Simultaneity of events inside a singularityby Alyx.Vox Tags: dimensionless, relativity, singularity, space, time 

#1
Jan2813, 04:53 PM

P: 5

Hello,
I was wondering if the following idea had been proposed in one form or another within a scientific community. Provided that the space within the singularity is dimensionless, that being 0 in length on all the axes (is it?) the following is in order. From this follows that the Planck's Length is zero, therefore the Planck's Time is zero as well. All that means that if whatever happens, if it happens at all inside singularity must happen at the exact same instance as all the other events happening inside the same singularity (and every other singularity as well). Now, don't be too quick on throwing rotten tomatoes at me. My expertise lies within the realms of computer science. I am not educated into physics formally if you don't count highschool and my general interests (I might get a degree later on, however unlikely that seems to be). My thought rests on one assumption only: the lack of dimensions inside a singularity and I'm wondering if I'm wrong about that. If that assumption is correct the train of thought should be correct as well. Thank you. 



#2
Jan2813, 05:03 PM

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PF Gold
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#3
Jan2813, 05:03 PM

P: 181

If we can't talk about an inside of a singularity, any physics discussion there would be speculative, since we have no theory to guide us. 



#4
Jan2813, 05:25 PM

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PF Gold
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Simultaneity of events inside a singularity 



#5
Jan2813, 05:39 PM

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As others have explained, the question doesn't make sense within the theory of general relativity. However, there are a couple of related questions that the OP may be interested in, eg. the classification of singularities as spacelike or timelike, and the BKL conjecture for spacelike singularities.
"1. The first part of the conjecture states that spatial points decouple as one goes to a spacelike singularity in the sense that the evolution can be described by a collection of systems of ordinary differential equations with respect to time, one such system at each spatial point. (“A spacelike singularity is local.”) 2. The second part of the conjecture states that the system of ordinary differential equations with respect to time describing the asymptotic dynamics at any given spatial point can be asymptotically replaced by the billiard equations. If the matter content is such that the billiard table has infinite volume, the asymptotic behavior at each point is given by a (generalized) Kasner solution (“Kasnerlike spacelike singularities”). If, on the other hand, the matter content is such that the billiard table has finite volume, the asymptotic behavior at each point is a chaotic, infinite, oscillatory succession of Kasner epochs." http://relativity.livingreviews.org/...es/lrr20081/ 



#6
Jan2913, 05:52 AM

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To lessen the confusion, let me use different names and call r = T and t = Z. The Schwarzschild metric is then ds^{2} = (1  2m/T)dZ^{2}  (1  2m/T)^{1} dT^{2}  T^{2}d^{2}Ω where d^{2}Ω is solid angle. T^{2}d^{2}Ω is still the metric on a sphere, but the radius is now T. As T goes to zero the sphere shrinks to zero circumference and zero radius. Rearranging things slightly, ds^{2} = (2m/T  1)^{1} dT^{2}  (2m/T  1)dZ^{2}  T^{2}d^{2}Ω And approximating T ≈ 0, ds^{2} = (T/2m) dT^{2}  (2m/T) dZ^{2}  T^{2}d^{2}Ω What is happening? Inside the event horizon the spacetime is no longer time independent. Rather it has a translational symmetry. In fact the spatial part of the metric has cylindrical symmetry. It's a world in which the radius is collapsing, but the distance along the axis Z is stretching. Particles that came in at different times t will hit the singularity at different places Z. 



#7
Jan2913, 06:32 AM

P: 5

A lot of different explanations were given, but I think this one...
Now, the question is: if they all happen at the same time, but not at the same place... Then where do they happen? Multiuniverses? Other dimensions? I have very little to no knowledge of quantum mechanics, so that part of the discussion is over for me, at least for the time being, but please be free to try and elaborate it to me if you feel the need and I'll try to understand them on my part (hmm, I thought nobody understood quantum mechanics :P ). Oh, yes, one more question concerning Planck's Length. In the context of the singularity "prior" to Big Bang, could it be that Planck's Length was initially set just as any other natural constant and that it "was" therefore undefined "before" the BB? 



