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10th April 2023, 12:04 PM | #1 |
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Black Holes, 10'th verse
So I'm still thinking about black holes, but hey, you can't blame a guy for thinking about holes, right?
Which actually brings me to a previous thing I STILL don't understand. Which probably won't surprise anyone, since I'm still not a trained physicist. So I'm probably missing something, and I KNOW that, so please explain slowly and in simple words, like for Pixie Of Key So: premise 1: gravity propagates at the speed of light. This was empyricaly proven recently when the gravity waves from a merger reached us at the same time as the light. Premise 2: inside the event horizon all light cones lead to the centre. Even light can't go towards the outside at all. It seems to me like if the matter were concentrated in the centre (either singularity, Planck density, or really anything smaller than the event horizon) then the information that there's some mass there distorting space couldn't actually reach any matter that just crossed the event horizon. That would involve something moving at the speed of light going outwards. Which it can't. And yes, I know, the event horizon is only a coordinate singularity, only in Schwarzschild coordinates, etc. You explained that to me already. I think I get it. But no matter what coordinates I use, information still can't go outwards without going superluminal. (Unless I'm missing something. Which I probably am.) It seems to me like the only way something behaving almost like one from outside could possibly form, is to never actually form a black hole. Like, stop at the Schwarzschild radius + 1 Planck length, or something like that. That's the only way that information that there's a big mass there can possibly flow outwards without going superluminal. As usual, I'm not actually Pixie Of Key or such, so I realize that if my understanding differs from that of actual physicists, it means I must be the one who's wrong. I'm not gonna go crackpot here and play Secret Socrates or anything. But that leaves me wondering WTH do I get wrong there. Anyone who can explain in simple words, I'd be most grateful. |
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10th April 2023, 12:12 PM | #2 |
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Very briefly, the fact that gravitational waves propagate at the speed of light doesn’t mean that the gravitational field behaves in the same way. In fact a steady state field doesn’t propagate at all.
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10th April 2023, 12:49 PM | #3 |
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If you look at from the quantum perspective, where gravity is mediated by a graviton, then you could make some rules like this:
1. gravitons act on photons 2. photons don't act on gravitons 3. gravitons don't act on gravitons Then what we will see is gravity bending the trajectories of light, but we won't see light bouncing off of gravity. Gravitons should be able to leave the black hole oblivious to what's happening to the photons. |
10th April 2023, 03:12 PM | #4 |
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Yes, but how would that steady field even form? The last wave to deform it to the final state, that last Planck length to the event horizon, would take longer than the age of the universe to get there. Or ok, it's there, it's stable. One more grain of sand falls in, event horizon expands. How does that information even reach the new event horizon, when all light cones lead to the centre?
As I was saying, not trying to claim I disproved it. I just feel like I'm missing something important there... Which I probably am... It's just... The black hole side of GR and some of QM is fascinating because it breaks my brain. I'm trying to understand what I'm missing. Like where did my brain fly off the hook and into dada land. |
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10th April 2023, 07:42 PM | #5 |
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I don't mean to be pedantic, but I recently learned that gravity waves and gravitational waves are not the same thing. What you meant was the latter. I don't really know how to answer your question though.
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10th April 2023, 07:52 PM | #6 |
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Heh. Kind of reminds me of when I was a kid and I thought a "gravity bomb" had to be some cool SF device where the explosion caused a burst of gravity that would destroy everything nearby, or something like that. How disappointing to learn that the phrase just means bombs that fall when you drop them because, you know, there's gravity. In other words, ordinary air-dropped bombs. |
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10th April 2023, 10:55 PM | #7 |
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10th April 2023, 11:57 PM | #8 |
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Well what is gravity exactly? Isn't it essentially just a curvature of spacetime? A field. If we think of spacetime as a kind of stretchy fabric, like spandex, gravitational waves pass through the fabric, but the wave is not the fabric and the fabric is not the wave.
I don't know if this helps answer the OP's question, but it's how I think about it. There is no experimental evidence for the existence of gravitons, and Wikipedia says the following:
Quote:
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11th April 2023, 01:07 AM | #9 |
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From the point of view of an outside observer the object never appears to enter the black hole, it just gets smeared out until it 'disappears' at the event horizon. Once inside it enters a closed area of space where every direction leads inside. In effect it has become part of the 'universe' inside the black hole.
