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Consider an object which is a spherical one-way mirror, and let's call it the "Sphere".

For the needs of the thought experiment, suppose that:

  • the Sphere is perfectly spherical
  • the mirror is perfeclty one-way
  • the reflection of the mirror is perfect (in particular no Joule effect)
  • the Sphere is perfectly unbreakable and perfectly dimensionally stable.
  • the inside of the Sphere is perfectly empty (and at absolute zero if simpler and zero gravity)

Now we put a diffuse light source outside the Sphere (like the Sun).

Classically, the light (and so the energy) should accumulate linearly inside the Sphere, ad infinitum.

Question: What should really happened inside the Sphere (in the quantum mechanics framework)?
Is it possible that at a given density of photons, a part of them transform into (massive) particles which next accumulate too?

Bonus question: Is it possible to experiment that with today's (or close future) technology (with all the "perfect" above replaced by "quasi-perfect" in a reasonable sense)?

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    $\begingroup$ One-way mirrors don't exist. Any supposed one-way mirror you've seen is actually just a partially-reflective pane of glass with more light on one side than the other. $\endgroup$
    – Jahan Claes
    Commented Aug 18, 2015 at 17:32
  • $\begingroup$ @JahanClaes: ok but suppose it exists for simplifying the thought experiment. $\endgroup$
    – Sebastien Palcoux
    Commented Aug 18, 2015 at 17:40
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    $\begingroup$ So, suppose something unphysical exists and predict the physics that will occur? That makes no sense, and does not make for a good physics question. $\endgroup$
    – Jon Custer
    Commented Aug 18, 2015 at 18:50
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    $\begingroup$ No, the bonus question is not very interesting - it is no different than a high gain laser cavity. Yes, intensity will build up until the flux in equals the flux out. Physics thought experiments are fine as long as they are based on real physics. If based on unreal physics than you will get an unreal answer. $\endgroup$
    – Jon Custer
    Commented Aug 18, 2015 at 19:42
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    $\begingroup$ @JonCuster of course this would lead to an unreal answer, but sometimes this helps understanding situations which are more real. I would not be so discouraging with this type of questions, usually there is something beyond to consider. $\endgroup$
    – rmhleo
    Commented Aug 18, 2015 at 23:05

2 Answers 2

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This situation would lead to an accumulation of the photons inside this sphere. Quantum mechanics has no prohibitions for bosons, like photons, to occupy the same space under the same quantum numbers, so the photons would just build up continuously. But at no moment any of them should create other particles, since this would require interactions if charges or strong fields created by charges, but this cannot happen spontaneously.

But interestingly, if we are going to think big, at some point you would have an enormous density of photons inside, like a gas of them exerting pressure over the walls of the sphere. So in my mind, I think this sphere would behave as having mass, provided the number of photons is high enough, and it could even gravitate to the Sun?!?!

But I would like to check the equations and see if there is this possibility, at least in theory. And I will get back and improve this answer with some estimates.

Update So in searching a reliable way to make the estimation, I found this discussion where different approaches are given. I think this is better than any estimation I can sketch at this point.

As for the feasibility of all this, I think the closest you would get is having a material with very high reflection for a wide range of the EM spectrum, but still will absorb a fraction, even a tiny one. Thus it would heat up and radiate part of the energy to the exterior, until some stationary situation is achieved where a balance is determined by the actual values of the absorption/reflection coefficients.

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    $\begingroup$ This sounds plausible. You will have a bose-gas of photons as you say. Eventually the energy density would be so great that the enclosed energy density of the photons would make a considerable contribution to curvature of space time around the sphere, as if the sphere has gained mass. The radiation pressure inside the sphere would be phenomenal. So not only must the sphere be a (unphysical) perfect one-way mirror, it also needs to be made of a (even more unphysical) unbreakable material. $\endgroup$
    – gleedadswell
    Commented Aug 19, 2015 at 3:06
  • $\begingroup$ @gleedadswell: So "theoretically" the inside of the sphere can become a massless black hole! $\endgroup$
    – Sebastien Palcoux
    Commented Aug 20, 2015 at 8:43
  • $\begingroup$ Well, the more you get into physics the more you realize that the distinction between mass and energy is meaningless. So I wouldn't say that such a black hole was massless. $\endgroup$
    – gleedadswell
    Commented Aug 20, 2015 at 23:41
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Let's just say that given a sufficient density of photons, you would expect things like pair production to occur with some probability. However, these massive particles will occur as particle-antiparticle pairs, thus won't "accumulate" since they'll annihilate each other if there are too many of them. They might also annihilate with your mirrored sphere.

As for "real life" examples: since a one-way mirror is impossible, this is hard to do. The number of photons in the sphere will just be proportional to the flux you're shining on the sphere, and not increase linearly with time, since a photon inside the sphere has as much probability to go out as a photon outside the sphere has to go in.

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    $\begingroup$ Pair production will only occur if the photons have sufficient energy that the energy of two photons is greater than the rest mass of the particle pair produced (1.02 MeV) for electron-positron pairs. So pair production would require X-rays. Are these one-way mirrors so perfect that they are even one-way for X-rays? $\endgroup$
    – gleedadswell
    Commented Aug 19, 2015 at 3:02
  • $\begingroup$ @gleedadswell Good point! And I don't know, one-way mirrors don't exist to begin with! $\endgroup$
    – Jahan Claes
    Commented Aug 19, 2015 at 3:28

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