Did the big bang create an infinite number of photons?

We will always be able to see the cosmic microwave background (CMB) at about [the age of the universe] light years away.

Always.

Does that mean that infinite photons were created at that time? If not, how can we keep receiving new light from that event?

• Answer number one: possibly Aleph-null, definitely not Aleph-one . Answer number two: yes, but the photino birds at most of them. //I'll let myself out now – Carl Witthoft Nov 8 '18 at 15:24
• Isn't the real reason we can always see the CMB because space is so empty that most of the original photons from the Big Bang haven't run into anything yet? I mean, if you look at the surface of the Earth, you certainly can't see CMB hitting and being absorbed by the other side of the Earth. – Michael Nov 8 '18 at 23:12

As Ben Crowell already answered, the number of photons could be finite or infinite depending on whether the universe is finite. But I want to comment on the underlying assumption:

We will always be able to see the Cosmic Microwave Background at about [age of universe] light years away. Always.

It is possible that the expansion of the universe eventually stops then reverses and the unverse then recollapses, leading to a Big Crunch. This could happen, for example, if the universe is spatially closed, but there are other possibilities which result in Big Crunch. If that happens, the average density of matter would be increasing then and all the photons of the Cosmic Microwave Background would be eventually absorbed by heated (and opaque) matter. Of course, many new photons would be created at the same time, but those would not be the relics of the Big Bang.

If instead the expansion would continue indefinitely, then not only the number of CMB photons in a given constant volume would decrease in time, their wavelengths would also stretch, and this would mean that eventually it would not be possible to detect them. Assuming that the expansion would continue with approximately the same Hubble parameter, about every $$10^{10}$$ years the wavelength of CMB photon would grow by a factor of $$e$$. This means, that in $$10^{30}$$ years the wavelength of a typical CMB photon would be in excess of 10 light-years and in $$10^{40}$$ years wavelenth of CMB photons would exceed the size of de Sitter horizon, which also means that the CMB radiation by that time would be drowned in Gibbons–Hawking radiation coming from de Sitter horizon, and thus by then it would be impossible to detect CMB even in principle.

• Is it a realistic third option that we're in a low-comological constant bubble of an eternal inflation-universe and the expansion within our bubble is so small that we'll eventually see the edge? – JollyJoker Nov 8 '18 at 9:39
• Photon number (or particle number for any other massless particle) is ill-defined. Realistic distributions are Poisson-like, and are probabilistic, but with a non-zero probability for any possible number. So "finite" or "infinite" are both equally wrong, and the question is just meaningless. – AccidentalFourierTransform Nov 8 '18 at 14:52
• @AccidentalFourierTransform: while I agree with the first part of your statement in principle, for the FLRW closed cosmology, the number of photons as measured by a system of comoving observers could only be finite since there are builtin cutoffs both IR and UV here, with finite total energy. Likewise, for open cosmology the number is infinity by virtue of infinite volume withe finite density. – A.V.S. Nov 8 '18 at 15:31
• @JollyJoker: I would not call this a separate option, it is possible to have a bubble with a local crunch, or one expanding indefinitely, and most observers living inside one expanding bubble would never encounter another bubble. Bubble walls will have constant acceleration, so they tend to have ultrarelativistic velocities and either would move away from observer (so she could see for example reflection of a CMB photons from such a wall in the past) or they move toward observer at almost the speed of light (which would be bad for her well-being). For details see arXiv:hep-th/0606114 – A.V.S. Nov 8 '18 at 17:31

The cosmological evidence is currently consistent with either a closed or an open universe. A closed universe is spatially finite, has always been spatially finite, and always will be. An open universe is spatially infinite, has always been and always will be.

Current models are homogeneous. If the universe is homogeneous and infinite, then it contains infinitely many photons. If finite, finitely many.

The fact that you can observe photons forever does not automatically mean that there are infinitely many. Their flux is decreasing with time, and you could observe them at a decreasing rate.

• Photon number (or particle number for any other massless particle) is ill-defined. Realistic distributions are Poisson-like, and are probabilistic, but with a non-zero probability for any possible number. So "finite" or "infinite" are both equally wrong, and the question is just meaningless. – AccidentalFourierTransform Nov 8 '18 at 14:52
• Query: on what scale (spatial and/or temporal) do the current models consider the universe to be homogeneous? – Carl Witthoft Nov 8 '18 at 15:26
• "The fact that you can observe photons forever does not automatically mean that there are infinitely many. Their flux is decreasing with time, and you could observe them at a decreasing rate." Given a finite number of photons, there must be a last one. That photon has some time of observation. By definition of it being the last photon, there are no photon observed after the time of observation of the last photon. – Acccumulation Nov 8 '18 at 16:44
• "there must be a last one. That photon has some time of observation." That doesn't follow. The last photon is almost certainly not the last observed photon. – Beanluc Nov 8 '18 at 17:26
• @AccidentalFourierTransform: You're right that it's probabilistic, but I don't think that makes the question of finiteness ill-defined. The number of quanta within a given finite volume will be probabilistic. (I'll take your word for it that it's Poisson for blackbody radiation.) But if the total volume is finite, then the sum of finitely many IID Poisson variables is finite, with probability 1. Similarly, the sum of infinitely many IID Poisson variables is infinite with probability 1. – Ben Crowell Nov 8 '18 at 20:21