Jarek Duda
12-17-11, 06:14 AM
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:
http://dl.dropbox.com/u/12405967/loop.jpg
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 (http://en.wikipedia.org/wiki/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 (http://en.wikipedia.org/wiki/Eternalism_%28philosophy_of_time%29) - 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 (http://en.wikipedia.org/wiki/Cyclic_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) ...
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:
http://dl.dropbox.com/u/12405967/loop.jpg
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 (http://en.wikipedia.org/wiki/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 (http://en.wikipedia.org/wiki/Eternalism_%28philosophy_of_time%29) - 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 (http://en.wikipedia.org/wiki/Cyclic_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) ...