Thread: Thermodynamical thought experiment with time reversing loop?

There is some thought experiment constructed to help finding intuitions about the 'conflict' between CPT conservation and 2nd law of thermodynamics. Like for wormhole loops, I see it completely unrealistic - I only think it is inspiring mind exercise and may lead to some better understanding of thermodynamics (and temporal logic).
General Relativity Theory determines shape and rotation of light cones in each point of spacetime (like near black hole), but it is time (and CPT) symmetric - doesn't directly distinguish between past and future of such light cones. Without any additional reasons like entropy gradient, we could time-flip the light cones.
Another from 2nd law of thermodynamics way to distinguish past and future of such light cones is by continuity ... but let us imagine there is some loop on which GRT makes that light cones have configuration like that:

Where the start and the beginning have the same position, but may be shifted in time. Of course it would require some really nasty singularity inside such loop - even more than in the center of black hole where spacetime is no longer a manifold.
There are rather completely no reasonable scenarios to obtain such singularity, maybe mathematics could forbid such global solution (but black holes require hypothesis: cosmic censorship hypothesis) ...

Only for this thought experiment, let us assume for a moment that there exists such time reversing loop - and a rocket flied through it and returned back to Earth orbit.
If someone really doesn't like such loop concept, one can imagine that this rocket was transformed by CPT symmetry - it would be made of antimatter, but it would be enough for thermodynamical considerations.

Ok, let's get to the main subject - thermodynamics.
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.
So it seems that 2nd law doesn't only emphasize just e.g. entropy gradient direction, but can work in both - depending on reason-result chains ... ?

This thought experiment becomes real mind feast if we allow the astronaut to land (not antimatter case)
Time reversed molecules are nearly the same, temperature is average energy so it also shouldn't depend on time direction - he should be able to just breath in our atmosphere (??)
His body should be in thermal equilibrium with environment - heat exchange should work normally, so I don't see a reason his time-reversed metabolism should work improperly (??)
So it would seem that he could also eat our food ... but there appears a problem - from his time perspective, it could need turning e.g. back into a chicken

The situation is really really strange - great mind exercise - I would gladly hear your comments, expansions ...
I think the only reasonable causality understanding here is Einstein's block universe - that like in GRT, the spacetime is already created and 'we only travel to our future there'.
So eventual time-loops are already made self-consistent, like in good SF movies (e.g. Twelve monkeys) - if one would like to kill his grandfather in the past, there would happen something that he couldn't do it.
If you disagree, how do you understand the conflict between CPT conservation and 2nd law?

How would look such contact of time-opposite natural reason-result chains? (theoretically allowed by CPT conservation)
For example some believe in cyclic universe model - that our universe will finally collapse into nearly a point.
From the perspective of CPT conservation, such Big Collapse point would be Big Bang it reversed time - low entropy state (spatially localized) creates entropy gradient (2nd law), starts reason-result chains ... and so evolution of universe in reversed time direction ... which should finally meet with ours in some far far future.
Why against current acceleration growth, it should finally start collapsing? Because of energy conservation - gravity pulls together (1/r^2), while some 'dark energy' push it out, but its density (and so strength) should decrease with the volume (1/r^3) ...

I've just found 2002 "The orientability of spacetime" paper from Classical and Quantum Gravity Journal: The orientability of spacetime
Here is arxiv version: http://arxiv.org/PS_cache/gr-qc/pdf/0202/0202031v4.pdf

It occurs that the lack of such time-reversing curves is precisely called time-orientability (there is required a distinction in semi-riemannian manifolds) and the author even propose a test:
"In a true test of time orientability on a region R through which time cannot be oriented, the clock readings would increase steadily along the path taken by the clock. Before entering R the observer sees the time values increasing on the clock. When the clock exits at a time /rho the increasing clock times would be at ever decreasing values for the observer time. The observer would still see a backwards counting clock, but only at times before /rho"

I personally don't threat their existence so serious - I only needed such thought experiment to show intuition about that there isn't a conflict between 2nd law and CPT conservation.
What lead me to that thermodynamics also doesn't really emphasize any time direction (what would contradict more fundamental CPT conservation), is new approach to thermodynamical modeling I was developing e.g. for my current PhD thesis: [1111.2253] From Maximal Entropy Random Walk to quantum thermodynamics
It shows why Brownian motion is often an approximation - makes some unjustified assumptions - only approximate maximizing uncertainty. If we do it right - using recent Maximal Entropy Random Walk and expansions, it for example doesn't longer disagree with thermodynamical predictions of quantum mechanics (leads to quantum ground state stationary probability density), naturally explains Born's rules ... or e.g. shows a deeper time symmetry of thermodynamics.

