I Black hole singularity vs. quantum mechanics

[Jyrioffinland]

TL;DR Summary

I'm wondering why QM does not deny singularities from happening (given they do exist).

I'm wondering about some aspects about black holes (BH) and singularities, but since all my questions have to do mostly with quantum mechanics, I placed this thread in here.

OK, let's assume there IS a singularity in the middle of a BH.

A) Pauli exclusion principle (PEP) says no two fermions can occupy the same quantum state (QS). Why can it be out-ruled by immense gravity? Shouldn't there be a non-singular stack/ball of fermions in different QS's instead of the singularity? How much gravity is enough to throw PEP in the thrash? Mathematically, it should not be possible.

B) The elementary particles are not point-like, but rather wave-package-like in spacetime. They do, and the singularity should also, obey the Heisenberg's uncertainty principle. Since its momentum is measurable to a pretty exact degree, there should be enough wiggle room spatially for it to have a non-zero volume. Why does it still vanish?

C) Also, those wave-packages should not have an infinite gravitational pull towards each other when they come close enough. When they completely overlap, the gravitational pull should go to zero (as then all gravity gets canceled out). Thus, there would be no gravitational pull in the middle of the BH if all matter were in an (all-but-)point-like singularity.

I wish you can show me why I'm wrong (or, hopefully, correct) here.

 

[PeterDonis]

let's assume there IS a singularity in the middle of a BH.

No, we can't assume that, because you are using the term "singularity" to refer to "a thing that is there", but it isn't. The "singularity" itself is not part of the spacetime. What physicists really mean when they say "there is a singularity inside a black hole" is that objects that fall into the hole will see the spacetime curvature in their vicinity increasing without bound in a finite time by their own clocks. They do not mean that the singularity is a "thing".

The above invalidates everything you say in your post.

 

[Jyrioffinland]

No, we can't assume that, because you are using the term "singularity" to refer to "a thing that is there", but it isn't. The "singularity" itself is not part of the spacetime. What physicists really mean when they say "there is a singularity inside a black hole" is that objects that fall into the hole will see the spacetime curvature in their vicinity increasing without bound in a finite time by their own clocks. They do not mean that the singularity is a "thing".

The above invalidates everything you say in your post.

Well, my point was exactly that there can be no singularity as a "thing". My questions (A–C) are possible reasons for singularity not being able to exist as a "thing".

Maybe this a stupid question, sorry.

 

[PeroK]

Maybe this a stupid question, sorry.

What you need is a valid theory of quantum gravity.

 

[PeterDonis]

My questions (A–C) are possible reasons for singularity not being able to exist as a "thing".

GR already proves that the singularity can't be a "thing". There is no need to introduce additional reasons from QM.

That said, your proposed reasons are still based on erroneous assumptions. The increase without bound of spacetime curvature experienced by objects that fall into a black hole does not imply any of the following:

(1) That in the limit multiple fermions would have to occupy the same state;

(2) That in the limit the uncertainty principle would have to be violated;

(3) That in the limit wave packets describing different particles would have to completely overlap.

So you cannot argue that the singularity can't be a "thing" on any of the grounds you propose.

One other comment:

infinite gravitational pull

...is not a property of the singularity in GR. ("Gravitational pull" is not even a well-defined concept anywhere inside a black hole horizon.) What increases without bound inside a black hle is tidal gravity, but that is not the same as "gravitational pull".

 

[PeterDonis]

(1) That in the limit multiple fermions would have to occupy the same state;

(2) That in the limit the uncertainty principle would have to be violated;

(3) That in the limit wave packets describing different particles would have to completely overlap.

All of these items seem to me to be based on a more fundamental misconception, that anything that falls into a black hole gets "squeezed to zero volume" as the singularity is approached. That is not the case, and the fact that the areal radius $r$ goes to $0$ as the singularity is approached should not be misconstrued to imply that it is.

Objects that fall into a black hole and experience tidal gravity increasing without bound get squeezed in some directions but stretched in others. The worldlines that describe the different particles inside the object do not all end up at "the same point".

 

[Demystifier]

Maybe this a stupid question, sorry.

Not at all, this is one of the most profound questions in theoretical physics. It is widely believed that quantum gravity somehow eliminates the classical black hole singularity, but nobody knows how exactly it does so because we still don't have a full quantum theory of gravity.