In the weak field limit, we have(adsbygoogle = window.adsbygoogle || []).push({});

[itex]dt = (1 + 2\phi)^{-\frac{1}{2}}d\tau[/itex]

where the usual meaning of the symbols applies. This means that in GR dτ < dt analogous to SR. Let suppose we measure the period dt_{S}of a photon emitted at the surface of the Sun as well as the same photon, i.e. same atomic process, in a lab on Earth where the period is dt_{E}. Therefore we have two relationships w.r.t. to dτ such that

[itex]dt_{S} = (1 + 2\phi_{S})^{-\frac{1}{2}}d\tau[/itex]

and

[itex]dt_{E} = (1 + 2\phi_{E})^{-\frac{1}{2}}d\tau[/itex]

Taking the ratio we find that

[itex]dt_{E} = \sqrt{\frac{1 + 2\phi_{S}}{1 + 2\phi_{E}}}dt_{S}[/itex]

because φ < 0 and |φ_{E}| << |φ_{S}|

we find that dt_{E} < dt_{S}

This is not what I would expect, surely the Sun's greater gravity means that the coordinate time interval there would be less than the same quantity measured in Earth's lesser gravity? Even though this gives the right relationship for gravitational redshift, I am still very confused.

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# Ratio of time dilation relation in different potentials

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