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Everything posted by elfmotat

  1. You caught us! How did you find out? Did someone tip you off? I've already informed my Illuminati bosses of the existence of this thread, so I hope you went through at least seven proxies!
  2. It seems the wiki is wrong, or at least poorly worded. If you compress a mass to its Schwarzschild radius it certainly will collapse, but that is not at all its defining characteristic. As I've said, collapse will become inevitable before it is compressed to its Schwarzschild radius. Somebody should probably fix that. EDIT: Upon re-reading, the wiki is not really wrong. The article does not actually mention gravitational collapse, it just says that a mass smaller than its Schwarzschild radius will have an event horizon, which is true. I still think it's a bit badly worded though.
  3. Except that they are (for a black hole with no angular momentum or charge), by the definition of the Schwarzschild radius.
  4. You have it reversed. The Schwarzschild radius does not define at what radius something will become a black hole. That may vary depending on the specifics of the star/mass/whatever that's undergoing collapse. The radius at which you are guaranteed collapse is at 9/8 its Schwarzschild radius. For a BH with zero angular momentum the event horizon does correspond to its Schwarzschild radius. No. It means the matter will collapse in on itself due to its own gravity to form a black hole. A "horizon" means "point of no return." As ajb previously mentioned, the specifics involving the formation of horizons are still not completely known.
  5. This is why it's important to learn the math. Intuition is not a good guide for physical matters. Falling into a supermassive black hole would be better. The tidal forces at the horizon would be negligible, and you would pass right through without noticing a thing. Nothing special happens there, it's just a point of no return. As for how to maximize your time of survival: do precisely nothing. Geodesics are paths of maximal proper time. Trying to fight your way out will only make you die faster. Mass, volume, and energy are all observables. I.e. you can measure them. You can't measure a vector. There are different types of vectors, and some of them have absolutely nothing whatsoever to do with physics. The point at which gravitational collapse becomes inevitable is at 9/8 the Schwarzschild radius. This is known as Buchdahl's Theorem -- Schutz's textbook has a section on it. After the mass has collapsed into a black hole, its event horizon will be located at its Schwarzschild radius (assuming it has no angular momentum).
  6. A vector is a mathematical object. It is not a "thing" that exists. I recommend picking up an introductory Newtonian physics textbook. For a black hole with zero angular momentum (called a "Schwarzschild black hole") the event horizon is at [math]R_{EH}=R_S=2GM/c^2[/math]. This radius is called the "Schwarzschild radius." For a black hole with angular momentum (called a "Kerr black hole") the event horizon is not at its Schwarzschild radius. Instead, it is found at: [math]R_{EH} = \frac{GM}{c^2}+ \sqrt{\left ( \frac{GM}{c^2} \right )^2 - \left (\frac{J}{Mc} \right )^2} = \frac{R_S}{2}+ \sqrt{\left ( \frac{R_S}{2} \right )^2 - \left ( \frac{J}{Mc} \right )^2}[/math] If you take a ball of mass M and compress it down to a radius of less than [math]R=9GM/4c^2 = 9 R_S / 8[/math], the internal pressure required to counteract gravity and prevent collapse into a black hole becomes infinite. In other words, if you compress a mass down to less than 9/8 its Schwarzschild radius, it has no choice but to become a black hole. I believe that probably answers most of your questions.
  7. I wouldn't exactly call that an "interaction" by any usual definition of the word. Superposition is not an interaction. I didn't say "mass and gravity don't exist," I said you can treat the gravitational interaction as being zero if the masses involved are sufficiently small. Which you can.
