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Lets say we had a spaceship sitting on earth under the influence of gravity.

Light travels from the ship's floor to the ceiling. An observer 'A' stands near the ceiling.

Hence the light loses gravitational potential energy, and therefore decreases in frequency.

m g Δs = h Δf

where m = 'mass' of light, g = gravitational field strength, s = distance between ceiling and floor, h = Planck's constant, f = frequency of light

Replacing 'm' with its equivalent in terms of f, h and c (speed of light), we get,

**(h f / c^2)**g Δs = h Δf

And we end up with:

Δf / f = g Δs /c^2

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Now what I dont quite get is the bolded bit.

we use the equations below and substitute for 'm'...

m = E/c^2, E = h f

But why do we use the initial frequency 'f' to substitute for 'm'? Why not Δf (although that would cause the Δf's to cancel out..)? Could someone elaborate?

Or is this an oversimplification?