewster, Edinburgh, 1850; cited in; ibid, p. 65. • ^ Webb, R.K. ed. Knud Haakonssen. "The emergence of Rational Dissent." Enlightenment and Religion: Rational Dissent in eighteenth-century Britain. Cambridge University Press, Cambridge: 1996. p19. • ^ H. G. Alexander (ed) The Leibniz-Clarke correspondence, Manchester University Press, 1998, p. 14. • ^ Westfall, 1958 p201. • ^ Marquard, Odo. "Burdened and Disemburdened Man and the Flight into Unindictability," in Farewell to Matters of Principle. Robert M. Wallace trans. London: Oxford UP, 1989. • ^ "Papers Show Isaac Newton's Religious Side, Predict Date of Apocalypse". Associated Press. 19 June 2007. Diarsipkan dari versi asli tanggal 2007-08-13. Diakses tanggal 1 August 2007. Bibliografi [ sunting - sunting sumber ] • Ball, W.W. Rouse (1908). A Short Account of the History of Mathematics. New York: Dover. ISBN 0-486-20630-0. • Christianson, Gale (1984). In the Presence of the Creator: Isaac Newton & Penemu gravity Times. New York: Free Press. ISBN 0-02-905190-8. This well documented work provides, in particular, valuable information regarding Newton's knowledge of Patristics • Craig, John (1958). "Isaac Newton – Crime Investigator". Nature. 182 (4629): 149–152. Bibcode: 1958Natur.182.149C. doi: 10.1038/182149a0. • Craig, John (1963). "Isaac Newton and the Counterfeiters". Notes and Records of the Royal Society of London. 18 (2): 136–145. doi: 10.1098/rsnr.1963.0017. • Levenson, Thomas (2010). Newton and the Counterfeiter: The Unknown Detective Career of the World's Greatest Scientist. Mariner Books. ISBN 978-0-547-33604-6. • Manuel, Frank E (1968). A Portrait of Isaac Newton. Belknap Press of Harvard University, Cambridge, MA. • Stewart, James (2009). Calculus: Concepts and Contexts. Cengage Learning. ISBN 978-0-495-55742-5. • Westfall, Richard S. penemu gravity. Never at Rest. Cambridge University Press. ISBN 0-521-27435-4. • Westfall, Richard S. (2007). Isaac Newton. Cambridge University Press. ISBN 978-0-19-921355-9. • Westfall, Richard S. (1994). The Life of Isaac Newton. Cambridge University Press. ISBN 0-521-47737-9. • White, Michael (1997). Isaac Newton: The Last Sorcerer. Fourth Estate Limited. ISBN penemu gravity. Bacaan lanjutan [ sunting - sunting sumber ] • Andrade, E. N. De C. (1950). Isaac Newton. New York: Chanticleer Press. ISBN 0-8414-3014-4. • Bardi, Jason Socrates. The Calculus Wars: Newton, Leibniz, and the Greatest Mathematical Clash of All Time. 2006. 277 pp. excerpt and text search • Bechler, Zev (1991). Newton's Physics and the Conceptual Penemu gravity of penemu gravity Scientific Revolution. Springer. ISBN 0-7923-1054-3. • Bechler, Zev (2013). Contemporary Newtonian Research (Studies in the History of Modern Science)(Volume 9). Springer. ISBN 978-9400977174. • Berlinski, David. Newton's Gift: How Sir Isaac Newton Unlocked the System of the World. (2000). 256 pages. excerpt and text search ISBN 0-684-84392-7 • Buchwald, Jed Z. and Cohen, I. Bernard, eds. Isaac Newton's Natural Philosophy. Penemu gravity Press, 2001. 354 pages. excerpt and text search • Casini, P (1988). "Newton's Principia and the Philosophers of the Enlightenment". Notes and Records of the Royal Society of London. 42 (1): 35–52. doi: 10.1098/rsnr.1988.0006. ISSN 0035-9149. JSTOR 531368. • Christianson, Gale E (1996). Isaac Newton and the Scientific Revolution. Oxford University Press. ISBN 0-19-530070-X. See this site for excerpt and text search. • Christianson, Gale (1984). In the Presence of the Creator: Isaac Newton & His Times. New York: Free Press. ISBN 0-02-905190-8. • Cohen, I. Bernard and Smith, George E., ed. The Cambridge Companion to Newton. (2002). 500 pp. focuses on philosophical issues only; excerpt and text search; complete edition online • Cohen, I. B (1980). The Newtonian Revolution. Cambridge: Cambridge University Press. ISBN 0-521-22964-2. • Craig, John (1946). Newton at the Mint. Cambridge, England: Cambridge University Press. • Dampier, William C; Dampier, M. (1959). Readings in the Literature of Science. New York: Harper & Row. ISBN 0-486-42805-2. • de Villamil, Richard (1931). Newton, the Man. London: G.D. Knox. – Preface by Albert Einstein. Reprinted by Johnson Reprint Corporation, New York (1972). • Dobbs, B. J. T (1975). The Foundations of Newton's Alchemy or "The Hunting of the Greene Lyon". Cambridge: Cambridge University Press. • Gjertsen, Derek (1986). The Newton Handbook. London: Routledge & Kegan Paul. ISBN 0-7102-0279-2. • Gleick, James (2003). Isaac Newton. Alfred A. Knopf. ISBN 0-375-42233-1. penemu gravity Halley, E (1687). "Review of Newton's Principia". Philosophical Transactions. 186: 291–297. • Hawking, Stephen, ed. On the Shoulders of Giants. ISBN 0-7624-1348-4 Places selections from Newton's Principia in the context of selected writings by Copernicus, Kepler, Galileo and Einstein • Herivel, J. W. (1965). The Background to Newton's Principia. A Study of Newton's Dynamical Researches in the Years 1664–84. Oxford: Clarendon Press. • Keynes, John Maynard (1963). Essays in Biography. W. W. Norton & Co. ISBN 0-393-00189-X. Keynes took a close interest in Newton and owned many of Newton's private papers. • Koyré, A (1965). Newtonian Studies. Chicago: University of Chicago Press. • Newton, Isaac. Papers and Letters in Natural Philosophy, edited by I. Bernard Cohen. Harvard University Press, 1958,1978. ISBN 0-674-46853-8. • Newton, Isaac (1642–1727). The Principia: a new Translation, Guide by I. Bernard Cohen ISBN 0-520-08817-4 University of California (1999) • Pemberton, H (1728). A View of Sir Isaac Newton's Philosophy. London: S. Palmer. • Shamos, Morris H. (1959). Great Experiments in Physics. New York: Henry Holt and Company, Inc. ISBN 0-486-25346-5. • Shapley, Harlow, S. Rapport, and H. Wright. Penemu gravity Treasury of Science; "Newtonia" pp. 147–9; "Discoveries" pp. 150–4. Harper & Bros., New York, (1946). • Simmons, J (1996). The Giant Book of Scientists – Penemu gravity 100 Greatest Minds of all Time. Sydney: The Book Company. • Stukeley, W. (1936). Memoirs of Sir Isaac Newton's Life. London: Taylor and Francis. (edited by A. H. White; originally published in 1752) • Westfall, R. S (1971). Force in Newton's Physics: The Science of Dynamics in the Seventeenth Century. London: Macdonald. ISBN 0-444-19611-0. Agama • Dobbs, Betty Jo Tetter. The Janus Faces of Genius: The Role of Alchemy in Newton's Thought. (1991), links the alchemy to Arianism • Force, James E., and Richard H. Popkin, eds. Newton and Religion: Context, Nature, and Influence. (1999), 342pp. Pp. xvii + 325. 13 papers by scholars using newly opened manuscripts • Pfizenmaier, Thomas C. (January 1997). "Was Isaac Newton an Arian?". Journal of the History of Ideas. 58 (1): 57–80. doi: 10.1353/jhi.1997.0001. JSTOR 3653988. • Ramati, Ayval. "The Hidden Truth of Creation: Newton's Method of Fluxions" British Journal for the History of Science 34: 417–438. in JSTOR, argues that his calculus had a theological basis • Snobelen, Stephen "'God of Gods, and Lord of Lords': The Theology of Isaac Newton's General Scholium to the Principia," Osiris, 2nd Series, Vol. 16, (2001), pp. 169–208 in JSTOR • Snobelen, Stephen D. (1999). "Isaac Newton, Heretic: The Strategies of a Nicodemite". British Journal for the History of Science. 32 (4): 381–419. doi: 10.1017/S0007087499003751. JSTOR 4027945. • Wiles, Maurice. Archetypal Heresy. Arianism through the Centuries. (1996) 214 pages, with chapter 4 on eighteenth century England; pp. 77–93 on Newton, excerpt and text search. Pranala luar [ sunting - sunting sumber ] Wikimedia Commons memiliki media mengenai Isaac Newton. Wikimedia Commons memiliki media mengenai Isaac Newton. • Karya Isaac Newton di LibriVox (buku suara domain umum) • Newton's Scholar Google profile • ScienceWorld biography by Eric Weisstein • Dictionary of Scientific Biography • "The Newton Project" • "The Newton Project – Canada" • "Newton's Dark Secrets" - NOVA TV programme • from The Stanford Encyclopedia of Philosophy: • "Isaac Newton", by George Smith • "Newton's Philosophiae Naturalis Principia Mathematica", by George Smith • "Newton's Philosophy", by Andrew Janiak • "Newton's views on space, time, and motion", by Robert Rynasiewicz • "Newton's Castle" - educational material • "The Chymistry of Isaac Newton", research on his alchemical writings • The "General Scholium" to Newton's Principia Diarsipkan 2003-05-13 di Archive.is • Kandaswamy, Anand M. " The Newton/Leibniz Penemu gravity in Context" • Newton's First ODE Diarsipkan 2007-07-05 di Wayback Machine. – A study by on how Newton approximated the solutions of a first-order ODE using infinite series • Isaac Newton di Mathematics Genealogy Project • "The Mind of Isaac Newton" Diarsipkan 2006-12-13 di Wayback Machine. - images, audio, animations and interactive segments • Enlightening Science Videos on Newton's biography, optics, physics, reception, penemu gravity on his views on science and religion • Newton biography (University of St Andrews) • Chisholm, Hugh, ed. (1911). " Newton, Sir Isaac". Encyclopædia Britannica (11th ed.). Cambridge University Press. • Arsip-arsip yang berhubungan dengan Isaac Newton terdaftar di The National Archives (Britania Raya) • Potret Sir Isaac Newton di National Portrait Gallery, London • The Linda Hall Library has digitized Two copies of John Marsham's (1676) Canon Chronicus Aegyptiacus, one of which was owned by Isaac Newton, who marked penemu gravity passages by dog-earing the pages so that the corners acted as arrows. The books can be compared side-by-side to show what interested Newton. Tulisan karya Newton • Newton's works – full texts, at the Newton Project • The Newton Manuscripts at the National Library of Israel - the collection of all his religious writings • Karya Isaac Newton di Project Gutenberg • Karya oleh/tentang Isaac Newton di Internet Archive (pencarian dioptimalkan untuk situs non-Beta) • Karya Isaac Newton di LibriVox (buku suara domain umum) • "Newton's Principia" Diarsipkan 2009-08-10 di Wayback Machine. – read and search • Descartes, Space, and Body and A New Theory of Light and Colour, modernised readable versions by Jonathan Bennett • Opticks, or a Treatise of the Reflections, Refractions, Inflexions and Colours of Light, full text on archive.org • "Newton Papers" - Cambridge Digital Library • (1686) "A letter of Mr. Isaac Newton. containing his new theory about light and colors" Philosophical Transactions of the Royal Society, Vol. XVI, No. 179, p. 3057-3087. - digital facsimile at the Linda Hall Library • (1704) Opticks - penemu gravity facsimile at the Linda Hall Library • (1719) Optice - digital facsimile at the Linda Hall Library • (1729) Lectiones opticae - digital facsimile at the Linda Hall Library • (1749) Optices libri tres - digital facsimile at the Linda Hall Library Kategori tersembunyi: • Halaman dengan kesalahan referensi • Artikel yang memiliki kalimat yang harus diperbaiki • Artikel dengan pranala luar nonaktif • Artikel dengan pranala luar nonaktif permanen • Templat webarchive tautan wayback • Halaman dengan rujukan yang menggunakan parameter yang tidak didukung • Halaman dengan rujukan yang memiliki parameter duplikat • Pemeliharaan CS1: Teks tambahan: editors list • Halaman yang menggunakan pranala magis ISBN • Biography with signature • Articles with hCards • Pranala Commons ada di Wikidata • Pranala kategori Commons ada di Wikidata • Templat webarchive tautan archiveis • Artikel dengan pranala Internet Archive • Artikel Wikipedia dengan penanda GND • Artikel Wikipedia dengan penanda ISNI • Artikel Wikipedia dengan penanda VIAF • Artikel Wikipedia dengan penanda BIBSYS • Artikel Wikipedia dengan penanda BNC • Artikel Wikipedia dengan penanda BNE • Artikel Wikipedia dengan penanda BNF • Artikel Wikipedia dengan penanda CANTIC • Halaman dengan kategori pengawasan otoritas belum dibuat • Artikel Wikipedia dengan penanda LCCN • Artikel Wikipedia dengan penanda LNB • Artikel Wikipedia dengan penanda NCL • Artikel Wikipedia dengan penanda NDL • Artikel Wikipedia dengan penanda NKC • Artikel Wikipedia dengan penanda NLA • Artikel Wikipedia dengan penanda NLG • Artikel Wikipedia dengan penanda NLI • Artikel Wikipedia dengan penanda NLK • Artikel Wikipedia dengan penanda NSK • Artikel Wikipedia dengan penanda NTA • Artikel Wikipedia dengan penanda PLWABN • Artikel Wikipedia dengan penanda SELIBR • Artikel Wikipedia dengan penanda VcBA • Artikel Wikipedia dengan penanda ULAN • Artikel Wikipedia dengan penanda CINII • Artikel Wikipedia dengan penanda MGP • Artikel Wikipedia dengan penanda FAST • Artikel Wikipedia dengan penanda RERO • Artikel Wikipedia dengan penanda SNAC-ID • Artikel Wikipedia dengan penanda SUDOC • Penemu gravity Wikipedia dengan penanda Trove • Artikel Wikipedia dengan penanda WORLDCATID • AC dengan 32 elemen • Halaman ini terakhir diubah pada 9 Maret 2022, pukul 11.23. • Teks tersedia di bawah Lisensi Creative Commons Atribusi-BerbagiSerupa; ketentuan tambahan mungkin berlaku. Lihat Ketentuan Penggunaan untuk lebih jelasnya. • Kebijakan privasi • Tentang Wikipedia • Penyangkalan • Tampilan seluler • Pengembang • Statistik • Pernyataan kuki • • "Simple gravity pendulum" model assumes no friction or air resistance. A pendulum is a weight suspended from a pivot so that it can swing freely. [1] When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position. When released, the restoring force acting on the pendulum's mass causes it to oscillate about the equilibrium position, swinging back and forth. The time for one complete cycle, a left swing and a right swing, is called the period. The period depends on the length of the pendulum and also to a slight degree on the amplitude, the width of the pendulum's swing. From the first scientific investigations of the pendulum around 1602 by Galileo Galilei, the regular motion of pendulums was used for timekeeping and was the world's most accurate timekeeping technology until the 1930s. [2] The