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Author Topic: By reversing the laws of physics, can we reverse the arrow of time?  (Read 1385 times)

ARVIND

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If the thermodynamic arrow of time reverses, the laws of physics should be reversed.
Eg: A spaceship enters the event horizon of black hole, it has no chance of escaping the gravitational forceof the black hole. But. if time rewinds, the spaceship escapes the blackhole.
So, if we reverse the laws of physics, and by some means, make it work, is it possible to rewind time?     

Jarek Duda

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There is great thought experiment about it - while I completely don't see it as a realistic possibility, it is really great to understand "conflict" between 2nd law of thermodynamics and CPT symmetry conservation - that in fact there is none.
Specifically, general relativity doesn't distinguish between past and future light cones - so there appears question if spacetime has to be (time-)orientable?
... and it occurs that there are known solutions - using wormholes or slowly rotating black hole ( http://iopscience.iop.org/0264-9381/19/17/308/ , http://arxiv.org/PS_cache/gr-qc/pdf/0202/0202031v4.pdf ) which are not time orientable - there exist loops exchanging past and future light cones:


Imagine we have sent a rocket through such trajectory and it has returned ...
Inside this rocket, the astronaut shouldn't feel a difference - he could e.g. just break a mug ... but from our perspective it would be time reversed: pieces would get together into the mug.
Everything (like mugs) have tendency to get into higher entropic state (broken), but our things (mugs) came from past reason-result chains, so such state change (breaking) can only have e.g.: unbroken state toward past time direction and broken toward future.
In contrast, reason-result chain of mugs from the rocket came from our future time direction, so it can increase entropy only while breaking toward our past.

Great model to understand the asymmetry you are talking about is Kac ring - black and white balls in a ring and there are some marked positions. Now in each step rotate it by one position, changing color while going through marked positions.
Natural statistical assumption ("Stoßzahlansatz"): that total proportion of colors correspond to proportions before the marked positions, says it should tend to equal distribution of colors (maximal entropy) ... however, making two full rotations you get the initial setting - entropy has to finally start decreasing - here is nice paper about it.
We can prove e.g. Boltzmann H-theorem that in classical mechanics entropy always grows ... but making time symmetry of the system we would get opposite conclusion - contradiction. Such "theorems" for time symmetric evolution need to have some hidden extremely subtle assumption, called Stoßzahlansatz.

So in fact 2nd law works as well in both directions - if we know that in given moment all particles are in the left part of the tank, the safest/thermodynamical assumption for both later and earlier is entropy increase.
We need to find some separate explanation for asymmetry - if it is not written in fundamental equations, it has to be a property of a specific solution of physics we live in: being close to spatially localized Big Bang.

Pmb

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If the thermodynamic arrow of time reverses, the laws of physics should be reversed.
Eg: A spaceship enters the event horizon of black hole, it has no chance of escaping the gravitational forceof the black hole. But. if time rewinds, the spaceship escapes the blackhole.
So, if we reverse the laws of physics, and by some means, make it work, is it possible to rewind time?     
The laws of physics describe what we observer in nature. Since rewinding time has never been observed physics can say nothing about it.

But what would that mean anyway? How would one observer such a rewinding in time?

Jarek Duda

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Pmb, if one believes in Einstein's general relativity, he should also treat seriously its theoretical consequences, like living in infinitely thin submanifold of multidimensional something, black holes with infinite density matter state, wormholes connecting two places of spacetime, warp drive ... or time reversing loops - which theoretically would allow to literally observe "rewinding the time".

If someone (like me) doesn't like such exotic and philosophically problematic possibilities, all experimental conformations of GRT, including frame dragging of Gravity Probe B, uses in fact its approximation: gravitomagnetism ( http://en.wikipedia.org/wiki/Gravitoelectromagnetism ).
It was introduced by Heaviside in 1893 to make Newton force Lorentz invariant in analogy to electromagnetism and in opposite to GRT, doesn't need additional dimensions and doesn't allow for such exotic possibilities.

Pmb

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Quote from: Jarek Duda
Pmb, if one believes in Einstein's general relativity, he should also treat seriously its theoretical consequences, like living in infinitely thin submanifold of multidimensional something,
I don’t know what you’re talking about. Can you please be specific and give an example of “like living in infinitely thin submanifold of multidimensional”?

Quote from: Jarek Duda
black holes with infinite density matter state, wormholes connecting two places of spacetime, warp drive ... or time reversing loops - which theoretically would allow to literally observe "rewinding the time".
That’s not necessarily true. While one can describe the spacetime of such things it need not follow that there exist in nature ways of accomplishing such things. Relativity predicts certain things given certain assumptions. E.g. Yes. I know that there is a metric which describing Warp Drive but nobody knows yet if its theoretically possible to construct one. As I recall the outer surface of the warp drive cannot be causally connected to the inside surface. Therefore there may be no way of controlling such a warp drive. As far as ‘time reversing loops” go they might exist in theory but may not be able to exist in practice. Something similar holds for wormholes.

