Like Riemann, he wanted a closed universe one whose volume and circumference were perfectly finite and measurable without a boundary; he also chose the hypersphere to model the spatial part of the Universe. In truth, the cosmological solutions of relativity allow complete freedom for one to imagine a space which expands or contracts over the course of time: this was demonstrated by the Russian theorist Alexander Friedmann, between and At the same time, the installment of the large telescope at Mount Wilson, in the United States, allowed for a radical change in the cosmic landscape.

In , the observations of Edwin Hubble proved that the nebula NGC was situated far beyond our galaxy. Very rapidly, Hubble and his collaborators showed that this was the case for all of the spiral nebulae, including our famous neighbor, the Andromeda nebula: these are galaxies in their own right, and the Universe is made up of the ensemble of these galaxies. Beyond this spatial enlargement, the second major discovery concerned the time evolution of the Universe. In , indications accumulated which tended to lead one to believe that other galaxies were systematically moving away from ours, with speeds which were proportional to their distance.

This is the fourth of a series of 6 posts devoted to the analysis of some of the scientific aspects of the film, adapted from a paper I published last spring in Inference : International Review of Science. The elasticity of time is a major consequence of relativity theory, according to which time runs differently for two observers with a relative acceleration — or, from the Equivalence Principle, moving in gravitational fields of different intensities.

Thus, close to the event horizon of a black hole, where the gravitational field is huge, time dilation is also huge, because the clocks will be strongly slowed down compared to farther clocks. This corresponds to a time dilation factor of 60, Although the time dilation tends to infinity when a clock tends to the event horizon this is precisely why no signal can leave it to reach any external observer , at first sight a time dilation as large as 60, seems impossible for a planet orbiting the black hole on a stable orbit. Intuitively, even an expert in general relativity would estimate impossible to reconcile an enormous time differential with a planet skimming up the event horizon and safely enduring the correspondingly enormous gravitational forces.

However Thorne did a few hours of calculations and came to the conclusion that in fact it was marginally possible although very unlikely. A rotating black hole, described by the Kerr metric, behaves rather differently from a static one, described by the Schwarzschild metric. The time dilation equation derived from the Kerr metric takes the form:. Although my various books have been translated in 14 languages including Chinese, Korean, Bengali… , only 4 of my essays have been translated in English. The sense of a systematic assault on the weak-field predictions of GR has been supplanted to some extent by an opportunistic approach in which novel and unexpected and sometimes inexpensive tests of gravity have arisen from new theoretical ideas or experimental techniques, often from unlikely sources.

Instead, much of the focus has shifted to experiments which can probe the effects of strong gravitational fields. These are the regimes of strong gravity. At one extreme are the strong gravitational fields associated with Planck-scale physics. Will unification of the forces, or quantization of gravity at this scale leave observable effects accessible by experiment?

Dramatically improved tests of the equivalence principle, of the inverse square law, or of local Lorentz invariance are being mounted, to search for or bound the imprinted effects of Planck-scale phenomena. At the other extreme are the strong fields associated with compact objects such as black holes or neutron stars. Astrophysical observations and gravitational wave detectors are being planned to explore and test GR in the strong-field, highly-dynamical regime associated with the formation and dynamics of these objects. In this Living Review, we shall survey the theoretical frameworks for studying experimental gravitation, summarize the current status of experiments, and attempt to chart the future of the subject.

We shall not provide complete references to early work done in this field but instead will refer the reader to the appropriate review articles and monographs, specifically to Theory and Experiment in Gravitational Physics [ ], hereafter referred to as TEGP.

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## New light on the Einstein-Hilbert priority question | SpringerLink

Additional recent reviews in this subject are [ , , , 71 , 98 , ]. References to TEGP will be by chapter or section, e. The principle of equivalence has historically played an important role in the development of gravitation theory. Newton regarded this principle as such a cornerstone of mechanics that he devoted the opening paragraph of the Principia to it.

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In , Einstein used the principle as a basic element in his development of general relativity. We now regard the principle of equivalence as the foundation, not of Newtonian gravity or of GR, but of the broader idea that spacetime is curved. Much of this viewpoint can be traced back to Robert Dicke, who contributed crucial ideas about the foundations of gravitation theory between and These ideas were summarized in his influential Les Houches lectures of [ 93 ], and resulted in what has come to be called the Einstein equivalence principle EEP. In the simplest case of dropping two different bodies in a gravitational field, WEP states that the bodies fall with the same acceleration this is often termed the Universality of Free Fall, or UFF.

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The outcome of any local non-gravitational experiment is independent of the velocity of the freely-falling reference frame in which it is performed. The outcome of any local non-gravitational experiment is independent of where and when in the universe it is performed. For example, a measurement of the electric force between two charged bodies is a local non-gravitational experiment; a measurement of the gravitational force between two bodies Cavendish experiment is not. In local freely falling reference frames, the non-gravitational laws of physics are those written in the language of special relativity.

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The argument that leads to this conclusion simply notes that, if EEP is valid, then in local freely falling frames, the laws governing experiments must be independent of the velocity of the frame local Lorentz invariance , with constant values for the various atomic constants in order to be independent of location. General relativity is a metric theory of gravity, but then so are many others, including the Brans-Dicke theory and its generalizations. Theories in which varying non-gravitational constants are associated with dynamical fields that couple to matter directly are not metric theories.