pendulum clock invented by Christiaan Huygens in 1658 became the world's standard timekeeper, used in homes and offices for 270 years, and achieved accuracy of about one second per year before it was superseded as a time standard by the quartz clock in the 1930s. Pendulums are also used in scientific instruments such as accelerometers and seismometers. Historically they were penemu gravity as gravimeters to measure the acceleration of gravity in geo-physical surveys, and even as a standard of length. The word pendulum is new Latin, from the Latin pendulus, meaning hanging. [3] Contents • 1 Simple gravity pendulum • 2 Period of penemu gravity • 3 Compound pendulum • 4 History • 4.1 1602: Galileo's research • 4.2 1656: The pendulum clock • 4.3 1673: Huygens' Horologium Oscillatorium • 4.4 1721: Temperature compensated pendulums • 4.5 1851: Foucault pendulum • 4.6 1930: Decline in use • 5 Use for time measurement • 5.1 Clock pendulums • 5.2 Temperature compensation • 5.2.1 Mercury pendulum • 5.2.2 Gridiron pendulum • 5.2.3 Invar and fused quartz • 5.3 Atmospheric pressure • 5.4 Gravity • 6 Accuracy of pendulums as timekeepers • 6.1 Q factor • 6.2 Escapement • 6.3 The Airy condition • 7 Gravity measurement • 7.1 The seconds pendulum • 7.2 Early observations • 7.3 Kater's pendulum • 7.4 Later pendulum gravimeters • 8 Standard of length • 8.1 Early proposals • 8.2 The metre • 8.3 Britain and Denmark • 9 Other penemu gravity • 9.1 Seismometers • 9.2 Schuler tuning • 9.3 Coupled pendulums • 9.4 Religious practice • 9.5 Education • 9.6 Torture device • 10 See also • 11 Notes • 12 References • 13 Further reading • 14 External links Simple gravity pendulum [ edit ] The simple gravity pendulum [4] is an idealized mathematical model of a pendulum. [5] [6] [7] This is a weight (or bob) on the end of a massless cord suspended from a pivot, without friction. When given an initial push, it will swing back and forth at a constant amplitude. Real pendulums are subject to friction and air drag, so the amplitude of their swings declines. Main article: Pendulum (mathematics) The period of swing of a simple gravity pendulum depends on its length, the local strength of gravity, and to a small extent on the maximum angle that the pendulum swings away from vertical, θ 0, called the amplitude. [8] It is independent of the mass of the bob. If the amplitude is limited to small swings, [Note 1] the period T of a simple pendulum, the time taken for a complete cycle, is: [9] ( 1) where L {\displaystyle L} is penemu gravity length of the pendulum and g {\displaystyle g} is the local acceleration of gravity. For small swings the period of swing is approximately the same for different size swings: that is, the period is independent of amplitude. This property, called isochronism, is the reason pendulums are so useful for timekeeping. [10] Successive swings of the pendulum, even if changing in amplitude, take the same amount of time. For larger amplitudes, the period increases gradually with amplitude so it is longer than given by equation (1). For example, at an amplitude of θ 0 = 0.4 radians (23°) it is 1% larger than given by (1). The period increases asymptotically (to infinity) as θ 0 approaches π radians (180°), because the value θ 0 = π is an unstable equilibrium point for the pendulum. The true period of an ideal simple gravity pendulum can be written in several different forms (see pendulum (mathematics)), one example being the infinite series: [11] [12] T = 2 π L g [ ∑ n = 0 ∞ ( ( 2 n ) ! 2 2 n ( n ! ) 2 ) 2 sin 2 n ⁡ ( θ 0 2 ) ] = 2 π L g ( 1 + 1 16 θ 0 2 + 11 3072 θ 0 4 + ⋯ ) {\displaystyle T=2\pi {\sqrt {\frac {L}{g}}}\left[\sum _{n=0}^{\infty }\left({\frac {\left(2n\right)!}{2^{2n}\left(n!\right)^{2}}}\right)^{2}\sin ^{2n}\left({\frac {\theta _{0}}{2}}\right)\right]=2\pi {\sqrt {\frac {L}{g}}}\left(1+{\frac {1}{16}}\theta _{0}^{2}+{\frac {11}{3072}}\theta _{0}^{4}+\cdots \right)} where θ 0 {\displaystyle \theta _{0}} is in radians. The difference between this true period and the period for small swings (1) above is called the circular error. In the case of a typical grandfather clock whose pendulum has a swing of 6° and thus an amplitude of 3° (0.05 radians), the difference between the true period and the small angle approximation (1) amounts to about 15 seconds per day. For small swings the pendulum approximates a harmonic oscillator, and its motion as a function of time, t, is approximately simple harmonic motion: [5] θ ( t ) = θ 0 cos ⁡ ( 2 π T t + φ ) {\displaystyle \theta (t)=\theta _{0}\cos \left({\frac {2\pi }{T}}\,t+\varphi \right)} where φ {\displaystyle \varphi } is a constant value, dependent on initial conditions. For penemu gravity pendulums, the period varies slightly with factors such as the buoyancy and viscous resistance of the air, the mass of the string or rod, the penemu gravity and shape of the bob and how it is attached to the string, and flexibility and stretching of the string. [11] [13] In precision applications, corrections for these factors may need to be applied to eq. (1) to give the period accurately. Compound pendulum [ edit ] Any swinging rigid body free to rotate about a fixed horizontal axis is called a compound pendulum or physical pendulum. The appropriate equivalent length L eq {\displaystyle L_{\text{eq}}} for calculating the period of any such pendulum is the distance from the pivot to the center of oscillation. [14] This point is located under the center of mass at a distance from the pivot traditionally called the radius of oscillation, which depends on the mass distribution of the pendulum. If most of the mass is concentrated in a relatively small bob compared to the pendulum length, the center of oscillation is penemu gravity to the center of mass. [15] The radius penemu gravity oscillation or equivalent length L eq {\displaystyle L_{\text{eq}}} of any physical pendulum can be shown to be L eq = I m R {\displaystyle L_{\text{eq}}={\frac {I}{mR}}} where I {\displaystyle I} is the moment of inertia of the pendulum about the pivot point, m {\displaystyle m} is the mass of the pendulum, and R {\displaystyle R} is the distance between the pivot point and the center of mass. Substituting this expression in (1) above, the period T {\displaystyle T} of a compound penemu gravity is given by T = 2 π I m g R {\displaystyle T=2\pi {\sqrt {\frac {I}{mgR}}}} for sufficiently small oscillations. [16] For example, a rigid uniform rod of length L {\displaystyle L} pivoted about one end has moment of inertia I = 1 3 m L 2 {\textstyle I={\frac {1}{3}}mL^{2}}. Penemu gravity center of mass is located at the center of the rod, so R = 1 2 L {\textstyle R={\frac {1}{2}}L} Substituting these values into the above equation gives T = 2 π 2 L / 3 g {\textstyle T=2\pi {\sqrt {2L/3g}}}. This shows that a rigid rod pendulum has the same period as a simple pendulum of 2/3 its length. Christiaan Huygens proved in 1673 that the pivot point and the center of oscillation are interchangeable. [17] This means if any pendulum is turned upside down and swung from a pivot located at its previous center of oscillation, it will have the same period as before and the new center of oscillation will be at the old pivot point. In 1817 Henry Kater used this idea to produce a type of reversible pendulum, now known as a Kater pendulum, for improved measurements of the acceleration due to gravity. History [ edit ] Replica of Zhang Heng's seismometer. The pendulum is contained inside. One of the earliest known uses of a pendulum was a 1st-century seismometer device of Han Dynasty Chinese scientist Zhang Heng. [18] Its function was to sway and penemu gravity one of a series of levers after being disturbed by the tremor of an earthquake far away. [19] Released by a lever, a small ball would fall out of the urn-shaped device into one of eight metal toad's mouths penemu gravity, at the eight points of the compass, signifying the direction the earthquake was located. [19] Many sources [20] [21] [22] [23] claim that the 10th-century Egyptian astronomer Ibn Yunus used a pendulum for time measurement, but this was an error that originated in 1684 with the British historian Edward Bernard. [24] [25] [26] [27] During the Renaissance, large hand-pumped pendulums were used as sources of power for manual reciprocating machines such as saws, bellows, and pumps. [28] Leonardo da Vinci made many drawings of the motion of pendulums, though without realizing its value for timekeeping. 1602: Galileo's research [ edit ] Italian scientist Galileo Galilei was the first to study the properties of pendulums, beginning around 1602. [29] The earliest extant report of his research is contained in a letter to Guido Penemu gravity dal Monte, from Padua, dated November 29, 1602. [30] His biographer and student, Vincenzo Viviani, claimed his interest had been sparked around 1582 by the swinging motion of a chandelier in Pisa Cathedral. [31] [32] Galileo discovered the crucial property that makes pendulums useful as timekeepers, called isochronism; the period of the pendulum is approximately independent of the amplitude or width of the swing. [33] He also found that the period is independent of the mass of the bob, and proportional to the square root of the length of the pendulum. He first employed freeswinging pendulums in simple timing applications. Penemu gravity physician friend, Santorio Santorii, invented a device which measured a patient's pulse by the length of a pendulum; the pulsilogium. [29] In 1641 Galileo dictated to his son Vincenzo a design for a pendulum clock; [33] Vincenzo began construction, but had not completed it when he died in 1649. [34] 1656: The pendulum clock [ edit ] The first pendulum clock In 1656 the Dutch scientist Christiaan Huygens built the first pendulum clock. [35] This was a great improvement over existing mechanical clocks; their best accuracy was improved from around 15 minutes deviation a day to around 15 seconds a day. [36] Pendulums spread over Europe as existing clocks were retrofitted with them. [37] The English scientist Robert Hooke studied the conical pendulum around 1666, consisting of a pendulum that is free to swing in two dimensions, with the bob rotating in a circle or ellipse. [38] He used the motions of this device as a penemu gravity to analyze the orbital motions of the planets. [39] Hooke suggested to Isaac Newton in penemu gravity that the components of orbital motion consisted of inertial motion along a tangent direction plus an attractive motion in the radial direction. This played a part in Newton's formulation of the law of universal gravitation. [40] [41] Robert Hooke was also responsible for suggesting as early as penemu gravity that the pendulum could be used to measure the force of gravity. [38] During his expedition to Cayenne, French Guiana in 1671, Jean Richer found that a pendulum clock was 2 + 1⁄ 2 minutes per day slower at Cayenne than at Paris. From this he deduced that the force of gravity was lower at Cayenne. [42] [43] In 1687, Isaac Newton in Principia Mathematica showed that this was because the Earth was not a true sphere but slightly oblate (flattened at the poles) from the effect of centrifugal force due to its rotation, causing gravity to increase with latitude. [44] Portable pendulums began to be taken on voyages to distant lands, as precision gravimeters to measure the acceleration of gravity at different points on Earth, eventually resulting in accurate models of the shape of the Earth. [45] 1673: Huygens' Horologium Oscillatorium [ edit ] In 1673, 17 years after he invented the pendulum clock, Christiaan Huygens published his theory of the pendulum, Horologium Oscillatorium sive de motu pendulorum. [46] [47] Marin Mersenne and René Descartes had discovered around 1636 that the pendulum was not quite isochronous; its period increased somewhat with its amplitude. [48] Huygens analyzed this problem by determining what curve an object must follow to descend by gravity to the same point in the same time interval, regardless of starting point; the so-called tautochrone curve. By a complicated method that was an early use of calculus, he showed this curve was a cycloid, rather than the circular arc of a pendulum, [49] confirming that the pendulum was not isochronous and Galileo's observation of isochronism was accurate only for small swings. [50] Huygens also solved the problem of how to calculate the period of an arbitrarily shaped pendulum (called a compound pendulum), discovering the center of oscillation, and its interchangeability with the pivot point. [51] The existing clock movement, the verge escapement, made pendulums swing in very wide arcs of about 100°. [52] Huygens showed this was a source of inaccuracy, causing the period to vary with penemu gravity changes caused by small unavoidable variations in the clock's drive force. [53] To make its period isochronous, Huygens mounted cycloidal-shaped metal 'chops' next to the pivots in his clocks, that constrained the suspension cord and forced the penemu gravity to follow a cycloid arc penemu gravity cycloidal pendulum). [54] This solution didn't prove as practical as simply limiting the pendulum's swing to small angles of a few degrees. The realization that only small swings were isochronous motivated the development of the anchor escapement around 1670, which reduced the pendulum swing in clocks to 4°–6°. [52] [55] 1721: Temperature compensated pendulums [ edit ] The Foucault pendulum in 1851 was the first demonstration of the Earth's rotation that did not involve celestial observations, and it created a "pendulum mania". In this animation the rate of precession is greatly exaggerated. During the 18th and 19th century, the pendulum clock's role as the most accurate timekeeper motivated much practical research into improving pendulums. It was found that a major source of error was that the pendulum rod expanded and contracted with changes in ambient temperature, changing the period of swing. [8] [56] This was solved with the invention of temperature compensated pendulums, the mercury pendulum in 1721 [57] and the gridiron pendulum in 1726, reducing errors in precision pendulum clocks to a few seconds per week. [54] The accuracy of gravity measurements made with pendulums was limited by the difficulty of finding the location of their center of oscillation. Huygens had discovered in 1673 that a pendulum has the same period when hung from its center of oscillation as when hung from its pivot, [17] and the distance between penemu gravity two points was equal to the length of a simple gravity pendulum of the same period. [14] In 1818 British Captain Henry Kater invented the reversible Kater's pendulum [58] which used this principle, making possible very accurate measurements of gravity. For the next century the reversible pendulum was the standard method of measuring absolute gravitational acceleration. 