Question about reversability/arrow of time

[eloheim]

Hi I have a question that hopefully isn't too hard. I couldn't find exactly what I was looking for in previous threads, and please move this if there is a better section for it (I wasn't sure).

Say I break an egg. Just from a classical or Newtonian view, if I could magically reverse the momentum of each individual particle in time, would it look like the paths of all the different particles 'conspire' to come back together into the form of original, unbroken egg? I say conspire because the entropy would dictate the bits of a broken egg are very unlikely to reform a whole egg by chance (or when the time continued forward as normal).

If this is right my question is if taking this problem quantum mechanically, using probabilities for the "future" paths of the reversed broken egg bits, would still end up with the same result of the original egg, or a very similar egg, or something else? I'm kind of wondering if the probabilistic aspect of this version would 'eat away' at the drop in entropy associated with reforming the unbroken egg (compared with the deterministic version).

My apologies if this question doesn't make sense and any poor terminology. Thanks!

 

[Demystifier]

Assuming that a true wave-function collapse does not exist, the wave function of the reversed quantum egg would evolve from a broken egg to the original unbroken egg.

The crucial questions, about which there is no consensus in the quantum-foundations community, are the following ones:
- Is there a true wave function collapse?
- Is the egg the same thing as the wave function of the egg?
Without answering those crucial questions first, it is impossible to answer your question.

 

[naima]

I found no recipe to cook a wave function.

 

[eloheim]

@Demystifier thanks for the reply. I wasn't thinking through the actual observation of the quantum egg part in terms of the measurement problem (etc.) so I'll be thinking about that.

@naima is that in response to Demystifier's "is the egg wave function the same as the egg question?" Or just hungry? :-)

 

[naima]

@naima is that in response to Demystifier's "is the egg wave function the same as the egg question?" Or just hungry? :-)

Interesting question about duality!

 

[Nugatory]

As Demystifier has pointed out, quantum mechanics refuses to answer the question "Could the egg reassemble itself?".

Classical mechanics says "the egg could reassemble itself, but it never will". If you think about this for a moment, you may decide that "could it happen?" is the wrong question, or at least one for which there is no useful answer. Much more important is that both quantum and classical mechanics give the same answer - a clear "No" - to the more useful question "Will the egg reassemble itself".

 

[A. Neumaier]

I found no recipe to cook a wave function.

Not every wave function can be cooked. But didn't you know :-) that wave functions of a certain form ''have'' an egg, just as an electron ''has'' a wave function? It is enough to put the egg of such a wave function into hot water.

 

[A. Neumaier]

My apologies if this question doesn't make sense and any poor terminology.

For an improved question of the same sort and associated terminology see spin echo reversal.

 

[naima]

This remark about hot water is significant. In his recent book Rovelli wrote that reversible movement does not emit heat. in a backwards movie the movement of the egg in the air does not look weirds. It is on when it jumps from the ground that you see that it is backwards. A that moment in real life heat is emitted. That is why he talks about "thermal time". Every increase of entropy is accompanied by heat. Even black holes (the symbol of irreversibility) have a surface temperature.

 

[A. Neumaier]

It is on when it jumps from the ground that you see that it is backwards. A that moment in real life heat is emitted.

Well, to reverse, you also need to reverse the motion of all atoms that make up the heat...

 

[A. Neumaier]

Rovelli wrote that reversible movement does not emit heat.

Indeed. But each time a wave function collapses, the entropy of the environment increases. Collapse is irreversible.

I found no recipe to cook a wave function.

But an egg is not described by a wave function but by a density matrix (since it has a temperature). Density matrices can be ''cooked''. The ''cooking process'' is described by a Lindblad equation, which describes irreversible quantum behavior.

 

[naima]

Yes and Irreversibility is linked to entropy and you find heat in the definition of entropy.
I would like to ask you a question:
In QM we have stationary states. How can we calculate if they are stable or unstable?

 

[eloheim]

@A. Neimaier thanks for the tip on the similar question. I will check it out.

I'm also thinking about Demystifier's advice to consider the quantum measurement of my possible re-formed egg. Is this very important for my original question though? I would assume I could just use any standard experimental procedure here because all I care is if the egg is macroscopically back again after t more seconds (being the length of time it took to smash it the first time).

Okay maybe the collapse question is related to comparing between the classical and quantum versions of the "reversal" (which was the point of my actual question)... That would make more sense :-)

As Demystifier has pointed out, quantum mechanics refuses to answer the question "Could the egg reassemble itself?".

Classical mechanics says "the egg could reassemble itself, but it never will". If you think about this for a moment, you may decide that "could it happen?" is the wrong question, or at least one for which there is no useful answer. Much more important is that both quantum and classical mechanics give the same answer - a clear "No" - to the more useful question "Will the egg reassemble itself".

Okay you're right to say I'm not wondering what COULD happen to the broken egg. I know very many things 'can' happen that are FAPP impossible (with infinitesimal probabilities), and that's not what I'm wondering about.

Also though, are you saying that in either case (classical/quantum) the reversed egg-goop particles will proceed toward equal or increasing entropy (more-or-less as normal), and certainly NEVER toward some future lower entropy whole-egg configuration?

This reminds me of readings about the arrow of time considered cosmologically. I think the idea was that for a generic lower entropy configuration, both directions of time would look symmetrical and tend toward higher entropy states in either direction ("past/future"). I think going against an intuition that if considering a universe starting with 'here', and from 'here' you see entropy increasing into the future, then you'd expect (wrongly) that the PAST states from this 'here' will be likely even lower entropy still ("so they could give birth to the 'here' that continues toward the future as was just considered"). In truth though that's wrong; it's plain more improbable for entropy to decrease no matter the direction.

Hopefully, if I'm understanding Nugatory correctly, this is kind of analogous to my egg situation(?). And reversing a bunch of particle trajectories doesn't do anything to change it.