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Consider a radiation emitted by star at rest and reach then earth and the earth moves away .If we assume that the photon has a particle character . Since the star is at rest and and earth is revolving and relative to source. And the doppler shift occurs. My question is that when then photon is emitted if just travel against the gravity of the star . If we Consider the equivalent principle , accleration causes the same effect as the gravitation up to certain limit. Hence gravitation must reduce the energy of light. Then the frequency of the light reduce and if shift towards red colour. Is my argument is correct . If it is wrong anyone explain me Why

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Yes, if one ignores the strange wording and grammar, what you sketched is the derivation of the so-called gravitational redshift which is indeed linked to the Doppler shift by the equivalence principle

http://en.wikipedia.org/wiki/Gravitational_redshift

See also the 2nd part of the following blog entry for a derivation along the lines of your sketch:

http://motls.blogspot.com/2012/09/albert-einstein-1911-12-1922-23.html?m=1

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