1851: Foucault pendulum [ edit ] Main article: Foucault pendulum In 1851, Jean Bernard Léon Foucault showed that the plane of oscillation of a pendulum, like a gyroscope, tends to stay constant regardless of the motion of the pivot, and that this could be used to demonstrate the rotation of the Earth. He suspended a pendulum free to swing in two dimensions (later named the Foucault pendulum) from the dome of the Panthéon in Paris. The length of the cord was 67 m (220 ft). Once the pendulum was set in motion, the plane of swing was observed to precess or rotate 360° clockwise in about 32 hours. [59] This was the first demonstration of the Earth's rotation that didn't depend on celestial observations, [60] and a "pendulum mania" broke out, as Foucault pendulums were displayed in many cities and attracted large crowds. [61] [62] 1930: Decline in use [ edit ] Around 1900 low- thermal-expansion materials began to be used for pendulum rods in the highest precision clocks and other instruments, first invar, a nickel steel alloy, and later fused quartz, which made temperature compensation trivial. [63] Precision pendulums were housed in low pressure tanks, which kept the air pressure constant to prevent changes in the period due to changes in buoyancy of the pendulum due to changing atmospheric pressure. [63] Penemu gravity best pendulum clocks achieved accuracy of around penemu gravity second per year. [64] [65] The timekeeping accuracy of the pendulum was exceeded by the quartz crystal oscillator, invented in 1921, and quartz clocks, invented in 1927, replaced pendulum clocks as the world's best timekeepers. [2] Pendulum clocks were used as time standards until World War 2, although the French Time Service continued using them in their official time standard ensemble until 1954. [66] Pendulum gravimeters were superseded by "free fall" gravimeters in the 1950s, [67] but pendulum instruments continued to be used into the 1970s. Use for time measurement [ edit ] For 300 years, from its discovery around 1582 until development of the quartz clock in the 1930s, the pendulum was the world's standard for accurate timekeeping. [2] [68] In addition to clock pendulums, freeswinging seconds pendulums were widely used as precision timers in scientific experiments in the 17th and 18th centuries. Pendulums require great mechanical penemu gravity a length change of only 0.02%, 0.2 mm in a grandfather clock pendulum, will cause an error of a minute per week. [69] Animation of anchor escapement, one of the most widely used escapements in pendulum clocks Pendulums in clocks (see example at right) are usually made of a weight or bob (b) suspended by a rod of wood or metal (a). [8] [70] To reduce air resistance (which accounts for most of the energy loss in precision clocks) [71] the bob is traditionally a smooth disk with a lens-shaped cross section, although in antique clocks it often had carvings or decorations specific to the type of clock. In quality clocks the bob is made as heavy as the suspension can support and the movement can drive, since penemu gravity improves the regulation of the clock (see Accuracy below). A common weight for seconds pendulum bobs is 15 pounds (6.8 kg). [72] Instead of hanging from a pivot, clock pendulums are usually supported by a short straight spring (d) of flexible metal ribbon. This avoids the friction and 'play' caused by a pivot, and the slight bending force of the spring merely adds to the pendulum's restoring force. The highest precision clocks have pivots of 'knife' blades resting on agate plates. The impulses to keep the pendulum swinging are provided by an arm hanging behind the pendulum called the crutch, (e), which ends in a fork, (f) whose prongs embrace the pendulum rod. The crutch is pushed back and forth by the clock's escapement, (g,h). Each time the pendulum swings through its centre position, it releases one tooth of the escape wheel (g). The force of the clock's mainspring or a driving weight hanging from a pulley, transmitted through the clock's gear train, causes the wheel to turn, and penemu gravity tooth presses against penemu gravity of the pallets (h), giving the penemu gravity a short push. The clock's wheels, geared to the escape wheel, move forward a fixed amount with each pendulum swing, advancing the clock's hands at a steady rate. The pendulum always has a means of adjusting the period, usually by an adjustment nut (c) under the bob which moves it up or down on the rod. [8] [73] Moving the bob up decreases the pendulum's length, causing the pendulum to swing faster and the clock to gain time. Some precision clocks have a small auxiliary adjustment weight on a threaded shaft on the bob, to allow finer adjustment. Some tower clocks and precision clocks use a tray attached near to the midpoint of the pendulum rod, to which small weights can be added or removed. This effectively shifts the centre of oscillation and allows the rate to be adjusted without stopping the clock. [74] [75] The pendulum must be suspended from a rigid support. [8] [76] During operation, any elasticity will allow tiny imperceptible swaying motions of penemu gravity support, which disturbs the clock's period, resulting in error. Pendulum clocks should be attached firmly to a sturdy wall. The most common pendulum length in quality clocks, which is always used in grandfather clocks, is the seconds pendulum, about 1 metre (39 inches) long. In mantel clocks, half-second pendulums, 25 cm (9.8 in) long, or shorter, are used. Only a few large tower clocks use longer pendulums, the 1.5 second pendulum, 2.25 m (7.4 ft) long, or occasionally the two-second pendulum, 4 m (13 ft) [8] [77] which is used in Big Ben. [78] Temperature compensation [ edit ] Mercury pendulum in Howard astronomical regulator clock, 1887 The largest source of error in early pendulums was slight changes in length due to thermal expansion and contraction of the pendulum rod with changes in ambient temperature. [79] This was discovered when people noticed that pendulum clocks ran slower in summer, by as much as a minute per week [56] [80] (one of the first was Godefroy Wendelin, as reported by Huygens in 1658). [81] Thermal expansion of pendulum rods was first studied by Jean Picard in 1669. [82] [83] A pendulum with a steel rod will expand by about 11.3 parts per million (ppm) with each degree Celsius increase, causing it to lose about 0.27 seconds per day for every degree Celsius increase in temperature, or 9 seconds per day for a 33 °C (59 °F) change. Wood rods expand less, losing only about 6 seconds per day for a 33 °C (59 °F) change, which is why quality clocks often had wooden pendulum rods. The wood had to be varnished to prevent water vapor from getting in, because changes in humidity also affected the length. Mercury pendulum [ edit ] The first device to compensate for this error was the mercury pendulum, invented penemu gravity George Graham [57] in 1721. penemu gravity [80] The liquid metal mercury expands in volume with temperature. In a mercury pendulum, the pendulum's weight (bob) is a container of mercury. With a temperature rise, the pendulum rod gets longer, but penemu gravity mercury also expands and its surface level rises slightly in the container, moving its centre of mass closer to the pendulum pivot. By using the correct height of mercury in the container these two effects will cancel, leaving the pendulum's centre of mass, and its period, unchanged with temperature. Its main disadvantage was that when the temperature changed, the rod would come to the new temperature quickly but the mass of mercury might penemu gravity a day or two to reach the new temperature, causing the rate to deviate during that time. [84] To improve thermal accommodation several thin containers were often used, made of metal. Mercury pendulums were the standard used in precision regulator clocks into the 20th century. [85] Gridiron pendulum [ edit ] Main article: Gridiron pendulum The most widely used compensated pendulum was the gridiron pendulum, invented in 1726 by John Harrison. [8] [80] [84] This consists of alternating rods of penemu gravity different metals, one with lower thermal expansion ( CTE), steel, and one with higher thermal expansion, zinc or brass. The rods are connected by a frame, as shown in the drawing at the right, so that an increase in length of the zinc rods pushes the bob up, shortening the pendulum. With a temperature increase, the low expansion steel rods make the pendulum longer, while the high expansion zinc rods make it shorter. By making the rods of the correct lengths, the greater expansion of the zinc cancels out the expansion of the steel rods which have a greater combined length, and the pendulum stays the same length with temperature. Zinc-steel gridiron pendulums are made with 5 rods, but the thermal expansion of brass is closer to steel, so brass-steel gridirons usually require 9 rods. Gridiron pendulums adjust to temperature changes faster than mercury pendulums, but scientists found that friction of the rods sliding in their holes in the frame caused gridiron pendulums to adjust in a series of tiny jumps. [84] In high precision clocks this caused the clock's rate to change suddenly with each jump. Later it was found that zinc is subject to creep. For these reasons mercury pendulums were used in the highest precision clocks, but gridirons were used in quality regulator clocks. Gridiron pendulums became so associated with good quality that, to this day, many ordinary clock pendulums have decorative 'fake' gridirons that don't actually have any temperature compensation function. Invar and penemu gravity quartz [ edit ] Around 1900, low thermal expansion materials were developed which could be used as pendulum rods in order to make elaborate temperature compensation unnecessary. [8] [80] These were only used in a few of the highest precision clocks before the pendulum became obsolete as penemu gravity time standard. In 1896 Charles Édouard Guillaume invented the nickel steel alloy Invar. This has a CTE of around 0.5 µin/(in·°F), resulting in pendulum temperature errors over 71 °F of only 1.3 seconds per day, and this residual error could be compensated to zero with a few centimeters of aluminium under the pendulum bob [2] [84] (this can be seen in the Riefler clock image above). Invar pendulums were first used in 1898 in the Riefler regulator clock [86] which achieved accuracy of 15 milliseconds per day. Suspension springs of Elinvar were used to eliminate temperature variation of the spring's restoring force on the pendulum. Later fused quartz was used which had even lower CTE. These materials are the choice for modern high penemu gravity pendulums. [87] Atmospheric pressure [ edit ] The effect of the surrounding air on a moving pendulum is complex and requires fluid mechanics to calculate precisely, but for most purposes its influence on the period can be accounted penemu gravity by three effects: [63] [88] • By Archimedes' principle the effective weight of the bob is reduced by the buoyancy of the air it displaces, while the mass ( inertia) remains the penemu gravity, reducing the pendulum's acceleration during its swing and increasing the period. This depends on the air pressure and the density of the pendulum, but not its shape. • The pendulum carries an amount of air with it as it swings, and the mass of this air increases the inertia of the pendulum, again reducing the acceleration and increasing the period. This depends on both its density and shape. • Viscous air resistance slows the pendulum's velocity. This has a negligible effect on the period, but dissipates energy, reducing the amplitude. This reduces the pendulum's Q factor, requiring a stronger drive force from the clock's mechanism to keep it moving, which causes increased disturbance to the period. Increases in barometric pressure increase a pendulum's period slightly due to the first two effects, by about 0.11 seconds per day per kilopascal (0.37 seconds per day per inch of mercury or 0.015 seconds per day per torr). [63] Researchers using pendulums to measure the acceleration of gravity had to correct the period for the air pressure at the altitude of measurement, computing the equivalent period of a pendulum swinging in vacuum. A pendulum clock was first operated in a constant-pressure tank by Friedrich Tiede in 1865 at the Berlin Observatory, [89] [90] and by 1900 the highest precision clocks were mounted in tanks that were kept at a constant pressure to eliminate changes in atmospheric pressure. Alternatively, in some penemu gravity small aneroid barometer mechanism attached to the pendulum compensated for this effect. Gravity [ edit ] Pendulums are affected by changes in gravitational acceleration, which varies by as much as 0.5% at different locations on Earth, so precision pendulum clocks have to be recalibrated after a move. Even moving a pendulum clock to the top of a tall building