Neither, in this narrow sense, is superstring theory see Section 2.

## Tag Archives: General Relativity

It is important to point out, however, that there is some ambiguity in whether one treats such fields as EEP-violating gravitational fields, or simply as additional matter fields, like those that carry electromagnetism or the weak interactions. Still, the notion of curved spacetime is a very general and fundamental one, and therefore it is important to test the various aspects of the Einstein equivalence principle thoroughly. We first survey the experimental tests, and describe some of the theoretical formalisms that have been developed to interpret them. For other reviews of EEP and its experimental and theoretical significance, see [ , ].

It is being developed by the French space agency CNES for a possible launch in March, , for a one-year mission [ 59 ]. The drag-compensated satellite will be in a Sun-synchronous polar orbit at km altitude, with a payload consisting of two differential accelerometers, one with elements made of the same material platinum , and another with elements made of different materials platinum and titanium.

An alternative concept for a space test of WEP is Galileo-Galilei [ ], which uses a rapidly rotating differential accelerometer as its basic element. In addition to these direct experiments, there was the Dirac equation of quantum mechanics and its prediction of anti-particles and spin; later would come the stunningly successful relativistic theory of quantum electrodynamics.

Special relativity has been so thoroughly integrated into the fabric of modern physics that its validity is rarely challenged, except by cranks and crackpots. It is ironic then, that during the past several years, a vigorous theoretical and experimental effort has been launched, on an international scale, to find violations of special relativity. And in models such as string theory, the presence of additional scalar, vector, and tensor long-range fields that couple to matter of the standard model could induce effective violations of Lorentz symmetry.

These and other ideas have motivated a serious reconsideration of how to test Lorentz invariance with better precision and in new ways. Such a Lorentz-non-invariant electromagnetic interaction would cause shifts in the energy levels of atoms and nuclei that depend on the orientation of the quantization axis of the state relative to our universal velocity vector, and on the quantum numbers of the state. The presence or absence of such energy shifts can be examined by measuring the energy of one such state relative to another state that is either unaffected or is affected differently by the supposed violation.

The Michelson-Morley, Joos, Brillet-Hall and cavity experiments test the isotropy of the round-trip speed of light. The centrifuge, two-photon absorption TPA and JPL experiments test the isotropy of light speed using one-way propagation. The most precise experiments test isotropy of atomic energy levels. Also included for comparison is the corresponding limit obtained from Michelson-Morley type experiments for a review, see [ ].

## Einstein's General Relativity and Gravitation

One of these is the Brillet-Hall experiment [ 46 ], which used a Fabry-Perot laser interferometer. In a recent series of experiments, the frequencies of electromagnetic cavity oscillators in various orientations were compared with each other or with atomic clocks as a function of the orientation of the laboratory [ , , , 12 , ].

The c 2 framework focusses exclusively on classical electrodynamics. A variety of clock anisotropy experiments have been carried out to bound the electromagnetic parameters of the SME framework [ ]. Direct comparisons between atomic clocks based on different nuclear species place bounds on SME parameters in the neutron and proton sectors, depending on the nature of the transitions involved. Mattingly [ ] gives a thorough and up-to-date review of both the theoretical frameworks and the experimental results for tests of LLI.

After almost 50 years of inconclusive or contradictory measurements, the gravitational redshift of solar spectral lines was finally measured reliably. During the early years of GR, the failure to measure this effect in solar lines was siezed upon by some as reason to doubt the theory. Unfortunately, the measurement is not simple.

The secret is to use strong, symmetrical lines, leading to unambiguous wavelength measurements. Successful measurements were finally made in and TEGP 2. In , LoPresto et al. The most precise standard redshift test to date was the Vessot-Levine rocket experiment that took place in June [ ]. A hydrogen-maser clock was flown on a rocket to an altitude of about 10, km and its frequency compared to a similar clock on the ground. Two hydrogen maser clocks and an ensemble of three superconducting-cavity stabilized oscillator SCSO clocks were compared over a day period.

This bound has been improved using more stable frequency standards, such as atomic fountain clocks [ , , 23 ]. Modern advances in navigation using Earth-orbiting atomic clocks and accurate time-transfer must routinely take gravitational redshift and time-dilation effects into account. For example, the Global Positioning System GPS provides absolute positional accuracies of around 15 m even better in its military mode , and 50 nanoseconds in time transfer accuracy, anywhere on Earth.

If these effects were not accurately accounted for, GPS would fail to function at its stated accuracy. This represents a welcome practical application of GR! Bounds on cosmological variation of fundamental constants of non-gravitational physics. For an in-depth review, see [ ]. Clock comparisons [ , 31 , , ]. Oklo Natural Reactor [ 72 , , ]. Spectra in distant quasars [ , ].

Spectra in distant quasars [ , 51 ]. Oklo Natural Reactor [ 72 ]. Big Bang nucleosynthesis [ , ]. Spectra in distant quasars [ ]. The main example of the former type is the clock comparison test, in which highly stable atomic clocks of different fundamental type are intercompared over periods ranging from months to years variants of the null redshift experiment.