I4 The Experiment of Rebka and Pound
We have already seen in G4 that Schwarzschild attempted beginning in 1913 to demonstrate a ‘red-shift’ in the absorption lines of the sun’s spectrum. With this Einstein had hoped to obtain a first experimental confirmation of his theory. However, the evidence would not have specifically confirmed the GTR but rather the conservation of energy:
As a photon flies from x1 to x2 its potential energy increases and it therefore needs to release a bit of its internal energy E1 = h • f1 (where h is Planck's constant). At location x2 it has the smaller energy
E2 = h • f2, the frequency of the radiation is thus slightly smaller and the wavelength (due to the formula
c = f • λ) becomes somewhat bigger. The wavelength thus shifts in the direction of the red end of the optical spectrum, from whence the name ‘red-shift’ comes. For a small rise of the photon from x1 to x2 applies
Putting this together we get
For very small uplifts in the earth’s surface this can be further simplified: x1 • x2 ≈ rE2 , for the difference x1 - x2 we write Δx , and G • M / rE2 is simply the gravitational acceleration g at the earth's surface. Thus we get the formula
This result – albeit with a different justification – was already derived in G4! There we also calculated that at a height difference Δx of 22.6 meters we have a ratio Δf / f in the range of 10-15.
The two American physicists R.V. Pound and G.A. Rebka succeeded in 1960 in experimentally measuring this tiny effect with an accuracy of about 10%. In 1964 Pound and J.L. Snider increased the accuracy to 1%. They used the extremely sharp spectral lines of radioactive cobalt atoms, which due to their embedding in a crystal lattice of iron atoms are emitting and absorbing virtually recoil-free (keyword Mössbauer effect). The height difference of 22.6 meters was enough to put the source and absorber out of resonance. Then using a screw thread the absorber was moved so ‘fast’ (a few millimeters per hour, see problem 9) in the direction of the source until the Doppler effect again put it in resonance with the source. The speed needed for the maximum resonance was then measured to calculate the frequency shift Δf!
The picture shows Glen Rebka at the lower end of the Jefferson Towers, Harvard University