Does Gravity affect the frequency of an electromagnetic wave? If so, does it increases or decreases it?

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Marlene Welch · Accepted Answer

If we describe a plane-wave (or a single photon) by its wave vector:                    k                  μ                    =      (      ω              /            c      ,                        k          →                    )        k^{mu} = (omega/c, vec k)  what pops out is that the frequency is the time-like part of a 4-vector. We can look at energy and momentum:                    p                  μ                    =      ℏ              k                  μ                    =      (      E              /            c      ,                        p          →                    )        p^{mu} = hbar k^{mu} = (E/c, vec p)  to try to find a natural rest frame:                    p                  μ                            p                  μ                    =              1                  c          2                    [      (      E              )        2            −              |                    |            p              |                              |                2                    c        2            ]      =                        ℏ          2                          c          2                    [              ω        2            −      (      c      k              )        2            ]      =      0        p^{mu}p_{mu} = frac 1 {c^2}[(E)^2-||p||^2c^2] = frac {hbar^2} {c^2}[omega^2 - (ck)^2] = 0  so that there is no rest frame.Energy is a property of the observer&#039;s frame, not the wave. The wave just goes at       c    c  , locally.

Does Gravity affect the frequency of an electromagnetic wave? If so, does it increases or decreases it?

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