  8. Gravity is different from the other three forces in a number of important ways: It is described by a rank-2 tensor field. The other three forces are described by rank-1 tensor fields, AKA vector fields. This translates into photons, gluons, and the weak bosons having spin-1, while the theoretical graviton is predicted to have spin-2. It couples to all other fields/matter. Anything with energy-momentum will generate a gravitational field. Electromagnetism only couples to fields/matter with charge. The weak force only couples to fields/matter with weak charge, and the strong force only couples to fields/matter with color charge. If there's a particle, you can bet it's effected by gravity. Gravity is incompatible with modern Quantum Field Theory, the basis of the Standard Model. The other three forces have descriptions in terms of quantum fields. In particular, General Relativity has been proven to be non-renormalizable. A successful quantum field theory of gravity has yet to be developed, though there are a number of well-known approaches to solve this problem -- String Theory and Loop Quantum Gravity being the most recognizable. Gravity is a geometric force. The other three forces are described in terms of fields on a background spacetime. With gravity, the field is spacetime itself. This property gives rise to the equivalence principle, which is why heavy objects and light objects will fall at the same rate. This may in fact turn out to be less of a distinction than you might think. Kaluza-Klein type theories can also describe the other forces/matter in terms of geometry, though they require extra spatial dimensions. For example, gravity + adding a fourth spatial dimension in a particular way gives rise to electromagnetism, with electric charge being the conserved momentum through the extra dimension. Gravity is much much much weaker than the other three forces. I've heard this example used before: a tiny fridge magnet is strong enough to overcome the force of the entire Earth pulling down on it. You too; you can walk around the surface of the planet with relative ease, lift objects, etc. Ever tried to pull apart two strong magnets? I'm not entirely sure what you mean by "absolute lower limit." I'm not aware of any such thing in QFT. If two masses are sufficiently small, you can indeed treat the gravitational interaction between them as zero. This is what is done in quantum theory -- the masses involved are so small and gravity is so weak that it is completely negligible.
  9. That's not very fair. I put my time and effort into giving you informative responses, and I'd like to think I've been very patient. I can't help if you aren't willing to learn.
  10. Anyone without a mental handicap.** So did you learn from your mistake? Did you realize that having the right answer doesn't make you right? The process by which you get to the answer is often more important than the answer itself. That's cool, I guess. I just don't know why you're making it a matter of pride that you don't understand that math. Why anyone would be proud of their ignorance is beyond me. Are you just trying to give us the impression that you have overwhelming levels of raw intelligence? Please do. To be honest, no, you're not really doing OK. Your posts are riddled with misconceptions and strange leaps of logic, all of which are quite tedious to correct. That's why I suggested picking up a textbook -- to avoid what's happening right now. Okay. I don't understand how you're getting from "some of the BH's energy is stored in its angular momentum" to "therefore its event horizon is smaller." The two seem utterly disconnected. This is absolutely 100% false. Energy is not a vector. Energy is a scalar quantity. It has magnitude and no direction. This is why it's important not to use terminology you do not understand. I don't know that there's an intuitive explanation. It comes from the Kerr solution to the Einstein Field Equations, which describes the geometry of spacetime around a black hole with angular momentum. I don't think it's possible to reach such a conclusion based solely on energy considerations. The energy of the gravitational field is not well-defined in general relativity, so this argument truly makes no sense. Gravity is an attractive force. It takes more energy to hold two objects apart than to bring them together. I don't know what you mean by this. Are you talking about Fourier analysis? I fail to see how that's relevant to the conversation.
  11. https://www.khanacademy.org/math/differential-calculus Trust me. Watch through a few of those videos and you'll do fine.
  12. Agreed. Except that the math can make sense to anyone if they put the time into learning it. I'm trying very hard to understand what you're saying, but there doesn't seem to be any logical connection between any of your arguments and your conclusion. This also makes no sense to me. Do you agree that supernovae can create BH's or not? A young student is trying to simplify the fraction 16/64. He notices that there's a six in the numerator and denominator. He remembers from class that you can cancel numbers that appear in the numerator and denominator. This is how he solves the problem: [math]\frac{16}{64} = \frac{1 \! \! \not{} \! 6}{\not{} \! 6 4} = \frac{1}{4}[/math] This is the right answer, as you can check, but the logic the went into obtaining it was faulty. Right answer, wrong reason. I don't understand. All I said was that this is the way BH's usually form, by our current understanding. That's all you need? I'd be very curious to watch you create a black hole with your finger... from a safe distance of course. From Mars, maybe. What energy to reduce its volume? You're jumping from one seemingly disconnected point to another. http://en.wikipedia.org/wiki/Type_II_supernova#Core_collapse All the links you'll ever need can be found in the citations of that article. I thought I already explained that collapse becomes inevitable at 9/8 the Schwarzschild radius. I'm also not completely sure what point you're trying to make. Thank you, o' chosen one, for gracing us commonfolk with your vast intellect. Okay. I agree with you that such a radius does indeed exist. Why would that automatically translate into a smaller event horizon? Explain how you're getting from A to B. I agree that the EH will be smaller, but I still don't see the logic here. Energy doesn't "move" anything. Energy is a property, not a thing. Why does that translate into a smaller event horizon? This also makes little sense.
