Is the concept of "wave function collapse" obsolete?

[DarMM]

Yes basically, so if you detect a particle to be in a spin state (however you do it) and then to be in a spin state associated with another direction it has "jumped states" in a way not described by unitary evolution.

In the classical probabilistic case you wouldn't have this because you could just assume the subsequent measurements reduce the support of the probability distribution. It's not a jump to another ensemble, it's just a subensemble.

In a Bayesian view collapse is sort of Bayesian updating + necessary information loss.

So my point to vanhees is that we seem to need collapse for sequences of measurements, because quantum measurements are not just filtrations as in the classical probabilistic case.

You introduced the point of the momentum ancilla into this, I'm just not sure of its purpose. It's something to do with the detector?

 

[PeterDonis]

You introduced the point of the momentum ancilla into this, I'm just not sure of its purpose. It's something to do with the detector?

It's more just to emphasize that describing the process as "detecting a particle to be in a spin state" requires interpretation. In Bohmian mechanics, for example, you aren't doing that; you're just detecting the particle's position, and which output beam of a S-G magnet the particle is in is purely due to its position, not its spin ("spin" doesn't really exist in Bohmian mechanics).

 

[DarMM]

It's more just to emphasize that describing the process as "detecting a particle to be in a spin state" requires interpretation. In Bohmian mechanics, for example, you aren't doing that; you're just detecting the particle's position, and which output beam of a S-G magnet the particle is in is purely due to its position, not its spin ("spin" doesn't really exist in Bohmian mechanics).

Ah sorry I see now. Indeed my language should have been more neutral. What would be the correct phrasing do you think?

Instead of saying "the particle has gone from one state to another" the most neutral statement would be "our probability assignments have gone from one form to another"

 

[PeterDonis]

Instead of saying "the particle has gone from one state to another" the most neutral statement would be "our probability assignments have gone from one form to another"

That phrasing makes "collapse" a non-problem, since there is no requirement that our probability assignments must obey unitary evolution.

 

[DarMM]

What's an interpretation neutral phrasing then?

Our assignments outside of measurements have to obey unitary evolution I thought due to that being an automorphism of the observable algebra. If you read nothing more into the formalism than probability assignments for macroscopic outcomes (and I thought all interps allow you to do this, their common core would be this effective use of the formalism) it seems to me the above is what you would say.

 

[PeterDonis]

What's an interpretation neutral phrasing then?

The only really neutral phrasing is to just describe the macroscopic observation ("a spot was observed at such-and-such point on the detector screen") and leave it at that.

 

[DarMM]

The only really neutral phrasing is to just describe the macroscopic observation ("a spot was observed at such-and-such point on the detector screen") and leave it at that.

That's not a neutral phrasing of the quantum formalism though. It's not just interpretation of QM neutral it's theory neutral.

 

[PeterDonis]

That's not a neutral phrasing of the quantum formalism though.

I would say a neutral phrasing of the quantum formalism is to just write down the equations and leave it at that.

 

[DarMM]

I would say a neutral phrasing of the quantum formalism is to just write down the equations and leave it at that.

But you have to apply them to an experiment. You can't just write them down, that seems to be the opposite extreme. That's why I think a fairly neutral statement is to say that the probabilities for future macroscopic effects are updated after a seeing a specific macroscopic effect in a way described by state collapse. All the interpretations would agree on that pragmatic use, they'd disagree on what else might be going on and what the meanings of terms are beyond their pure pragmatics.

 

[PeterDonis]

the probabilities for future macroscopic effects are updated after a seeing a specific macroscopic effect in a way described by state collapse

Yes, but as I said, this makes "collapse" a non-problem because updating probabilities does not require anything to have "actually happened" to the system. (Perhaps instead of "non-problem" it could be termed an "interpretation-dependent problem", and one interpretation is simply that nothing "actually happens" during collapse, it's just that we update the probabilities we'll use for future predictions.)

 

[DarMM]

Collapse and whether it needs to be explained is an interpretation dependent issue.

The interpretation neutral thing is how it is applied, i.e. see macroscopic effect then update the state to give probabilities to future macroscopic effects. That's what is actually done. I don't think this necessarily makes it a non-issue, it's just how it is used.

 

[vanhees71]

I agree with all this of course. I was not so much concerned with how exactly the $S_x$ and $S_z$ measurements are done but that the $S_x$ preparation cannot be considered a sub-ensemble (in the probability theory sense) of the $S_z$ preparation it originates from and hence the non-filtering nature of the experiment is what is essentially collapse.

The problem with all these philosophical (in my opinion irrelevant) discussions on interpretation is precisely the refusal to discuss real-world experiments. The SG experiment is the most simple example, where everything can be (nearly) analytically calculated within standard QM, and I don't see any mystery left.

