Gravitational redshift

Graphic representing the gravitational redshift of a neutron star (not exact)

In physics, light or other forms of electromagnetic radiation of a certain wavelength originating from a source placed in a region of stronger gravitational field (and which could be said to have climbed "uphill" out of a gravity well) will be found to be of longer wavelength when received by an observer in a region of weaker gravitational field. A neutron star is a type of remnant that can result from the Gravitational collapse of a massive Star during a Type II, Type Ib or Type Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. Light, or visible light, is Electromagnetic radiation of a Wavelength that is visible to the Human eye (about 400–700 Electromagnetic radiation takes the form of self-propagating Waves in a Vacuum or in Matter. In Physics, a gravity well is the Gravitational potential field around a massive body (a particular kind of Potential well) If applied to optical wave-lengths this manifests itself as a change in the colour of the light as the wavelength is shifted toward the red (making it less energetic, longer in wavelength, and lower in frequency) part of the spectrum. This effect is called gravitational redshift and other spectral lines found in the light will also be shifted towards the longer wavelength, or "red," end of the spectrum. Gravitation is a natural Phenomenon by which objects with Mass attract one another In Physics and Astronomy, redshift occurs when Electromagnetic radiation – usually Visible light – emitted or reflected by This shift can be observed along the entire electromagnetic spectrum.

Light that has passed "downhill" into a region of stronger gravity shows a corresponding increase in energy, and is said to be gravitationally blueshifted. Blue shift is the shortening of a transmitted signal's Wavelength, and/or an increase in its Frequency, due to the Doppler Effect, which indicates that

1 Definition
2 History
3 Important things to stress
4 Initial verification
5 Application
6 Exact Solutions
7 Gravitational Redshift vs. Gravitational Time Dilation
8 Primary sources
9 See also

Definition

Redshift is often denoted with the variable $z\,$ . In Physics and Astronomy, redshift occurs when Electromagnetic radiation – usually Visible light – emitted or reflected by

$z=\frac{\lambda_o-\lambda_e}{\lambda_e}$

Where:

$\lambda_o\,$ is the wavelength of the electromagnetic radiation (photon) as measured by the observer. Electromagnetic radiation takes the form of self-propagating Waves in a Vacuum or in Matter. In Physics, the photon is the Elementary particle responsible for electromagnetic phenomena $\lambda_e\,$ is the wavelength of the electromagnetic radiation (photon) when measured at the source of emission. Electromagnetic radiation takes the form of self-propagating Waves in a Vacuum or in Matter. In Physics, the photon is the Elementary particle responsible for electromagnetic phenomena

Gravitational redshift, the displacement of light towards the red, can (for the case of a star) be predicted using the formula provided in the theory of General Relativity (Albert Einstein: Relativity - Appendix - Appendix III - The Experimental Confirmation of the General Theory of Relativity):

$z_{\mathit{approx}}=\frac{GM}{c^2r}$

where:

$z_{\mathit{approx}}\,$ is the displacement of spectral lines due to gravity as viewed by a far away observer in free space. General relativity or the general theory of relativity is the geometric theory of Gravitation published by Albert Einstein in 1916 Albert Einstein ( German: ˈalbɐt ˈaɪ̯nʃtaɪ̯n; English: ˈælbɝt ˈaɪnstaɪn (14 March 1879 – 18 April 1955 was a German -born theoretical Gravitation is a natural Phenomenon by which objects with Mass attract one another In Classical physics, free space is a concept of Electromagnetic theory, corresponding to a theoretically "perfect" Vacuum, and sometimes $G\,$ is Newton's gravitational constant (the variable used by Einstein himself). The gravitational constant, denoted G, is a Physical constant involved in the calculation of the gravitational attraction between objects with mass $M\,$ is the mass of the body which the light is escaping. Mass is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object $c\,$ is the speed of light. $r\,$ is the radius of star emitting the light.

GM/r is the gravitational potential at distance r, so the redshift is seen to be directly proportional to the gravitational potential. Using the energy-momentum equation relating energy and wavelength of a photon, the gravitational redshift is equivalent to a loss of energy of the photon.

