The top of a tower of height h emits light with frequency f, speed c and wavelength L (as measured by the emitter):

f = c/L

An observer on the ground measures the frequency to be f', the speed of light to be c' and the wavelength to be L':

f' = c'/L'

Let us assume for a moment that gravitational time dilation as defined in general relativity (clocks on the ground tick slower than clocks at the top of the tower) is the only factor changing the measured quantities (the gravitational field does not affect the light as it travels between the top of the tower and the ground). Then we would have:

f' = f(1+gh/c^2)

c' = c(1+gh/c^2)

L' = L

Numerically, this coincides with the prediction of Newton's emission theory of light where there is no gravitational time dilation but instead the light accelerates as it falls.

Now we can add effects the gravitational field may have on the travelling light. What effects does Einstein's relativity predict? f' cannot be changed further - this is the result confirmed by the Pound-Rebka experiment. Therefore, from a formal point of view, any prediction should be limited to c' and L' increasing or decreasing proportionally. "Decreasing" is not physically plausible - it implies deceleration of the light as it falls. "Increasing" is implausible as well - there is no reason why the wavelength should increase as the light falls.

Clearly there are two interpretations giving the correct results:

1. Gravitational time dilation does exist. The gravitational field does not affect the travelling light.

2. There is no gravitational time dilation. In a gravitational field, light accelerates as ordinary falling objects do.

Einstein's general relativity, if it predicts results different from c'=c(1+gh/c^2) and L'=L, is inconsistent.

Pentcho Valev