Quote:
As an analogy consider a rubber sheet stretched out over an open frame with ball bearings sitting on it. Each ball pushes into the surface making the sheet curve downwards near it. If another ball gets close it will fall down the slope towards it. The sheet doesn't change shape unless a ball moves or somehow gets lighter or heavier. When it does the change in depression spreads out at a speed determined by the mechanical properties of the sheet. But once that has happened and the sheet settles into its new shape, any objects that are in or enter the changed area will be affected instantly. "But", you say "if an object falls into a black hole it can't get out or even send light out of the hole, so any information it had is lost!". Not quite. Its mass is still having an affect, only now it's combined with all the other stuff in the black hole with no distinction. So when you measure the mass of a black hole you are measuring everything in it, ie. the mass of the 'universe' inside the black hole. But that's just a single number, which makes sense if everything has been squashed into a 'singularity' with no structure to carry information.
Quote:
My speculation is that the 'black hole becomes a white hole at the other end' theory is correct. Our universe purportedly started out as a singularity much like the one speculated to be inside a black hole. Some calculations show a remarkable correspondance between the estimated amount of matter in the Universe and its size, which is exactly what you would expect if it was originally a 'black hole'. Also you can do a simple thought experiment where black holes gobble up all the the matter in the universe and then eat each other. The result would be an enormous black hole the size and mass of the universe! Everything inside it would be its 'universe'. It's amazing to think of these things happening at a scale so mind boggling that it's scary. And here we are, the result of some complicated chemical reactions that occurred on a planet after a big lump of ice smashed into it and created oceans of water, then over 3 billion years or so 'evolved' into creatures with conscious minds that are trying to make some sense of it all. Black holes may eventually turn out to be one of the least difficult things to understand about the Universe. |
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11th April 2023, 03:38 AM | #10 |
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It formed before the black hole did. It doesn't disappear when the black hole forms.
In electromagnetism there's something called Gauss's law. Basically, the amount of electric field passing through a closed surface is proportional to the amount of charge inside that surface. Doesn't matter how you rearrange the charge, it still applies. There's an equivalent law for gravity in GR as well. There are closed surfaces around the black hole, and those surfaces already have the information about how much mass is inside, even before the black hole collapses. So no information needs to escape, it's all already outside the black hole. And BTW, for the same basic reason, charged black holes also have electric fields (and if they spin, magnetic fields too). Photons don't need to escape, the information is already outside. |
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11th April 2023, 04:02 AM | #11 |
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From the point of view of an observer outside, sure. We already had that discussion, and I get it. I'm talking about a point inside the black hole this time. At some point as matter falls in, a point inside must get the information that oh, wait, some more matter fell even deeper inside, the space-time is even more curved. That's not mass that was already within that radius, it's a change that must be propagated back. But that essentially involves information travelling back in time, since r now acts as t.
And, assuming you mean Birkhoff's theorem, just like the shell theorem, and Gauss, I don't understand how that would help, since essentially it just integrates the vector field. It doesn't deal with how fast the information gets there. It essentially already is there. Which, again, is fine for the outside of a black hole, but doesn't answer how the information gets there in the first place for such changes inside the black hole. |
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11th April 2023, 06:27 AM | #12 |
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When you're talking about a flow of information taking place entirely inside the event horizon, the event horizon is not a barrier to that flow of information.
As Ziggurat explained, matter falling inside the event horizon is already known outside the event horizon, so its existence and its effect on the universe outside the event horizon does not involve a flow of information across the event horizon. So you are contemplating a conundrum that is not a conundrum. The idea that r acts as t inside the event horizon is a really bad idea, based on nothing more than pushing symbols found within the Schwarzschild metric form. That metric form has a coordinate singularity at the event horizon, so there is no continuity between the metric form outside and the metric form inside. Unless you wish to consider disconnected charts (which is the really bad idea), you must regard the Schwarzschild metric form outside the event horizon as the metric form for a completely different chart than for any chart that covers any part inside the event horizon. Which means that, although it is indeed possible to regard the Schwarzschild metric form as the metric form for a chart inside the event horizon, the Schwarzschild time and radial coordinates of that chart have absolutely nothing to do with the time and radial coordinates of the Schwarzschild chart outside the event horizon. Suppose, for example, that Alexander Morgan resides in Kansas City, Kansas and Morgan Alexander resides in Kansas City, Missouri. Saying "r now acts as t" inside the event horizon is a lot like saying that, when you cross the Mississippi River, "Alexander now acts as Morgan and Morgan now acts as Alexander". In reality, the Morgan Alexander on the east side of the river has nothing to do with the Alexander Morgan on the west side. |
11th April 2023, 06:55 AM | #13 |
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I'm not saying that the event horizon is a barrier to anything inside of it. I'm just saying that inside it the it the space-time is too curved for information from a point at r1 to get to a point at r2, where r1<r2<rs. No matter where you are at r2, you're outside the light cone from any point at r1. It's not that the event horizon is in the way, because obviously it's not; it's greater than both r1 and r2. The event horizon is mentioned there just to say we're inside it, where space-time is even more curved.
