Collapse of particle wave function and single Universe wave function?

[PeterDonis]

I haven't seen Hilbert space used in the context of MWI

MWI proponents probably don't think it's necessary to belabor the fact that the wave function is an element of Hilbert space, since it's an obvious fact of basic QM.

 

[gentzen]

Is there a verifiable difference between a "collapse", e.g. an observed particle is no longer in the superposition of its states/positions, and a change in the probability distribution caused by interaction with wider QM system (observer)?

The typical "objective-collapse" theories do change the math, and lead to observable differences, see wikipedia and SEP. That is why they are typically called theories instead of interpretations, except for the Penrose interpretation.

You are probably thinking more about the infamous "consciousness causes collapse" interpretation (which should not be called von Neumann–Wigner interpretation despite wikipedia, because von Neumann and Wigner described something else). That is simply not a good interpretation.

The collapse in the Copenhagen interpretation is something completely different, without any verifiable observable differences. That collapse is rather related to how you interpret probabilities, especially in a non-ensemble context. The trouble is that nearly all current tests of QM are in an ensemble context. It is easier for normal probabilities to find examples which are far away from an ensemble context.

 

[DrChinese]

1. The typical "objective-collapse" theories do change the math, and lead to observable differences, see wikipedia and SEP. That is why they are typically called theories instead of interpretations, except for the Penrose interpretation.

2. The trouble is that nearly all current tests of QM are in an ensemble context. It is easier for normal probabilities to find examples which are far away from an ensemble context.

1. Agreed. There have been a number of attacks on the GRW-class. The Penrose interpretation apparently is subject to some exotic tests as well. Not sure if anyone will execute any of those. The idea contains a lot of speculation about the relationship between QM and gravity. Just the kind of thing that has led many down a rabbit hole.

2. Well, there is that ol' GHZ thing - no ensemble required. QM wins every time!

 

[Nugatory]

Why the conclusion is that superposition is gone rather than its probability distribution changed?

That’s just saying the same thing in two different ways. We calculate the probability distribution from the wave function; 50-50 is what we calculate from the pre-collapse wave function and 100-0 is what we calculate from the post-collapse wave function.

 

[timmdeeg]

50-50 is what we calculate from the pre-collapse wave function and 100-0 is what we calculate from the post-collapse wave function.

"100-0 is what we calculate from the post-collapse wave function." Isn't 100-0 just the measurement outcome which verifies one of the two possibilities "offered" by the wave function?

 

[Nugatory]

"100-0 is what we calculate from the post-collapse wave function." Isn't 100-0 just the measurement outcome which verifies one of the two possibilities "offered" by the wave function?

Sure, but that’s basically the same thing. We started with the wave function $\frac{\sqrt{2}}{2}(|\alpha\rangle+|\beta\rangle)$, we measure, we get $\alpha$, we know that the wave function has collapsed and now is $|\alpha\rangle$.

 

[yapi]

You are probably thinking more about the infamous "consciousness causes collapse" interpretation (which should not be called von Neumann–Wigner interpretation despite wikipedia, because von Neumann and Wigner described something else). That is simply not a good interpretation.

I now recall reading about this interpretation, but no, was not thinking about it. To me (uninitiated into "tech" QM) such interpretation makes no sense as it implies that either there were no WF "collapses" before consciousness or that consciousness has always existed.

My thinking was more along the lines of Relational quantum mechanics (RQM) interpretation and then, being confused, mixed it with single Universe wave function. I guess, it would be nice to read some up-to-day book/article which clearly sates what all people in the area of QM agree on and what is the subject of fighting with sticks and stones ...

I think I understand now where my mistake was due to misunderstanding of superposition, WF and "collapse" of WF that observed.

 

[yapi]

Sure, but that’s basically the same thing. We started with the wave function $\frac{\sqrt{2}}{2}(|\alpha\rangle+|\beta\rangle)$, we measure, we get $\alpha$, we know that the wave function has collapsed and now is $|\alpha\rangle$.

If I understood correctly what I have read, there are vast number of somewhat complex QM systems which still maintain superpositions of some/all of its QM objects like, for example, atoms and molecules(?). This seems to imply that interaction between even 100s of QM objects does not automatically lead to immediate collapse of that (isolated) QM system wave function(s).
It almost looks to me that in order for a WF of a QM system to "collapse" such interaction(s) must "leak" quantum state information into the "future light cone"/deisolate it.

 

[gentzen]

My thinking was more along the lines of Relational quantum mechanics (RQM) interpretation and then, being confused, mixed it with single Universe wave function. I guess, it would be nice to read some up-to-day book/article which clearly sates what all people in the area of QM agree on and what is the subject of fighting with sticks and stones ...

One such up-to-date (2019) book would be:
https://www.amazon.com/Do-Really-Understand-Quantum-Mechanics/dp/1108477003?tag=pfamazon01-20
The articles on SEP (Stanford Encyclopedia on Philosophy) are typically good in a "no-nonsense" way. However, both resources are more "polished" than the actual state of the field. To understand the actual chaos, wikipedia is probably more suitable, but only if you are already able to have a reasoned opinion of your own. So the reality is that people are still fighting with sticks and stones even over topics which are in princinple well understood since the 80s.