I believe what you are referring to with your "loop" is a closed time-like curve :

Closed timelike curve - Wikipedia, the free encyclopedia

What happens here is that a spaceship travelling along such a curve would eventually end up at the same place and at the same time as when & where it initially entered the curve, in relation to a stationary observer. In essence so the ship travels into the past. However, anyone on board the spaceship should not be able to observe anything special; their clocks still run forward, the loop is transversed in a finite time as measured by them. For an outside observer though, no time would have passed between the ship entering and exiting the curve. Crucially also, the ship's CPTs would not be reversed. when they exit the loop - their clocks still run forward.
Now how's this for a brainteaser ??

It doesn't necessarily need to be a spacetime loop - the paper I've just posted use just curve with the same spatial positions of endings (can be shifted in time) ... but if they would travel backward, the loop would be finally enclosed.

Yes - the funniest is that inside the rocket everything would be normal - but from our time perspective their mugs would break backward ... if they would provide a mug to the Earth, 2nd law would still give it tendency to increase entropy (break) - but this 'mug from future' could only break toward our past - in opposite direction to our 2nd law.
The purpose of this thought experiment is to understand that surprisingly 2nd law is also time-symmetric - depends only on reason-result chains ... which usually provide us with mugs from the past, so they can break only toward the future.
And the real brainteaser starts if you allow such astronaut to land

I am not entirely sure now what you mean by this...the clock in the spaceship will always run forward for both outside observer and spaceship crew. There is no motion you could perform in a smooth 4-dimensional manifold that would reverse the direction of the time arrow for any observer. The CPT theorem only says that these values are symmetrical, not that you can reverse them at will.

I am not entirely sure now what you mean by this...the clock in the spaceship will always run forward for both outside observer and spaceship crew.

Clock from this spaceship would look going backward for standard observer ... if you don't believe me, look at above citation from peer-reviewed paper ... ?

There is no motion you could perform in a smooth 4-dimensional manifold that would reverse the direction of the time arrow for any observer.

4 dimensional spacetime includes the time - it is static, doesn't longer evolve - the future is already there and while time passes we travel toward it.
Such natural for GRT view is called Einstein's block universe or eternalism: Eternalism (philosophy of time) - Wikipedia, the free encyclopedia

The CPT theorem only says that these values are symmetrical, not that you can reverse them at will.

Time/CPT symmetry says that given theory doesn't directly distinguish past and future.
Of course it doesn't mean that we can practically reverse them - there would be needed e.g. such nonrealistic loop for that.

ps. The author of mentioned paper refers a few peer-reviewed ones, for example in Sorkin R D 1977 J. Physics A 10 717–725 there should be constructed a non-orientable wormhole (asymptotically flat), but it's not accessible electronically.

[QUOTE=Jarek Duda;297710]

Clock from this spaceship would look going backward for standard observer ... if you don't believe me, look at above citation from peer-reviewed paper ... ?

There is no motion you could perform in a smooth 4-dimensional manifold that would reverse the direction of the time arrow for any observer.

Apparently you don't read what you write, since these two statements completely disagree

What do you mean? The second sentence was not mine, but I agree with it - as I've already mentioned, pure non time-orientability would require a very nasty singularity inside (non differentable like the center of black hole). Another theoretical possibility is to spoil orientability - in mentioned Sorkin there should be construction of such nonorientable wormhole (still asymptotcally flat).
I personally see such theoretical possibilities as completely nonrealistic - only as a tool for very educative thought experiment.

Originally Posted by Jarek Duda

What do you mean? The second sentence was not mine, but I agree with it - as I've already mentioned, pure non time-orientability would require a very nasty singularity inside (non differentable like the center of black hole). Another theoretical possibility is to spoil orientability - in mentioned Sorkin there should be construction of such nonorientable wormhole (still asymptotcally flat).
I personally see such theoretical possibilities as completely nonrealistic - only as a tool for very educative thought experiment.

A non-orientable wormhole...interesting idea. Unfortunately though there would need to be a singularity at each end of such a wormhole

I'm not sure if non orientable manifold have to be non time-orientable - I think it could have only a loop making P symmetry instead of T - e.g. transforming life into chiral life.
Non orientable means that ignoring metric, this manifold has such nontrivial topology ... non time-orientability uses the metric - such topologically trivial manifold would definitely directly require very nasty singularity, but non orientable wormhole might not require it directly ... but indeed theoretical realizations of wormholes often requires two singularities of stress-energy tensor.

Originally Posted by Jarek Duda

I'm not sure if non orientable manifold have to be non time-orientable - I think it could have only a loop making P symmetry instead of T - e.g. transforming life into chiral life.
Non orientable means that ignoring metric, this manifold has such nontrivial topology ... non time-orientability uses the metric - such topologically trivial manifold would definitely directly require very nasty singularity, but non orientable wormhole might not require it directly ... but indeed theoretical realizations of wormholes often requires two singularities of stress-energy tensor.

