Question

Pound and Rebeka at Harward performed an experiment to verify the Red shift predicted by general theory of Relativity. The experiment consisted of the use of 14 keV γ -ray 57Fe source placed on the top of a tower 22.6 m high and the absorber at the bottom. The red shift was detected by the Mosbauer technique. What velocity of the absorber foil was required to compensate the red shift, and in which direction?

Answer 1

The gravitational red shift is due to the change in the energy of a photon as it moves from one region of space to another differing gravitational potential. The photon carries an inertial as well as the gravitational mass given by h ν/c2. In its passage from a point where the gravitational potential is ϕ1 to another point where the potential is ϕ2 there will be expenditure of work given by hν/c2 times the potential difference (ϕ2 − ϕ1). This would result in an equivalent decrease in the energy content of the photon and hence its frequency.

ΔE = E(ϕ2 − ϕ1)/c2

A level difference of H near the earth’* surface would result in the fractional shift of frequency Δν/ν = gH/c

Now, Δν/ν = v/c = gH/c2

or v = gH/c = 9.8 × 22.6/3 × 108 = 7.38 × 10−7m/ = 7.38 × 10−4mm/

Thus resonance fluorescence would occur for downward velocity of the absorber of magnitude 7.38 mm/*.