State the principle of equivalence.

A gamma-ray photon is emitted from the base of a tower towards the top of the tower.

(i) Explain, using the principle of equivalence, why the frequency of the photon as measured at the top of the tower is less than that measured at the base of the tower.

(ii) The frequency of the photon at the base is 3.5×10¹⁸ Hz and the tower is 23 m high. Determine the shift Δf in the frequency of the photon at the top of the tower.

(iii) Suggest, using your answer to (b)(ii), why the photon frequency must be measured very precisely for this experiment to be successful.

inertial and gravitational effects are indistinguishable / a freely falling frame in a gravitational field is equivalent to an inertial frame far from all masses / an accelerating frame is equivalent to a frame at rest in a gravitational field;

(i) The question does not specifically state the location of the tower so allow any of the explanations below.
(the principle of equivalence predicts) photon energy decreases as it moves against a g field;
this energy is given by E=hf;
hence as E decreases, f must also decrease;

or

the tower is equivalent to a frame accelerating upwards;
the top of the tower is moving away from the light emitted from the base;
and so by the Doppler effect/red-shift the frequency at the top will be less;

or

in freely falling tower the frequency at the top and bottom would be the same;
an outside observer sees the top moving towards the light emitted from the base and so (by the Doppler effect) expects a blue-shift;
for the frequency to be the same at the top the light moving upwards must suffer an equal red-shift;

(ii) 8.8×10³Hz / 8.9×10³Hz / 9.0×10³Hz;

(iii) \(\frac{{\Delta f}}{f}\left( { = \frac{{8.8 \times {{10}^3}}}{{3.5 \times {{10}^{18}}}}} \right) \approx {10^{ - 15}}\) / the shift is very small compared to the original  frequency / the new frequency differs from the original in the 15th decimal place;