Watsisname wrote:Source of the post Example where this doesn't work in general relativity:
A classic test of general relativity is the gravitational lensing of light. The revelation is actually not that light rays bend, but that they bend twice as much! The Newtonian calculation predicts half of the correct lensing angle. Using general relativity and treating the effect as arising from time dilation also predicts half of the correct angle. Einstein himself initially fell for this trap when predicting the bending of light around the Sun (and was lucky to fix this before the observation was made!) The correct calculation requires the complete Schwarzschild metric where both time and space are distorted, and demonstrates that the spatial geometry is not Euclidean.
Watsisname wrote:Source of the post So I don't think it's good to be so married to a model as to avoid the potential for better ones. A better model describes a wider range of phenomena more accurately.
Terran wrote:Source of the post I tried to find Einstein's original equation to compare to the Schwarzchild metric but unfortunately the internet isn't very helpful. Do you by any chance know the equations for that model that predicted 1/2 what it was observed to be?
Terran wrote:Source of the post I don't doubt they will get the right answers, I just feel that they might be interpreting them incorrectly, like that story with the blind men and the elephant, but in reverse. Like creating the math equations for inertia but saying thats because mass gets tired, you get the right predictions but you answer with incorrect conclusions.
Terran wrote:Source of the post But it still isn't sitting with me the fact that you can observe said spatial distortion. A spatial distortion would be a topological distortion and would only be observable by an outside observer.
Perhaps if the intrinsic nature of the curvature created a compression and expansion but not a deflection... To make my life easier I reduced major equations to simple geometric ones.
Terran wrote:Source of the post And with quantum mechanics, it looks like what you would expect with multiple time components
Terran wrote:Source of the post yes, I could just be seeing what I want to see, but then again, if everyone saw the same thing no one would question if it was wrong or right, so I am going to try to prove them wrong, if they are wrong then I am right, if I am wrong they are right, I guess we'll see which is it in the future XD
Watsisname wrote:A-L-E-X wrote:Source of the post Yes, I love math too! Which is why I was so puzzled by it being called "gross." I mean raw sewage is gross (or sewage of any kind)- but math?! No!A-L-E-X wrote:Source of the post How long will it be before we understand the details of the collapse and rotating black holes do you think? Do we need a workable theory of quantum gravity first (perhaps that will also settle the question of black hole cosmology too.)
I think theorists are very slowly getting there, but it's an exceptionally difficult mathematics problem made more difficult by the weird property of rotating black holes which causes their interior geometry to depend on what happens in the future as well as in the past.
You can get a sense for why this is the case just by looking at the Kerr metric as is -- things that fall into it never hit the singularity, but rather cross relativistically with more matter falling in -- including itself. You end up with three singularites -- the initial one at the center, plus a "past" singularity which fell in after the hole formed but before you, and a "future" singularity which is coming in after you. Thus the interior of the black hole depends on what happens in the future!
That property still becomes relevant when studying what should actually happen in a real rotating black hole, not just the Kerr vacuum solution.
Rotating black holes are weird!
A further difficulty is, as you said, what actually happens to the matter distribution as it approaches singularity conditions, or when the space-time curvature becomes very large. A huge hurdle here is that different researchers have all sorts of ideas on how to approach the problem (how to bridge toward a theory of quantum gravitation), but they are enormously difficult to test experimentally.
So for the time being, when asked what really happens in an astrophysical, rotating black hole?A-L-E-X wrote:Source of the post I saw you were using transcendental math up there, what's your opinion of Stephen Hawking using Imaginary Time to eliminate the Big Bang singularity problem? This would also be workable for black holes.
I'm not too knowledgeable on this, and I'm definitely not as smart as Hawking, so I wouldn't know what to conclude about it. Sometimes very complex problems may have elegant solutions, but I have a difficult time knowing how that approach would be helpful for this one.
Watsisname wrote:If the gravitons can't escape, then they don't generate a black hole, and so they escape. If they escape, then they generate a black hole, and so they can't escape.
Paradox? It sure seems that way! Asking how gravitons escape a black hole is a bit like asking how gravity escapes itself -- a quick road into an endless loop. How do we break the loop? Abandon the notion that gravitons must escape from anything. Say instead that they are what make the black hole! Gravitons, or the fields they generate, are what give the marching orders to other masses in the vicinity.
Thinking in the context of general relativity (without gravitons) may help. How does an object near a black hole "know" that there is mass hidden away inside the horizon? It doesn't! It only knows the simplest rule: "always move straight". It moves on a locally straight line according to the space-time geometry of its immediate vicinity, and that geometry is warped. Why is the geometry warped?