History

The gravitational weakening of light from high-gravity stars was predicted by John Michell in 1783, using Isaac Newton's concept of light corpuscles (see: emission theory). John Michell ( December 25, 1724 – April 29, 1793) was an English natural philosopher and Geologist, whose work spanned Sir Isaac Newton, FRS (ˈnjuːtən 4 January 1643 31 March 1727) Biography Early years See also Isaac Newton's early life and achievements Emission theory (also called "emitter theory" was a competing theory for the Special theory of relativity, explaining the results of the Michelson-Morley experiment The effect of gravity on light was then explored by Laplace and Johann Georg von Soldner (1801), who predicted that some stars would have a gravity so strong that light would not be able to escape. Johann Georg von Soldner ( 16 July 1776 - 13 May 1833) was a German Physicist, Mathematician and Astronomer All of this early work assumed that light could slow down and fall, which was inconsistent with the modern understanding of light waves.

Once it became accepted that light is an electromagnetic wave, it was clear that the frequency of light should not change from place to place, since waves from a source with a fixed frequency keep the same frequency everywhere. The only way around this conclusion would be if time itself was altered--- if clocks at different points had different rates.

This was precisely Einstein's conclusion in 1911. Albert Einstein ( German: ˈalbɐt ˈaɪ̯nʃtaɪ̯n; English: ˈælbɝt ˈaɪnstaɪn (14 March 1879 – 18 April 1955 was a German -born theoretical He considered an accelerating box, and noted that according to the special theory of relativity, the clock rate at the bottom of the box was slower than the clock rate at the top. Special relativity (SR (also known as the special theory of relativity or STR) is the Physical theory of Measurement in Inertial Nowadays, this can be easily shown in accelerated coordinates. In Relativistic physics, the Rindler coordinate chart is an important and useful Coordinate chart representing part of flat Spacetime, also called the The metric tensor in units where the speed of light is one is:

$ds^2 = - r^2 dt^2 + dr^2 \,$

and for an observer at a constant value of r, the rate at which a clock ticks, R(r), is the square root of the time coefficient, R(r)=r. In Physics, natural units are Physical units of Measurement defined in terms of universal Physical constants, such that some chosen physical The acceleration at position r is equal to the curvature of the hyperbola at fixed r, and like the curvature of the nested circles in polar coordinates, it is equal to 1/r.

So at a fixed value of g, the fractional rate of change of the clock-rate, the percentage change in the ticking at the top of an accelerating box vs at the bottom, is:

${R(r+dr) - R(r) \over R} = {dr\over r} = g dr \,$

The rate is faster at larger values of R, away from the apparent direction of acceleration. The rate is zero at r=0, which is the location of the acceleration horizon. The horizon ( Ancient Greek ὁ ὁρίζων, /ho horídzôn/ from ὁρίζειν, "to limit" is the apparent line that separates Locally, the rate changes in the same way as the gravitational acceleration.

Using the principle of equivalence, Einstein concluded that the same thing holds in a gravitational field, that the rate of clocks R at different heights was altered according to the gravitational field g. The equivalence principle When g is slowly varying, it gives the fractional rate of change of the ticking rate. If the ticking rate is everywhere almost this same, the fractional rate of change is the same as the absolute rate of change, so that:

${dR \over dx} = g = - {dV\over dx} \,$

Since the rate of clocks and the gravitational potential have the same derivative, they are the same up to a constant. The constant is chosen to make the clock rate at infinity equal to 1. Since the gravitational potential is zero at infinity:

$R(x)= 1 - {V(x) \over c^2} \,$

where the speed of light has been restored to make the gravitational potential dimensionless.

The coefficient of the $d t 2$ in the metric tensor is the square of the clock rate, which for small values of the potential is given by keeping only the linear term:

$R^2 = 1 - 2V \,$

and the full metric tensor is:

$ds^2 = - ( 1 - {2V(r)\over c^2} )c^2 dt^2 + dx^2 + dy^2 + dz^2$

where again the c's have been restored. This expression is correct in the full theory of general relativity, to lowest order in the gravitational field, and ignoring the variation of the space-space and space-time components of the metric tensor, which only affect fast moving objects.