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11th April 2023, 07:33 AM | #14 |
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If r1<r2 and you are at r2 outside the light cone of an event at r1, then why should you care about that event at r1? You can't hear about it, sure, but it also can't affect you. To establish a conundrum here, you would have to explain why information needs to travel from some specific event e1 to some other specific event e2 that is separated from e1 by a space-like interval. |
11th April 2023, 07:50 AM | #15 |
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Hans believes that information about the mass of the black hole needs to travel across a space-like interval to observers, otherwise they will not be able to observe the gravitational influence of that mass.
The conundrum is, how can we observe the gravitational influence of black holes (and how can matter be attracted to black holes) if the information about their mass is trapped inside the event horizon. He's basically asking you to map the incomplete and inaccurate lay approximations of the actual physics back to the actual physics themselves, and then map them back out to a new lay approximation that while incomplete is at least accurate in regards to how information about the mass of a black hole is observed from outside the event horizon. As far as I can tell, Ziggurat has already done this. But since most of the mapping events take place on the other side of my event horizon of ignorance about physics, I can't really say for sure, or tell you how exactly it was done. My assumption is that information (about mass) isn't constrained by black hole event horizons the way the lay language seems to imply. Hans's assumption seems to be that the lay language suggests that the physics of black holes may not be what physicists say it is when they do physics. |
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11th April 2023, 08:10 AM | #16 |
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I'm saying it's kinda like this:
1. From outside, just to get that out of the way, since that's not what I'm asking: if, say, our sun collapsed into a black hole, as Ziggurat said, we as someone outside already have the space curvature for a mass there anyway. Assuming it's a circular collapse, no gravitational waves are needed (or indeed possible) for us to notice any difference. The mass inside a sphere with a radius of 1AU centered on the sun, which is all that influences us cf the shell theorem (or Birkhoff if you want to go GR) didn't change or anything. Space-time is just as curved for us as it was before. So that's not what I'm asking. 2. INSIDE the newly formed event horizon is where my understanding gets dicey. A point INSIDE the former sun would have to somehow "notice" that space there just got a lot more curved than before the collapse. Like, before it was chilling at, say, a comfy 20g (inside the sun, but not too deep) and now it just passed 1.6 trillion g as it went through the event horizon and it's going downhill (as in, steeper gravity well, or more g) from there. That's the kind of information I'm talking about there. Basically imagine one starship gets sucked into a black hole while fighting it as hard as it can with its impulse engines to delay the inevitable. Then 1s later another spaceship goes in from the other side going full impulse towards the centre. At some point starship 2 has gotten at a distance r1 from the singularity, while starship 1 is still at r2, where r1<r2. It too pulls starship 1 towards the centre. (I'm overlooking the rather important part that it's not a spherical distribution, but the basic principle applies.) Essentially my question is: how does starship 1 ever notice the pull from starship 2, since it's outside any light cone from starship 2? |
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11th April 2023, 08:37 AM | #17 |
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Hey, I have enough trouble understanding the actual physics. I just throw up my hands when it comes to understanding incomplete and inaccurate lay approximations to physics.
