3 dimensions of space and 1 of time

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I'm wondering if the perception of spacetime as "3 dimensions of space and 1 of time" is a symptom of our inability to maintain an objective view on the matter.

I believe the reason we separate them in our minds is because we seem to have some control over space but no control over time. But this is due to our limitations of velocity, right, not because spacetime is actually "3+1". Relative velocity is what gives control through space and time. Same thing, right? I mean, we don't even really have control over 3-dimensions of space. We only have control across Earth's surface and we only really have that control in 2-dimensions. We need to build machines (airplanes, etc.) to gain control of the 3rd dimension. We'd need another machine to gain control of the 4th. So couldn't we just as easily say that spacetime is "2+2"?

Do you think it would help us to view spacetime not as "3+1" or "2+2" but as it really is; as "4"?
 

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  • #2
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Experiments performed to date agree with the 3+1 model, not anything else.
 
  • #3
atyy
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http://arxiv.org/abs/gr-qc/0604027
Hamiltonian analysis of the double null 2+2 decomposition of Ashtekar variables
R. A. d'Inverno, P Lambert, J. A. Vickers

http://arxiv.org/abs/gr-qc/9510040
Covariant double-null dynamics: (2+2)-splitting of the Einstein equations
P. R. Brady, S. Droz, W. Israel, S. M. Morsink
 
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  • #4
Matterwave
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Well, time is definitely different. Whereas I can walk backwards and forwards in space with no difficulty, I can only move forward in time...unless H.G. Well's is right.
 
  • #5
atyy
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I suppose a spacetime is 3+1 or 2+2 if it is globally hyperbolic - are there physically important spacetimes that are not globally hyperbolic? I remember reading somewhere that the Schwarzschild solution isn't, but don't remember where, or if it is even true.

BTW, there is an interesting quote from Hawking about the canonical approach "However the split into three spatial dimensions and one time dimension seems contrary to the whole spirit of relativity. Moreover it restricts the topology of spacetime ..." http://books.google.com/books?id=pxA4AAAAIAAJ&dq=hawking+and+israel&source=gbs_navlinks_s
 
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  • #6
bcrowell
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  • #7
atyy
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Matterwave, I think your point hits the nail on the head as to why we make the 3+1 distinction. However, my point still stands. Our inability to travel backwards in time is OUR limitation and not a fundamental limitation of spacetime itself. Velocity moves us through space. Velocity also moves us through time - both forwards and back - IF we can acheive a relative velocity that equals or exceeds the speed of light. But we can't even gain enough velocity to leave Earth's surface without the aid of a machine. Doesn't it seem like we're projecting our limitations onto spacetime?
 
  • #9
atyy
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Matterwave, I think your point hits the nail on the head as to why we make the 3+1 distinction. However, my point still stands. Our inability to travel backwards in time is OUR limitation and not a fundamental limitation of spacetime itself. Velocity moves us through space. Velocity also moves us through time - both forwards and back - IF we can acheive a relative velocity that equals or exceeds the speed of light. But we can't even gain enough velocity to leave Earth's surface without the aid of a machine. Doesn't it seem like we're projecting our limitations onto spacetime?
While the 3+1, 2+2 or 4+0 views are all equivalent in certain regimes, I hope you know that the distinction between timelike and spacelike at every point in spacetime is absolute - it comes from the signature of the metric being 2?
 
  • #10
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When we make the 3+1 distinction, we are folliating one of the space dimensions as a hypersurface. So, we are actually trying to visualize "1 time dimension + 2 space dimensions." Wiki up '3+1 Formalism' and 'ADM.'
 
  • #11
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A good way of clearly seeing the difference between space and time is with the formula for computing the space-time interval in special relativity. The interval between two space-time events is the same for all reference frames. This interval is:
dS = sqrt (dX^2 + dY^2 + dZ^2 - dT^2)

Notice that the three space dimensions have + signs and the time dimension has a - sign.
The formula will not hold true if you put in four + signs or two + signs and two - signs.

I hope this helps clarify things.
 
  • #12
Matterwave
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Matterwave, I think your point hits the nail on the head as to why we make the 3+1 distinction. However, my point still stands. Our inability to travel backwards in time is OUR limitation and not a fundamental limitation of spacetime itself. Velocity moves us through space. Velocity also moves us through time - both forwards and back - IF we can acheive a relative velocity that equals or exceeds the speed of light. But we can't even gain enough velocity to leave Earth's surface without the aid of a machine. Doesn't it seem like we're projecting our limitations onto spacetime?
Our inability to reach the speed of light is not a practical limitation like space-travel, but a theoretical limitation put there by Special Relativity. According to SR, we will never be able to move at the speed of light. This speed limit is, as far as we know, absolute.
 
