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Assume there are 10 molecules per cubic meter, on average, in interstellar space--in effect, a very thin gas. Assume that the source of light is ten billion light years away, the tunnel through which it passes is one meter square, and space does not expand. If there are $9.46052840500002\times10^{25}$ meters in a direct path 10 billion light years long, the light will potentially interact with $9.46052840500002\times10^{26}$ molecules in the path.

Can gravitational lensing, scattering, propagation delay in photon-electron interaction, or any other process along the path cause light from the original source to arrive at the detector with lower frequency? In other words, will it be red-shifted?

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  • $\begingroup$ Light passing near a moving black hole (or other massive, compact object) could be redshifted or blueshifted. See this question. $\endgroup$ – Peter Shor Oct 12 '18 at 12:48
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    $\begingroup$ If you're trying to find an alternate explanation than the expansion of the universe for the redshift from distant objects, I am sure that any explanations that use only standard, known physics have already been considered and ruled out. $\endgroup$ – Peter Shor Oct 12 '18 at 12:51
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It is a usual practice in physics not to use more digits than required for a given problem. Since what you are making is an estimate, just an order of magnitude would suffice, say $10^{26}$ metres.

As to your question, all effects you recall could affect photon propagation and also change frequency, but in a rather random way, not only lowering it. I'm not able to quantitatively estimate these effects, but a posteriori would say they are irrelevant.

I say so because it is known that spectral lines from faraway stars have their frequencies displaced, e.g. by Doppler effect (not always decreasing), but frequencies of different lines are all displaced in the same relative amount. Any frequency changes by the same factor as all others for the same star.

It would be difficult to explain how this could possibly happen for every conceivable process that can affect propagation of photons.

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