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If there is a lamp $1$ meter away from me which is switched on at time $t_1$ and switched off at $t_2$, I'll start receiving the light at time $t_1+\frac{1}{c}$ and stop receiving it at $t_2+\frac{1}{c}$. So there is only a finite time $t_2-t_1$ during which I'll get the light.

CMB photons were created at a finite time in the past- the time of recombination when it was $380,000$ years old. If this moment can be compared with the switching on of a cosmic lamp, then from that moment, the CMB photons have started travelling towards us. Will we ever stop receiving these CMB photons here on earth? If not, why?

DavidH
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Solidification
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  • what if the lamp is receding at 0.99999917$c$? – JEB Jun 26 '20 at 02:09
  • @JEB - Drop a hot object into a black hole. We will see photons that are more and more red shifted arriving at a slower and slower rate. They correspond to photons emitted by the object in its own reference frame before it crosses the event horizon. Since there are a finite number of photons, one might expect there is a last one. Can one make a similar argument for the CMB? – mmesser314 Jun 26 '20 at 03:03
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    Does this answer your question? Will the CMB ever stop shining? – ProfRob Jun 26 '20 at 11:34
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    In particular, see Pela's answer to the question Rob linked. – PM 2Ring Jun 26 '20 at 11:53

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Short answer: it depends.

Edit: while I still disagree with Rob Jeffries on the conclusion, it's true that the main focus on your question shouldn't be on

Shall we ever stop receiving these CMB photons here on earth?

but indeed on

If this moment can be compared with the switching on of a cosmic lamp

because it shows a fundamental misconception. The answer to the "cosmic lamp" is, indeed, no, you can't compare it to a lamp, and the misconception is fundamental because it doesn't rely on expansion nor finiteness of the universe.

Try to think about it this way: the CMB happened everywhere at once. Neglecting the fact that it wasn't instantaneous, in the precise moment of the CMB you would have seen it from directly under your feet. A fraction of a second later, you would have seen it coming from a few meters away, and the reason for this isn't that in that point of the universe the CMB happened later: it's only because of the finite speed of light that we see it with this delay. If you keep this going, you'll arrive at 380000 years after those moments, and therefore receiving the CMB light from a very distant point. Now we're ready to answer the other question.

It depends on a high number of factors. It the universe is finite, then yes, you will see "the last CMB photon". If the universe is instead infinite, expansion becomes important: this answer by pela explains it very well.

Mauro Giliberti
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