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Common sense cannot be trusted on matters like these. Common sense is calibrated for reasoning over matters encountered in daily life. The further away we get from that, into more and more exotic phenomena, the less common sense can apply. Black holes are very far from the domain of common sense.
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I always suggest looking at the quantum eraser experiment to see how bad common sense works with quantum mechanics. It's fairly simple but intuition fails most people when it comes to explaining how it works.
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No need for funky stuff, just do the classic (lol) Young's slits experiment which should be more than enough oddness for anyone.

I was shown it at school, using microscope glass slides that we waved over a Bunsen burner running cold, to coat with soot. We then carefully etched parallel lines with a compass by hand. Our (~17 y/o) efforts were a bit random but we did get some smudgy banding results on the screen.

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Using a compass is interesting, use two razor blades taped together is much easier and it’s close enough to perfect parallel lines.
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The question of "what holds it up?" is where that leads to. There's an interesting history of answering that question again and again - and the discovery of new types of stars each time.

History of the Universe : What Is Hidden In The Core Of A Neutron Star? - https://youtu.be/YoYjkNQ27T8

That video goes into it... without getting mathy at any point.

One of the bits that you're having trouble with is the compression of matter to a point. There's a theoretical type of black hole known as a kugelblitz - https://en.wikipedia.org/wiki/Kugelblitz_(astrophysics)

    A kugelblitz is a theoretical astrophysical object predicted by general relativity. It is a concentration of heat, light, or radiation so intense that its energy forms an event horizon and becomes self-trapped. In other words, if enough radiation is aimed into a region of space, the concentration of energy can warp spacetime so much that it creates a black hole. This would be a black hole the original mass–energy of which was in the form of radiant energy rather than matter
Rather than compressing particles, would you have difficulty with converting it to incredibly large amounts of energy that wraps space time into a singularity? If you packed enough photons into one spot, that energy would curve space time enough to form a black hole.
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>Rather than compressing particles [...] If you packed enough photons into one spot

I haven't watched the video, but if we're compressing electrons, neutrons, or other fermions, I imagine if we want to keep compressing that down to an arbitrarily small radius, won't we pretty quickly find it favorable to shift those fermions to something else, probably photons, to respect Pauli exclusion?

Really, I don't know enough physics to figure out the reason why it shouldn't always end up in this incorporeal energy-curving-space situation either way, if we're compressing arbitrarily far.

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But then you "fill up all the photon slots" too (not literally because they are not fermions, but they do spontaneously convert back into things like electrons at that density) and you can work around the Pauli exclusion principle by stacking your electrons at higher and higher energy levels.

Pauli exclusion isn't an impenetrable force field - as you say, it's just often more favourable to do something else than to work around it. Consider an iron atom with however many electrons though - all those orbitals except the inner one are electrons working around Pauli.

I'm not a physicist either.

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Pauli exclusion is a QM thing. Black holes are a GR thing. Famously, we don’t know how to mix the two.
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We don't know how to mix the two in general. There are plenty of tame enough special cases where we know how a mixture has to look like.

Finding a tame enough special case was how Hawking discovered his radiation.

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Pauli Exclusion is just another “force” that can be overridden. Nature isn’t a list of rules
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As far as anyone knows, electrons are already point masses.
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A particle is a region of space where it's probable that a certain kind of interaction will happen. I don't see any reason why they can't overlap infinitely and then squeeze to the Dirac delta function: certain to be here, no error bars. That is, apart from the Pauli exclusion principle. But you have to leave that one behind if you're dealing with masses beyond the TOV limit.

Of course I'm missing something here. I've taken QM and not GR so I would have this interpretation.

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Some of the most interesting and fundamental ideas in science are counter-intuitive
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My rather pop-sci understanding is that when you start playing around with relativity math, trying various masses and densities you hit something rather worrisome. As you approach some great, but still possible, value the plot goes infinite, the singularity. This is bad for the theory because going asymptotic like that usually indicates a fundamental problem in the math. But relativity does so well everywhere else... What if it could? And thus the black hole was born.

The easy thing to miss, and blew my mind when I read it. is that general relativity is the concept of space-time, emphasis on the time, and this is also compressed by the mass, so if this singularity can actually occur it would also take an infinite amount of time to fall into it. So nothing can actually enter it. From the point of view of an astronaut(deliberately ignoring all the other relativistic implications) flying directly toward the event horizon. As you approach you will quickly see the rest of the universe age and die. and if hawking radiation is real the black hole will evaporate in front of you before you can reach it.

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I believe this is a misunderstanding based on inadequate coordinate systems, and that an astronaut would fall through the event horizon, die, and reach the singularity in finite time.

See https://physics.stackexchange.com/questions/82678/does-someo...

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AFAIK from the outside point of view it takes infinite time. We see the falling object redshift to infinity (blackshift, really) and merge into the black sphere we observe.

But in the object's own time coordinates the math says it does hit the singularity. If you fell in you wouldn't die of old age before you hit it.

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Does time accelerate just for the astronaut approaching the black hole (meaning they would be witnessing the future) or does it accelerate for everyone (meaning approaching a black hole is going to make everything end quicker)?
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If outside observers could watch the astronaut clearly, the astronaut would look like they're slowing down to a stop at the event horizon. The astronaut would not see themselves freezing in time, but they would see everything outside of the black hole speed up.

You could travel arbitrarily far into the future by getting close to a black hole's event horizon for a while without crossing it and then leaving, assuming you had the energy for it and you didn't get obliterated by all the mass and energy falling into the black hole in that timeframe.

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Time acceleration is dependent on the gravitational flux.

All objects within a given radius of the black hole (possibly modulo spin) would experience the same time dilation. Remote objects in the universe would not experience the dilation.