  • #13
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Matterwave, I believe the speed limit you are referring to is a restriction of matter, not spacetime itself. Black holes have a force that surpasses this speed limit. Entangled particles do to. And what information passes between two light particles that pass each other from opposite directions? All of these scenarios produce a net value that is greater than the speed of light and spacetime allows them all.

Kochanskij, I like the formula that you called upon. It speaks loudly and, although it leaves questions, it really puts those questions in a new light. I'll be pondering that one for a while. Thanks!
 
  • #14
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A good way of clearly seeing the difference between space and time is with the formula for computing the space-time interval in special relativity. The interval between two space-time events is the same for all reference frames. This interval is:
dS = sqrt (dX^2 + dY^2 + dZ^2 - dT^2)
But it would work equally well, wouldn't it, to make time the vector and length the scalar? Of course that would require a re-structuring of most equations.
 
  • #15
Fredrik
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But it would work equally well, wouldn't it, to make time the vector and length the scalar? Of course that would require a re-structuring of most equations.
That wouldn't actually change anything. If one of the terms in the line element has a different sign than the others, that variable takes the role of time in the theory regardless of what you call it.
 
  • #16
bapowell
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Black holes have a force that surpasses this speed limit. Entangled particles do to. And what information passes between two light particles that pass each other from opposite directions?
Black holes do not have a 'force' that surpasses the speed of light. Are you suggesting that they can accelerate infalling objects to greater than light speed? That's also not right. You should read up on some GR, the generalization of special relativity to non-inertial frames.

As far as being unable to surpass the speed of light: this is an axiom of special relativity. Surprisingly, it is not 'derived'. Special relativity (and its constancy of the speed of light) are not accepted theories because we've empirically noticed that, try as we might, we simply can't go faster than light. Instead, we test the consequences of relativity -- the consequences of a theory based on the supposition that there is an ultimate speed in the universe. The predictions of special relativity (and, by extension, general relativity) have been well tested (time dilation, photon deflection by stars, QED, etc...there are many examples.)

Lastly, your comment about entangled particles. Do you mean quantum entanglement of wavefunctions? If so, it's not immediately clear that entangled systems violate causality. Not my field, but I've read that the jury is still out on whether meaningful information can be transferred between the components of an entangled state.
 
  • #17
JesseM
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Lastly, your comment about entangled particles. Do you mean quantum entanglement of wavefunctions? If so, it's not immediately clear that entangled systems violate causality. Not my field, but I've read that the jury is still out on whether meaningful information can be transferred between the components of an entangled state.
It's definitely impossible for us to transmit information using measurements on entangled particles, see Eberhard's theorem. Whether or not there are some "hidden" FTL effects coordinating the behavior of the particles depends on your interpretation of quantum mechanics, Bohmian mechanics says there would be but the many-worlds interpretation says there wouldn't, for example.
 
  • #18
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Relativity says that no information can be sent faster than light. If we could, then a paradox would always result.
JesseM is correct in that we can never use quantum entanglement to send information faster than light.
Even at the event horizon or inside a black hole, nothing ever passes the locally measured speed of light. A photon will always pass you at the usual speed.
However, space itself can expand faster than light. It did so at the big bang during inflation. But still, this expansion can not be used to send information.

If an object or signal is sent thru a wormhole to another part of space, it could get there faster than light. This would lead to time travel into the past and all those paradoxes. So many physicists think wormholes would collapse so quickly that nothing could ever pass thru. It is still unknown if there is a way to hold a wormhole open using negative mass-energy.
 
  • #19
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It is still unknown if there is a way to hold a wormhole open using negative mass-energy.
You should read up on the http://arxiv.org/abs/gr-qc/9702049" [Broken].
 
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  • #20
JesseM
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You should read up on the http://arxiv.org/abs/gr-qc/9702049" [Broken].
This paper says that the Krasnikov tube also requires negative energy densities, and mentions that with multiple Krasnikov tubes GR would predict the possibility of closed timelike curves (so if you believe the chronology protection conjecture quantum gravity would somehow rule out this possibility)
 
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  • #21
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This paper says that the Krasnikov tube also requires negative energy densities, and mentions that with multiple Krasnikov tubes GR would predict the possibility of closed timelike curves (so if you believe the chronology protection conjecture quantum gravity would somehow rule out this possibility)
I don't want to bet causality on a conjecture. :wink:
Seriously, the only time I hear about NEGATIVE energy densities are in discussions of the ergoregion of a Kerr BH really close to the event horizon. Call me nutty, but I don't see those conditions being harnessed anytime soon. Then again, I DO find the CPC really very compelling. That also doesn't make it any more than a conjecture however...
 