The field equations of general relativity say that the singularity of the black hole distorts the geometry immediately around it, just like poking at a rubber sheet. But that distortion can't be localized. The singularity can't just cause a tiny dimple that suddenly cuts into flat geometry. Just as how your poking into a rubber sheet distorts the whole sheet, the distortion around the singularity must further distort the geometry around that, reaching out until the whole geometry is warped in a smooth manner given by the Schwarzschild metric. This is how the singularity extends its influence beyond the event horizon. It doesn't violate the one-way rule of the horizon, it makes the one-way rule of the horizon, by generating the geometry.
A quick detour:
We now know that there are gravitational waves, and that those also move at the speed of light. But gravitational waves definitely do not escape from inside a horizon. This is because gravitational waves are self-propagating changes in the space-time, rather than the static geometry attributed to the source mass. So they must follow the rules of the geometry that already exists around their source. They can't climb out of a black hole if they were generated inside one -- they are trapped.
In fact this must happen anytime two black holes merge together. Some of the gravitational waves will spiral around inside the resulting black hole and make a new, particularly nasty type of singularity -- one which not only has infinite curvature, but infinitely rapidly oscillating changes in curvature, like the function y=sin(1/x)/x. Those who read Kip Thorne's Science of Interstellar book may have seen it as the "BKL singularity".
A-L-E-X wrote:Source of the post Wat, that looks like something Einstein might have scribbled
A-L-E-X wrote:Source of the post Now I see why what you and Doc said and what I believe is the most elegant solution to all this, a universe in which past, present and future coexists. So you actually only have one singularity, but because of the way we perceive time, it seems like three. The three parts would be linked together through time but would really be one.
A-L-E-X wrote:Source of the post
Wat, what do you think of the theories that say that gravity leaks in from outside our universe (it is used to explain why it's so weak compared to the other forces.)
Watsisname wrote:A-L-E-X wrote:Source of the post Wat, that looks like something Einstein might have scribbled
It is not the longest calculation I've ever done, but it is definitely one of the most "oh god, the symbols..." reaction inducing ones. The calculation is basically just verifying that the expectation value of the energy of an electron whose wave function covers two states is just the average of the energies of those two states. Not particularly surprising or interesting, aside from the realization that a wave function for an electron being in two states is a valid solution in quantum mechanics. (In fact this is what happens during electron transitions -- the probability of being in one state or the other shifts smoothly over some transition time.)A-L-E-X wrote:Source of the post Now I see why what you and Doc said and what I believe is the most elegant solution to all this, a universe in which past, present and future coexists. So you actually only have one singularity, but because of the way we perceive time, it seems like three. The three parts would be linked together through time but would really be one.
I don't think this implies that past, present, and future coexist. It's analogous to saying that if someone dropped a coin in a wishing well yesterday, and you toss one in today, and another person will toss a third in tomorrow, then if those coins overlap it means yesterday today and tomorrow all exist simultaneously. I don't think that logically follows. They are different coins, and each being thrown into the well is a different event. The future event didn't influence the past or present events, it influenced the world lines that followed from them, because their paths are stuck in the well.A-L-E-X wrote:Source of the post
Wat, what do you think of the theories that say that gravity leaks in from outside our universe (it is used to explain why it's so weak compared to the other forces.)
It sounds good in a handwaving sense, not in a rigorous or predictively useful sense... at least as far as I'm aware. I don't spend much time thinking about theories if they are not testable.
Watsisname wrote:They could be, but I'm not aware of anything that convincingly pushes favor towards or against it besides personal philosophies and wish-casting. Like (or even highly related to) the various interpretations of quantum mechanics.
midtskogen wrote:In a multiverse one could perhaps argue that the past, present and future are fixed and predetermined, but our path through the multiple universes of the predetermined multiverse is not, perhaps fundamentally indeterminable.
Watsisname wrote:Source of the post Then calculate the deflection angle for when the light ray exactly skims the radial coordinate r=3GM/c^2.
Watsisname wrote:Source of the post Does it? Calculate the wave function for an electron in a 1-dimensional conductor of length L, using a theory with multiple time components. Normalize it and plot your result. What is the probability of a measurement finding the electron between L/3 and 2L/3?
Terran wrote:Source of the post Heres most of my math:
Terran wrote:Source of the post Maybe if I knew more calculus, and took more time on the problem, I might get something close to the actual solution. Don't have time and the patience to figure out how this math changes as the light changes position, I do realize thats one issue... But doing the math wrong at least gives me some insights into the problem, and its complexity.
Terran wrote:Source of the post Ah! You got me! I have made little effort into the math that would come from such a conclusion, so far what I have said was rather an observational "connection". Let me elaborate on my observation: