The Question of How You Build a Black Hole

‘If Ant-man can’t do it, how does it happen?’ After I finished working on that post yesterday, I was left with this question.

It’s kind of a squirrelly question if you stop and think about it. I made an argument by Uncertainty Principle that particles can’t be compressed into such a tiny space in order to be trapped within the black hole formed by the mass of a single human man, and yet individual particles of matter must be compressed to this degree in order to make a real astrophysical black hole. How does that actually happen?

For one thing, the matter forming Black Holes has a very specific hysteresis to it. In real terms, you can’t just jump to a black hole, you have to take a huge mass and basically work through the life cycle of a star. At the end of that, you end up going through a series of states where pressure of material on the outside is pushing down on material in the inside and there are no physical forces that are able to resist the drive toward compression. As such, there is definitely communication going on between many particles and the state of the matter as a whole will end up being a particular statistical mechanical construct based upon some quantum mechanical allowances. What those are, nobody exactly knows yet! Presumably, this is some sort of many-body coherent state, some kind of mega-boson where all the constituent matter is allowed to reside in the same quantum mechanical ground state, which is utterly different from the postulate of the man trying to crush an electron with his gravity.

One of the pivotal difficulties with addressing questions surrounding this state of matter is that Quantum Mechanics is difficult to reconcile with General Relativity. The Uncertainty Principle as I used it yesterday does not take into account relativistic effects. In fact, basic level Quantum Mechanics, like the Schrodinger Equation, are actually classical with how they look at energy. Schrodinger’s Equation is composed of direct kinetic and potential energy terms which only match to first order with the relativistic expression for energy, which is essentially like saying that Schrodinger’s Equation contains no allowances for the travel-time of information from one point to another –which is why you have to be careful about simultaneity on a global level when considering quantum mechanics. In the drive toward including Relativity in Quantum Mechanics, you end up in the territory of the Klein-Gordon and Dirac Equations, both of which expand on Schrodinger’s Equation to bring special relativity into quantum mechanics, much the way Schrodinger’s Equation brings Quantum Mechanics to Classical physics; within appropriate scales, both descriptions work. Schrodinger’s equation is not simply wrong, it just has a limit. The modern Quantum Field Theories that brought us the Standard Model of particle physics, producing things like the Higg’s Boson along the way, all are symmetric in such a way that they allow for Special Relativity.

General Relativity is much harder. There have not yet been any successful theories that completely meld gravity with quantum mechanics. I wish you could find such a thing on this blog, but I’m not that smart.

What a Black Hole ‘is’ internally is still very much a cryptic thing. We can look at them externally, but information only flows into them and doesn’t come back out. Hawking radiation allows a way that energy can leak out, but a Black Hole does not really communicate its structure into this radiation.

Supposing you can’t just build a Black Hole by waiting for a star to collapse, are there other ways one might be produced? One potential candidate is particle accelerators, like the LHC. The reason this could work is actually fairly superficial. When you’re accelerating particles, Special Relativity comes into play. From the laboratory looking at accelerated particles zipping by, because of Special Relativity, a scientist would think the particles are flattened along their direction of travel. This is because of the phenomenon of length contraction, which is where a particle traveling at nearly the speed of light appears to be foreshortened because measurements of length within the frame of reference of the particle do not match with those of the lab. If you accelerated that particle to a high enough speed, the Uncertainty Principle as worked from the lab frame would claim that the particle fits within the length of a Schwarzchild radius for some tiny mass of black hole and, if it were to have a collision with another such particle, they could stick together as a black hole. A secondary feature of this is mass-energy: at a high speed, 4-momentum makes the particle have much greater mass than it would have at rest, presumably increasing the gravity and therefore also increasing the Schwarzchild radius. I don’t know the balance of these effects mathematically (having not actually worked through them and having only trivial skill with the Einstein Equations), but one additional consideration here is that the distance contraction foreshortening is only along the direction of travel, meaning that the spacetime metric surrounding the collision of two such particles is not of Schwarzchild geometry (the metric that produces the black hole hypothesis in General Relativity) and it seems unlikely to me that such a collision can be anything but just a collision as a result. What I mean is that even though they are foreshortened in one length, their distributions are normal in other directions and they may ‘leak’ out of the collision without being compressed into a black hole.

From the basic structure of quantum mechanics, it would also be possible to make the argument that every particle is itself already a black hole. All particles intrinsically have particle-wave duality and the quantum mechanical wave function tells only of ‘likelihood with which you might find said particle at this or that location.’ Beyond the envelope which describes where you may find it in a given circumstance, an electron is itself is a featureless, dimensionless point mass and we can’t be certain if that ‘point’ is smaller than the Schwarzchild radius necessary for it to be a black hole. If there were a way to randomly reach out and ‘find’ it in a location smaller than it’s own Schwarzchild radius, it would be a black hole by definition if only for that moment –never mind that localized to so tiny a volume, the light a charge like an electron can radiate would have a ridiculously small wavelength. Again, we don’t know if there’s something special about the material inside a black hole and our only real definition is that a black hole be of such density that it’s irradiated light can’t escape it’s gravity well.

It’s a very complicated series of questions that have been the subject of a lot of careers in physics. Discarding the complexity or making blanket statements like ‘science supports this’ are massively oversimplifying the whole field. In reality, science is still deciding exactly what it supports.

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