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Author | Topic: Did the expansion rate of the universe exceed lightspeed? | |||||||||||||||||||||||||||
cavediver Member (Idle past 3671 days) Posts: 4129 From: UK Joined: |
It might be possible to put a non-positive definite metric on the sphere -- I don't have enough intuition about pseudo-Riemannian manifolds (or even a good basic knowledge) to determine whether the 2-sphere can be a pseudo-Riemannian manifold. Sure - coming up with a p-R metric on a given topolgy is not that difficult. Making it a solution of GR is the hard part! The closed FRW space-time is topologically a 4-sphere, but you still get the two singularities.
I mention this, because I can change the model from a sphere to an elliptic paraboloid (look it up to see what it looks like) in which our closed 1-d space expands forever; however, I think I've read that if the expansion does go on forever, then the spatial dimensions cannot be compact -- space must go on for infinity. So either an elliptic paraboloid cannot be given a Lorentzian metric consistent with GR, or 4-manifolds are different than 2-manifolds. In FRW space-time, then the perpetually expanding solutions are spatially infinite. However, you can compactify them using non-trivial spatial topology. Your elliptic paraboloid is essentially de-Sitter space, which is geometrically finite but expands for ever. The de-Sitter source is the cosmological constant, and the FLRW extension of FRW gives the same possibility, where we can be closed, yet expand for ever - by virtue of the CC dominating over the mass content.
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Straggler Member (Idle past 93 days) Posts: 10333 From: London England Joined: |
Cheers for your very clear and patient explanation. I think I amstrting to get it.
Now I will try and tackle Cavediver's last post!!
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Straggler Member (Idle past 93 days) Posts: 10333 From: London England Joined: |
I think I get the 4d velocity vector and the limit implied by the length of this. I also think I get the difference between a massles particle and a body with rest mass with this way of thinking of things.
The part that I don't get and would appreciate some further explanation of is -
Stationary observers watching you are still moving through time as normal, so you do not appear to have the near infinite velocity you are experiencing. They will see your vector as tipped 45 degrees, equal amounts in time and space. This is what we usually call 'the speed of light'. The idea of moving in time at the speed of light is in itself quite bizzarre.... So what does this tell us about the rate of the expansion of the universe? Or is the point that I was originally missing the very fact that this has nothing to do with the rate of the epansion of the universe and that the two have absolutely no bearing on each other?
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cavediver Member (Idle past 3671 days) Posts: 4129 From: UK Joined: |
but the short answer is that the forces of gravity cancel out. Careful - although a test particle will not be accelerated in any direction (obvious from simple consideration of symmetry), there is certainly curvature. In a space of uniform density, the actual concept of 'gravity' is not applicable, and one should stick to thinking in terms of curvature.
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Explorer Junior Member (Idle past 5896 days) Posts: 24 From: Sweden Joined: |
I must admit you lost me there again, Cavediver... lol. But please dont make an effort to further explain. I will understand in time. It might be that I actually did understand it but never understood it. How is that for a verbal paradox
One of my original questions... what would happen if "something" went faster than light speed? We have concluded that no one would detect it , right? But would there be any other changes to "it"? What would happen to the relative time IF something went FTL?
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Chiroptera Inactive Member |
Heh. I had to look up what FLWR meant. But thanks; I've learned something. Maybe I'll even become smarter than ICANT!
...Onward to Victory is the last great illusion the Republican Party has left to sell in this country, even to its own followers. They can't sell fiscal responsibility, they can't sell "values," they can't sell competence, they can't sell small government, they can't even sell the economy. -- Matt Taibbi
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cavediver Member (Idle past 3671 days) Posts: 4129 From: UK Joined: |
The part that I don't get and would appreciate some further explanation of is... Sorry, will have to leave this for now as I must work. But this is more difficult to understand.
So what does this tell us about the rate of the expansion of the universe? Nothing
Or is the point that I was originally missing the very fact that this has nothing to do with the rate of the epansion of the universe and that the two have absolutely no bearing on each other? Yes. Edited by cavediver, : No reason given.
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cavediver Member (Idle past 3671 days) Posts: 4129 From: UK Joined: |
One of my original questions... what would happen if "something" went faster than light speed? The point is - what does this mean? If travelling at the speed of light means you reach any destination in zero time, then what can 'faster' possibly mean? Whatever it is, it is something that cannot be described as a speed or velocity.
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Chiroptera Inactive Member |
what would happen if "something" went faster than light speed? Good question. Unfortunately, I don't think we have any real theories to tell us what would happen. Now in the case of the galaxies moving apart, the appearence of "motion" faster than light is kind of an illusion -- the distance between the galaxies is increasing at a rate faster than the speed of light, but the galaxies, in a sense, aren't really moving in space. The moral of the story: an change in the distance between two objects isn't necessarily due to spatial motion. Or something. ...Onward to Victory is the last great illusion the Republican Party has left to sell in this country, even to its own followers. They can't sell fiscal responsibility, they can't sell "values," they can't sell competence, they can't sell small government, they can't even sell the economy. -- Matt Taibbi
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Straggler Member (Idle past 93 days) Posts: 10333 From: London England Joined: |
Well that wraps things up strictly in terms of the OP I guess!!
If you do get a chance to explain further on the stationary observer's view I for on would be interested to hear this. Anyway - Thanks for your time so far. Interesting stuff.
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Dr Adequate Member (Idle past 312 days) Posts: 16113 Joined: |
One of my original questions... what would happen if "something" went faster than light speed? We have concluded that no one would detect it , right? But would there be any other changes to "it"? What would happen to the relative time IF something went FTL? Tachyons. Physics is weird.
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Explorer Junior Member (Idle past 5896 days) Posts: 24 From: Sweden Joined: |
Oh, yes... I remember those from some books I have read. Weird indeed.
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compmage Member (Idle past 5180 days) Posts: 601 From: South Africa Joined: |
quote: I was thinking the same a while ago when reading another thread here somewhere. Am I correct in saying that during the early dense phase of the universe the curvature was virtually the same everywhere? Or am I completely off the mark due to my layman's understanding?
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cavediver Member (Idle past 3671 days) Posts: 4129 From: UK Joined: |
Am I correct in saying that during the early dense phase of the universe the curvature was virtually the same everywhere? Yes, although we believe this is also true today at the largest scales of the Universe. Galaxies and clusters just make up localised bumps in the otherwise smooth curvature. These bumps were originally just the size of quantum fluctuations, but have been inflated and expanded into the current large-scale structure!
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LucyTheApe Inactive Member |
Percy writes: Even though the very early universe was incredibly dense, certainly sufficient to produce a black hole, it was incredibly dense everywhere throughout the universe. This means the net gravity at any given point in the early universe was the same, approximately zero, since equal amounts of matter existed in all directions. I'm not sure if I understand what your saying here Percy. If all matter came into existence at the big bang, then so did gravity. And the center of gravity would have been at the center of the big bang. If the universe expanded symmetrically the center of gravity is still in its original position and the total amount of gravity hasn't changed. But even if the universe expanded asymmetrically there's still a point in the middle of the universe that is the center of gravity with the same pulling force it had to start off with irrespective of the magnitude of the expanding universe.
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