Black hole singularity vs. quantum mechanics

In summary, 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.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
  • #1
Jyrioffinland
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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.
 
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  • #2
Jyrioffinland said:
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.
 
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  • #3
PeterDonis said:
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.
 
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  • #4
Jyrioffinland said:
Maybe this a stupid question, sorry.
What you need is a valid theory of quantum gravity.
 
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  • #5
Jyrioffinland said:
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:

Jyrioffinland said:
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".
 
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  • #6
PeterDonis said:
(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".
 
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  • #7
Jyrioffinland said:
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.
 
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Related to Black hole singularity vs. quantum mechanics

1. What is a black hole singularity?

A black hole singularity is a point of infinite density and zero volume at the center of a black hole, where the laws of physics as we know them break down.

2. How does quantum mechanics relate to black hole singularities?

Quantum mechanics is a branch of physics that describes the behavior of particles on a very small scale. It is used to study the properties of black hole singularities, as it may provide insight into how they behave and interact with other particles.

3. Can quantum mechanics explain what happens at the singularity of a black hole?

Currently, there is no complete theory that can fully explain what happens at the singularity of a black hole. However, some scientists believe that a combination of quantum mechanics and general relativity may provide a better understanding of this phenomenon.

4. How does the uncertainty principle apply to black hole singularities?

The uncertainty principle states that it is impossible to know both the position and momentum of a particle with absolute certainty. This principle may also apply to black hole singularities, as the extreme conditions near the singularity make it difficult to accurately measure and predict the behavior of particles.

5. Are there any theories that reconcile black hole singularities and quantum mechanics?

Several theories, such as loop quantum gravity and string theory, attempt to reconcile the laws of quantum mechanics with the behavior of black hole singularities. However, these theories are still being studied and debated, and there is currently no consensus on a definitive solution.

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