Many Worlds vs Classical Mechanics

[durant35]

I have a question regarding the ontology of the many-worlds interpretation which by my assumption shows some deficiencies in this way of thinking.

When many worlders describe branching and effects giving rise to multiple worlds they typically invoke Schrödinger cat-type experiments where from a micro state we get a meaningful superposition on a macro level and two distinct worlds.

But the problem with this is when they invoke the infamous "the splitting occurs all the time". Suppose a person tosses a die. This line of thinking implies that there would be six worlds where each outcome is realized.

But as far as we know, tossing a die is a classical process which is fundamentally distinct from a case of micro-macro entanglement. So when it is said - all possible outcomes occur - do they really, and how?

Note that this example doesn't invoke math and I would like to be based strictly on the example of the coin toss that I mentioned - since that example doesn't seem to imply many worlds.The second part of problem is the possibility of worlds where entropy spontaneously decreases. Suppose I have a broken glass. In classical mechanics it is possible for it to reform but you would have to wait a long, long time so the possibility is practically negligible. If the wavefunction is all there is it should also obey the second law of thermodynamics and you would have to wait an extremely long time before you get glasses reforming, no matter what world in the set of the worlds in the theory is in question.

But it seemse that due to quantum uncertainty there should be worlds where glasses spontaneously reform all the time, those worlds would be a complete violation of the 2nd law of thermodynamics.

Is this considered a part of the theory or there are no such worlds and all of the worlds must obey the 2nd law of thermodynamics because it would violate Schrödinger's equation if they didn't?

Thanks in advance

 

[PeterDonis]

Suppose a person tosses a die. This line of thinking implies that there would be six worlds where each outcome is realized.

Only if there is some quantum uncertainty involved in how the die lands.

as far as we know, tossing a die is a classical process

And if that is true, i.e., if there is no quantum uncertainty involved, then the MWI does not say there will be any splitting of worlds.

t seemse that due to quantum uncertainty there should be worlds where glasses spontaneously reform all the time

Yes, but they will have an extremely small measure.

those worlds would be a complete violation of the 2nd law of thermodynamics.

Yes, they would. The 2nd law is a statistical law, not a fundamental law.

 

[durant35]

Only if there is some quantum uncertainty involved in how the die lands.

But is there any? I think there is, so there would be many, many low probability branches where the die rolls on one side without any classical force being applied to it
Those branches would correspond to the small uncertainty. Likewise we would have one high amplitude branch which is correspondence with the laws of classical mechanics (e.g. die toss with a specific force applied, specific resistance of the air etc. so the outcome would be based on Newtonian mechanics).

Is this reasonable?

Yes, they would. The 2nd law is a statistical law, not a fundamental law.

But how do quantum probabilities/uncertainties play a role here?
Entropy increase is a classical effect and can be desribed through classical statistical mechanics.
How does quantum probability/uncertainty yield the same effect - or does it in fact replace something about classical probability for this?

Thanks for the answers!

 

[PeterDonis]

is there any?

I don't think we know for sure, but it certainly seems like there could be.

Is this reasonable?

If there is quantum uncertainty, then yes, the implications you describe seem reasonable.

Entropy increase is a classical effect

No, it's a statistical effect. There is quantum statistical mechanics just like there is classical statistical mechanics.

 

[Strilanc]

You seem to be assuming that all the "worlds" are equally likely, or something like that. But that's not how many-worlds works at all. For lack of a better way of saying it, more of you ends up in some worlds than others. The splits aren't equal, they're weighted.

You also seem to be assuming the worlds only depend on coarse-grained human-level stuff. But if you throw a die there's not just six "worlds", there's quadrillions upon quadrillions of weighted outcomes based on tiny little differences in how all the electrons and atoms and etc are decohering. In the many-worlds interpretation, there are many many worlds all constantly splitting and spreading out at an absurd rate onto their own little paths through configuration space. But because dice are so large, when you weigh up all the predicted resulting worlds and group them by which die roll happened, you will find that one outcome is over-represented by far. And it will match the die outcome predicted by the classical approximation.

And really MWI doesn't talk about worlds. It just drops the collapse postulate, implicitly saying "Just because we're no longer strongly interacting with the clump of configuration space where the other amplitude flowed to doesn't mean that amplitude suddenly became 0.".

 

[durant35]

You seem to be assuming that all the "worlds" are equally likely, or something like that. But that's not how many-worlds works at all. For lack of a better way of saying it, more of you ends up in some worlds than others. The splits aren't equal, they're weighted.

You also seem to be assuming the worlds only depend on coarse-grained human-level stuff. But if you throw a die there's not just six "worlds", there's quadrillions upon quadrillions of weighted outcomes based on tiny little differences in how all the electrons and atoms and etc are decohering. In the many-worlds interpretation, there are many many worlds all constantly splitting and spreading out at an absurd rate onto their own little paths through configuration space. But because dice are so large, when you weigh up all the predicted resulting worlds and group them by which die roll happened, you will find that one outcome is over-represented by far. And it will match the die outcome predicted by the classical approximation.

And really MWI doesn't talk about worlds. It just drops the collapse postulate, implicitly saying "Just because we're no longer strongly interacting with the clump of configuration space where the other amplitude flowed to doesn't mean that amplitude suddenly became 0.".

So there would be worlds with many nearly identical copies of yours which are distinguishable only by one position of a particle and the small micro effect of different positions of the atom, but all of the copies would have the same observations?

Isn' this a bit too much for a normal viewpoint?

 

[stevendaryl]

So there would be worlds with many nearly identical copies of yours which are distinguishable only by one position of a particle and the small micro effect of different positions of the atom, but all of the copies would have the same observations?

Isn' this a bit too much for a normal viewpoint?

Any time that a theory involves probability, it is possible to give an "ensemble" interpretation, where everything that has a nonzero probability happens. There really isn't much (if any) difference between saying:

1. There is only one world, and it evolves nondeterministically.
2. There are infinitely many worlds, and the whole shebang evolves deterministically, and probability is only involved because I don't know which one is "mine".