I think so too. Ah. You appear to have been taken in by some of those incomplete and inaccurate lay approximations. According to the physics, nothing much happens at the event horizon, just as someone who crosses the US Continental Divide doesn't notice anything particularly unusual. That continental divide concerns a global property: Does rain falling here eventually drain into the Pacific or the Atlantic? Local observations cannot answer that question. The event horizon of a black hole involves a global property: Is there any way at all for this falling raindrop to end up in an ocean other than the black hole? Local observations cannot answer that question. Presumably the gravitational pulls of starships 1 and 2 were affecting the trajectories of both starships even before either starship crosses the event horizon. They accomplish that by affecting the geometry of spacetime as quantified by the Einstein field equations. Their world lines are influenced by that geometry of spacetime. Their world lines continue to be influenced by the geometry of spacetime even after they have crossed the event horizon, and even after their actions are no longer able to influence each other. The geometry of spacetime records enough history of their past actions to influence their future worldlines. Whether a starship's influence upon the geometry of spacetime can happen fast enough to influence the world line of another starship depends on some complicated details. It sounds as though you may not be aware that a particle that crosses the event horizon on one side of the black hole can make its way around to the other side, remaining inside the event horizon the entire way and losing only a little "altitude" as it does so. The answer to your question depends upon details that are not made sufficiently precise by your phrasing of the question. To make your question sufficiently precise, you need to rephrase your question in terms of specific events, and you will need to provide impractically copious quantitative data concerning those events and also concerning the geometry of spacetime in which those events occur. Absent those details, the best I can say is that events separated by a spacelike interval cannot influence each other, whereas with events separated by a timelike interval it is possible for one of those events to influence the other. |
11th April 2023, 10:36 AM | #18 |
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Is that the "time becomes space" thing?
https://physics.stackexchange.com/qu...the-old-time-v I think one of Hans' assumptions is that the event horizon is a shell around some mass, but the mass is also concentrated inside that shell, so a smaller shell can be made around it, but still contains the same amount of mass as the larger shell. Is that a valid assumption? |
11th April 2023, 10:56 AM | #19 |
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hubble-telescope-black-hole report CNN
I don't know what caused these panelists to break up over a report on a black hole. Some kind of double entendre, perhaps? I also get the impression they're all "I don't get science and all this goes over my head, but it's kinda cool anyway." |
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12th April 2023, 08:32 AM | #20 |
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Well, more accurately space -- and at that only the radius component -- becomes time-LIKE, and time becomes space-LIKE. But then IIRC Clinger himself said in another thread that I should use that coordinate as time, if it's the one time-like, but that may well be one of the many things I misunderstood.
But basically the gist of it is that the universe has 4 dimensions: x, y, z and ct. Let's just focus on 2 of them for simplicity. The invariant is x2-(ct)2. Note the minus, unlike, say projecting a segment onto orthogonal coordinates, where you'd have a + (cf Pythagoras.) Inside a black hole, essentially the two switch sides. And yes, only in Schwarzschild coordinates. There are other coordinate systems that act differently, but we'd write a book if we go there. And I'm nowhere near qualified enough to write a book about GR or I wouldn't be asking dumb questions here in the first place Nobody knows if it actually is the actual time coordinate there, since nobody actually looked inside one. |
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12th April 2023, 08:37 AM | #21 |
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Never said anything special happens. Well, not in this thread. All I'm going on about this time is just that on one side space is less curved than a value, on the other side it's more curved.
It's like subsonic vs supersonic flow in a ram/scram-jet, if you will. It's still air, still made of the same particles, and obeys the same laws. Just in one setup pressure can propagate uphill, in the other it doesn't. Is all. But in a sense your continental divide analogy was already perfect. I'm only concerned with which direction stuff can flow. Just like in that divide. And in this case the stuff is basically any information. |
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12th April 2023, 08:40 AM | #22 |
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Well, after more thought about what I'm trying to say, and why (which I should have been doing before starting the thread), it's kinda like this: I don't expect that space gets more and more curved as you approach the singularity. I would expect that it more or less keeps those 1.6 trilion g from the event horizon all the way down, because once you get to that point, information, including gravitational waves, can only propagate in one direction, towards the centre. Information that more mass got in a smaller shell below your radius can't flow uphill.
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12th April 2023, 08:41 AM | #23 |
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Showerthoughts-mediated explanation:
We know from certain theories and their supporting observations that light is constrained to follow null geodesics in spacetime. And we know from certain theories and their supporting observations that mass concentrations define the curvature of null geodesics in spacetime. And we further know from these theories and observations that sufficiently dense concentrations of mass will define "circular" null geodesics at a certain radius from the center of that mass concentration. And we further know that as a corollary of this, null geodesics within that radius will be "more than circular". Therefore, we know that light falling within that radius will never again emerge beyond that radius. And light emitted within that radius will never emerge beyond that radius. Nothing in any of our theories or observations suggests that concentrations of mass cannot affect null geodesics beyond the radius at which light is constrained to "circular" or "more than circular" geodesics. No matter how dense that mass concentration happens to be. |
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12th April 2023, 08:45 AM | #24 |
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Not directly, no. All I'm saying is that distortions in space-time also propagate along the same geodesics. Which is what creates my problem.
