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Imagine a universe governed by the same physical laws as ours, i.e., the same fundamental forces, with the only caveat that there are no photons, hence no electromagnetic radiation in this universe. An empty universe is a trivial example of this, but I mean more than that. I do understand that if we just remove all the photons in our current universe magically, new photons would immediately be produced by decay of existing particles like neutrons. But not all massive particles decay. When I say there are no photons, I mean there are also no processes that produce photons. For example, consider a universe with only electrons, or only neutrinos, or some of the bosons that do not decay.

In such a universe, is the temperature of any system absolute zero? Because, if not, they should radiate black body radiation, but which is prohibited by the nature of the particles constituting the system.

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    $\begingroup$ So there is no electromagnetism but there are some things that you call electrons, although they are presumably uncharged? $\endgroup$
    – WillO
    Commented Jun 6 at 15:57
  • $\begingroup$ @WillO In fact I mentioned having electromagnetism; only that there aren't opposite charges available to release any photons. Now I see there shall always be virtual photons, in that case; but do they count as black body radiation? I guess not. $\endgroup$
    – N Unnikrishnan
    Commented Jun 6 at 17:42
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    $\begingroup$ No, temperature is not necessarily related to the presence of photons or electromagnetic interaction. You can even consider a gas of neutral particles and still it is possible to associate a temperature. Another important example is a gas a gluons and quaks (ignoring the electromagnetic sector), chech the "phase diagram" of QCD. Even abstract systems like the famous "Ising model" can have temperature. $\endgroup$
    – Quillo
    Commented Jun 6 at 20:19

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A universe filled with only dark matter would contain no photons at non-zero temperature. It requires matter that is coupled to the electromagnetic field to generate radiation.

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    $\begingroup$ OK, so my understanding that anything above absolute zero radiates like a black body is wrong; only matter coupled to EM field does. Dark matter, for eg., does NOT radiate black body radiation. Is that right? $\endgroup$
    – N Unnikrishnan
    Commented Jun 7 at 4:53
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Temperature is just another word for "mean kinetic energy". Not being able to radiate heat would certainly lead to strange phenomena such as a heated body retaining its temperature indefinetely if placed in an absolute vacuum, but I don't see how "no radiation" implies "no temperature".

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  • $\begingroup$ I was under the impression that anything above absolute zero radiates like a black body. But no, as you all point out, only matter that couples to the EM field does. $\endgroup$
    – N Unnikrishnan
    Commented Jun 7 at 4:58
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Rather than a lack of photons, you could consider inside a black hole where photons just don't move. Motion leads to heat. In such a case it would be very close to absolute zero in a one-solar sized black hole and even colder in a massive black hole. Check out this answer in Astronomy Stack Exchange https://astronomy.stackexchange.com/questions/26427/why-black-holes-are-extremely-cold

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    $\begingroup$ "where photons just don't move" Have you a reference for that claim? $\endgroup$
    – Jeanbaptiste Roux
    Commented Jun 6 at 16:57
  • $\begingroup$ @JeanbaptisteRoux time has stopped inside a black hole. Nothing moves down to the quantum level. If you look at the reference it talks about being at absolute zero or even lower. $\endgroup$
    – foolishmuse
    Commented Jun 6 at 19:20
  • $\begingroup$ Everything inside of a black hole is doomed to move towards the singularity the same way we are doomed to move forward in time. Furthermore, you did not provide any references. Calculate the null geodesics for the Schwarzschild metric in Schwarzschild coordinates, and you'll see that photons do move. $\endgroup$
    – Jeanbaptiste Roux
    Commented Jun 7 at 5:54
  • $\begingroup$ @JeanbaptisteRoux it is only from the inside frame of reference that things move. From our frame of reference outside the black hole, nothing moves. And since we are measuring temperature from out here, there is no movement and therefore no temperature. $\endgroup$
    – foolishmuse
    Commented Jun 7 at 13:11
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Once you remove photons (and so, incidentally, remove the electromagnetic force) then you have a very strange universe in which all fundamental particles are neutral and there are no inelastic collisions. Since you have removed the possibility of any form of electromagnetic radiation, there is certainly no black body radiation in such a universe.

You could still assign a "temperature" to an individual particle by virtue of its kinetic energy. However, in the absence of inelastic collisions, I don't see how any population of particles would reach thermodynamic equilibrium, so the notion of temperature as a parameter that determines the distribution of energies within a population of particles via Maxwell-Boltzmann statistics would not apply.

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