[Physics] Gravitational Time Dilation and Gravitational Redshift - two separate things?

[Ilja Schmelzer]

No, the signal will be blue-shifted only once.

This can be best seen if one replaces the wave by a hand-waving person
and looks at the time when the light signal of "hand up" and "hand
down" arrive.

If we look at this in coordinates which are natural for a stable
configuration, thus, a metric of the form g_mn (x^i) dx^m dx^n with
the metric coefficients depending only on the spatial coordinates, and
assume the handwaving guy as well as the observer at rest, the light
rays for "hands up" and for "hands down" are the same trajectories,
only with a shift in the time coordinate t.

Thus, from point of view of the background time coordinate, there is
no change in the frequency.  Thus, the only change in the frequency is
because of the clocks (which have to be used to measure the frequency
of the hand-waving).   So, they are the same thing.

2018-12-04 22:12 GMT+01:00, Doug Marett <dm88dm at gmail.com>:
> Hi All,
>
>     This just came up in a question I had to my website - it has to do with
> the Pound-Rebka experiment and whether gravitational time dilation of
> clocks and gravitational redshift of EM are two different things or the
> same thing. The problem is set out by L.B. Okun is plain language in an
> article here: https://arxiv.org/pdf/hep-ph/0010256.pdf
>    The essence of it is that if you take a clock and move it from the
> ground to the top of a tower, the clock should speed up in it's rate at the
> higher altitude. If you then send an EM signal from this clock back to the
> ground, Einstein says that the EM should be blue-shifted. However, this
> would mean that the signal sent to the ground has now been blue-shifted
> TWICE, once due to the clock speeding up,  and once due to the fall of the
> EM through the gravitational gradient.
> However, the Pound-Rebka experiment finds that it is blue-shifted only
> once. So which effect is redundant, gravitational time dilation of clocks
> or gravitational red-shift of light? They can't be the same thing, since
> the latter is an operation performed on the EM during transit, and is
> supposed to make it bend. And the former is something which happens to
> clocks independent of EM signals sent between them.
> Interestingly, the experiment proposed by Okun to answer the question was
> performed in a slightly different form by Tom Van Baak as described here:
>
> http://leapsecond.com/great2005/
>
> Another link that is useful is the paper here which examines the math used
> in the Pound-Rebka experiment and finds it is full of errors!
>
> http://milesmathis.com/pound.html
>
> Just wondering if anyone else is aware of this apparent contradiction in
> the relativistic thinking : )
>
> Doug
>