Jarek Duda

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I don’t know what you’re talking about. Can you please be specific and give an example of “like living in infinitely thin submanifold of multidimensional”?
Imagine 2D sheet with constant positive internal curvature - it just has to enclose into a sphere ... where this sphere is?
It is infinitely thin 2D submanifold of 3D - even if we use only internal curvature like in GRT, it can create structures clearly requiring higher dimensions - Whitney theorem says we need about 8 dimensions here.
So accordingly to GRT, our spacetime is infinitely thin something in mutidimensional something - with what it completely doesn't interact (any interaction would be seen thermodynamically - our heat would be running away).
I see it very philosophically disturbing - e.g. why it remains infinitely flat?
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That’s not necessarily true. While one can describe the spacetime of such things it need not follow that there exist in nature ways of accomplishing such things. Relativity predicts certain things given certain assumptions. E.g. Yes. I know that there is a metric which describing Warp Drive but nobody knows yet if its theoretically possible to construct one. As I recall the outer surface of the warp drive cannot be causally connected to the inside surface. Therefore there may be no way of controlling such a warp drive. As far as ‘time reversing loops” go they might exist in theory but may not be able to exist in practice. Something similar holds for wormholes.
Of course theoretical existence does not imply real existence, but for complete/coherent theory, we should be able to understand its all hypothetical consequences.
From one side because even the most exotic consequence surprisingly could be realized, e.g. be an explanation of some strange phenomena ... from the other because being able to lead to a nonsense is a way to disprove a theory (by contradiction).
And so accordingly to GRT, internal curvature caused by well placed huge amount of mass could theoretically create wormhole of chosen shape ... even if it is completely not realizable by us.

Such wormhole is a tube joining two places of spacetime. Imagine starting such tube, but instead of gluing it in standard way, let it go through the spacetime in some higher dimension and then glue from the other side like in (nonorientable) Klein bottle:

Going through such wormhole could switch our past and future light cones (eventually left and right like in chiral life concept) - I absolutely agree it is completely impossible to realize in practical way, but still we need to understand such possibilities ...
Especially it is really great thought exercise to understand thermodynamics :)
« Last Edit: 14/01/2013 20:42:22 by Jarek Duda »

Pmb

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Quote from: Jarek Duda
Imagine 2D sheet with constant positive internal curvature - it just has to enclose into a sphere ... where this sphere is?
FYI – The term that you’re looking for here is “intrinsic curvature” not “internal curvature”. See definition at http://mathworld.wolfram.com/IntrinsicCurvature.html

Quote from: Jarek Duda
It is infinitely thin 2D submanifold of 3D - even if we use only internal curvature like in GRT, it can create structures clearly requiring higher dimensions –
Thanks. I’m well versed with these notions. It was the way you expressed yourself that I found to be confusing. E.g. “living in infinitely thin submanifold”. One would normally say that a 2d manifold is a submanifold of a 3d manifold. Calling it infinitely thin is confusing since nobody ever says that.

Quote from: Jarek Duda
So accordingly to GRT, our spacetime is infinitely thin something in mutidimensional something
I see no reason to make a statement that spacetime is a subspace of something if you can’t define that something and its usefulness.

Quote from: Jarek Duda
And so accordingly to GRT, internal curvature caused by well placed huge amount of mass could theoretically create wormhole of chosen shape ... even if it is completely not realizable by us.
You’ve said here that it takes a huge amount of mass to create a wormhole. What you neglected to say is that the matter must be exotic since the mass density must be negative.  It is not yet know whether this is possible or not. Thorne et al explains

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Wormhole creation, … must be accompanied by closed timelike curves … and also a violation of the “weak energy condition”. .. it is not known whether the stress-energy tensors required by the Einstein equations in those spacetimes are permitted by quantum field theory.
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Jarek Duda

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Quote from: Jarek Duda
So accordingly to GRT, our spacetime is infinitely thin something in mutidimensional something
I see no reason to make a statement that spacetime is a subspace of something if you can’t define that something and its usefulness.

Having only 2D sheet with constant positive internal/intrinsic curvature, it encloses into a sphere - so where it is happening? What it divides into two parts - interior and exterior?
It is not about usefulness, but that you just cannot avoid these additional dimensions while defining something only through intrinsic curvature.
Indeed mathematically it is just simple looking submanifold ... but in physics we additionally need to ask what these mathematical abstracts mean physically - and it is literally being infinitely thin, not true?
Physics doesn't like infinitely thin objects - they are not continuous in orthogonal direction. Physicists got used to them, but it doesn't mean there is not a problem here.
E.g. they try to model particles as infinitely small point abstracts ... but ultraviolet divergence shows that it's wrong.
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Wormhole creation, … must be accompanied by closed timelike curves … and also a violation of the “weak energy condition”. .. it is not known whether the stress-energy tensors required by the Einstein equations in those spacetimes are permitted by quantum field theory.
Honestly, as I have said, I absolutely don't see it realistic. 
This is only thought experiment - theoretical possibility useful to understand 2nd law of thermodynamics - that there is no conflict with time/CPT symmetry conservation of Lagrangian mechanics we use on all scales: from QFT to GRT.

 

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