The changing rates of clocks allowed Einstein to conclude that light waves change frequency as they move, and the frequency/energy relationship for photons allowed him to see that this was best interpreted as the effect of the gravitational field on the mass-energy of the photon. In Physics, mass–energy equivalence is the concept that for particles slower than light any Mass has an associated Energy and vice versa.

Einstein was accused by Philipp Lenard of plagiarism for not citing Soldner's earlier work - a baseless accusation motivated by Lenard's vocal anti-semitism. Philipp Eduard Anton von Lénárd ( June 7, 1862 &ndash May 20, 1947) was a German physicist and the winner of the Antisemitism (alternatively spelled anti-semitism or anti-Semitism; also rarely known as judeophobia) is the Prejudice against or hostility Einstein's result was based on gravitational time dilation, an idea which had no antecedant in any earlier work, and without which a correct theory of gravitational light deflection is impossible. Gravitational time dilation is the effect of time passing at different rates in regions of different Gravitational potential; the higher the local distortion of Spacetime

Important things to stress

The receiving end of the light transmission must be located at a higher gravitational potential in order for gravitational redshift to be observed. Potential energy can be thought of as Energy stored within a physical system In other words, the observer must be standing "uphill" from the source. If the observer is at a lower gravitational potential than the source, a gravitational blueshift can be observed instead. Blue shift is the shortening of a transmitted signal's Wavelength, and/or an increase in its Frequency, due to the Doppler Effect, which indicates that

Tests done by many universities continue to support the existence of gravitational redshift.

Gravitational redshift is not only predicted by general relativity. General relativity or the general theory of relativity is the geometric theory of Gravitation published by Albert Einstein in 1916 Other theories of gravitation require gravitational redshift, although their detailed explanations for why it appears vary. (Any theory that includes conservation of energy and mass-energy equivalence must include gravitational redshift. In Physics, the law of conservation of energy states that the total amount of Energy in an isolated system remains constant and cannot be created although it may In Physics, mass–energy equivalence is the concept that for particles slower than light any Mass has an associated Energy and vice versa. )

Gravitational redshift does not assume the Schwarzschild metric solution to Einstein's field equation - in which the variable $M\;$ cannot represent the mass of any rotating or charged body. In Einstein's theory of General relativity, the Schwarzschild solution (or the Schwarzschild vacuum) describes the Gravitational field outside The Einstein field equations ( EFE) or Einstein's equations are a set of ten equations in Einstein 's theory of General relativity in which the

Initial verification

A number of experimenters initially claimed to have identified the effect using astronomical measurements, and the effect was eventually considered to have been finally identified in the spectral lines of the star Sirius B by W.S. Adams in 1925. Sirius is the brightest star in the night sky with a visual Apparent magnitude of &minus1 Walter Sydney Adams ( December 20 1876 &ndash May 11 1956) was an American Astronomer. However, measurements of the effect before the 1960s have been critiqued by (e. g. , by C. M. Will), and the effect is now considered to have been definitively verified by the experiments of Pound, Rebka and Snider between 1959 and 1965.

The Pound-Rebka experiment of 1959 measured the gravitational redshift in spectral lines using a terrestrial 57Fe gamma source. The Pound-Rebka experiment is a well known experiment to test Albert Einstein 's theory of General relativity. This was documented by scientists of the Lyman Laboratory of Physics at Harvard University. A commonly-cited experimental verification is the Pound-Snider experiment of 1965.