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12th April 2023, 08:54 AM | #25 |
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Why are you saying that, though?
Nothing in GR predicts that mass will stop having a gravitational effect if it exceeds a certain density. Nothing we have observed suggests that this might be the case. The solution to your problem is to acknowledge that you're begging the question. |
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12th April 2023, 09:29 AM | #26 |
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Look, it's like this: imagine you're pumping an ideal gas into a tank. Nothing stops you from reaching ludicrious pressures, right?
Now imagine you're lighting an afterburner behind a scramjet. Like, mother of all afterburners, a lot of fuel, creating a lot of pressure. Can that affect the pressure uphill? No, because it's a supersonic flow and the sound waves that propagate that information can't travel faster than the speed of sound. There's nothing forbidding a higher pressure per se at the front of the engine. Just the pressure from the back of the engine would have to propagate as a wave faster than sound speed. THAT's what's preventing it. Same issue here. You have exactly the equivalent of that supersonic flow. Except here you'd need superluminal flow for the gravitational distortion to propagate uphill. |
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13th April 2023, 05:25 PM | #27 |
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No, because the gravitation is already defined when you get to the event horizon. Once inside it doesn't change for an outside observer. The gravity wave doesn't have to propagate uphill at all from inside the hole. If it did then we would be able to tell what was going on inside a black hole by detecting localized gravity sources inside it, which we can't. From our point of view any mass thrown at it never actually gets inside anyway, it stops at the 'surface'. At that point it is 'pulling' at space just like the same (total) mass would be from inside.
Going back to the rubber sheet analogy, a ball has a certain diameter that causes the sheet to be dragged down around its surface. We don't have to consider distortion of the sheet where it is touching the ball, because that part is stuck to the ball. (yes, analogies can only take you so far...). At the point where our ball becomes a 'black hole' it has stretched the sheet so far down that the sides are vertical. Nothing that falls in can get out because no matter how fast it orbits it can never gain height on a vertical surface. Inside the ball 'gravity' (slope of the rubber sheet) has no meaning, it's just an object with mass and diameter and that is all. According to thermodynamic theory the gravity at the surface of a non-rotating black hole is constant over its entire surface. So even if there were objects moving around inside it, they would have no external effect. The inside is its own universe, closed off from ours by the event horizon. It can't have any effect on us apart from its total mass and diameter (which have a fixed relationship to each other). When you combine that with the obvious conclusion that all the matter in the universe must be inside its own event horizon, interesting possibilities emerge. For example, what happens inside a black hole when matter is thrown into it? It gets bigger. That means the space inside it must expand. What do we notice about our own universe? It's expanding. Another thing we see is that our universe apparently originated from a singularity, with all matter and energy concentrated in an infinitely small amorphous point, just like is assumed to be at the center of a black hole. But what if that never actually happened? what if mass is constantly entering our universe and being smeared out in it, making the CMB that we interpret as originating in the 'big bang'? What if the real 'big bang' was the point in time when our universe was created by something in a larger universe (perhaps even our own one) becoming a black hole? According to big bang theory the Universe rapidly inflated from a singularity into a small universe that then formed stars and galaxies etc. like we see today, and the light from those stars is red-shifted due to slower further expansion. Telescopes are now getting so powerful that we can see galaxies from close to that time. I predict that in the future we will be able to see even further back, and the galaxies from before then will still look like they do today. Astronomers will react by pushing the inflation phase further back to account for this anomaly, rather than admit that there was no singularity that inflated. |
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13th April 2023, 05:34 PM | #28 |
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14th April 2023, 04:49 AM | #29 |
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If I thought you needed that analogy and STILL don't see why it applies, then, sorry, the problem is on your end: you're not qualified to be judging it or really posting here in the first place. The issue was already described in non-analogous terms before that, and it flew right over your head. That's why you got the analogy. So I'm not too fussed about that. I'll keep asking those who do understand. It was a very specific physics problem, so it's ok to not understand it. Posting just that your comprehension finally started and promptly stopped at "ooh, that looks like an analogy" is not contributing anything of value.
