How can a gravitational singularity exist if it violates quantum physics?

Question

I have never understood this, granted I have never been a quantum physicist, but I am about to graduate a mechanical engineer at one of the the top 3 schools in the country, so I feel that I have the capacity to grasp some of the concepts and certainly could learn it.

If, according to quantum laws, no particle can occupy a space smaller than it's wavelength then how can the center of a black hole, or the universe, have dimensions of 0m X 0m X 0m? or am I misunderstanding? if so, please provide math showing how to calculate the dimensions. an example would be very much appreciated.

Furthermore, if the notion of "infinities" being present at the center of energetic accretions exceeding the criteria defined by: gravity > c, was derived from General Relativity, which makes no reconciliation with quantum laws because, correct me if I'm wrong, they were not established when it was formulated...so, other than the fact that "it works...most of the time", why is it simply accepted as fact? or does it work all the time? please explain how we know that it works all the time or show math proving that it works all the time.

I feel like general relativity may be similar to Newton's Gravity, which provides an almost always accurate result, but because certain laws (e.g. those regarding light) did not exist when he formulated it, it has limitations of applicability. In this case, Einstein's formula was constructed before certain laws were known and thus may not always be right, such as in the case of singularities.

My thought process has always been that energy/matter; no matter if it's a quark, a string, or whatever lies lower; resists being compressed by an applied force (sort of like a spring constant) wherein compression to a dimensionless entity (e.g. infinite compression is required to achieve 0 volume) would require infinite Force (from Gravity in the case of a black hole and the big bang), which would require infinite mass, and, as should be beyond obvious, infinite mass does not exist because matter/energy is finite. Am I wrong about "compression"? if so, please show math (or words) that explains how a wave (or a string) can occupy a space smaller than it's wavelength (or whatever the technical word characterizing strings is).

I might be asking for math that is deserving of nothing less than a nobel prize, but if that's the case then why is the notion of a singularity accepted as fact instead of explored as wrong and in need of improvement?

If I have asked for math please do me the favor of carrying out calculations so I can see the numbers. If a solution would require an iterative numerical method to solve, please just set up the initial iteration. If it is more cumbersome than that (e.g. a system of equations that requires numerical iterations), just leave it as simply the general equations. If a solution would require numerical (as opposed to analytical) integration/differentiation, don't even worry about (from personal experience, those are a real pain in the ***), simply the general equations would again be greatly appreciated though. Basically, if the solution would be more cumbersome than analytical methods and/or some slight rearrangements, don't waste your time. Obviously, you don't have to do anything, but as someone who feels capable of understanding the theories (words and math) but incapable (due to current school obligations) of dedicating the time to learn them, it would be greatly appreciated.

Also if you actually plan on doing any of this, please leave an initial answer that says "give me a few minutes" or something, just so I know that my question is going to (attempt) to be answered.





some background: this question arises from my inability to understand how time "stops" (and space...ceases to exist??? or am I wrong?...equations illustrating these notions would be awesome too!) at the beginning of the universe. I don't understand why it is impossible for that big ball of energy to have just kind of remained in equilibrium for 1, 10, 100, 1000 billion years, hell, it could have been just an hour of equilibrium or no equilibrium at all because the system was decaying the entire "non-existent time" before expansion (due to Hawking Radiation...or some other phenomena necessitated by the 2nd Law, or rather, whatever laws were governing the system before the emergence of different governing laws, including the ones that govern the current era) and then, BAM! -some random (and improbable?) fluctuation (governed by stochastic physics) happens- and --> Expansion!

Answer 1

I'm not sure I can fully answer your question. There are some interesting facts about stellar remnants. Both white dwarfs and neutron stars are quantum mechanical objects. Using nothing more than Newtonian gravity you can find the energy of electrons packed into a tight volume and balance that against the gravitational energy of a solid sphere (of constant density).



This means that given the remnants mass, you can calculate the size using quantum mechanics. I believe that this formulation agrees very well with experimental results.



So a white dwarf stops at the electron degeneracy pressure. That is the star is not massive enough to push the electrons together any further. In neutron stars the electrons are pushed so closed together that they will start getting absorbed by the protons producing neutrons. Now instead of electrons, we have a quantum mechanical object of neutrons. Because neutrons are so much more massive, they can be pushed together much further and indeed produce much smaller remnants than white dwarfs--in fact a neutron star is already dense enough that it starts behaving similar to a black hole (but there is no theoretical event horizon--in actuality if you got very close it would be difficult to escape). Neutron stars spins so fast that they not only stretch but twist space-time around them--this effect is not predicted from Newtonian gravity.





So we know that there are some stars which collapse "below" the point of a neutron star, to a black hole. It's quite possible (and probable as you stated) that this is not an actual geometric singularity. It's probably some smaller quantum object made up of something else besides neutrons (quarks, I suppose). But whatever it is, it creates an extremely dense object--dense enough to behave as a black hole. Furthermore, the size of this object would be so much less than the event horizon, that from the event horizon and beyond (i.e. where we can observe) this object appears as a point particle.

Answer 2

Who says the volume of a black hole is 0 m^3?



We can't "measure" the volume, even though we can assume that it acts like a point mass. Usually, we use the schwartzshild radius as the physical size of the black hole (actually, the event horizon), and even that has a few conditions, like non-rotating and zero charge.



Since we can't 'see' inside the event horizon, everything else is speculation, including the idea of zero volume and infinite density, so we don't know that even our most esoteric maths can handle the structure.



One thing for sure: what goes in doesn't seem to come out, despite Hawking radiation...



Oh, about time and black holes.... Again, because light gets red-shifted as it approaches the schwartzschild radius, this is what gets assumed as time slowing down. We haven't got near enough to a black hole to test it. And Relativity says that the curvature of space is caused by gravity, hence the greater the mass (and closeness to it) the greater (sharper?) the curvature becomes. So, maybe, the wavelength is still the same, but "spaghettified" parallel or inside the black hole, which keeps the same rules as before, but 'vectored'

Answer 3

"How can a gravitational singularity exist if it violates quantum physics?"



Easy. It doesn't. There is no spacetime, mass, or gravitation in quantum physics, so this problem is transparent to quantum physics. Doesn't that help?



"If, according to quantum laws, no particle can occupy a space smaller than it's wavelength then how can the center of a black hole, or the universe, have dimensions of 0m X 0m X 0m? or am I misunderstanding?"



You are mixing metaphors. As far as a black hole contained in this Universe, the event horizon is as constrained as the contents can be for uncertainty relations. That you feel that all the mass is piled at the geometric center, is not Nature's problem. Some believe that this Universe is inside one-or-more black holes in a Universe that contains ours. In this model, the "central singularity" is a cold, dark, infinitely diffuse future, in which no particle will have any other particle in its future. Perfect for quantum tunneling back into the container Universe, from essentially a Bose Einstein condensate state.



You will come across a lot of flatlanders that will think they can know all there is to know about the interior of a black hole, and we clearly cannot. So do not let them flare your Asperger's into a tizzy, with their naivete.