# Gravitational time dilation with a unit of time corresponding to the period of a light wave

How is it that time runs faster at regions further out from the center of a gravitational field if:

A clock's arm is made to make one cycle for a complete wavelength of a particular light beam. Consider the clock moving upwards from the surface of the earth as the light also moves up. Since the wavelength of the light increases as it loses energy, then the frequency must decrease:

$$c = λν$$

c is a constant, therefore

$$λ ∝ \frac{1}{ν}$$

But the frequency is the number of cycles the light beam makes in a second: this number reduces. Since the period — the duration of time for once wavelength of the light (one cycle of the clock's arm) — is

$$T = \frac{1}{f}$$

it increases for a decrease in frequency. Therefore, the duration of time for one cycle increases; the clock runs slower. Thus the clock runs slower with increased de-energisation of the light as it moves further away from the center of the gravitational field.

I get that experimental evidence differs, but I'm having a hard time finding the fault in the above claim.

• There are several flaws in your question. The main one is that you don't have a defined frame of reference, in which you would evaluate your equations: "Consider the clock moving upwards from the surface of the earth as the light also moves up" - No frame can be defined at the speed of light. Secondly: "c is a constant" - No, the speed of light is variable in General Relativity. It is constant only locally, but you don't have a frame, in which c would be local. Finally: "light [...] loses energy" - No, it doesn't. This thinking is a result of you not having a defined frame of reference. – safesphere Sep 29 '19 at 18:43