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I've been reading several threads here and online articles trying to absorb the current understanding of observations of far galaxies receding faster than the speed of light, it is said because the expansion of space unlike of wave/particles is not constrained to the speed of light, and specifically because the most distant galaxies are redshifted corresponding to a speed up to several times the speed of light. My problem is understanding how observations of such motion are conceived of as detectable and detected.

My understanding from my old studies is that in special relativity as objects move from you at speeds asymptotically approaching the speed of light, the moving object from our vantage asymptotically slows time toward zero, increases mass toward infinity, and thins in the direction of movement toward zero. Is this wrong? But light always moves at the speed of light and so travels to us at the same speed but at a red-shifted lower energy; thus as galaxies move away at faster speeds their stellar spectra are increasingly redshifted.

My first specific question considering any galaxy currently believed observed traveling away from us at faster than the speed of light, is how the individual photons are conceived. Here is my understanding so you can hopefully clear up my misunderstanding. My understanding is that an object moving away at the speed of light is the limiting case for photon energy, that is, as the speed of light away is reached its emitted photons' wavelengths are stretched to infinity and the photon's energy to zero, to indetectibility. In this understanding, even if a galaxy is moving away from us at faster than light speed no photons from it could reach us. Yet the claim is these photons are being observed. What am I not getting here?

Secondly, regarding redshift, my understanding though vaguer was that as speed away increased toward the speed of light, red shift increases toward infinity, so how can red shift show anything more than closeness to approach of the speed of light? I suspect whatever I don't get here is related to the photon question.

ps I also have questions about inflation which actually led to these but this is my first question here and I think this is enough to test whether my questions fit here. Thanks!

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  • $\begingroup$ Far away galaxies do not recede at speeds faster than light. In fact, in general relativity speed is not well defined in this case and it is actually the expansion of spacetime that causes this perception. This is well explained in e.g. Carroll’s book. $\endgroup$
    – Oбжорoв
    Commented Dec 25, 2021 at 22:47
  • $\begingroup$ What astronomers are actually seeing is atomic spectral lines (often hydrogen) shifted to lower ("redder") frequencies than they are in a lab and predicted by theory. So they are not seeing "infinitely redshifted photons." And a better way to think of it is that the photons carrying this information have been redshifted by their journey through expanding spacetime, and we use this info to infer the structure of the space around us $\endgroup$
    – RC_23
    Commented Dec 26, 2021 at 3:37

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