Does the momentum and energy of photon change when it travels from distant galaxies through the Space?
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It does. Have a look at https://en.wikipedia.org/wiki/Gravitational_redshift – anna v Sep 24 '21 at 07:22
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OP is not talking about photons climbing out of a gravitational well. – joseph h Sep 24 '21 at 07:51
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@josephh I noted "when it travels from distant galaxies " , distant galaxies are gravitational wells. – anna v Sep 24 '21 at 08:46
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Clearly the OP is referring to universal expansion redshift not gravitational redshift. Cheers. – joseph h Sep 24 '21 at 08:49
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This question is missing context: Where did you get the claim that momentum and energy of a photon don't change from? – ACuriousMind Sep 24 '21 at 11:52
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https://physics.stackexchange.com/a/667740/311056 From here – A.M. Sep 24 '21 at 11:58
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A photon traveling through intergalactic distances in space does lose energy and momentum, due to spacetime expansion (universal expansion). This is termed cosmological redshift where the wavelength at which the light is originally emitted becomes lengthened as it travels through an expanding universe, meaning the photon loses energy.
The energy of a photon is given by $$E = \frac{hc}{\lambda}$$ where $h$ is Planck’s constant, $c$ is the speed of light, and $\lambda$ is the photon’s wavelength. So if $\lambda$ increases, energy decreases.
The momentum of photon is $$p=\frac{E}{c}=\frac{h}{\lambda}$$ which means it also loses momentum due to universal expansion.
Here we assume the photon moves through empty space and does not interact (and redshift) with gravitational fields of massive objects. That is, energy loss is due to universal expansion only (the photon "interacts" with the expanding universe only).
joseph h
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Where does it loses the Energy and momentum to? And if it does why can we still se it!? – A.M. Sep 24 '21 at 07:39
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1Hi A.M. That's actually a question that has been debated many times. Energy conservation in cosmological models is far from clear. In fact, energy conservation in General Relativity has always been problematic. Have a look at this question and the answers/links therein. Cheers. – joseph h Sep 24 '21 at 07:48
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There is gravitational redshift, too. Is cosmological redshift not some Doppler effect? What you describe sounds much more exciting than the life saving automobiles (the formula refer to gravitational, not cosmological redshift, the latter is Doppler effect, the former isn't). – Peter Bernhard Nov 12 '22 at 18:39
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@PeterBernhard Gravitational redshift occurs when electromagnetic waves travel out of a gravitational well. Cosmological redshift occurs due to expansion of the universe. Note that Doppler shifting usually refers to relative motion between source and observer. Which formulas are you referring to? I have listed two equations that express the energy and momentum of photons. – joseph h Nov 12 '22 at 20:47
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Wikipedia you link to says "To derive the redshift effect, use the geodesic equation for a light wave, which is ... ", followed by some formula that does not correspond to the ones you listed. - Admittingly, at time above, I was wrong about cosmological redshift being considered as a pure Doppler effect. They seem to consider cosmological redshift as some kind of gravitational redshift, to tell from the formula I wasn't able to past and copy in (from the Wikipage linked to). In my mind, that formula you did not list does not refer to gravitational redshift nor Doppler redshift. – Peter Bernhard Nov 13 '22 at 08:05
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@PeterBernhard Right. As per my last comment, those equations above are general and describe the energy and momentum of quantum particles. They have nothing to do with redshift as such. Cheers. – joseph h Nov 13 '22 at 08:14