  13. I agree with the conclusion, not the logic that went into forming it. Your explanation still makes no sense to me. A sometimes but not always creates B. Therefore A never creates B. That's probably the worst logic I've ever heard.
  14. I was being a bit sloppy with my language earlier when I called a Kerr BH a "rotating" BH. I should have been more precise and just called it "a BH with angular momentum." Unfortunately this isn't nearly as easy to explain as simply calling it "rotating," because the latter evokes nice (albeit probably misleading) imagery in the mind. Yes, but earlier you were saying that you must add energy to form a black hole, which is simply not true.
  15. Except the event horizon is not a "thing" that requires energy to move. It's a location in space. Black holes do not have extended volumes, so it doesn't really make sense to think of it as "spinning." It's probably more apt to just consider it an intrinsic property, much like spin in quantum physics. Nothing is "really" spinning, but the angular momentum is still there.
  16. That's not how black holes form. They (usually) form when the core of a large star collapses in on itself due to its own gravity. There's no "added energy." If anything lots and lots of energy is lost because the outer layers of the star will (usually) explode in an event called a supernova. Also, just to add to the conversation, the Schwarzschild radius is not the radius at which gravitational collapse is inevitable. That actually occurs at [math]R=9GM/4c^2 = 9 R_S / 8[/math], which is a bit larger than the Schwarzschild radius. At that radius the internal pressure required to prevent gravitational collapse becomes infinite. No problem
  17. I don't understand the logic that went into this, but you're correct. A black hole with angular momentum will have a smaller event horizon than a non-rotating black hole with equivalent mass. The event horizon of a rotating black hole is given by: [math]R_{EH} = \frac{GM}{c^2}+ \sqrt{\left ( \frac{GM}{c^2} \right )^2 - \left (\frac{J}{Mc} \right )^2}[/math] where M is the BH's mass and J is its angular momentum. As you can see, adding angular momentum shrinks the event horizon. The maximum occurs at J=0, which is equivalent to a Schwarzschild BH with its event horizon given by the Schwarzschild radius. It's not quite that simple. The event horizon of a Kerr BH is no longer given by its Schwarzschild radius -- it is given by the equation above. In the case of Kerr BH's we also have a second, larger horizon to deal with called the ergosphere. Inside the ergosphere everything must rotate with the BH. Both the ergosphere and the event horizon shrink with increasing angular momentum.
  18. Are you watching the same video as me? When did anyone say otherwise? This seems very tangential. To prove any of what? I have no idea what you mean by "complimentary forces" and "frame forces." I've never encountered those terms before.
  19. I'm sorry to tell you, but you're not going to get any direct meaningful responses to posts like these. It's so full of vague concepts and misconceptions that you're better off addressing what isn't wrong with it than what is. I think you need to start from scratch, ridding your brain of any popsci analogies/explanations you may have come across. This again makes no sense. I don't know what you mean by "a grid," or "disables GR geometry." Such a terms are far too vague to be meaningful. Plus, there is space and time at the event horizon. Who told you there isn't?
  20. Math is the only way to unambiguously, quantitatively, numerically predict something. Math is the language of physics. Physics consists of mathematical models compared with experimental/observational data. Below is a video you may find informative. Pay close attention to the part at 5:00, where he discusses vague theories and why they are not scientific.
  21. Frustrating income That's all well and good. It's good to be intrigued by the unknown. Unfortunately, knowing how to push the boundaries of the unknown takes years and years of learning and training. It's based on General Relativity, which is so far the best, most accurate theory of gravity we have. Extrapolating our theories to the unknown is part of physics. You take what's known, extrapolate, then compare to reality. A good approximation of empty space is intergalactic space, which is indeed approximately Minkowskian. This is what I meant by ill-defined nonsensical questions. I don't know how to answer because it's not really a meaningful question. I don't know what this is supposed to mean either. Geometry is geometry, not vectors. Vectors can be useful mathematical objects, but they certainly don't define the geometry of spacetime. This also makes little sense to me. This doesn't make any sense either. At least, it's a poorly formed question. No motion according to who? Why would there need to be motion for curvature? Vectors are mathematical objects. There are types of vectors that have absolutely nothing to do with motion, relativity, or even physics. I can't follow this either. That's kind of a problem if you ever want to actually learn any physics. Physics is not philosophy. Physics is mathematical models of reality, which can be falsified by experiment. I don't really know if I like that description. It seems to imply that energy-momentum causes spacetime curvature, which is simply not true by any common understanding. Einsteinian curvature and energy-momentum are equivalent, i.e. if you have one you have the other. Asking which causes which is sort of nonsensical. They both cause and effect each other. The geometry effects the matter, and the matter effects the geometry.
