Tensors and Relativity: Chapter 5

The gravitational redshift experiment

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This ``gedänken'' experiment was first suggested by Einstein . Suppose we have a tower of height h on the surface of the earth.

figure210


Figure 5.1: The Gravitational redshift experiment.

A particle of rest mass m is dropped from the top of the tower and falls freely with acceleration g [ see Figure 5.1 ]. It reaches the ground with a velocity tex2html_wrap_inline734 , so its total energy E, as measured by an observer at the foot of the tower is

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Suppose the observer has some magical method of converting all this energy into a photon of the same energy [ this is a thought experiment after all! ]. Upon its arrival at the top of the tower with energy tex2html_wrap_inline738 the photon is again magically changed into a particle of rest mass tex2html_wrap_inline740 . It must be that tex2html_wrap_inline742 ; otherwise, perpetual motion  could result, so tex2html_wrap_inline744 . We therefore obtain:

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and since tex2html_wrap_inline746 and tex2html_wrap_inline748 we find:

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We therefore predict that a photon climbing in the earths gravitational field will lose energy and will consequently be redshifted. The redshift is:

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This was tested by Pound and Snider  in 1965 using the Mossbauer effect [ photons from atomic decay peak sharply at a particular frequency ]. They measured the redshift experienced by a 14.4 Kev tex2html_wrap_inline752 rays from the decay of tex2html_wrap_inline754 Fe in climbing up a 20 m tower by determining the speed at which a detector at the top must be moved in order to maximize the detection rate i.e. the velocity blueshift balances the gravitational redshift . They found:

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This experimental verification of Einstein's thought experiment is a death- blow of one's chances of finding a simple special relativistic theory of gravity!