Can anyone else not read the title of this thread without breaking into song?
Black holes: where does the matter go?
Hawking and Feynman have both had a crack although
Even now it still seems that no-one knows
Though, it is true, holes have hair
You can get crabs from a black hole?
That’s only true if all four dimensions are both macroscopic and accessible to normal matter, a scenario which is already ruled out by everyday experience.
QM doesn’t fall out of string theory (maybe you meant to write GR?). Rather, string theory is pretty much an ordinary quantum theory – it can be obtained by applying a quantization procedure to the oscillations of a classical (relativistic) string, as in one-dimensional extended object (while taking care of a couple of oddities that arise along the way).
Supposedly it eventually all leaks out in the form of Hawking radiation (energy and matter really being the same thing). As to what “state” it takes within the black hole, my (limited) understanding is that our conceptions of space and time are completely out of sync with what would be happening within a black hole. For instance, it’s somewhat intuitive that all the matter/energy falling into a black hole will fall through the event horizon and form some sort of super-dense “ball” at the center. But at that point the shape of space itself is so warped that our concept of “ball” has no meaning. A straight line would no longer describe the closest distance between two points. The angles of a triangle would no longer add up to 180 degrees, etc.
Gravity is curving space and time and warping the topology of spacetime to such a degree, which seems analogous to warping our observation of spacetime—going from a flat projection (baseline spacetime) to a sort of Riemann sphere/complex-manifold (“singularity-like” spacetime). Matter/energy, of course, have to follow these paths anywhere from P(∞) to P(0) or P(-∞) that appear to converge to 0.
What happens at the event horizon this gravitational boundary (such as the wavelength of light will have to shrink to zero as it crosses) I find especially interesting, because I believe it to be an observable projection of this sort of warp of spacetime.
Even Penrose’s Twistor Theory of 3+1 spacetime (Minkowski space) suggests that perhaps the various spins of quantum particles are undergoing Möbius transformations, as gravity is curving spacetime into some Riemann sphere-like topology.
I’m talking in circles, or Riemann spheres, aren’t I?
I’m actually contemplating to spend some free time to figure out a concise way to CG animate these ideas/theories. This is the sort of stuff pop-science shows or magazines never attempt to explain or visualize; it’s always umpteen shows watering down these things and stopping just as the physics and geometry of our universe really become interesting.
Which is more dense: a black hole or the universe at the time of the Big Bang? Or are they the same? If the Big Bang was more dense, at what point in time was the universe as dense as a black hole?
Where are you taking these things from? Gravity doesn’t have anything to do with topology, it only affects the geometry of spacetime. I’m not sure what you’re trying to make of the Riemann sphere specifically – the geometry used in general relativity is (pseudo-)Riemannian, but those are distinct concepts. The Riemann sphere is also the set of states of a spin-1/2 particle (or more generally, any two-level quantum system). Penrose makes much of the fact that the ‘heavenly sphere’ – i.e. the set of all light rays intersecting a particular point – is a Riemann sphere, and that its automorphisms (the Möbius transformations) are equivalent to the Lorentz transformations of special relativity; this has some connection to twistor theory since any event, i.e. space-time point, is essentially represented in twistor space as a Riemann sphere if memory serves, but I’m not sure I see the sense in how you combined these concepts…
From the perspective (reference frame) of a black hole denizen, would space appear, locally, to be bizarre and contorted or flat and simple? Can we communicate with the interior, for instance, throw stuff in and look for a response? And how long would we have to wait for that response?
The troubling thing about black holes, for me, is the curvature at the event horizon. Effectively, relative to us, time stops at this boundary. From outside, nothing can ever be seen to cross this boundary, so any black holes that formed in the past thirteen billion years or so cannot be seen by us to have finished forming, we can only observe the period of their formation through the time-dilated lens of their gravity well, up to the boundary of the light sphere, if that exists in a region we can observe.
There is nothing special about the curvature of the event horizon of a black hole. For a star-sized black hole, the curvature at the horizon will be extreme, but then, it’ll also be extreme well outside of the horizon. For a very large black hole, the curvature at the horizon can be quite moderate. And it’s even possible to cross the event horizon of a black hole while in a region of perfectly flat space (i.e., with zero curvature).
As for “black hole denizen”, well, that’s a rather problematic notion. Once you’re past the event horizon, it’s guaranteed that you’ll reach the singularity at the center in very short order. You can’t just stick around and wait in there. If you just mean that you’ve got an infalling observer making measurements during that brief window of time, the curvature will generally increase as you get closer to the center, and eventually will be extreme enough to kill you and destroy your measuring apparatus, but when that happens won’t have any particular relationship to where the horizon is: It might be inside or outside, depending on how sturdy you are and on the size of the hole.
To be honest, I had started to explain further where I’m coming from and just ended up making more of a mess of my thinking and visualization.
As for claiming that spacetime has geometry, but no projected topology depending on where you are, how fast your moving, will place you in a more or less curved spacetime geometry and the projected topology of such will present it’s self to you as slower clocks, relativistic shortening, or even Einstein rings… If not, where am I wrong? Now I’m !