  22. I recommend purchasing an introductory GR textbook. Asking questions usually isn't the difficult part -- it's knowing which questions to ask that can be hard. A good textbook will do that for you. Otherwise you might end up wasting people's time by asking nonsensical or ill-defined questions. Schutz and Hartle, together, are probably your best bet. Schutz focuses more on the underlying math, has a wonderful section at the beginning to go over special relativity, vectors, dual vectors, tensors, etc., for people who may not be familiar with differential geometry. The first half gives you a great intuition for the notation, the basics of differential geometry, and the ideas that led to the Einstein Field Equations. The second half is about solutions to the field equations, approximation methods like linearized gravity, gravitational waves, etc. Hartle focuses mostly on solutions to the EFE's, and how to extract meaning from different metrics. My favorite book on GR is Carroll's, but it may be a bit beyond a first-time-learner's level if they aren't already somewhat familiar with the formalism. For reference texts, MTW and Wald are great. MTW goes over hundreds of topics in great detail, though it is admittedly a bit outdated. Wald is more up to date and has a very formal mathematical approach to things. If you have any specific questions, this forum can often be very helpful. There are a number of people here who are familiar with GR. For very technical questions, I might redirect you to the physics stack exchange.
  23. You didn't "predict" it, you just stated it. That's not the same thing. If you wanted me to, I could go through all the calculations in GR which actually predict (i.e. numerically, quantitatively, non-ambiguously) that spacetime converges to a singularity as t goes to zero. Can you do the same with your ideas? Unfortunately, this is because your "points" are rather vague and ill-defined. It's hard to address questions that don't really make much physical sense. If you had asked more concrete questions then I would have given concrete answers to those questions. Instead, your OP seems more like existential musings rendered into prose. I did the best I could with what you provided -- I gave concrete answers to the general sentiment of the post. If you want me to go through line by line and address each point individually, my response will mostly consist of "please define X," or "X doesn't make sense," or "what do you mean by X?"
  24. General Relativity says that energy-momentum and spacetime curvature are equivalent. Neither "creates" the other. The field equation of GR is: [math]G_{\mu \nu} = \frac{8 \pi G}{c^4} \, T_{\mu \nu}[/math] the left hand side is spacetime curvature, T is energy-momentum density, and they are related by a constant. As for quantum gravity, the straightforward approach you would expect to use for a quantum field theory of gravity simply does not work. For the other three forces + matter, you take the Lagrangian of the theory and plug it into the path integral. After some very clever and tedious calculations you will be able to use this to make numerical predictions about different types of interactions that might take place by using a process called renormalization. It was mathematically proven a number of years ago that GR simply is not renormalizable. I.e. QFT and GR are simply not compatible as-is. Either our theory of gravity needs to be reconsidered, or our approach to QFT, or both. There are a number of approaches which purport to solve this problem, String Theory and Loop Quantum Gravity being the most well-known, though none has been completely successful. That being said, we are not completely at a loss. There are a number of things we can do which we can be reasonably confident about. For example, semi-classical gravity, where the stress-energy tensor in the GR field equation is replaced by the expectation value of the stress-energy operator: [math]G_{\mu \nu} = \frac{8 \pi G}{c^4} \, \langle \hat{T}_{\mu \nu} \rangle[/math] This gives an approximation method for finding the gravitational field generated by a quantum field, though we are still considering spacetime as a classical object. We are also able to do QFT calculations on curved background spacetimes, giving us a good approximation of how quantum fields behave in the vicinity of, for example, a black hole. This is how things like Hawking radiation and black-hole entropy are rigorously analyzed. I believe Strange answered your question regarding the Big Bang. GR predicts spacetime was a singularity at t=0. I.e. GR predicts that space and time simply did not exist "before" t=0. This obviously seems a bit unphysical. Until there's a successful quantum theory of gravity we probably won't know much about what was actually going on.
  25. Good point. It's hard to sneak 50 useless posts past everyone. That seems like a simple problem to fix though: no exceptions. Everyone needs to stick around until the quota is met. That would ensure two things: 1) that members aren't signing up only to start religious debates, and 2) that they actually have some knowledge or curiosity about science, which is, after all, the theme of the website.
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