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Re: Gravitational redshift and clocks



On Mon, 1 Sep 2003, Savinainen Antti wrote:
>>General Relativity predicts that when a light ray leaves the
>>ground and rises higher its frequency gets smaller (i.e., light
>>is redshifted).

OK.

On 09/01/2003 03:24 PM, Stephen Speicher wrote:
> No. General relativity does not predict a gravitational effect on
> the frequency itself, i.e., the frequency does not itself "get[s]
> smaller." In general relativity the frequency is not intrinsic to
> the object -- it does not itself get smaller or get larger -- but
> rather it is a _relationship_ between observer and object. The
> observed redshift is a consequence of the nonlocal path through
> the curvature of the spacetime manifold, not due to any change in
> the local frequency itself.

That's mostly wrong and entirely irrelevant.

There is a perfectly well-defined notion of local
frequency. One needs to specify who's measuring
what frequency in which reference frame, but that's
just routine housekeeping.

To first order (which is all that matters here)
the redshift depends on the potential difference
phi(X) - phi(Y)
with no other dependence on the "nonlocal path
through the curvature of the spacetime manifold"
that the photon took getting from X to Y.

Specifically,
delta(lambda) / lambda = delta(phi)