Thermodynamical thought experiment with nonorientable spacetime?

[Duda Jarek]

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.

Here is some 2002 paper from Classical and Quantum Gravity Journal about nonorientable specitime (precisely not time-orientable), here is its arxiv version.

 

They are probably completely unrealistic, but 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 only 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) ...

[michel123456]

First of all I have a personnal axiom: never mess living things with physics. If you put a living chicken in a physics equation, you'll get peculiar results. If you put a cat, as Schroedinger did, you'll get also a peculiar result. Living entities are not good examples of physical phenomenas: a bird can build a nest, something that physical randomness would forbid. Man build cars: cars are not an example of the result of some strict physical process.

 

Likewise, a mug is not a good example, neither a broken mug, because a mug is the result of living human elaboration.

Also, a human being breathing is not a good example, because it is part of a vital process.

 

I am not sure that when you consider strict physical process like water evaporation, you will not find that it is perfectly reversible.

 

Secondly, in your sympathetic diagram, you have a curve and a counter-curve. The counter-curve is not very clear, but appears at the right beginning on the left side. You should have an explanation on why the curve goes one way, then for some reason gets flat, then turns the other way. What are the physics behind that?

 

Thirdly, if someone could go into the past, which I think is impossible, but even if he could, why would he be an exception not following the laws of physics? Of course he cannot be an exception. So if someone goes 10 years in the past, he will find himself 10 years younger. If he goes thirty years in the past, he will eventually transforms into a spermatozoid. In any case, he will never be able to kill his own grandfather.

Edited December 18, 2011 by michel123456

[Duda Jarek]

First of all, I totally agree that considering living things with fundamental physics is extremely inconvenient ... but it doesn't mean that there can be a contradiction between these totally different points of views.

The problem you are talking about is mainly the conflict between:

- looking time asymmetric 2nd law of (effective) thermodynamics and

- CPT symmetric more fundamental physics.

The main purpose of this thought experiment is to understand why there is no conflict here - 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.

Inside the rocket everything would be normal - but from our time perspective their mugs would break backward ... if they would provide such 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.

 

If you don't like human origin mugs, you could e.g. crush a boulder or mix two different liquids - also a result of some reason-result chain (like liquid separation), what is the base of 2nd law. Simpler objects like a uniform liquid are thermodynamically time symmetric or reversible like many phase transitions.

 

Secondly, it doesn't necessarily need to be a spacetime loop - ending points can be shifted in time, like in Hadley's peer-reviewed paper. I personally don't see it too realistic, only as thought experiment to understand thermodynamics, but you could get such loop for example by attaching mirror image to the left of black hole picture:

 

Thirdly, why do you see here some exception of laws of physics?? It was intended to understand them, not contradict ...

I completely agree that one couldn't go back and kill his grandfather - physics wouldn't allow him. The only natural for GRT point of view is the Einstein's block universe or eternalism ( http://en.wikipedia.org/wiki/Eternalism_%28philosophy_of_time%29 ) - that spacetime is already chosen - such that eventual time-loops would be already self-consistent.

 

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.

Edited December 18, 2011 by Duda Jarek

[michel123456]

(...) like in Hadley's peer-reviewed paper.

 

Great paper. Thanks.

 

The best part from your link IMHO is

It would appear that the existence or otherwise of a time reversing region is dependent upon the observer.

 

Everything is relative! Even the arrow of time, why not, indeed?

[Duda Jarek]

I'm not sure what do you mean? - orientability is global property - if there is some small local loop reversing time directions, from some distant point we could go to this region, make the loop and then go back to the starting point ... also reversing our time directions.

 

About "Everything is relative", it's not so simple.

Our normal mugs objectively can break only toward our future.

There are even substances with clearly defined time arrow - for example unstable isotopes (created thanks of supernovas in our past) decreases radioactivity while time passes ... while their time reversed versions would increase radioactivity instead.

Very interesting would be mixing such two versions of the same isotope - our would decay and then recombine into the time reversed version ... and such substance would have no well defined time arrow.

 

But there are also much simpler substances without objective time arrow - for example simple fluid in thermodynamical equilibrium - shouldn't its time reversed version look exactly the same? ... could we distinguish them?

In other words: could the reversed astronaut from the thought experiment breath with our atmosphere?

Edited December 31, 2011 by Duda Jarek

[ajb]

What is the correct notion of the CPT theorem on a curved space-time? I am not at all sure, but I would not at all be suprised if time orientability features heavily.

[Duda Jarek]

Unless being in a singularity like a center of black hole or BB, general relativity says spacetime is semi-riemanian manifold: locally is Minkowski space (up to second order: curvature) - from microscopic QFT point of view (which CPT concerns), differences could appear on some hundreds decimals.

GRT alone is both T and P symmetry.

 

There indeed appears a problem with that CP symmetry is believed to be violated ... but I'm not entirely convinced that it is on fundamental level (equations) not symmetry breaking on solution level, like Higgs potential is symmetric while its solutions aren't? (...or fundamental physics is CPT symmetric, while its solution we live in has thermodynamical time arrow...).

The question is how such T or P loop would transform particles?

Ok, short living kaons could be transformed in long living ones - I would say they look the same in our description, but they are just different particles?

But would transformed nucleons/electrons be different than ours?

I don't think so - the eventual violation is on about tenth decimal, while we know there are no different stable field configurations (particles) so near ?

Edited January 1, 2012 by Duda Jarek

[ajb]

Unless being in a singularity like a center of black hole or BB, general relativity says spacetime is semi-riemanian manifold: locally is Minkowski space (up to second order: curvature) - from microscopic QFT point of view (which CPT concerns), differences could appear on some hundreds decimals.

 

One could certainly heuristically argue that via the equivalence principle: "The short distance behaviour of the quantum field theory should be the same as the corresponding quantum field theory on Minkowski space-time ".

 

Anyway, I am very doubtful that a general global notion of CPT can be formulated, a general curved Lorentzian manifold does not have isometries that are analogous to C or T. However, if we have spacial and temporal orientation then there is such a notion of CPT in generally covariant field theory [1].

 

Hollands (and Wald) have also formulated a CPT theorem in curved space-times via the operator product expansion [2]. The warning is that the theorem Hollands gives is really for the short distance behaviour within an algebraic formalism. We have to scratch our heads here and ponder if this is the correct full replacement.

 

Really this is all beyond my expertise, but it is interesting to think about the correct replacement for the Wightman axioms, CPT and the spin-statistics theorem on a curved space-time.

 

References

 

[1] Romeo Brunetti, Klaus Fredenhagen, Rainer Verch. The generally covariant locality principle -- A new paradigm for local quantum physics, Commun.Math.Phys. 237:31-68,2003.

 

[2] S. Hollands. The Operator Product Expansion For Perturbative Quantum Field Theory In Curved Spacetime, Commun. Math. Phys. 273, 1-36, 2007.

Edited January 2, 2012 by ajb