# 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.

**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 , so its total energy *E*, as measured by an observer at the foot of the tower is

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 the photon is again magically changed into a particle of rest mass . It must be that ; otherwise, perpetual motion could result, so . We therefore obtain:

and since and we find:

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

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 rays from the decay of 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:

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!