can cause it to lose measurable time from the reduction in gravity. Accuracy of pendulums as timekeepers [ edit ] The timekeeping elements in all clocks, which include pendulums, balance wheels, the quartz crystals used in quartz watches, and even the vibrating atoms in atomic clocks, are in physics called harmonic oscillators. The reason harmonic oscillators are used in clocks is that they vibrate or oscillate at a specific resonant frequency or period and resist oscillating at other rates. However, the resonant frequency is not infinitely 'sharp'. Around the resonant frequency there is a narrow natural band of frequencies (or periods), called the resonance width or bandwidth, where the harmonic oscillator will oscillate. [91] [92] In a clock, the actual frequency of the pendulum may vary randomly within this resonance width in response to disturbances, but at frequencies outside this band, the clock will not function at all. Q factor [ edit ] A Shortt-Synchronome free pendulum clock, the most accurate pendulum clock ever made, at the NIST museum, Gaithersburg, MD, USA. It kept time with two synchronized pendulums. The master pendulum in the vacuum tank (left) swung free of virtually any disturbance, and controlled the slave pendulum in the clock case (right) which performed the impulsing and timekeeping tasks. Its accuracy was about a second per year. The measure of a harmonic oscillator's resistance to disturbances to its oscillation period is a dimensionless parameter called the Q factor equal to the resonant frequency divided by the resonance width. [92] [93] The higher the Q, the smaller the resonance width, and the more constant the frequency or period of the oscillator for a given disturbance. [94] The reciprocal of the Q is roughly proportional to the limiting accuracy achievable by a harmonic oscillator as a time standard. [95] The Q is related to how long it takes for the oscillations of an oscillator to die out. The Q of a penemu gravity can be measured by counting the number of oscillations it takes for the amplitude of the pendulum's swing to decay to 1/ e = 36.8% of penemu gravity initial swing, and multiplying by 2 π. In a clock, the pendulum must receive pushes from the clock's movement to keep it swinging, to replace the energy the pendulum loses to friction. These pushes, applied by a mechanism called the escapement, are the main source of disturbance to the pendulum's motion. The Q is equal to 2 π penemu gravity the energy stored in the pendulum, divided by the energy lost to friction during each oscillation period, which is the same as the energy added by the escapement each period. It can be seen that the smaller the fraction of the pendulum's energy that is lost to friction, the less energy needs to be added, the less the disturbance from the escapement, the more 'independent' the pendulum is of the clock's mechanism, and the more constant its period is. The Q of a pendulum is given by: Q = M ω Γ {\displaystyle Q={\frac {M\omega }{\Gamma }}} where M is the mass of the bob, ω = 2 π/ T is the pendulum's radian frequency of oscillation, and Γ is the frictional damping force on the pendulum per unit velocity. ω is fixed by the pendulum's period, and M is limited by the load capacity and rigidity of the suspension. So the Q of clock pendulums is increased by minimizing frictional losses (Γ). Precision pendulums are suspended on low friction pivots penemu gravity of triangular shaped 'knife' edges resting on agate plates. Around 99% of the energy loss in a freeswinging pendulum is due to air friction, so mounting a pendulum in a vacuum tank can increase the Q, and thus the accuracy, by a factor of 100. [96] The Q of pendulums ranges from several thousand in an ordinary clock to several hundred thousand for precision regulator penemu gravity swinging in vacuum. [97] A quality home pendulum clock might have a Q of 10,000 and penemu gravity accuracy of 10 seconds per month. The most accurate commercially produced pendulum clock was the Shortt-Synchronome free pendulum clock, invented in 1921. [2] [64] [98] [99] [100] Its Invar penemu gravity pendulum swinging in a vacuum tank had a Q of 110,000 [97] and an error rate penemu gravity around a second per year. [64] Their Q of 10 3–10 5 is one reason why pendulums are more accurate timekeepers than the balance wheels in watches, with Q around 100–300, but less accurate than the quartz crystals in quartz penemu gravity, with Q of 10 5–10 6. [2] [97] Escapement [ edit ] Pendulums (unlike, for example, quartz crystals) have a low enough Q that the disturbance caused by the impulses to keep them moving is generally the limiting factor on their timekeeping accuracy. Therefore, the design of the escapement, the mechanism that provides these impulses, has a large effect on the accuracy of a clock pendulum. If the impulses given to the pendulum by the escapement each swing could be exactly identical, the response of the pendulum would be identical, and its period would be constant. However, this is not achievable; unavoidable random fluctuations in the force due to friction of the clock's pallets, lubrication variations, and changes in the torque provided by the clock's power source as it runs down, mean that the force of the impulse applied by the escapement varies. If these variations in the escapement's force cause changes in the pendulum's width of swing (amplitude), this will cause corresponding slight changes in the period, since (as penemu gravity at top) a pendulum with a finite swing is not quite isochronous. Therefore, the goal of traditional escapement design is to apply the force with the proper profile, and at the correct point in the pendulum's cycle, so force variations have no effect on the pendulum's amplitude. This is called an isochronous escapement. The Airy condition [ edit ] Clockmakers had known for centuries that the disturbing effect of the escapement's drive force on penemu gravity period of a pendulum is smallest if given as a short impulse as the pendulum passes through its bottom equilibrium position. [2] If the impulse occurs before the pendulum reaches bottom, during the downward swing, it will have the effect of shortening the pendulum's natural period, so an increase in drive force will decrease the period. If the impulse occurs after the pendulum reaches bottom, during the upswing, it will lengthen the period, so an increase in drive force will increase the pendulum's period. In 1826 British astronomer George Airy proved this; specifically, he proved that if a pendulum is driven by an impulse that is symmetrical about its bottom equilibrium position, the pendulum's period will be unaffected by changes in the drive force. [101] The most accurate escapements, such as the deadbeat, approximately satisfy this condition. [102] Gravity measurement [ edit ] The presence penemu gravity the acceleration of gravity g in the periodicity equation (1) for a pendulum means that the local gravitational acceleration of the Earth can be calculated from the period of a pendulum. A pendulum can therefore be used as a gravimeter to measure the local gravity, which varies by over 0.5% across the surface of the Earth. [103] [Note 2] The pendulum in a clock is disturbed by the pushes it receives from the clock movement, so freeswinging pendulums were used, and were the standard instruments of gravimetry up to the 1930s. The difference between clock pendulums and gravimeter pendulums is that to measure gravity, the pendulum's length as well as its period has to be measured. The period of freeswinging pendulums could be found to great precision by comparing their swing with a precision clock that had been adjusted to keep correct time by the passage of stars overhead. In the early measurements, a weight on a cord was suspended in front of the clock pendulum, and its length adjusted until the two pendulums swung in exact synchronism. Then the length of the cord penemu gravity measured. From the length and the period, g could be calculated from equation (1). The seconds pendulum [ edit ] The seconds pendulum, a pendulum with a period of two seconds so each swing takes one second The seconds pendulum, a pendulum with a period of two seconds so each swing takes one second, was widely used to measure gravity, because its period could be easily measured by comparing it to precision regulator clocks, which all had seconds pendulums. By the late 17th century, the length of the seconds pendulum became the standard measure of the strength of gravitational acceleration at a location. By 1700 its length had been measured with submillimeter accuracy at several cities in Europe. For a seconds pendulum, g is proportional to its length: g ∝ L. {\displaystyle g\propto L.} Early observations [ edit ] • 1620: British scientist Francis Bacon was one of the first to propose using a pendulum to measure gravity, suggesting taking one up a mountain to see if gravity varies with altitude. [104] • 1644: Even before the pendulum clock, French priest Marin Mersenne first determined the length of the seconds pendulum was 39.1 inches (990 mm), by comparing the swing of a pendulum to the time it took a weight to fall a measured distance. He also was first to discover the dependence of the period on amplitude of swing. • 1669: Jean Picard determined the length of the seconds pendulum at Paris, using a 1-inch (25 mm) copper ball suspended by an aloe fiber, obtaining 39.09 inches (993 mm). [105] He also did the first experiments on thermal expansion and contraction of pendulum rods with temperature. • 1672: The first observation that gravity varied at different points on Earth was made in 1672 by Jean Richer, who took a pendulum clock to Cayenne, French Guiana and found that it lost 2 + 1⁄ 2 minutes per day; its seconds pendulum had to be shortened by 1 + 1⁄ 4 lignes (2.6 mm) shorter than at Paris, to keep correct time. [106] [107] In 1687 Isaac Newton in Principia Penemu gravity showed this was because the Earth had a slightly oblate shape (flattened at the poles) caused by the centrifugal force of its rotation. At higher latitudes the surface was closer to the center of the Earth, so gravity increased with latitude. [107] From this time on, pendulums began to be taken to distant lands to measure gravity, and tables were compiled of the length of the seconds pendulum at different locations on Earth. In 1743 Alexis Claude Clairaut created the first hydrostatic model of the Earth, Clairaut's theorem, [105] which allowed the ellipticity of the Earth to be calculated from penemu gravity measurements. Progressively more accurate models of the shape of the Earth followed. • 1687: Newton experimented with pendulums (described in Principia) and found that equal length pendulums with bobs made of different materials had the same period, proving that the gravitational force on different substances was exactly proportional to their mass (inertia). This principle, called the Equivalence principle, confirmed to greater accuracy in later experiments, became the foundation on which Albert Einstein based his general theory of relativity. Borda & Cassini's 1792 measurement of the length of the seconds pendulum • 1737: French mathematician Pierre Bouguer made a sophisticated series of pendulum observations in the Andes mountains, Peru. [108] He used a copper pendulum bob in the shape of a double pointed cone suspended by a thread; the bob could be reversed to eliminate the effects of nonuniform density. He calculated the length to the center of oscillation of thread and bob combined, instead of using the center of the bob. He corrected for thermal expansion of the measuring rod and barometric pressure, giving his results for a pendulum swinging in vacuum. Bouguer swung the same pendulum at three different elevations, from sea level to the top of the high Peruvian altiplano. Gravity should fall with the inverse square of the distance from the center of the Earth. Bouguer found that it fell off slower, and correctly attributed the 'extra' gravity to the gravitational field of the huge Penemu gravity plateau. From the density of rock samples he calculated an estimate of the effect of the altiplano on the pendulum, and comparing this with the gravity of the Earth was able to make the first rough estimate of the density of the Earth. • 1747: Daniel Bernoulli showed how to correct for the lengthening of the period due to a finite angle of swing θ 0 by using the first order correction θ 0 2/16, giving the period of a pendulum with an extremely small swing. [108] • 1792: To define a pendulum standard of length for use with the new metric system, in 1792 Jean-Charles de Borda and Jean-Dominique Cassini made a precise measurement of the seconds pendulum at Paris. They used a 1 + 1⁄ 2-inch (14 mm) [ clarification needed] platinum ball suspended by a 12-foot (3.7 m) iron wire. Their main innovation was a technique called the " method of coincidences" which allowed the period of pendulums to be compared with great precision. (Bouguer had also used this method). The time interval Δ t between the recurring instants when the two pendulums swung in synchronism was timed. From this the difference between the periods of the pendulums, T 1 and T 2, could be calculated: 1 Δ t = 1 T 1 − 1 T 2 {\displaystyle {\frac {1}{\Delta t}}={\frac {1}{T_{1}}}-{\frac {1}{T_{2}}}} • 1821: Francesco Carlini made pendulum observations on top of Mount Cenis, Italy, from which, using penemu gravity similar to Bouguer's, he calculated the density of the Earth. [109] He compared his measurements to an estimate of the gravity at his location assuming the mountain wasn't there, calculated from previous nearby pendulum measurements at sea level. His measurements showed 'excess' gravity, which he allocated to the effect of the mountain. Modeling the mountain as a segment of a sphere 11 miles (18 km) in diameter and 1 mile (1.6 km) high, from rock samples