Yeah...you see, you need the singularity to actually make the wormhole in the first place. And once singularities are there they have a nasty habit of sticking around until they evaporate via Hawking radiation, which takes a very long time for the type of singularity needed to create a wormhole big enough to permit travel using a spaceship...
I applaud you anyway for bringing this up, it does need a nice bit of mental acrobatics to think about these things

I'm not sure if making that spacetime has nontrivial topology really requires localized singularities? Couldn't it be made on global level?
For example imagine a 2D riemannian manifold with small positive Gaussian curvature (kind of cosmological constant) - it make that it should enclose into a sphere - without local internal curvature singularities, we get nontrivial global topology ... ?

And maybe we should finally take these mental acrobatics to the next step and allow the astronaut to land ...
For example: could he breath with our atmosphere? (I think he could)
Now the sad part: from our perspective, he would completely lose his free will (???) - we would knew earlier what he will do in his future ...
He wouldn't really have any choice, because we would already knew what fate physics has prepared for him (usually we don't know it) ... and oppositely - he would already know what we our future will bring us ... ???
This is very a nasty example of killing free will ...
As a mental warm up, I propose exercising with 'just' allowing sending information back in time (using e.g. CPT transformation of free electron laser).

Originally Posted by Jarek Duda

I'm not sure if making that spacetime has nontrivial topology really requires localized singularities? Couldn't it be made on global level?
For example imagine a 2D riemannian manifold with small positive Gaussian curvature (kind of cosmological constant) - it make that it should enclose into a sphere - without local internal curvature singularities, we get nontrivial global topology ... ?

And maybe we should finally take these mental acrobatics to the next step and allow the astronaut to land ...
For example: could he breath with our atmosphere? (I think he could)
Now the sad part: from our perspective, he would completely lose his free will (???) - we would knew earlier what he will do in his future ...
He wouldn't really have any choice, because we would already knew what fate physics has prepared for him (usually we don't know it) ... and oppositely - he would already know what we our future will bring us ... ???
This is very a nasty example of killing free will ...
As a mental warm up, I propose exercising with 'just' allowing sending information back in time (using e.g. CPT transformation of free electron laser).

Are you confusing topology with geometry ? They are different things.
The short answer is no, you will most likely not be able to create a wormhole without having a singularity at each end. Also, even if you could, the wormhole would not be stable, and would collapse before anything could travel through it...

Of course geometry and topology are connected, but different points of view ... but orientability is rather topological one ...
I'm not convinced ... choosing internal curvature (stress-energy tensor) as for some higher dimensional analogue of Klein bottle, would it have to be orientable?
Ok - matter distribution creating it would be probable very nonstable, but there is also e.g. cosmological constant ... I totally agree that it wouldn't be too realistic (neither wormholes are), but what you are mathematically saying is definitely too strong ... (?)

Originally Posted by Jarek Duda

Of course geometry and topology are connected, but different points of view ... but orientability is rather topological one ...
I'm not convinced ... choosing internal curvature (stress-energy tensor) as for some higher dimensional analogue of Klein bottle, would it have to be orientable?
Ok - matter distribution creating it would be probable very nonstable, but there is also e.g. cosmological constant ... I totally agree that it wouldn't be too realistic (neither wormholes are), but what you are mathematically saying is definitely too strong ... (?)

A 4-dimensional Klein bottle ? That's a very interesting idea...such a topology has never occured to me. I know that a Klein bottle is a surface in 4-dimensional space, but can you actually boost the surface itself into 4 dimensions while retaining the basic topology ? I don't have the answer to this, will need to think about it for a while...
It's definitely an interesting idea.

I'm not so fluent with higher dimensional (differential) topology, but with the growth of dimension, usually the space of possibilities grows really fast - for example one dimensional compact manifold is only a circle, two dimensional orientable compact manifolds are sphere and toruses with some natural genus ... while as I remember, for three dimensional there is not known complete classification (?)
Some examples to get compact four-dimensional 'Klien-like': you could for example multiply Klein by sphere, or twice by circle (2D torus) ... or straightforward analogously to Klein - it is S^1\times [0,1] cylinder glued not like torus, but in nonorientable way (through interior) - you can do the same using S^3 instead (Whitney theorem says that it would definitely fit in 8 dimensions, but I think 6 would be enough).
Simple representation of such construction (not with sphere) is to draw a cube of given number of dimensions and draw arrows (as its dimension) on its faces - then imagine that opposite faces are glued accordingly to the arrows (orientation) - if all arrows agrees, you get torus and in other cases some kind of (higher dimensional) Klein bottles.
Here is 2D case:
torus.jpg

But it's only abstract math ... let's go back to the topic: much more interesting thermodynamics (and causality) ...