I look at a black hole, and see two singularities. The most obvious is the one at the center. The other, the threshold of the event horizon (look familiar?). Regardless or not that you may not notice anything special about crossing that particular singularity, it seems to me to be the central singularity’s opposite, but equal phenomena.
My above posts are nothing more than raw bits and pieces I pick up from a myriad of papers, theses, books, my own study and experience in my career with geometry and complex space, etc.
It’s too much and scattershot, now. We’ve acquired so much evidence in QM and GR, yet it’s painfully clear the Standard Model frustratingly inadequate. It’s resulted in modern physics becoming so esoteric that I feel we’ve hit a true dead end. Of course, the jury’s still out on the Higgs, but it’ll just be another quantum particle that begs the same questions as all the other fundamental particles.
It’s gone stale, and we’ve lost the scent. Yet, I, some schmuck on the internet care“ enough, just out of raw passion and curiosity about these fundamentals, to just toss some abstract connections around.
I just watched a video today called Athene’s Theory of Everything. It’s really more of an essay and hypothesis hybrid, but the important point is that I think he has some interesting points, that put into words the very things I’ve been struggling to communicate (half-baked as it is, anyhow).
So, this is the first I’ve heard of it, and can’t vouch for the veracity of any of it or the people involves as I haven’t looked into it yet, but I do recommend at least taking the 40 mins to watch it—it’s at least well produced, interesting and offers some serious thought provoking stuff to actually ponder depending on how finely calibrated your cynicalizer is. There’s even some impressive (to me at least) novel ideas touched on.
Anyhow, I’ll let the video speak for itself, but to quote his closing remarks:
If you were aware of this, I apologize. If so, or if you or anyone else decides to watch it, I’d love to hear some criticisms and opinions.
It’s late, this is, again tl;dr, and before I go unconscious, I just want to say I’m rooting for those of you that have and are doing the actual research, and have put in the investment of time, money and effort to pursue one of the greatest tools mankind has: The scientific method.
Goodnight, moon… Zzzzzzzz…
Nonsense. Science, in the sense of developing basic theory that determines all other results, is open to almost no one. This has been true for more than a century. Back then, the trope was that only a dozen people in the world understood Einstein. This was wrong in many ways, but correct in that it recognized that the math and physics was so advanced that only specialists who made it their lives had any chance of affecting future basic theory.
It is equally true today. You are throwing words around without the underlying math. That’s not science. There are many times more professional theoretical scientists today than in 1905 so the actual number of people who understand is comparatively large, but no one who isn’t one of them has anything to say on the subject. The most you can do is spew blather on the internet and have someone correct your mistakes. (You’re also showing ignorance of the last 100 years of philosophy that has commented on modern physics but we have fewer people able to correct that.)
Let me make this as blunt as possible. Everything that can be said on this subject is expressed in the language of math. If you’re using words, people can stop immediately without losing anything of value.
Agreed—to a degree.
I couldn’t be a more staunch supporter of the scientific method. True, mathematically modeled theories are of the most esoteric and abstract fields of any human endeavor.
Yet, you do not start to form a theory without first forming a hypothesis [a supposition or proposed explanation made on the basis of limited evidence as a starting point for further investigation].
Today, there are an order of magnitude of minds on the planet than there were in Newton’s time.
Most of the physics that are evident on the human level and intuition has been sorted out, and now were drilling in [QM] or out [GR] into the fundamental fabric of reality itself. There’s so many theories now, in different states of validity, each one a plausible model of the universe, yet all with their issues, gaps, or incompatibilities.
To even get up to speed on QM/GR takes years, if not decades just to merely stand on the shoulders of the Standard Model and the required math/notation. We have isolated theories to the point that we can’t decide which one is the most likely lead to furthering progress in the next era of physics: Unification.
Mathematics are imperative to diving deeper into the fundamental nature of reality. No question. But, aren’t we’re getting lost in the abstracts of it all? Too much of any theory based off of QM or GR is purely mathematically abstract, which is a problem, with no foreseeable ways to test any predictions.
For instance, look at the amount of cost and effort in particle physics. The LHC and Fermilab’s Tevatron are on the forefront, bleeding edge of testable, fundamental physics.
The math of the Standard Model predicts the Higgs Boson. I can’t wait, myself, to see what comes out of the discovery of a new boson this past summer.
And granted, if we find this boson to be the Higgs and/or any of its possible related particles, then research will have a narrower focus, which is looking very likely (with a significance of 5.9 sigma).
But we all know we’re going to need a new theory that explains why the current mathematics of particle physics and relativity don’t jive. I guess that’s why I keep coming back to the black hole. It’s the one, confirmed object that shows us there is a TOE, and any hypothesis or theories that seem to relate could be the key. I believe the underlying “geometry” of reality is key.
We need a new perspective, and it can come from anywhere: Be it mathematics, geometry, topology, experimentation, or making connections from previously abstract phenomena of logic and nature. forming novel perspectives.