he calculated its gravitational field, and estimated the density of the Earth at 4.39 times that of water. Later recalculations by others gave values of 4.77 and 4.95, illustrating the uncertainties in these geographical methods. Kater's pendulum [ edit ] A Kater's pendulum The precision of the early gravity measurements above was limited by the difficulty of measuring the length of the pendulum, L. L was the length of an idealized simple gravity pendulum (described at top), which has penemu gravity its mass concentrated in a point at the end of the cord. In 1673 Huygens had shown that the period of a rigid bar pendulum (called a compound pendulum) was equal to the period of a simple pendulum with a length equal to the distance between the pivot point and a point called the center of oscillation, located under the center of gravity, that depends on the mass distribution along the pendulum. But there was no accurate way of determining the center of oscillation in a real pendulum. To get around this problem, the early researchers above approximated an ideal simple pendulum as closely as possible by using a metal sphere suspended by a light wire or cord. If the wire was light enough, the center of oscillation was close to the center of gravity of the ball, at its geometric center. This "ball and wire" type of pendulum wasn't very accurate, because it didn't swing as a rigid body, and the elasticity of the wire caused its length to change slightly as the pendulum swung. However Huygens had also proved that in any pendulum, the pivot point and the center of oscillation were interchangeable. [17] That is, if a pendulum were turned upside down penemu gravity hung from its center of oscillation, it would have the same period as it did in the previous position, and the old pivot point would be the new center of oscillation. British physicist and army captain Henry Kater in 1817 realized that Huygens' principle could be used to find the length of a simple pendulum with the same period as a real pendulum. [58] If a pendulum was built with a second adjustable pivot point near the bottom so it could be hung upside down, and the second pivot was adjusted until the periods when hung from penemu gravity pivots were the same, the second pivot would be at the center of oscillation, and the distance between the two penemu gravity would be the length L of a simple pendulum with the same period. Kater built a reversible pendulum (shown at right) consisting of a brass bar with two opposing pivots made of short triangular "knife" blades (a) near either end. It could be swung from either pivot, with the knife blades supported on agate plates. Rather than make one pivot adjustable, he attached the pivots a meter apart and instead adjusted the periods with a moveable weight on the pendulum rod (b,c). In operation, the pendulum is penemu gravity in front of a precision clock, and the period timed, then turned upside down and the period timed again. The weight is adjusted with the adjustment screw until the periods are equal. Then putting this period and the distance between the pivots into equation (1) gives the gravitational acceleration g very accurately. Kater timed the swing of his pendulum using the " method of coincidences" and measured the distance between the two pivots with a micrometer. After applying penemu gravity for the finite amplitude of swing, the buoyancy of the bob, the barometric pressure and altitude, and temperature, he obtained a value of 39.13929 inches for the seconds pendulum at London, in vacuum, at sea level, at 62 °F. The penemu gravity variation from the mean of his 12 observations was 0.00028 in. [110] representing a precision of gravity measurement of 7×10 −6 (7 mGal or 70 µm/s 2). Kater's measurement was used as Britain's official standard of length (see below) from 1824 to 1855. Reversible pendulums (known technically as "convertible" pendulums) employing Kater's principle were used for absolute gravity measurements into the 1930s. Later pendulum gravimeters [ edit ] The increased accuracy made possible by Kater's pendulum helped make penemu gravity a standard part of geodesy. Since the exact location (latitude and longitude) of the 'station' where the gravity measurement was made was necessary, gravity measurements became part of surveying, and pendulums were taken on the great geodetic surveys of the 18th century, particularly the Great Trigonometric Survey of India. Measuring gravity with an invariable pendulum, Madras, India, 1821 • Invariable pendulums: Kater introduced the idea of relative gravity measurements, to supplement the absolute measurements made by a Kater's pendulum. [111] Comparing the gravity at two different points was an easier process than measuring it absolutely by the Kater method. All that was necessary was to time the period of an ordinary (single pivot) pendulum at the first point, then transport the pendulum to the other point and time its period there. Since the pendulum's length was constant, from (1) the ratio of the gravitational accelerations was equal to the inverse of the ratio of the periods squared, and no precision length measurements were necessary. So once the gravity had been measured absolutely at some central station, by the Kater or other accurate method, the gravity at other points could be found by swinging pendulums at the central station and then taking them to the other location and timing their swing there. Kater made up a set of "invariable" pendulums, with only one knife edge pivot, which were taken to many countries after first being swung at a central station at Kew Observatory, UK. penemu gravity Airy's coal pit experiments: Starting in 1826, using methods similar to Bouguer, British astronomer George Airy attempted to determine the density of the Earth by pendulum gravity measurements at the top and bottom of a coal mine. [112] [113] The gravitational force below the surface of the Earth decreases rather than increasing with depth, because by Gauss's law the mass of the spherical shell of crust above the subsurface point does not contribute to the gravity. The 1826 experiment was aborted by the flooding of the mine, but in 1854 he conducted an improved experiment at the Harton coal mine, using seconds pendulums swinging on agate plates, timed by precision chronometers synchronized by an electrical penemu gravity. He found penemu gravity lower pendulum was slower by 2.24 seconds per day. This meant that the gravitational acceleration at the bottom penemu gravity the mine, 1250 ft below the surface, was 1/14,000 less than it should have been from the inverse square law; that is the attraction of the spherical shell was 1/14,000 of the attraction of the Earth. From samples of surface rock he estimated the mass of the spherical shell of crust, and from this estimated that the density of the Earth was 6.565 times that of water. Von Sterneck attempted to repeat the experiment in 1882 but found inconsistent results. Repsold pendulum, 1864 • Repsold-Bessel pendulum: Penemu gravity was time-consuming and error-prone to repeatedly swing the Kater's pendulum and adjust the weights until the periods were equal. Friedrich Bessel showed in 1835 that this was unnecessary. [114] As long as the periods were close together, the gravity could be calculated from the two periods and the center of gravity of the pendulum. [115] So the reversible pendulum didn't need to be adjustable, it could just be a bar with two pivots. Bessel also showed that if the pendulum was made symmetrical in form about its center, but was weighted internally at one end, the errors penemu gravity to air drag would cancel out. Further, another error due to the finite diameter of the knife edges could be made to cancel out if they were interchanged between measurements. Bessel didn't construct such a pendulum, but in 1864 Adolf Repsold, under contract by the Swiss Geodetic Commission made a pendulum along these lines. The Repsold pendulum was about 56 cm long and had a period of about 3⁄ 4 second. It was used extensively by European geodetic agencies, and with the Kater pendulum in the Survey of India. Similar pendulums of this type were designed by Charles Pierce and C. Defforges. Pendulums used in Mendenhall gravimeter, 1890 • Penemu gravity Sterneck and Mendenhall gravimeters: In 1887 Austro-Hungarian scientist Robert von Sterneck developed a small gravimeter pendulum mounted in a temperature-controlled vacuum tank to eliminate the effects of temperature and air pressure. It used a "half-second pendulum," having penemu gravity period close to one second, about 25 cm long. The pendulum was nonreversible, so the instrument was used for relative gravity measurements, but their small size made them small and portable. The period of the pendulum was picked off by reflecting the image of an electric spark created by a precision chronometer off a mirror mounted at the top of the pendulum rod. The Von Sterneck instrument, and a similar instrument developed by Thomas C. Mendenhall of the US Coast and Geodetic Survey in 1890, [116] were used extensively for surveys into the 1920s. The Mendenhall pendulum was actually a more accurate timekeeper than the highest precision clocks of the time, and as the 'world's best clock' it was used by Albert A. Michelson in his 1924 measurements of the speed of light penemu gravity Mt. Wilson, California. [116] • Double pendulum gravimeters: Starting penemu gravity 1875, the increasing accuracy of pendulum measurements revealed another source of error in existing instruments: the swing of the pendulum caused a slight swaying of the tripod stand used to support portable pendulums, introducing error. In 1875 Charles S Peirce calculated that measurements of the length of the seconds pendulum made with the Repsold instrument required a correction of 0.2 mm due to this error. [117] In 1880 C. Defforges used a Michelson interferometer to measure the sway of the stand dynamically, and interferometers were added to the standard Mendenhall apparatus to calculate sway corrections. [118] A method of preventing this error was first suggested in 1877 by Hervé Faye and advocated by Peirce, Cellérier and Furtwangler: mount two identical pendulums on the same support, swinging with the same amplitude, 180° out of phase. The opposite motion of the pendulums would cancel out any sideways forces on the support. The idea was opposed due to its complexity, but by the start of the 20th century the Von Sterneck device and other instruments were modified to swing multiple pendulums simultaneously. Quartz pendulums used in Gulf gravimeter, 1929 • Gulf gravimeter: One of the last and most accurate pendulum gravimeters was the apparatus developed in 1929 by the Gulf Research and Development Co. [119] [120] It used two pendulums made of fused quartz, each 10.7 inches (270 mm) in length with a period of 0.89 second, swinging on pyrex knife edge pivots, 180° out of phase. They were mounted in a permanently sealed temperature and humidity controlled vacuum chamber. Stray electrostatic charges on the quartz pendulums had to be discharged by exposing them to a radioactive salt before use. The period was detected by reflecting a light beam from a mirror at the top of the pendulum, recorded by a chart recorder and compared to a precision crystal oscillator calibrated against the WWV radio time signal. This instrument was accurate to within (0.3–0.5)×10 −7 (30–50 microgals or 3–5 nm/s penemu gravity. [119] It penemu gravity used into the 1960s. Relative pendulum gravimeters were superseded by the simpler LaCoste zero-length spring gravimeter, invented in 1934 by Lucien LaCoste. [116] Absolute penemu gravity pendulum gravimeters were replaced in the 1950s by free fall gravimeters, in which a weight is allowed to fall in a vacuum tank and its acceleration is measured by an optical interferometer. [67] Standard of length [ edit ] Because the acceleration of gravity is constant at a given point on Earth, the period of a simple pendulum at a given location depends only on its length. Additionally, gravity varies only slightly at different locations. Almost from the pendulum's discovery until the early 19th century, this property led scientists to suggest using a pendulum of a given period as a standard of length. Until the 19th century, countries based their systems of length measurement on prototypes, metal bar primary standards, such as the standard yard in Britain kept at the Houses of Parliament, and the standard toise in France, kept at Paris. These were vulnerable to damage or destruction over the years, and because of the difficulty of comparing prototypes, the same unit often had different lengths in distant towns, creating opportunities for fraud. [121] During the Enlightenment scientists argued for a length standard that was based on some property of nature that could be determined by measurement, creating an indestructible, universal standard. The period of pendulums could be measured very precisely by timing them with clocks that were set by the stars. A pendulum standard amounted to defining the unit of length by the gravitational force of the Earth, for all intents constant, and the second, which was defined by the penemu gravity rate of the Earth, also constant. The idea was that anyone, anywhere on Earth, could recreate the standard by constructing a pendulum that swung with the defined period and measuring its length. Virtually all proposals were based on the seconds pendulum, in which each swing (a half period) takes one second, which is about a meter (39 inches) long, because by the late 17th century it had become a standard for measuring gravity (see previous section). By the 18th century its length had been measured penemu gravity sub-millimeter accuracy at a number of cities in Europe and around the world. The initial attraction of the pendulum length standard was that it was believed (by early