What happens with electromagentic waves that are emitted into intergalactic space, but reach not any object because of inflation? Lets assume that photon A and photon B are emitted. Photon B hits some object, photon A enters a gigantic void or simply has nothing in its path, and heads for the horizon, so to say.

Relativity tells that A and B do not "feel" time passing. From our point of view B travels a finite time, while in the frame of B the object is reached instantly. However, since A will be eternally underway, what is going to happen? We have kind of a zero*infinity travelling time in the frame of A.

Do our models make statements about this? Or is there some explanation

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    $\begingroup$ Interesting read regarding photon lifetimes physicsworld.com/cws/article/news/2013/jul/24/… $\endgroup$ – Dean Mar 17 '16 at 22:15
  • $\begingroup$ IIUC the universe is flat (i.e. 2-dimensional) seen from a reference frame moving with light speed. The photon is everywhere on its path at the same time, form its perspective (that is, there is no path). $\endgroup$ – Peter - Reinstate Monica Mar 18 '16 at 20:07

Infinities are a type of singularity. As soon as you introduce an actual infinity into any kind of mathematical model you can't expect it to make useful predictions. Mathematical models can't deal with infinite time. Similarly, using a frame that moves at the speed of light, with infinite rapidity, is singular.

In the particular case you describe, in a regular frame, the photon becomes progressively redshifted by the expansion of spacetime, its energy (to an observer in a inertial frame) becomes lower and lower.

  • $\begingroup$ Since redshift is ~proportional to the scale factor, unless the wavelength of the photon was comparable to the diameter of the Universe to begin with, it will never be. But since its path length will never actually reach infinity, there will never be a singularity. $\endgroup$ – pela Mar 18 '16 at 8:15
  • $\begingroup$ Ok I'll edit that. $\endgroup$ – James K Mar 18 '16 at 16:58
  • $\begingroup$ So the answer is: we don't know, our models can't tell? $\endgroup$ – Rainer Glüge Mar 18 '16 at 20:24
  • $\begingroup$ What is going to happen is that the photon is going to travel indefinitely. But you can't sensibly ask what will happen after infinitely many years, in anyone's frame of reference. Actual photons will be doing lots of quantum stuff as they travel. $\endgroup$ – James K Mar 18 '16 at 20:37
  • $\begingroup$ Can you please explain what Quantum stuff is going to happen? That would probably answer the question. $\endgroup$ – Rainer Glüge Mar 21 '16 at 14:54

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