# Infinite Light Box

1. Jan 27, 2014

### MichaelJ

Here's the scenerio: you have box (shape is not necessarily important, but for simplicity we'll say its a cube), within the cube is a vacuum and the inside of the box consists of "perfect" mirrors, meaning that no light is absorbed (obviously this is not possible in the real world), however light can enter the box through the outside of the walls. If you place the box out in the light what would happen?
I have only studied up to Introduction Physics in university as I am a Bio major, so I am unsure of the affect that one photon can have on another. So would the box infinitely "absorb" the light into itself and nothing would ever "happen" or would there be a threshold point that could be reached at which point "something" would happen, or lastly is there always a small affect occurring that would simply be magnified the more light enters the box?
Also the light could be "natural" as in a mix of different types of light (visible and nonvisible). Or it could be specifically gamma rays or UV etc... If the difference in energy levels will affect the end result of the hypothetical experiment.

Last edited: Jan 27, 2014
2. Jan 27, 2014

### .Scott

All practicalities aside:

The first problem is that there is no mirror that will reflect 100% of the light on one side while allowing light to enter from the other side. But there are other ways of getting the light in there, so we can skip that.

The next problem will be the force that is building up on the inside of the box. When the mirrors reflects the light, there is a recoil in the mirror. Eventually that recoil would break the box.

The next problem is that all of that light has mass and soon gravitation will become an issue. In the extreme, a black hole will form.

3. Jan 27, 2014

### Mentz114

4. Jan 27, 2014

### Staff: Mentor

The cube would absorb light and increase in internal energy until the pressure became too great and the box explodes releasing both the pressure and the light.

5. Jan 27, 2014

### MichaelJ

Lets say that since this is a "perfect" mirror, the photons do not lose any of their momentum when being reflected, therefore their would be no increase in internal energy or pressure, plus the fact that it is a vacuum means that their are no interactions within the interior of the box.

6. Jan 27, 2014

### Mentz114

Impossible. The more light that reflects the greater the change of momentum which is the force.

7. Jan 27, 2014

### MichaelJ

Correct me if I'm wrong, but doesn't light have momentum, but no mass? and for the sake of the "perfect mirror" we are assuming that the momentum of the photons are not lost on the inside of the box, though if they were than under a normal outside light situation, the amount of light coming in would not be a great enough stream to overcome the loss of momentum from the reflections, so the loss of momentum of the photons within the box would gradually "sluff off" the energy coming into the box, but at a rate that should not be able to exert much force at once.

8. Jan 27, 2014

### MichaelJ

Okay I understand that, I guess my question is more about what happens when you infinitely increase the amount photons within a given space, would their interactions become important at some point? And if so what would the interactions result in.

9. Jan 27, 2014

### Staff: Mentor

I am assuming perfect mirrors. Light exerts pressure on a perfect mirror. In fact, it exerts more pressure on a mirror than on an absorber. When a photon is reflected its momentum reverses, this change in momentum of the photon necessarily results in an impulse on the mirror.

As I said above, the pressure would build as light entered the container until the container can no longer handle the pressure.

Last edited: Jan 27, 2014
10. Jan 27, 2014

### Mentz114

Weinberg tells us what happens if the walls are strong enough to let the interior get to very, very high temperatures before giving way. Obviously we can't get to infinite energy.

11. Jan 27, 2014

### .Scott

Please don't do this. Infinitely increasing the photon density within a container would instantly create both a black hole and an infinitely potent gravity wave that would travel through the universe at the speed of light destroying everything. Is that a sufficient "interaction" for your purposes?

12. Jan 27, 2014

### pervect

Staff Emeritus
If you consider only the gravitational interaction between photons, you'd expect the metric to exhibit gravitational blueshifting as you approach the center of the box. And you'd expect the solutions to converge to a black hole like solution if you put enough photons in the box.

If you're interested in the non-gravitational interaction between photons, you're in the wrong forum, GR isn't the right theory to handle that.

13. Jan 27, 2014

### pervect

Staff Emeritus
A small part of this is true - infinitely increasing the photon density within a container would eventually create a black hole, but I it's wrong to describe this as an "instant" process.

Furthermore Birkhoff's theorem would prevent the emission of gravity waves if this was done in a spherically symmetric fashion (which the described process is), so the part about "infinitely potent gravity waves" is also wrong.

14. Jan 27, 2014

### Staff: Mentor

:rofl:

15. Jan 27, 2014

### PAllen

Well, if we're being technical, no manifold with EM can be exactly spherically symmetric. Now, you could say that the classical analog of photons is null dust rather than EM radiation, but ... if you're ruling out gravity waves on that basis it's not quite fair. The OP described a cube, anyway ...

16. Jan 27, 2014

### .Scott

Someone should forward this to "The Big Bang Theory" writers,

17. Jan 27, 2014

### pervect

Staff Emeritus
Well, the original quote I was responding to was:

I thought that was a bit "over the top". But I suppose my response was a bit off the mark.

The class of candidates that we expect to generate gravity waves are not uniform collapses, which would suppress gravity waves to a high extent (total suppression via Birkhoff's theorem if the collapse was totally symmetrical), but rather rotational inspirals involving two massive bodies where gravity wave production is not suprressed in this manner, and are much more effective at producing gravity waves than the scenario being described.

And those inspiral events, which would produce much stronger gravity waves , due to both the lack of suppresion of gravity waves , AND by the fact that the inspiraling bodies have a lot more mass than the proposed mass needed to make (for definiteness) a 1m^3 box collapse, have so far have eluded our detection with our most senstive instruments.

Thus, suggesting that gravity waves from the box case would "destory the universe" seems to me to be downright silly.

18. Jan 28, 2014

### PAllen

I agree - the GW would be minimal.

19. Jan 28, 2014

### .Scott

I still don't think we should let MichaelJ perform the experiment. There are a limited number of ways that you can create infinite mass. I was assuming God-like abilities where he simply increased the mass to infinite without transferring the mass from anywhere else. I don't think you could count on Birkoff's protection in this case.

Birkoff was considering a finite pulsating mass, one that could be enclosed in a finite Schwarzschild metric. In this case we are instantly expanding the Schwarzschild metric to infinity. BTW, there is no other way to get to infinite mass other than "instantly".

20. Jan 28, 2014

### PAllen

Your first post on this said infinite density, not infinite amount. If you imagine continuing the process until 'disaster', the disaster would be BH formation accompanied by extremely tiny emission of gravity waves. You would have infinite density on approach to the singularity. If you continued adding photons to the BH, you would just get a bigger BH with undetectable levels of GW.

As for making an infinite amount of photons appear at once, that is simply ruled out by GR field equations. I'm not sure whether you could have an infinite FLRW solution ending in a big crunch, but this is not a BH anyway.

Thus any way of 'in principle' doing this, would produce BH - yes, measurable GW - no.