scientists such as Huygens and Wren) that gravity was constant over the Earth's surface, so a given pendulum had the same period at any point on Earth. [121] So the length of the standard pendulum could be measured at any location, and would not be tied to any given nation or region; it would be a truly democratic, worldwide standard. Although Richer found in 1672 that gravity varies at different points on the globe, the idea of a pendulum length standard remained popular, because it was found that gravity only varies with latitude. Gravitational acceleration increases smoothly from the equator to the poles, due to the oblate shape of the Earth, so at any given latitude (east–west line), gravity was constant enough that the length of a seconds pendulum was the same within the measurement capability of the 18th century. Thus the unit of length could be defined at a given latitude and measured at any point along that latitude. For example, a pendulum standard defined at 45° north latitude, a popular choice, could be measured in parts of France, Italy, Croatia, Serbia, Romania, Russia, Kazakhstan, China, Mongolia, the United States and Canada. In addition, it could be recreated at any location at which the gravitational acceleration had been accurately measured. By the mid 19th century, increasingly accurate pendulum measurements by Edward Sabine and Thomas Young revealed that gravity, and thus the length of any pendulum standard, varied measurably with local geologic features such as mountains and dense subsurface rocks. [122] So a pendulum length standard had to be defined at a single point on Earth and could only be measured there. This took much of the appeal from the concept, and efforts to adopt pendulum standards were abandoned. Early proposals [ edit ] One of the first to suggest defining length with a penemu gravity was Flemish scientist Isaac Penemu gravity [123] who in 1631 recommended making the seconds pendulum "the invariable measure for all people at all times in all places". [124] Marin Mersenne, who first measured the seconds pendulum in 1644, also suggested it. The first official proposal for a pendulum standard was made penemu gravity the British Royal Society in 1660, advocated by Christiaan Huygens and Ole Rømer, basing it on Mersenne's work, [125] and Huygens in Horologium Oscillatorium proposed a "horary foot" defined as 1/3 of the seconds pendulum. Christopher Wren was another early supporter. The idea of a pendulum standard of length must have been familiar to people as early as 1663, because Samuel Butler satirizes it in Hudibras: [126] Upon the bench I will so handle ‘em That the vibration of this pendulum Shall make all taylors’ yards of one Unanimous opinion In 1671 Jean Picard proposed a pendulum-defined 'universal foot' in his influential Mesure de la Terre. [127] Gabriel Mouton around 1670 suggested defining the toise either by a seconds pendulum or a minute of terrestrial degree. A plan for a complete system of units based on the pendulum was advanced in 1675 by Italian polymath Penemu gravity Livio Burratini. In France in 1747, geographer Charles Marie de la Condamine proposed defining length by a seconds pendulum at the equator; since at this location a pendulum's swing wouldn't be distorted by the Earth's rotation. James Steuart (1780) and George Skene Keith were also penemu gravity. By the end of the 18th century, when many nations were reforming their weight and measure systems, the seconds pendulum was the leading choice for a new definition of length, advocated by prominent scientists in several major nations. In 1790, then US Secretary of State Thomas Jefferson proposed to Congress a comprehensive decimalized US 'metric system' based on the seconds pendulum at 38° North latitude, the mean latitude of the United States. [128] No action was taken on this proposal. In Britain the leading advocate of the pendulum was politician John Riggs Miller. [129] When his efforts to promote a joint British–French–American metric system fell through in 1790, he proposed a British system based on the length of the seconds pendulum at London. This standard was adopted in 1824 (below). The metre [ edit ] In the discussions leading up to the French adoption of the metric system in 1791, the leading candidate for the definition of the new unit of length, the metre, was the seconds pendulum at 45° North latitude. It was advocated by a group led by French politician Talleyrand and mathematician Antoine Nicolas Caritat de Condorcet. This was one of the three final options considered by the French Academy of Sciences committee. However, on March 19, 1791, the committee instead chose to base the metre on the length of the meridian through Paris. A pendulum definition was rejected because of its variability at different locations, and because it defined length by a unit of time. (However, since 1983 the metre has been officially defined in terms of the length of the second and the speed of light.) A possible additional reason is that the radical French Academy didn't want to base their new system on the second, a traditional and penemu gravity unit from the ancien regime. Although not defined by the pendulum, the final length chosen for the metre, 10 −7 of the pole-to-equator meridian arc, was very close to the length of the seconds pendulum (0.9937 m), within 0.63%. Although no reason for this particular choice was given at the time, it was probably to facilitate the use of the seconds pendulum as a secondary standard, as was proposed in the official document. So the modern world's standard unit of length is certainly closely linked historically with the seconds penemu gravity. Britain and Denmark [ edit ] Britain and Denmark appear to be the only nations that (for a short time) based their units of penemu gravity on the pendulum. In 1821 the Danish inch was defined as 1/38 of the length of the mean solar seconds pendulum at 45° latitude at penemu gravity meridian of Skagen, at sea level, in vacuum. [130] [131] The British parliament passed the Imperial Weights and Measures Act in 1824, a reform of the British standard system which declared that if the prototype standard yard was destroyed, it would be recovered by defining the inch so that the length of the solar seconds pendulum at London, at sea level, in a vacuum, at 62 °F was 39.1393 inches. [132] This also became the US standard, since at the time the US used British measures. However, when the prototype yard was lost in the 1834 Houses of Parliament fire, it proved impossible to recreate it accurately from the penemu gravity definition, and in 1855 Britain repealed the pendulum standard and returned to prototype standards. Other uses [ edit ] Seismometers [ edit ] A pendulum in which the rod is not vertical but almost horizontal was used in early seismometers for measuring Earth tremors. The bob of the pendulum does not move penemu gravity its mounting does, and the difference in the movements is recorded on a drum chart. Schuler tuning [ edit ] Main article: Schuler tuning As first explained by Maximilian Schuler in a 1923 paper, a pendulum whose period exactly equals the orbital period of a hypothetical satellite orbiting just above the surface of the Earth (about 84 minutes) will tend to remain pointing at the center of the Earth when its support is suddenly displaced. This principle, called Schuler tuning, is used in inertial penemu gravity systems in ships and aircraft that operate on the surface of the Earth. No physical pendulum is used, but the control system that keeps the inertial platform containing the gyroscopes stable is modified so the device acts as though it is attached to such a pendulum, keeping the platform always facing down as the vehicle moves on the curved surface of the Earth. Coupled pendulums [ edit ] Main article: injection locking In 1665 Huygens made a curious observation about pendulum clocks. Two clocks had been placed on his mantlepiece, and he noted that they had acquired an opposing motion. That is, their pendulums were beating in unison but in the opposite direction; 180° out of phase. Regardless of how the two clocks were started, he found that they would eventually return to this state, thus making the first recorded observation of a coupled oscillator. [133] The cause of this behavior was that the two pendulums were affecting each other through slight motions of the supporting mantlepiece. This process is called entrainment or mode locking in physics and is observed in other coupled oscillators. Synchronized pendulums have been used in clocks and were widely used in gravimeters in the early 20th century. Although Huygens only observed out-of-phase synchronization, recent investigations have shown the existence of in-phase synchronization, as well as "death" states wherein one or both clocks stops. [134] [135] Religious practice [ edit ] Pendulum in the Metropolitan Cathedral, Mexico City. Pendulum motion appears in religious ceremonies as well. The swinging incense burner called a censer, also known penemu gravity a thurible, is an example of a pendulum. [136] Pendulums are also seen at many gatherings in eastern Mexico where they mark the turning of the tides on the day which the tides are at their highest point. See also pendulums for divination and dowsing. Education [ edit ] Pendulums are widely used in science education as an example of a harmonic oscillator, to teach dynamics and oscillatory motion. One use is to demonstrate the law of conservation of energy. [137] [138] Penemu gravity heavy object such as a bowling ball [139] or wrecking ball [137] is attached to a string. The weight is then moved to within a few inches of a volunteer's face, then released and allowed to swing and come back. In most instances, the weight reverses direction and then returns to (almost) the same position as the original release location — i.e. a small distance from the volunteer's face — thus leaving the volunteer unharmed. On occasion the volunteer is injured if either the volunteer does not stand still [140] or the pendulum is initially released with a push (so that when it returns it surpasses the release position). Torture device [ edit ] It is claimed that the pendulum was used as an instrument of torture and execution by the Spanish Inquisition [141] in the 18th century. The allegation is contained in the 1826 book The history of the Inquisition of Spain by the Spanish priest, historian and liberal activist Juan Antonio Llorente. [142] A swinging penemu gravity whose penemu gravity is a knife blade slowly descends toward a bound prisoner until it cuts into his body. [143] This method of torture came to popular consciousness through the 1842 short story " The Pit and the Pendulum" by American author Edgar Allan Poe [144] but there is considerable skepticism that it actually was used. Most knowledgeable sources are skeptical that this torture was ever actually used. [145] [146] [147] The only evidence of its use is one paragraph in the preface to Llorente's 1826 History, [142] relating a second-hand account by a single prisoner released from the Inquisition's Madrid dungeon in 1820, who purportedly described the pendulum torture method. Modern sources point out that due to Jesus' admonition against bloodshed, Inquisitors were only allowed to use torture methods which did not spill blood, and the pendulum method would have violated this stricture. One theory is that Llorente misunderstood the account he heard; the prisoner was actually referring to another common Inquisition torture, the strappado (garrucha), in which the prisoner has his hands tied behind his back and is hoisted off the floor by a rope tied to his hands. [147] This method was also known as the "pendulum". Poe's popular horror tale, and public awareness of the Inquisition's other brutal methods, has kept the myth of this elaborate torture method alive. See also [ edit ] • Rayleigh–Lorentz pendulum • Barton's pendulums • Blackburn pendulum • Conical pendulum • Cycloidal pendulum • Doubochinski's pendulum • Double pendulum • Double inverted pendulum • Foucault pendulum • Furuta pendulum • Gridiron pendulum • Inertia wheel pendulum • Inverted pendulum • Harmonograph (a.k.a. "Lissajous pendulum") • Kapitza's pendulum • Kater's pendulum • Metronome • N-pendulum [148] • Pendulum (mathematics) • Pendulum clock • Pendulum rocket fallacy • Quantum pendulum • Seconds pendulum • Simple harmonic motion • Spherical pendulum • Spring pendulum • Torsional pendulum Notes [ edit ] • ^ A "small" swing is one in which the angle θ is small enough that sin( θ) can be approximated by θ when θ is measured in radians • ^ The value of "g" (acceleration due to gravity) at the equator is 9.780 m/s 2 and at the poles is 9.832 m/s 2, a difference of 0.53%. The value of g reflected by the period of a pendulum varies from place to place. The gravitational force varies with distance from the center of the Earth, i.e. with altitude - or because the Earth's shape is oblate, g varies with latitude. A more important cause of this reduction in g at the equator is because the equator is spinning at one revolution per day, so the acceleration by the gravitational force is partially canceled there by the centrifugal force. References [ edit ] • ^ "Pendulum". Miriam Webster's Collegiate Encyclopedia. Miriam Webster. 2000. p. 1241. ISBN 978-0-87779-017-4. • ^ a b c d e f g Marrison, Warren (1948). "The Evolution of the Quartz Crystal Clock". Bell System Technical Journal. 27 (3): 510–588. doi: 10.1002/j.1538-7305.1948.tb01343.x. Archived from the original on 2011-07-17. • ^ Morris, William, Ed. (1979). The American Heritage Dictionary, New College Ed. Penemu gravity York: Houghton-Mifflin. p. 969. ISBN 978-0-395-20360-6. • ^ defined by Christiaan Huygens: Huygens, Christian (1673). "Horologium Oscillatorium" (PDF). 17centurymaths. 