#8
Jan2913, 08:30 AM

P: 16

The Singularity and the Big Bang Bang are the biggest unsolved problems in modern physics. The closest thing to the Big Bang that we can observe is about 300000 years after the big bang (the cosmic microwave background radiation). We only know that the universe was expanding from some point but we don't know what was the big bang what caused it, how it hapen, was there space and time, were the laws of physics valid and so on. In the begining physicist were thinking that the BB was some event from which everything including space time and the laws of physics appeared from nothing and it was the begining of everything. However this was only an assumption and nowadays many theories as Inflation, String/MTheory discribe the big bang as an event happening in much larger Universe and possibly only one of many such events. Nothing of this is proven or well known it can turn out to be anything. BTW you can try to search in youtube for Leonard Susskind's Lectures(General/Special Relativity,Quantum Mechanics, Classical Mechanics, Cosmology, Particle Physics). They are very very good source of real physics unlike the most things that are on the internet today. I am just like you Computer Scientist interested in physics so in my spare time I watch them sometimes. You can find them interesting too. The best thing is that they are made for people who know math and want to see the real physics but at the same time don't have too much time to spend.(They tell you stuff realy fast) 



#9
Jan2913, 09:23 AM

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As for "where" all those events happen, they happen in spacetime. There's no need for multiuniverses or other dimensions. Inside the event horizon, "space" is infinite, so there's plenty of room for an infinite number of events that all happen "at the same time". (A technical point: all of these statements are really dependent on adopting a particular set of coordinates to describe spacetime inside the event horizon. There are other coordinates that have different properties: for example, there are coordinates in which "r" is still spacelike inside the horizon, and "space" is not infinite inside the horizon, and events with the same "r" coordinate don't all happen "at the same time". So things are actually even weirder than we've been describing. ) 



#10
Jan2913, 10:46 AM

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#11
Jan2913, 11:37 AM

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Quantum mechanically, as has already been said, we don't have a good theory, and we can really only speculate about what happens to spacetime once curvature gets large enough (roughly, when the radius of curvature of spacetime gets small enough to be of the same order as the Planck length), or whether "spacetime" is even the right description at that scale, as opposed to something completely different. 



#12
Jan3013, 10:41 AM

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#13
Jan3013, 11:00 AM

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Outside the event horizon, it is possible to maintain a constant r, and not proceed toward the singularity. The force required to hold constant r approaches infinity as r approaches the horizon (from outside; from inside, even infinite force would do no good). 



#14
Jan3013, 11:15 AM

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Perhaps this will clarify somewhat: (1) Outside the event horizon, a curve of constant r (and constant theta, phibut I'll assume throughout this post that the angular coordinates are constant) is timelike: that means it can be thought of as describing "a point in space" existing for an infinite time (from t = minus infinity to t = infinity). "Space" outside the horizon extends out to r = infinity, so "space" is also infinite outside the horizon; we can think of a curve of constant t as describing a "space" extending from r = 2M (the horizon) to r = infinity. (2) The event horizon itself is a curve of constant r = 2M (where M is the mass of the hole and G = c = 1) which is null: it describes an outgoing light ray. (3) Inside the event horizon, a curve of constant r is spacelike: that means it can be thought of as describing an "instant of time" that extends infinitely in space (from t = minus infinity to t = infinity). If we want to emphasize this, we rename the coordinates inside the horizon, r > T and t > R, and we say that a curve of constant T describes an instant of time that extends infinitely in space from R = minus infinity to R = infinity. 



#15
Jan3013, 01:22 PM

P: 5

Well all I learned from this is that I'm quite a dummy when it comes to anything outside of classical mechanics in the context of physics. All this is starting to make my brain hurt...



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