From the perspective of the astronaut falling toward the singularity, the rest of the Universe would age at an ever-increasing rate.

From the perspective of a remote observer, the astronaut falling toward the singularity would be experiencing time at an ever-decreasing rate.

The notion of relativity is that time-perception is relative, and dependent on acceleration, whether from motion (as on a spaceship) or from gravitational acceleration (as near a black hole). Objects in orbit around Earth, further from Earth's centre, and hence subject to reduced gravitational acceleration, age more quickly than objects on Earth's surface. This is actually measurable using atomic clocks, though the effect is quite small. It is sufficient that GPS satellites require time correction.

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My rather limited understanding is that. first there is a lot going on and due to the forces and gravitational gradients involved, matter itself probably would not survive the journey that close to the horizon. But ignoring that, When in compressed time, from the point of view of someone freefalling, timewise everything is normal, the rest of the universe has accelerated and in the case of a black hole has just aged out and died but you are fine. from the external point of view they are taking forever to get there.

Where my imagination fails(above my pay grade) is in the face of infinity, what are the implications of infinite time compression?(everything happens at once?)

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> external point of view

So time is localised? I’m not sure what localised time means but I’m hoping the question makes sense.

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I can only guess as well, infinite time compression might result in a big bang when it applies to everything. All black holes could lead to the same moment causing the bang.
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There are a lot of curious coincidences between properties of black holes and properties of the whole universe that lead some physicists to the idea that they could be connected. There's also that Penrose diagram showing another universe beyond a black hole. (Seems like a copout to me though. Penrose diagrams are drawn in 1D space, so the black hole cuts the universe in half. If you had 2D or better space couldn't you just travel around behind the black hole to the other side of it?)
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Yeah, wouldn't this cause trouble with Pauli exclusion principle?
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Only if they all had the same energy level.

And if they didn't form a superconductor. I'm not sure why they would but if they did they would violate it. That's actually what makes superconductors superconducting - the really weird state where electron pairs act like bosons.

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It's a complete violation of good sense to invoke common sense here. You talk about "particles" but that's not what the world is made of. Also, particle/wave duality. Also, any number of bosons can occupy the same position. Also black holes evaporate. And on and on.
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> … you cannot compress particles to an absolute point.

What do you mean by “particle” here? This kind of handwaving is fundamentally classical, and breaks down in the presence of quantum physics.

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Common sense - the experience gained from your common everyday experience of reality - does not apply in black holes.

Common sense would tell you they can't exist at all because you can't compress atoms - you have lived your entire life with atoms being entirely incompressible for the practical purpose of anything you do.

Leaning on common sense to discuss fundamental physics has been wrong since round about the start of the practice of physics.

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Funnily enough, technical speaking atoms are a small minority of ordinary matter, that is already excluding dark matter.

That's because a lot of the ordinary mass in the universe is ionised or in other weirder states.

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Common sense actually says that atoms don't exist and if you squish cheese really hard you just get really hard and slightly smaller cheese, or maybe you invent a new type of dairy product.
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This needs a joke about unbelievable denseness.
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Aren't fundamental particles like electrons and quarks treated as points?
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If you really treated them as points the theory would blow up because the electrostatic potential energy of a point charge is infinite. This is dealt with by “renormalization” which is roughly: assume the theory isn’t really valid all the way to a zero length scale and that we can average out everything that happens below some cutoff size and that it doesn’t really matter where we place the cutoff because the theory works the same if you change the cutoff and change the other parameters accordingly.
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They are, but there are some interesting theories about their internal structure. Be aware that this is probably junk science but I have currently been enjoying this effort to describe them via the em field.

https://quicycle.com/understanding-electrons/

And the video essay on the subject https://www.youtube.com/watch?v=hYyrgDEJLOA (Huygens Optics: Williamson & Van der Mark electron model | Are electrons made of light?)

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Points are a realist view - there's a real object there.

Although some physicists disagree, QM slants very anti-realist. There are no objects anywhere, no particles, no waves, only probabilistic interactions, some of which can be snapshotted into localised partially definite results.

So there are only interactions between probability distributions in space and time, and "particle-like events."

No pointy objects, and no need for them.

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Wouldn't it be both? Electrons occupy probability clouds, but the overall probabilities of things happening are summed over the whole cloud as if, at each point, the electron was a point particle at that point?
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QM slanting anit-realist is because some prominent physicists like Neils Bohr gave the math that interpretation, and they were more persuasive than the realists like Einstein, Schrodinger, Everett.

The agnostic view is it's just a mathematical model that makes accurate probabilistic predictions when measurements are made, which says nothing about what's really going on.

Of course treating particles as points is also mathematical.

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Kind of, but not really.. though there are simple models with electrons as a point charge, a more accurate model involves the electron field describing the probability of an electron existing at any region in space (not to be confused with the electromagnetic field, the medium in which photons propagate).
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Sure the position of an electron is not definite, but neither is that of a buckyball, but a buckyball has a shape we can describe, an internal structure we regard as extended over space, in a way that is separate from the indeterminacy of its center of mass position. This is unlike an electron, for which, if we set aside the uncertainty as to its center of mass, my understanding is that the only internal degrees of freedom it has left (in the Standard Model) are its spin and whether it is left or right handed, with no other structure to it.

It is in this sense that, AIUI, electrons are modeled as point particles.

Of course, that doesn’t mean that if we zoom in enough, probing at higher and higher energy scales, that it can’t turn out to have some non-zero fundamental size outside of just uncertainty in its center of mass position. I think string theory would say that at the string scale it would be a string.

But, AIUI, no experiment has shown it to have the kind of extent that would make it be called not a point particle (an extent in a sense beyond just uncertainty in COM position)

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