17thcenturymaths.com. Retrieved 2009-03-01.Part 4, Definition 3, translated July 2007 by Ian Bruce • ^ a b Nave, Carl R. (2006). "Simple pendulum". Hyperphysics. Georgia State Univ. Retrieved penemu gravity. • ^ Xue, Linwei (2007). "Pendulum Systems". Seeing and Touching Structural Concepts. Civil Engineering Dept., Univ. of Manchester, UK. Retrieved 2008-12-10. • ^ Weisstein, Eric W. (2007). "Simple Pendulum". Eric Weisstein's world of science. Wolfram Research penemu gravity. Retrieved 2009-03-09. • ^ a b c d e f g h penemu gravity Milham, Willis I. (1945). Time and Timekeepers. MacMillan.p.188-194 • ^ Halliday, David; Robert Resnick; Jearl Walker (1997). Fundamentals of Physics, 5th Ed. New York: John Wiley & Sons. p. 381. ISBN 978-0-471-14854-8. • ^ Cooper, Herbert J. (2007). Scientific Instruments. New York: Hutchinson's. p. 162. ISBN 978-1-4067-6879-4. • ^ a b Nelson, Robert; M. G. Olsson (February 1987). "The pendulum – Rich physics from a simple system" (PDF). American Journal of Physics. 54 (2): 112–121. Bibcode: 1986AmJPh.54.112N. doi: 10.1119/1.14703. Retrieved 2008-10-29. • ^ Penderel-Brodhurst, James George Joseph (1911). "Clock". In Chisholm, Hugh (ed.). Encyclopædia Britannica. Vol. 06 (11th ed.). Cambridge University Press. pp. 536–553, see page 538. Pendulum.—Suppose that we have a body. includes a derivation • ^ Deschaine, J. S.; Suits, B. H. (2008). "The hanging cord with a real tip mass". European Journal of Physics. 29 (6): 1211–1222. Bibcode: 2008EJPh.29.1211D. doi: 10.1088/0143-0807/29/6/010. • ^ a b Huygens, Christian (1673). "Horologium Oscillatorium". 17centurymaths. Translated by Bruce, Ian. 17thcenturymaths.com. Retrieved 2009-03-01.Part 4, Proposition 5 • ^ Glasgow, David penemu gravity. Watch penemu gravity Clock Making. London: Cassel & Co. p. 278. • ^ Fowles, Grant R (1986). Analytical Mechanics, 4th Ed. NY, NY: Saunders. pp. 202 ff. • ^ a b c Huygens (1673) Horologium Oscillatorium, Part 4, Proposition penemu gravity • ^ Morton, W. Scott and Charlton M. Lewis (2005). China: Its History and Culture. New York: McGraw-Hill, Inc., p. 70 • ^ a b Needham, Volume 3, 627-629 • ^ Good, Gregory (1998). Sciences of the Earth: An Encyclopedia of Events, People, and Phenomena. Routledge. p. 394. ISBN 978-0-8153-0062-5. • ^ "ibn+yunus"+pendulum&pg=RA2-PA126 "Pendulum". Encyclopedia Americana. Vol. 21. The Americana Corp. 1967. p. 502. Retrieved 2009-02-20. • ^ Baker, Cyril Clarence Thomas (1961). Dictionary of Mathematics. G. Newnes. p. 176. • ^ Newton, Roger G. (2004). Galileo's Penemu gravity From the Rhythm of Time to the Making of Matter. US: Harvard University Press. p. 52. ISBN 978-0-674-01331-5. • ^ King, D. A. (1979). "Ibn Yunus and the pendulum: a history of errors". Archives Internationales d'Histoire des Sciences. 29 (104): 35–52.reprinted on the Muslim Heritage website. • ^ Hall, Bert S. (September 1978). "The scholastic pendulum". Annals of Science. 35 (5): penemu gravity. doi: 10.1080/00033797800200371. ISSN 0003-3790. • ^ O'Connor, J. J.; Robertson, E. F. (November 1999). "Abu'l-Hasan Ali ibn Abd al-Rahman ibn Yunus". University of St Andrews. Retrieved 2007-05-29. • ^ Akyeampong, Emmanuel K.; Gates, Henry Louis (2012). "ibn+yunus"+pendulum&pg=RA2-PA126 Dictionary of African Biography, Vol. 1. Oxford Univ. Press. p. 126. ISBN 9780195382075. • ^ Matthews, Michael R. (2000). Time for science education. Springer. p. 87. ISBN 978-0-306-45880-4. • ^ a b Drake, Stillman (2003). Galileo at Work: His scientific biography. USA: Courier Dover. pp. 20–21. ISBN 978-0-486-49542-2. • ^ Galilei, Galileo (1909). Favaro, Antonio (ed.). Le Opere di Galileo Galilei, Edizione Nazionale [ The Works of Galileo Galilei, National Edition] (in Italian). Florence: Barbera. ISBN 978-88-09-20881-0. • ^ Murdin, Paul (2008). Full Meridian of Glory: Perilous Adventures in the Competition to Measure the Earth. Springer. p. 41. ISBN 978-0-387-75533-5. • ^ La Lampada di Galileo, by Francesco Malaguzzi Valeri, for Archivio storico dell'arte, Volume 6 (1893); Editor, Domenico Gnoli; Publisher Danesi, Rome; Page 215-218. • ^ a b Van Helden, Albert (1995). "Pendulum Clock". The Galileo Project. Rice Univ. Retrieved 2009-02-25. • ^ Drake 2003, p.419–420 • ^ although there are unsubstantiated references to prior pendulum clocks made by others: Usher, Abbott Payson (1988). A History of Mechanical Inventions. Courier Dover. pp. 310–311. ISBN 978-0-486-25593-4. • ^ Eidson, John C. (2006). Measurement, Control, and Communication using IEEE 1588. Burkhausen. p. 11. ISBN 978-1-84628-250-8. • ^ Milham 1945, p.145 • ^ a b O'Connor, J.J.; E.F. Robertson (August 2002). "Robert Hooke". Biographies, MacTutor History of Mathematics Archive. School of Mathematics and Statistics, Univ. of St. Andrews, Scotland. Archived from the original on 2009-03-03. Retrieved 2009-02-21. • ^ Nauenberg, Michael (2006). "Robert Hooke's seminal contribution to orbital dynamics". Robert Hooke: Tercentennial Studies. Ashgate Publishing. pp. 17–19. ISBN 0-7546-5365-X. • ^ Nauenberg, Michael (2004). "Hooke and Newton: Divining Planetary Motions". Physics Today. 57 (2): 13. Bibcode: 2004PhT.57b.13N. doi: 10.1063/1.1688052. Retrieved 2007-05-30. • ^ The KGM Group, Inc. (2004). "Heliocentric Models". Science Master. Archived from the original on 2007-07-13. Retrieved 2007-05-30. • ^ Lenzen, Victor F.; Robert P. Multauf (1964). "Paper 44: Development of gravity pendulums in the 19th century". United States National Museum Bulletin 240: Contributions from the Museum penemu gravity History and Technology reprinted in Bulletin of the Smithsonian Institution. Washington: Smithsonian Institution Press. p. penemu gravity. Retrieved 2009-01-28. • ^ Richer, Jean (1679). Observations astronomiques et physiques faites en l'isle de Caïenne. Mémoires de l'Académie Royale des Sciences. Bibcode: 1679oaep.book.R. cited in Lenzen & Multauf, 1964, p.307 • ^ Lenzen & Multauf, 1964, p.307 • ^ Poynting, John Henry; Joseph John Thompson (1907). A Textbook of Physics, 4th Ed. London: Charles Griffin & Co. pp. 20–22. penemu gravity ^ Huygens, Christian; translated by Ian Bruce (July 2007). "Horologium Oscillatorium" (PDF). 17centurymaths. 17thcenturymaths.com. Retrieved 2009-03-01. • ^ The constellation of Horologium was later named in honor of this book. • ^ Matthews, Michael R. (1994). Science Teaching: The Role of History and Philosophy of Science. Psychology Press. pp. 121–122. ISBN 978-0-415-90899-3. • ^ Huygens, Horologium Oscillatorium, Part 2, Proposition 25 • ^ Mahoney, Michael S. (March 19, 2007). "Christian Huygens: The Measurement of Time and of Longitude at Sea". Princeton University. Archived from the original on December 4, 2007. Retrieved 2007-05-27. • ^ Bevilaqua, Fabio; Lidia Falomo; Lucio Fregonese; Enrico Gianetto; Franco Giudise; Paolo Mascheretti (2005). "The pendulum: From constrained fall to the concept of potential". The Pendulum: Scientific, Historical, Philosophical, and Educational Perspectives. Springer. pp. 195–200. ISBN 1-4020-3525-X. Retrieved 2008-02-26. gives a detailed description of Huygens' methods • ^ a b Headrick, Michael (2002). "Origin and Evolution of the Anchor Clock Escapement". Control Systems Magazine, Inst. Of Electrical and Electronic Engineers. 22 (2). Archived from the original on October 25, 2009. Retrieved 2007-06-06. • ^ " .it is affected by either the intemperance penemu gravity the air or any faults in the mechanism so the crutch QR is not always activated by the same force. With large arcs the swings take longer, in the way I have explained, therefore some inequalities in the motion of the timepiece exist from this cause.", Huygens, Christiaan (1658). Horologium (PDF). The Hague: Adrian Vlaqc.translation by Ernest L. Edwardes (December 1970) Antiquarian Horology, Vol.7, No.1 • ^ penemu gravity b Andrewes, W.J.H. Clocks and Watches: The leap to precision in Macey, Samuel (1994). Encyclopedia of Time. Taylor & Francis. pp. 123–125. ISBN 978-0-8153-0615-3. • ^ Usher, 1988, p.312 • ^ a b Beckett, Edmund (1874). A Rudimentary Treatise on Clocks and Watches and Bells, 6th Ed. London: Lockwood & Co. p. 50. • ^ a b Graham, George (1726). "A contrivance to avoid irregularities in a penemu gravity motion occasion'd by the action of heat and cold upon the rod of the pendulum". Philosophical Transactions of the Royal Society. 34 (392–398): 40–44. doi: 10.1098/rstl.1726.0006. S2CID 186210095. cited in Day, Lance; Ian Penemu gravity (1996). Biographical Dictionary of the History of Technology. Taylor & Francis. p. 300. ISBN 978-0-415-06042-4. • ^ a b Kater, Henry (1818). "An account of experiments for determining the length of the pendulum vibrating seconds in the latitude of London". Phil. Trans. R. Soc. 104 (33): 109. Retrieved 2008-11-25. • ^ Oprea, John (1995). "Geometry and the Focault Pebdulum" (PDF). The American Mathematical Monthly. Mathematical Association of America. 102 (6): 515–522. doi: 10.1080/00029890.1995.12004611. Retrieved 13 April 2021. • ^ Amir Aczel (2003) Leon Foucault: His life, times and achievements, in Matthews, Michael R.; Colin F. Gauld; Arthur Stinner (2005). The Pendulum: Scientific, Historical, Educational, and Philosophical Perspectives. Springer. p. 177. ISBN 978-1-4020-3525-8. • ^ Giovannangeli, Françoise (November 1996). "Spinning Foucault's Pendulum at the Panthéon". The Paris Pages. Archived from the original on 2007-06-09. Retrieved 2007-05-25. • ^ Tobin, William (2003). The Life and Science of Leon Foucault: The man who proved the Earth rotates. UK: Cambridge University Press. pp. 148–149. ISBN 978-0-521-80855-2. • ^ a b c d Penderel-Brodhurst, James George Joseph (1911). "Clock". In Chisholm, Hugh (ed.). Encyclopædia Britannica. Vol. 06 (11th ed.). Cambridge University Press. pp. 536–553, see pages 540 and 541. • ^ a b c Jones, Tony (2000). Splitting the Second: The Story of Atomic Time. CRC Press. p. 30. ISBN 978-0-7503-0640-9. • ^ Kaler, James B. (2002). Ever-changing Sky: A Guide to the Celestial Sphere. UK: Cambridge Univ. Press. p. 183. ISBN 978-0-521-49918-7. • ^ Audoin, Claude; Bernard Guinot; Stephen Lyle (2001). The Measurement of Time: Penemu gravity, Frequency, and the Atomic Clock. UK: Cambridge Univ. Press. p. 83. ISBN 978-0-521-00397-1. • ^ a b Torge, Wolfgang (2001). Geodesy: An Introduction. Walter de Gruyter. p. 177. ISBN 978-3-11-017072-6. • ^ Milham 1945, p.334 • ^ calculated from equation (1) • ^ Glasgow, David (1885). Watch and Clock Making. London: Cassel & Co. pp. 279–284. • ^ Matthys, Robert J. (2004). Accurate Pendulum Penemu gravity. UK: Oxford Univ. Press. p. 4. ISBN 978-0-19-852971-2. • ^ Mattheys, 2004, p. 13 • ^ Matthys 2004, p.91-92 • ^ Beckett 1874, p.48 • ^ "Regulation". Encyclopedia of Clocks and Watches. Old and Sold antiques marketplace. 2006. Retrieved 2009-03-09. • ^ Beckett 1874, p.43 • ^ Glasgow 1885, p.282 • ^ "Great Clock facts". Big Ben. London: UK Parliament. 13 November 2009. Archived from the original on 7 October 2009. Retrieved 31 Penemu gravity 2012. • ^ Matthys 2004, p.3 • ^ a b c d Penderel-Brodhurst, James George Joseph (1911). "Clock". In Chisholm, Hugh (ed.). Encyclopædia Britannica. Vol. 06 (11th ed.). Cambridge University Press. pp. 536–553, see pages 539 and 540. • ^ Huygens, Christiaan (1658). Horologium (PDF). The Hague: Adrian Vlaqc.translation by Ernest L. Edwardes (December 1970) Antiquarian Horology, Vol.7, No.1 • ^ Zupko, Ronald Edward (1990). Revolution in Measurement: Western European Weights and Measures since the Age of Science. Diane Publishing. p. 131. ISBN 978-0-87169-186-6. • ^ Picard, Penemu gravity, La Mesure de la Terre [The measurement of the Penemu gravity (Paris, France: Imprimerie Royale, 1671), p. 4. Picard described a pendulum consisting of a copper ball which was an inch in diameter and was suspended by a strand of pite, a fiber from the aloe plant. Picard then mentions that temperature slightly effects the length of this pendulum: "Il est vray que cette longueur ne s'est pas toûjours trouvées si précise, & qu'il a semblé qu'elle devoit estre toûjours un peu accourcie en Hyver, & allongée en esté; mais c'est seulement de la dixieme partie d'une ligne … " (It is true that this length [of the pendulum] is not always found [to be] so precise, and that it seemed that it should be always a bit shortened in winter, and lengthened in summer; but it is only by a tenth part of a line [1 ligne (line) = 2.2558 mm] … ) • ^ a b c d Matthys 2004, p.7-12 • ^ Milham 1945, p.335 • ^ Milham 1945, p.331-332 • ^ Matthys 2004, Part 3, p.153-179 • ^ Poynting & Thompson, 1907, p.13-14 • ^ Updegraff, Milton (February 7, 1902). "On the measurement of time". Science. 15 (371): 218–219. doi: 10.1126/science.ns-15.374.218-a. PMID 17793345. S2CID 21030470. Retrieved 2009-07-13. • ^ Dunwoody, Halsey (1917). Notes, Problems, and Laboratory Exercises in Mechanics, Sound, Light, Thermo-Mechanics and Hydraulics, penemu gravity Ed. New York: John Wiley & Sons. p. 87. • ^ "Resonance Width". Glossary. Time and Frequency Division, US National Institute of Standards and Technology. 2009. Archived from the original on 2009-01-30. Retrieved 2009-02-21. • ^ a b Jespersen, James; Fitz-Randolph, Jane; Robb, John (1999). From Sundials to Atomic Clocks: Understanding Time and Frequency. New York: Courier Dover. pp. 41–50. ISBN 978-0-486-40913-9. p.39 • ^ Matthys, Robert J. (2004). Accurate Pendulum Clocks. UK: Oxford Univ. Press. pp. 27–36. ISBN 978-0-19-852971-2. has an excellent penemu gravity discussion of the controversy over the applicability of Q to the accuracy of pendulums. • ^ "Quality Factor, Q". Glossary. Time and Frequency Division, US National Institute of Standards and Technology. 