I respectively disagree, to the point that there probably is a minimum level of math one needs to understand.
My scribblings in this thread is not the entirety of science, but yeh, I’m throwing around observations and evidence, taking the math underlying for granted (not unlike rigorous mathematical models throwing around equations without understanding the underlying nature). At some point, the logically abstract models that do explain reality, need to be translated into a human language, so it can be understood and taken further by some minds that have a better grasp on the visually abstract. Indeed, we already have non-mathematical language, visualizations and words for such things, and more will come; if someone can grok Minkowski Space in their mind, without being able to read or work with the notation, they can play out certain scenarios as thought experiments.
I’m not trying to form a new theory here, that’s ridiculous. But, pretty soon, physics will dissolve into the untestable, theoretical impasse. The energies required to experiment further are beyond human capabilities to probe as deep as any unifying theories will require.
So, all this said, juggling these known problems with known abstracts (words, visualizations, or math), in a manner of though experiments is something I think should be encouraged for anyone. That’s what science is about, fundamentally. A theory will arise if warranted, but that’s not necessarily my focus in general. But I do want to be corrected if I’m missing an important piece of evidence or aspect of reality.
So, if the answer to the question, “Where does the matter in a black hole go?” is “We don’t know.” That’s fine. But what’s the fun in stopping there?
Also, if you (or anyone) care to point out some of my ignorance on this front, I’d appreciate it. S’what I’m here for! 
Black holes do not have a singularity at the event horizon. Some of the more common ways of describing black holes have singularities there, but that’s a property of the description, not of the hole itself, and there are other descriptions that behave just fine there. This is what’s referred to as a “coordinate singularity”, and there’s nothing special about them: The North and South Poles are coordinate singularities of the latitude/longitude system, for instance, as is the origin of a polar coordinate system.
Setting aside the “fact” that “perfectly flat spacetime” is about as non-mythical as a “perfect vacuum”, what I read appears to contradict what you are suggesting: the event horizon is specifically defined as the boundary at which there are no paths that lead away from the singularity, meaning it is a spheroid of rather extreme curvature.
I misunderestimated human ingenuity once. Not a mistake I, personally, will make again. Observation has become so inferential and highly removed from the reality of experimentation, I seriously doubt that the discipline of physics will genuinely surpass the point of testability. The lag between theorization and substantiating evidence (“proof” will probably become to strong a word or will become diluted in meaning) will gradually or rapidly increase. If we cross the vaunted technological “singularity” and can employ sophisticated AI to race on ahead for us, perhaps the lag can be mitigated, but I have my doubts about either.
What if the singularity is NOT an infinitely dense geometric point?
The above-referenced Fuzzball
The Gravastar
Perhaps the singularity is a finitely-small, finitely-dense lump of Planck Density
of one Planck Mass per cubic Planck Length.
I’m not sure what you mean by ‘projected topology’. Usually, the topology of a space is roughly concerned with the question into which ‘forms’ it can be continuously deformed: so a cube can be deformed into a sphere, a coffee mug into a torus (donut), but not into a sphere – generally, two spaces of different topology have a different connectedness: the sphere has no hole, the torus one, etc. Relativity is concerned with the geometry defined on a given space, which gives us a measure of lengths and distances; all the effects you mention are due to this geometry.
No. In fact, the curvature of a sufficiently large black hole essentially vanishes at the event horizon; this does not change the fact that beyond the horizon, every future-directed path leads to the singularity. Take the analogy of a ‘dumb hole’: at some point, the flow speed of a fluid becomes greater than the speed of sound within the fluid, so beyond that point no sound can escape. However, the flow speed behind that point is only infinitesimally greater than immediately before; this difference in speed is analogous to the curvature.
And just for kicks, the explanation for how you can cross an event horizon while still being in zero curvature:
Imagine a spherical shell of photons, all coming from who-knows-where very far away, and all converging on a single point. When the shell gets small enough, it’ll be within the Schwarzschild radius corresponding to its mass, and thus will be a black hole. Let’s say, for the sake of argument, that the mass is such that its radius is 1 light-second. Now, an object at the central target point of this shell is clearly inside of the black hole, and can’t get out: It has therefore crossed over the event horizon. But it won’t get any information at all about that infalling shell of photons for another second: Any way that information could reach that point, including propagating effects of the curvature, is limited to the speed of light, and thus couldn’t get there any sooner than the light itself. So if the unfortunate target was sitting in flat space before, it’s still sitting in flat space as it crosses the singularity, and indeed right up until the exact moment when the singularity forms right on top of it.
Topology has many different subfields. I know this is very scattered, but bare with me.
Here I’m still referring to a closed topology (no holes), but in a far more abstract, algebraic definition. More specifically, I’m focusing on a three-sphere (S[sup]3[/sup]) embedded in a 4 dimensional Riemannian geometry (R[sup]4[/sup]).
I’m typing up a more explanatory post, but I’ll need to take my time in trying to convey my point. Damn, I need Mathematica. It’d be so much easier just showing the geometry.