More information can be seen at Tests of general relativity. At its introduction in 1915 the general theory of relativity did not have a solid empirical foundation

Application

Gravitational redshift is studied in many areas of astrophysical research. Astrophysics is the branch of Astronomy that deals with the Physics of the Universe, including the physical properties ( Luminosity,

Exact Solutions

A table of exact solutions of the Einstein field equations consists of the following:

	Non-rotating	Rotating
Uncharged	Schwarzschild	Kerr
Charged	Reissner-Nordström	Kerr-Newman

The more often used exact equation for gravitational redshift applies to the case outside of a non-rotating, uncharged mass which is spherically symmetric. The Einstein field equations ( EFE) or Einstein's equations are a set of ten equations in Einstein 's theory of General relativity in which the In Einstein's theory of General relativity, the Schwarzschild solution (or the Schwarzschild vacuum) describes the Gravitational field outside In General relativity, the Kerr metric (or Kerr vacuum) describes the geometry of Spacetime around a rotating massive body In Physics and Astronomy, the Reissner-Nordström metric is a solution to the Einstein field equations in empty space which corresponds to the gravitational The Kerr-Newman metric is a solution of Einstein's General relativity field equation that describes the spacetime geometry in the region surrounding a charged The equation is:

$z=\frac{1}{\sqrt{1-\left(\frac{2GM}{rc^2}\right)}}-1$ , where

$G\,$ is the gravitational constant,
$M\,$ is the mass of the object creating the gravitational field,
$r\,$ is the radial coordinate of the observer (which is analogous to the classical distance from the center of the object, but is actually a Schwarzschild coordinate), and
$c\,$ is the speed of light. The gravitational constant, denoted G, is a Physical constant involved in the calculation of the gravitational attraction between objects with mass Mass is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object In the theory of Lorentzian manifolds Spherically symmetric spacetimes admit a family of nested round spheres.

Gravitational Redshift vs. Gravitational Time Dilation

When using special relativity's relativistic Doppler relationships to calculate the change in energy and frequency (assuming no complicating route-dependent effects such as those caused by the frame-dragging of rotating black holes), then the Gravitational redshift and blueshift frequency ratios are the inverse of each other, suggesting that the "seen" frequency-change corresponds to the actual difference in underlying clockrate. Special relativity (SR (also known as the special theory of relativity or STR) is the Physical theory of Measurement in Inertial The relativistic Doppler effect is the change in Frequency (and Wavelength) of Light, caused by the relative motion of the source and the observer (as in In Theoretical physics, the issue of route-dependence deals with whether a selected differential between two points is taken as absolute, or as being partly a Albert Einstein 's theory of General relativity predicts that rotating bodies drag Spacetime around themselves in a phenomenon referred to as frame-dragging Black hole#Major features of rotating black holes A rotating black hole is a Black hole that possesses Angular momentum. Blue shift is the shortening of a transmitted signal's Wavelength, and/or an increase in its Frequency, due to the Doppler Effect, which indicates that Gravitational time dilation is the effect of time passing at different rates in regions of different Gravitational potential; the higher the local distortion of Spacetime Route-dependence due to frame-dragging may come into play, which would invalidate this idea and complicate the process of determining globally-agreed differences in underlying clock rate. Albert Einstein 's theory of General relativity predicts that rotating bodies drag Spacetime around themselves in a phenomenon referred to as frame-dragging

While gravitational redshift refers to what is seen, gravitational time dilation refers to what is deduced to be "really" happening once observational effects are taken into account. Gravitational time dilation is the effect of time passing at different rates in regions of different Gravitational potential; the higher the local distortion of Spacetime

Primary sources

John Michell "On the means of discovering the distance, magnitude etc. of the fixed stars" Philosophical Transactions of the Royal Society (1784) 35-57, & Tab III

Albert Einstein, "The effect of gravity on light" (1911)

Albert Einstein, "Relativity: the Special and General Theory. " (@Project Gutenberg).

R. V. Pound and G. A. Rebka, Jr. "Gravitational Red-Shift in Nuclear Resonance" Phys. Rev. Lett. 3 439-441 (1959)

R. V. Pound and J. L. Snider "Effect of gravity on gamma radiation" Phys. Rev. 140 B 788-803 (1965)

R. V. Pound, "Weighing Photons" Classical and Quantum Gravity 17 2303-2311 (2000)

Dictionary

gravitational redshift

-noun

(astronomy),(physics) a shift to longer wavelengths of spectral lines emitted by atoms in a strong gravitational field

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