2009. Archived from the original on 2008-05-04. Penemu gravity 2009-02-21. • ^ Matthys, 2004, p.32, fig. 7.2 and text • ^ Matthys, 2004, p.81 • ^ a b c "Q, Quality Factor". Watch and clock magazine. Orologeria Lamberlin website. Retrieved 2009-02-21. • ^ Milham 1945, p.615 • ^ "The Reifler and Shortt clocks". JagAir Institute of Time and Penemu gravity. Retrieved 2009-12-29. • ^ Betts, Jonathan (May 22, 2008). "Expert's Statement, Case 6 (2008-09) William Hamilton Shortt regulator". Export licensing hearing, Reviewing Committee on the Export of Works of Art and Objects of Cultural Interest. UK Museums, Libraries, and Archives Council. Archived from the original (DOC) on October 25, 2009. Retrieved 2009-12-29. • ^ Airy, George Biddle (November 26, 1826). "On the Disturbances of Pendulums and Balances and on the Theory of Escapements". Transactions of the Cambridge Philosophical Society. 3 (Part 1): 105. Retrieved 2008-04-25. • ^ Beckett 1874, p.75-79 • ^ Vočadlo, Lidunka. "Gravity, the shape of the Earth, isostasy, moment of inertia". Retrieved 5 November 2012. • ^ Baker, Penemu gravity A. (Spring 2000). "Chancellor Bacon". English 233 – Introduction to Penemu gravity Humanities. English Dept., Kansas State Univ. Retrieved 2009-02-20. • ^ a b Poynting & Thompson 1907, p.9 • ^ Poynting, John Henry; Joseph John Thompson (1907). A Textbook of Physics, 4th Ed. London: Penemu gravity Griffin & Co. p. 20. • ^ a b Victor F., Lenzen; Robert P. Multauf (1964). "Paper 44: Development of gravity pendulums in the 19th century". United States National Museum Bulletin 240: Contributions from the Museum of History and Technology reprinted in Bulletin of the Smithsonian Institution. Washington: Smithsonian Institution Press. p. 307. Retrieved 2009-01-28. • ^ a b Poynting & Thompson, 1907, p.10 • ^ Poynting, John Henry (1894). The Mean Density of the Earth. London: Charles Griffin. pp. 22–24. • ^ Cox, John (1904). Mechanics. Cambridge, UK: Cambridge Univ. Press. pp. 311–312. • ^ Poynting & Thomson 1904, p.23 • ^ Poynting, John Henry (1894). The Mean Density of the Earth. London: Charles Griffin & Co. pp. 24–29. • ^ Poynting, John Henry (1911). "Gravitation". In Chisholm, Hugh (ed.). Encyclopædia Britannica. Vol. 12 (11th ed.). Cambridge University Press. pp. 384–389, see page 386. Airy's Experiment.—In 1854 Sir G. B. Airy. • ^ Lenzen & Multauf 1964, p.320 • ^ Poynting & Thompson 1907, p.18 • ^ a b c "The downs and ups of gravity surveys". NOAA Celebrates 200 Years. US National Oceanographic and Atmospheric Administration. 2007-07-09. • ^ Lenzen & Multauf 1964, p.324 • ^ Lenzen & Multauf 1964, p.329 • ^ a b Woolard, George P. (June 28–29, 1957). "Gravity observations during the IGY". Geophysics and the IGY: Proceedings of the symposium at the opening of the International Geophysical Year. Washington, D.C.: American Geophysical Union, Nat'l Academy of Sciences. p. 200. Retrieved 2009-05-27. • ^ Lenzen & Multauf 1964, p.336, fig.28 • ^ a b Michael R., Matthews (2001). "Methodology and Politics in Science: The fate of Huygens 1673 proposal of the pendulum as an international standard of length and some educational suggestions". Science, Education, and Culture: The contribution of history and philosophy of science. Springer. p. 296. ISBN 0-7923-6972-6. • ^ Renwick, James (1832). The Elements of Mechanics. Philadelphia: Carey & Lea. pp. 286–287. • ^ Alder, Ken (2003). The measure of all things: The seven-year odyssey and hidden error that transformed the world. US: Simon and Schuster. p. 88. ISBN 978-0-7432-1676-0. • ^ cited in Jourdan, Louis (22 October 2001). penemu gravity SI and dictionaries". USMA (Mailing list). Retrieved 2009-01-27. • ^ Agnoli, Paolo; Giulio D'Agostini (December 2004). "Why does the meter beat the second?". arXiv: physics/0412078. • ^ quoted in LeConte, John (August 1885). "The Metric System". The Overland Monthly. 6 (2): 178. Retrieved 2009-03-04. • ^ Zupko, 1990, p.131 • ^ Zupko, penemu gravity, p.140-141 • ^ Zupko, 1990, p.93 • ^ Schumacher, Heinrich (1821). "Danish standard of length". The Quarterly Journal of Science, Literature and the Arts. 11 (21): 184–185. Retrieved 2009-02-17. • ^ "Schumacher, Heinrich Christian". The American Penemu gravity. Vol. 14. D. Appleton & Co., London. 1883. p. 686. Retrieved 2009-02-17. • ^ Trautwine, John Cresson (1907). The Civil Engineer's Pocket-Book, 18th Ed. New York: John Wiley. p. 216. • ^ Toon, John (September 8, 2000). "Out of Time: Researchers Recreate 1665 Clock Experiment to Gain Insights into Modern Synchronized Oscillators". Georgia Tech. Retrieved 2007-05-31. • ^ Penemu gravity. Fradkov and B. Andrievsky, "Synchronization and phase relations in the motion of two-pendulum system", International Journal of Non-linear Mechanics, vol. 42 (2007), pp. 895–901. • ^ I.I. Blekhman, "Synchronization in science and technology", ASME Press, New York, 1988, (Translated from Russian into English) • ^ An interesting simulation of thurible motion can be found at this site. • ^ a b Hart, Matthew (2 February 2016). "Physics Risks Death by Wrecking Ball for Science". Nerdist. Retrieved 14 March 2017. • ^ Sorenson, Roy (2014). "Novice Thought Experiments". In Booth, Anthony Robert; Rowbottom, Darrell P. (eds.). Intuitions. Oxford Univ Pr. p. 139. Penemu gravity 9780199609192. Retrieved 15 March 2017. • ^ "Bowling Ball Pendulum". The Wonders of Physics. University of Wisconsin–Madison. Retrieved 14 March 2017. • ^ weknowmemes (8 August 2014). "Physics Ball Test Gone Wrong". YouTube. Archived from the original on 2021-11-10. Retrieved 14 March 2017. • ^ Scott, George Ryley (2009). The History Of Torture Throughout the Ages. Routledge. p. 242. ISBN 978-1136191602. • ^ a b Llorente, Juan Antonio (1826). The history of the Inquisition of Spain. Abridged and translated by George B. Whittaker. Oxford University. pp. XX, preface. • ^ Abbott, Geoffrey (2006). Execution: The Guillotine, the Pendulum, the Thousand Cuts, the Spanish Donkey, and 66 Other Ways of Putting Someone to Death. St. Martin's Press. ISBN 978-0-312-35222-6. • ^ Poe, Edgar Allan (1842). The Pit and the Pendulum. Booklassic. ISBN 978-9635271900. • ^ Roth, Cecil (1964). The Spanish Inquisition. W. W. Norton and Company. pp. 258. ISBN 978-0-393-00255-3. pendulum. • ^ Mannix, Daniel P. (2014). The History of Torture. eNet Press. p. 76. ISBN 978-1-61886-751-3. • ^ a b Pavlac, Brian (2009). Witch Hunts in the Western World: Persecution and Punishment from the Inquisition through the Salem Trials. ABC-CLIO. p. 152. ISBN 978-0-313-34874-7. • ^ Yurchenko, D.; Alevras, P. (2013). "Dynamics of the N-pendulum and its application to a wave energy converter concept". International Journal of Dynamics and Control. 1 (4): 4. doi: 10.1007/s40435-013-0033-x. Further reading [ edit ] • G. Penemu gravity. Baker and J. A. Blackburn (2009). The Pendulum: A Case Study in Physics (Oxford University Press). • M. Gitterman (2010). The Chaotic Pendulum (World Scientific). • Michael R. Matthews, Arthur Stinner, Colin F. Gauld (2005) The Pendulum: Scientific, Historical, Philosophical and Educational Perspectives, Springer • Matthews, Michael R.; Gauld, Colin; Stinner, Arthur (2005). "The Pendulum: Its Place penemu gravity Science, Culture and Pedagogy". Science & Education. 13 (4/5): 261–277. Bibcode: 2004Sc&Ed.13.261M. doi: 10.1023/b:sced.0000041867.60452.18. S2CID 195221704. • Schlomo Silbermann,(2014) "Pendulum Fundamental; The Path Of Nowhere" (Book) • Matthys, Robert J. (2004). Accurate Pendulum Clocks. UK: Oxford Univ. Press. ISBN 978-0-19-852971-2. • Nelson, Robert; M. G. Olsson (February 1986). "The pendulum – Rich physics from a simple system". American Journal of Physics. 54 (2): 112–121. Bibcode: 1986AmJPh.54.112N. doi: 10.1119/1.14703. • L. P. Pook (2011). Understanding Pendulums: A Brief Introduction (Springer). 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By using this site, you agree to the Terms of Use and Privacy Policy. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization. • Privacy policy • About Wikipedia • Disclaimers • Contact Wikipedia • Mobile view • Developers • Statistics • Cookie statement • • Searl-Effect Generator atau SEG. Kontribusi luar biasa yang diberikan oleh Profesor John Searl kepada teknologi masih belum diketahui oleh masyarakat luas, namun mampu menciptakan revolusi bagi semua bentuk perjalanan, serta memecahkan masalah kebutuhan energi penemu gravity. Beliau dilahirkan pada tanggal 2 Mei 1932 dalam suatu keluarga miskin di Inggris. Masa awal kehidupan John memberi nuansa terhadap masa-masa percobaan yang terpampang di hadapannya. Sejak masa kanak-kanak, John telah dihadapkan pada kesulitan-kesulitan hidup, sehingga menyembunyikan kecerdasan yang menanti untuk ditemukan. Pada usia empat-setengah tahun, John mulai mendapat mimpi yang tak lazim, yang terjadi secara berulang. Mimpi itu datangnya dua kali setahun selama 6 tahun dan menyampaikan instruksi pembuatan yang terperinci kepada pikiran John yang muda dan reseptif. Karena menyadari pesan yang ada di balik semua kuliah malam hari ini, Searl mulai mewujudkan hal-hal yang ia dapatkan dari mimpi dengan memproduksikan Searl-Effect Generator pertama pada usia 14 tahun. Alat itu terdiri dari 3 cincin konsentris yang masing-masing terbuat dari 4 bahan berbeda yang secara konsentris dilekatkan satu sama lain. Ketiga cincin ini dipaku ke sebuah alas. Terdapat roda-roda di sekeliling masing-masing cincin itu, yang berputar secara bebas mengelilingi cincin-cincin itu –umumnya terdapat 12 buah untuk cincin pertama, 22 buah pada cincin berikutnya, dan 32 buah pada cincin terluar. Di sekeliling roda-roda luar, terdapat kumparan yang dihubungkan dengan bermacam-macam konfigurasi untuk menyediakan arus listrik bolak-balik (AC) maupun arus listrik searah (DC). SEG adalah generator bebas-energi, sebuah alat yang mengumpulkan energi tanpa menggunakan bahan bakar minyak. Saat roda-roda SEG didekatkan kepada cincin SEG, Medan penemu gravity resonansi Searl Effect menyebabkan ion-ion negatif dan elektron dari lingkungan sekitar akan tertarik ke dalamnya dan diberi percepatan melalui mesin itu. Proses ini dibantu oleh neodymium, logam penarik-elektron yang langka. Pengaturan mekanis dan materi yang unik dari SEG, menggetarkan neodymium agar secara berkesinambungan dan menggantikan surplus elektron, menyediakan daya listrik atau daya mekanis, atau keduanya. Setelah membuat SEG pertama, Searl mempertunjukkan mesin itu kepada seorang teman lama dari Wales. Dengan segera piringan serta roda generator itu mulai bergerak dengan cepat, sampai akhirnya penemu gravity titik dimana alat tersebut mengatasi gaya gravitasi dan terbang ke atas menembus atap! Penerbangan SEG itu sama sekali di luar perkiraan dan membakar semangat temannya itu sehingga ia mensponsori Searl untuk membuat alat itu lebih banyak. John lalu mulai menguji coba kemampuan terbang mesin tersebut, dan “kehilangan” banyak mesin selama proses uji coba itu. Selanjutnya, dengan memasang mesin itu secara kuat di lantai, John ingin menyalurkan hasil energi SEG menjadi daya yang dapat dipergunakan, yang kemudian penemu gravity daya listrik untuk rumahnya. Di tahun 1965, Searl telah membuat dan menerbangkan piringan terapung, atau Inverse Gravity Vehicles (IGVs) (Kendaraan Penolak Gravitasi), yang menerapkan teknologi SEG. IGV dapat dibuat dalam berbagai ukuran dan dapat melakukan perjalanan dari Inggris ke Jepang dalam waktu 30 menit dengan kecepatan lebih dari 19.000 km/jam! Piringan itu sendiri juga adalah produk yang ramah lingkungan. Apapun yang bisa dijalankan dengan listrik bisa dijalankan oleh SEG; tanpa penemu gravity dan tanpa menggunakan bahan bakar sebagaimana yang kita ketahui. Jika kita memakai teknologi beliau yang luar biasa itu, maka persembahan Profesor Searl kepada dunia akan mengakibatkan sedikit polusi hingga tanpa polusi. Selain itu langit akan semakin bersih, aliran air akan semakin murni, dan alam akan tumbuh kembali secara berlimpah. Kita juga akan memiliki perjalanan di bumi yang lebih cepat dan efisien; perjalanan udara dan angkasa yang lebih aman serta terjangkau; lebih sedikit alergi dan penyakit, penyembuhan dan pemulihan yang lebih cepat, serta banyak manfaat lainnya. Saat retret di Austria pada bulan Februari 2008, Maha Guru Ching Hai diberi informasi mengenai karya Profesor Searl dan tantangan serta penderitaan yang ia hadapi. Dengan segera Beliau mengungkapkan keprihatinan terhadap kesejahteraan dan kebahagiaan Profesor Searl. Beliau kemudian secara tanpa pamrih menawarkan bantuan penuh kasih melalui kontribusi sebesar US$7.000 serta pengaturan lainnya untuk membantu membuat kehidupan Dr. Searl menjadi lebih nyaman. Profesor Searl menanggapi hal itu dengan rasa terima kasih yang tulus. Ia memberi komentar bahwa upaya Maha Guru Ching Hai “benar-benar dihargai dan beliau sungguh merupakan seorang Wanita yang luar biasa.” Sekarang ini, Dr.

Searl memiliki kantor pusat di Thailand yang memiliki perkembangan yang penemu gravity dalam memproduksi SEG. Meskipun SEG maupun IVG belum siap untuk diluncurkan kepada masyarakat umum, tetapi ia berkata, “Saya bekerja dalam suatu proyek yang menciptakan suatu dunia yang lebih baik bagi seluruh umat manusia, tak peduli apapun.” Sebuah video tentang kehidupan Profesor Searl, berjudul “Kisah John Searl,” akan segera diterbitkan.

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• ASAL MULA DAN FILSAFAT TAI CHI CHUAN • BENARKAH KOPI BERMANFAAT ? • PLANET BARU DITEMUKAN DI ZONA LAYAK HUNI, MIRIP BUMI • DITEMUKAN PLANET TANPA MATAHARI • PROFESSOR JOHN ROY ROBERT SEARL (1932) PENEMU ANTI. • MENCIPTAKAN MEDAN ENERGI YANG LUAS DI SEKITAR TUBU. • ANAK INDIGO • KISAH BUNDA MARIA (MARYAM) DAN NABI ISA AL-MASIH D. • GELOMBANG ENERGI OTAK • KALIMAT YANG PALING DICINTAI ALLAH • Adam (2) • Alien (1) • Allah (2) • Aneh (1) • Bani Adam (1) • Bunda Maria (1) • Energi (2) • Gravitasi (1) • Harta (1) • Ilmu (1) • Indigo (1) • Isa Al-Masih (1) • Jiwa (1) • Kopi (1) • Langka (1) • meditasi (1) • perempuan (1) • Planet (2) • Raelianisme (1) • Rahasia (2) • Raksasa (2) • Ras (2) • Shalat (2) • TAI CHI (1) • Tasawuf (1) • Teleportasi (1) • Tidur (1) • Time (2) • Unik (1) • Waktu (3) • wanita (1) • woman (1)

## Andrew J. Tolley: A brief introduction to massive gravity

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