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Under Newton, a photon has gravitational mass m, for which it's affectedThe problem is that this doesn't work. Two observers at different heights would see differing numbers of waves passing their respective locations per unit time. The observers would conclude that waves were accumulating between their two locations, or somehow just vanishing.
by gravity.
1) A photon with energy E, falling under gravity effects from height h,
increases its energy by an amount
ΔE = +mgh
Using the equivalence m = E/c^2, its energy when it reaches ground is E
+ ΔE:
E + ΔE = E (1 + gh/c^2)
Using Planck's equivalence E = hf, it gives
f + Δf = f (1 + gh/c^2)
Then, under Newton, the frequency change is
Δf/f = +gh/c^2
The frequency of the photon increase by falling, and is blue-shifted.
On the other way around, if a photon is escaping from ground, at an
height h its frequency has decreased by
Δf/f = -gh/c^2 (red-shifted)
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No relativity here. Only requires to accept the existence of
gravitational mass and a given equivalence mass-energy.
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