  • #22
JesseM
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I don't want to bet causality on a conjecture. :wink:
Seriously, the only time I hear about NEGATIVE energy densities are in discussions of the ergoregion of a Kerr BH really close to the event horizon. Call me nutty, but I don't see those conditions being harnessed anytime soon.
Usually when physicists talk about speculations like holding a wormhole open with negative energy, they mention the Casimir effect which allows a region of space between two parallel plates to have an energy density lower than the vacuum energy of quantum field theory. Of course the vacuum energy itself is usually treated as being greater than zero in GR, so this doesn't necessarily mean the space between plates actually has a negative energy in the GR sense--according to this the vacuum energy is probably about 9*10^-10 joules per cubic centimeter if we assume the vacuum energy is responsible for the cosmological constant. But hellfire said in post #51 of this thread that the energy density between plates could be lower than the vacuum energy by an amount even greater than the vacuum energy is assumed to be greater than zero in cosmology, as long as the plates were less than about 10^-5 meters apart, so that would suggest that for sufficiently small separations the energy density between plates can be negative in the GR sense. I suppose there's no way to be completely confident about this without a theory of quantum gravity though!
 
  • #23
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Bapowell,

Black holes do not have a 'force' that surpasses the speed of light. Are you suggesting that they can accelerate infalling objects to greater than light speed?
Um, yes? There are two forces at work here: 1) gravity, 2) lights own velocity. From what I understand, the theory of relativity has linked these forces in a balanced way. Let's use the example of a "disappearing" Sun. If the Sun suddenly disappeared, it wouldn't be there to exert a gravitational influence on the Earth, but the effects of this wouldn't be seen until spacetime flattened out at Earth's location. This "flattening" of spacetime begins at the Sun's old location and "ripples" out until it reaches Earth. This happens at the speed of light. However, these changes in gravity don't affect the light. The light maintains it's own velocity; it still travels and without any blue or red-shifting. This is why I say that the forces of gravity and light are linked "harmoniously". They move at the same rate but maintain independance. Not so with a black hole...

Light looses it's independance around black holes. So, if light maintains independance from gravity when their forces are equal, then what does that say about the force of gravity when light looses it's independance? It says that force of gravity has surpassed that of light.
 
  • #24
JesseM
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Um, yes? There are two forces at work here: 1) gravity, 2) lights own velocity. From what I understand, the theory of relativity has linked these forces in a balanced way. Let's use the example of a "disappearing" Sun. If the Sun suddenly disappeared, it wouldn't be there to exert a gravitational influence on the Earth, but the effects of this wouldn't be seen until spacetime flattened out at Earth's location. This "flattening" of spacetime begins at the Sun's old location and "ripples" out until it reaches Earth. This happens at the speed of light. However, these changes in gravity don't affect the light. The light maintains it's own velocity; it still travels and without any blue or red-shifting. This is why I say that the forces of gravity and light are linked "harmoniously". They move at the same rate but maintain independance. Not so with a black hole...

Light looses it's independance around black holes. So, if light maintains independance from gravity when their forces are equal, then what does that say about the force of gravity when light looses it's independance? It says that force of gravity has surpassed that of light.
The http://www.aei.mpg.de/einsteinOnline/en/spotlights/equivalence_principle/index.html [Broken].
 
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  • #25
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Usually when physicists talk about speculations like holding a wormhole open with negative energy, they mention the Casimir effect which allows a region of space between two parallel plates to have an energy density lower than the vacuum energy of quantum field theory. Of course the vacuum energy itself is usually treated as being greater than zero in GR, so this doesn't necessarily mean the space between plates actually has a negative energy in the GR sense--according to this the vacuum energy is probably about 9*10^-10 joules per cubic centimeter if we assume the vacuum energy is responsible for the cosmological constant. But hellfire said in post #51 of this thread that the energy density between plates could be lower than the vacuum energy by an amount even greater than the vacuum energy is assumed to be greater than zero in cosmology, as long as the plates were less than about 10^-5 meters apart, so that would suggest that for sufficiently small separations the energy density between plates can be negative in the GR sense. I suppose there's no way to be completely confident about this without a theory of quantum gravity though!
Exactly! That Planck scale is a real killer for current theories. I'm familiar with the Casimir Effect, but even if we assume that kind of "closeness" and a subsequent negative... I don't see how it could be applied in this case. You'd need to shape and control that 'region' of negative density relative to surroundings, and I can't even imagine how that could be accomplished.

The region of lower density is after all, confined between the plates which give rise to the effect. The only time I can still think of negative energy densities being seriously discussed on a macroscopic scale (in the classic sense, not the term of art) really is in the ergoregion. Even then, the uncertainty about whether or not LOWERING density ever reaches NEGATIVE density is just as you say. Ah well...

EDIT: @Hoku: You might find some reading into "Spacetime Geodesics" and "Degrees of Freedom" and "Refraction" both helpful and quite interesting. I'm not being sarcastic; I really believe that those topics will help you to come to a better understanding of the relationship between... hmmm... the "riverbed" and "the water" if you catch my drift.
 

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