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14th April 2023, 04:50 AM | #30 |
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14th April 2023, 04:59 AM | #31 |
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A quick (less technical) digression...
There's a clearer picture of the black hole been published. It's still a bright do-nut around a dark centre, I assume it's light from the stuff being absorbed. Why does it form a do-nut shape rather than a sphere around the black-hole? Something to do with the black-hole rotating? |
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14th April 2023, 05:05 AM | #32 |
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That's not per se from the matter falling in, it's from the accretion disk. Matter swirls down the drain, so to speak, in a disc around the black hole, heats up, and that's what that doughnut glow is. (Well, there are also the beams at the poles, but you don't see those unless you're in their way.)
It tends to look more or less like a doughnut even if you're not looking directly perpendicular to it, because light bends around a black hole and you can essentially see the part of the disk that's behind it too. |
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14th April 2023, 05:30 AM | #33 |
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Yes, it's the disk bit I was wondering about. I suppose, thinking more about it, that it's because most of the matter is in the plane of the galaxy. If you see what I mean.
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14th April 2023, 09:23 PM | #34 |
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Well as I said before, the math breaks down once you get inside. It is presumed that the mass collects in the center as a singularity. Under those conditions gravity becomes even stronger as you go to the center. Light would still be able to move outwards, but would curve around more as it got closer to the center.
However there are theories that make quite different predictions. According to Knot Physics all the mass is concentrated at the event horizon, and the inside is 'flat' (ie. no local gravitational field), like the eye of a hurricane. If that is true then the only question is what happens to matter that was already inside when the black hole formed? If spacetime inside it is 'flat', then the answer is no change from what it was like before. A small black hole would be like a neutron star - extremely dense throughout. A very large black hole would have more reasonable density, perhaps not much higher than the space outside. Extrapolate to a black hole containing everything in the Universe and it would be just like it is now. Light and gravity waves would propagate just like they do now, and we would not notice any overall curvature of space due to the event horizon. Or would we? Planck evidence for a closed Universe
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14th April 2023, 11:31 PM | #35 |
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At least according to our models, it doesn't really matter how an accretion started, it ends up a disk. If it's a cloud going chaotically around, particles bump into each other, and momentum and angular momentum gets redistributed. Eventually it ends up as something where they don't bump into each other much, and that happens to be a disk.
Well, that's at least for the main disk. Of course there's also stars and even other black holes orbiting a supermassive black holes, and those go in other planes too. But it's rare for one to pass close enough to be outright gobbled by the black hole from another orientation. More often ("more" being relative) they pass through the edges of the accretion disk and interact with that one. |
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15th April 2023, 02:27 AM | #36 |
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Thanks for the info.
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15th April 2023, 02:52 AM | #37 |
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Yeah, had a thread about that some time ago. In fact, I'm fairly convinced that it would look exactly like what we see now, from big bang to big rip, with cosmic inflation and everything. In fact, the "dark energy" would be just us falling into it.
Last I remember, though, there the matter density math was barely off for a big rip, and a black hole universe needs a big rip. But I haven't followed that data in a long time, so I'm not sure if and how that has changed. |
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15th April 2023, 02:59 AM | #38 |
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15th April 2023, 03:03 AM | #39 |
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The problem there is that we don't yet really have a theory of quantum gravity. We have some quantum hypotheses, really. And it's kinda hard to do much about it at the moment, since at quantum levels gravity is pretty much homeopathic in strength at best, compared to the other forces. So it may be true, don't get me wrong, or it may not. We don't really know.
The idea of using uncertainty and the exclusion principle isn't limited to it, though. There are other ideas around that limiting maximum matter compressibility, even without going quantum gravity. |
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15th April 2023, 03:08 AM | #40 |
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In a sense ALL particles are variation on a theme. They're all resonances of the various fields, essentially. E.g., a photon is really just going in a circle in the magnetic and electric coordinates. IF there is any such thing as a graviton, yeah, I would expect it to be yet another variation on the same theme.
But it moving at the speed of light just tells us that it too has no mass, i.e., that it doesn't interact with the Higgs field. It really doesn't reveal any other similarity. Which may exist, don't get me wrong, but it's not how we'd determine it. |
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