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In all of my reading in physics, I have been surprised by the number of times that I read "this can't exist" or "that can't exist" because of the Heisenberg Uncertainty Principle. Every time it comes up, I am left to wonder "has anybody actually tested it in this (or that) particular instance? Or are we just making an assumption based on a 100 year old theory?"

This morning I read this article about singularities and I am left thinking how the heck can we claim that because of the HUP, a singularity can't exist at the centre of a black hole. Obviously the physics inside a black hole is very complex and currently beyond our understanding.

I realize that we can rely on the HUP in our day to day lives working at CERN. But is it not a stretch to make this claim about black holes? Do we have enough evidence about the HUP to say that we can rely on it as truth, even in these extreme situations?

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    $\begingroup$ I'm not really sure what you want as an answer to this question. Are you asking about any specific claim in the article you linked? Alas, why you'd expect an article on "bigthink.com" to be scientifically rigorous is beyond me in the first place - there isn't really any scientifically precise claim there one could criticize (it's also saying things like "Here, gravity itself goes to infinity.", which is perhaps acceptable for math-free pop-science, but a very poor turn of phrase when you actually want to be precise). $\endgroup$
    – ACuriousMind
    Apr 28 at 17:47
  • $\begingroup$ In any case, the strange bit about a "100 year old theory" is a strange bit to include in a question on a physics site. The age of a theory has nothing directly to do with its usefulness or applicability, and it reads very much as if you picked a pop-science strawman to construct some distorted picture about what "we" in "physics" do. $\endgroup$
    – ACuriousMind
    Apr 28 at 17:50
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    $\begingroup$ Singularities can't exist simply due to the way language works and what it means to say that something is a singularity. It precisely means that our theory predicts non-sensical values (such as infinite curvature) and is thus inadequate to faithfully describe nature in the relevant situation. So singularities are in our theories -- not in nature, by construction. $\endgroup$
    – ACat
    Apr 28 at 18:04
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    $\begingroup$ "Do we have enough evidence about the HUP to say that we can rely on it as truth?" --- Which step in the proof of the HUP do you find less than totally convincing? Do you count it as evidence that many thousands of people have studied this proof and none has found an issue with it? $\endgroup$
    – WillO
    Apr 28 at 18:59
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    $\begingroup$ Minor comment to the post (v3): Please consider to mention explicitly author, title, etc. of link, so it is possible to reconstruct link in case of link rot. $\endgroup$
    – Qmechanic
    Apr 28 at 19:03

2 Answers 2

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A key tenet of quantum theory is that the position and momentum of a particle are determined in a probabilistic way by its wave function. The HUP is a mathematical consequence of that- it is not a standalone assumption. So when people say that such and such is not possible because of the HUP, they really mean that it is not possible because of the fundamental implications of quantum theory.

So if someone says that a singularity cannot exist inside a black hole because of the HUP, what they mean is that if quantum theory applies at the centre of a black hole then there cannot be a singularity there. Of course, we can't yet prove what happens at the centre of a black hole, so it is all a matter of conjecture.

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  • $\begingroup$ Thanks. When I combine it with the link that Anna V gave, it gives me the complete picture. $\endgroup$ Apr 28 at 19:14
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The history of the HUP is spread over time, and since its first proposal the theory of quantum mechanics and quantum field theory have been validated over and over again with myriads of experiments. It can be shown that the commutator relations in the theory of quantum mechanics lead to the HUP, for example here.

Thus the validation of quantum theory is also a validation, i.e. experimental verification of the HUP.

Do we have enough evidence about the HUP to say that we can rely on it as truth, even in these extreme situations?

Now cosmological models use quantum mechanics in modeling the early stages of the universe, trying to avoid the singularities of classical mechanics, and the HUP is an envelope, order of magnitude estimate of how with quantum mechanics singularities are avoided. If we invoke quantum mechanics for singularities we also invoke the HUP.

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  • $\begingroup$ Fantastic answer. The math is beyond me, but I pick up the key meaning: The Heisenberg Uncertainty Principle exists as a fundamental mathematical relationship between two operators that are not compatible. If two observables are compatible, their commutator is zero and thus there is no uncertainty in their measurement. However, if two observables aren't compatible there will be an inherent uncertainty in the measurement. To see that this has physical meaning and is not just a mathematical trick, look at Heisenberg's gamma ray telescope thought experiment. $\endgroup$ Apr 28 at 19:10

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