Can Black Holes Swallow Quantum Numbers? Investigating the Entropy Problem

[danAlwyn]

The first question I've dared to post on this forum, and unfortunately it's pretty horrible. I also don't know if it belongs in this section.

My friends and I were speculating a while back about what would happen if nanoscopic black holes were produced (as possibly theorized) in the first run of the LHC, and Hawking radiation didn't work right, so the black holes stuck around for a while. The question came up about whether such a black hole could swallow an electron. Classically it could not, since the electron is a fundamental particle and the radius of the black holes is much, much smaller than the radius of the electron. Someone pointed out that the electron is a point particle in quanum mechanics, but that still makes sense because the wave function of an electron is sufficiently dispersed that it would be larger than the black hole. Even if it were somehow "trapped", it should be able to tunnel out immediately.

However, if a black hole eats quantum numbers, then this might not be true. An electron would go in, and something else might be able to pop out. I know that the setup is totally unrealistice, but does anybody know of any proposed tests for whether quantum numbers are conserved by black holes (I think it might be testable at the LHC, but I can't think of how)? Where would I look to find a brief explanation of the current state of theory on this subject?

Thanks,
-dA

 

[selfAdjoint]

I don't know what you mean about Hawking radiation not working. The HR is derived from the nature of spacetime around a BH and if you deny that, there's not much basis for answering other questions.

When an electron position is observed in QM, it is a definite point, the wave function is "collapsed". So I would say that even a tiny BH would have no problem swallowing an electron. And nothing would "pop out"! Hawking radiation happens near the event horizon, not right down on it. Nothing, not even HR, escapes a BH.

 

[danAlwyn]

I don't know what you mean about Hawking radiation not working. The HR is derived from the nature of spacetime around a BH and if you deny that, there's not much basis for answering other questions.

I admit, I don't expect this to be true. It was a silly little digression from reality. What it comes down to is that normally the evaporation time of a miniature BH should be too short for it to swallow anything. We were wondering what would happen if that was not the case.

From what you're saying I suspect that my flaw was treating particles inside a black hole as QM objects, just as if they were inside an infinite well. If the BH really does swallow particles like that whole, than it also probably does not conserve most quantum numbers-and that's a conjecture I feel a bit uncomfortable making without a better theoretical background.

Hopefully we'll be able to poke around at these BHs and see what they actually do conserve.

Thanks,

 

[lonelyphysicist]

The HR is derived from the nature of spacetime around a BH and if you deny that, there's not much basis for answering other questions.

This may be a little too strong a statement, as though HR follows very naturally from GR and QFT. As long as we have not observed directly radiation from black holes we cannot assume it has to exist.

I've also recently come across theoretical objections to the existence of black hole radiation. See, for instance:

Adam D Helfer 2003 Rep. Prog. Phys. 66 943-1008

I've not read thru the paper myself, but perhaps more knowledgeable people here can comment on it?

 

[James Jackson]

This all comes down to the problem of entropy in black hole system, really. 'Loss' of quantum numbers = decrease in entropy. Hawking (and others) have a lot to say on this - search for papers!