Why you want to call blocking a partial beam of silver atoms by putting something in its way "collapse" I don't know. For sure looking at the experimental setup you immediately see that this "collapse" works with the usual local interactions of the silver atoms with the matter making up the "blocker". Nothing acts instantaneously at a distance! I call simply blocking a partial beam of silver atoms blocking this partial beam, and the partial beam defines indeed a subensemble of silver atoms with definite $S_x$ which have been prepared to have a definite $S_z=+1/2$. Of course, QT tells you that then $S_z$ doesn't take a definite value anymore, and you even understand it from the dynamics why this must be so!

 

[DarMM]

The problem with all these philosophical (in my opinion irrelevant) discussions on interpretation is precisely the refusal to discuss real-world experiments. The SG experiment is the most simple example, where everything can be (nearly) analytically calculated within standard QM, and I don't see any mystery left

This isn't philosophical or related to interpretations. I'm not even saying there is a mystery. You're the one saying there is no collapse, part of the textbook formalism of the theory. Yes I can easily calculate the whole set up in standard QM and as per textbook QM (Weinberg, Peres, Shankar) it uses the collapse postulate.

Why you want to call blocking a partial beam of silver atoms by putting something in its way "collapse" I don't know. For sure looking at the experimental setup you immediately see that this "collapse" works with the usual local interactions of the silver atoms with the matter making up the "blocker". Nothing acts instantaneously at a distance!

Nobody is saying there is instantaneous action at a distance. Where is this even coming from?

 

[Michael Price]

Nobody is saying there is instantaneous action at a distance. Where is this even coming from?

The collapse is a non-local, instaneous, action-at-a-distance effect. That's why a lot of us don't believe in it. That's also in the textbooks.

 

[DarMM]

defines indeed a subensemble of silver atoms with definite $S_x$ which have been prepared to have a definite $S_z=+1/2$.

It's not a subensemble in the the sense of probability theory that's literally a fact coming from the differences between quantum and classical probability.

 

[vanhees71]

Nowhere in the calculations you use the collapse postulate. You solve an initial-value problem of a partial differential equation. That's it.

The word "collapse" implies "spooky action at a distance", and Einstein rightfully critizised this. The irony is that you don't need the collapse, and to postulate it contradicts the very fundamental construction of relativistic QFT. So why using it?

 

[DarMM]

The collapse is a non-local, instaneous, action-at-a-distance effect. That's why a lot of us don't believe in it. That's also in the textbooks.

If you accept the wave-function as an ontic element and collapse as real then it would imply a non-local effect. However interpretations that view the wavefunction as ontic typically don't have collapse and interpretations that have collapse don't view the wavefunction as ontic. So usually this is a non-issue. Textbook QM (a form of Copenhagen) doesn't have the wavefunctions as ontic.

 

[DarMM]

Nowhere in the calculations you use the collapse postulate. You solve an initial-value problem of a partial differential equation. That's it

So you can obtain the results of a $S_z$ measurement followed by an $S_x$ measurement purely with unitary dynamics?

 

[vanhees71]

It's not a subensemble in the the sense of probability theory that's literally a fact coming from the differences between quantum and classical probability.

It depends on, what you call a subensemble. I simply call choosing a part of a given ensemble according by some selection a subensemble. I also don't know, what you mean by quantum vs. classical probability.

I think, probabilities are probabilities, following a general axiomatic definition like, e.g., Kolmogorov's system, though this system doesn't determine the concrete probabilities for a given situation, which is provided by quantum theory.

 

[vanhees71]

So you can obtain the results of a $S_z$ measurement followed by an $S_x$ measurement purely with unitary dynamics?

Sure, why not?

 

[DarMM]

Sure, why not?

That would constitute a solution to the measurement problem. Where is there an account of this?

 

[DarMM]

I also don't know, what you mean by quantum vs. classical probability.

I think, probabilities are probabilities, following a general axiomatic definition like, e.g., Kolmogorov's system, though this system doesn't determine the concrete probabilities for a given situation, which is provided by quantum theory

Quantum Probability doesn't obey Kolmogorov's axioms. It's a generalisation of probability theory.

 

[Michael Price]

That would constitute a solution to the measurement problem. Where is there an account of this?

Any MWI textbook. Everett solved the measurement problem over sixty years ago. No collapse, just unitary evolution.

 

[DarMM]

Any MWI textbook. Everett solved the measurement problem over sixty years ago.

I doubt @vanhees71 is referring to MWI and Everett did not "solve" the measurement problem as he assumes a massive amount structure first and his derivation of the statistical rules, even as improved by DeWitt has gaps and the limits don't work. Hence the work of Wallace, Zurek and others.

 

[vanhees71]

That would constitute a solution to the measurement problem. Where is there an account of this?

Here is a nice paper:

https://arxiv.org/abs/quant-ph/0409206

 

[Michael Price]

I doubt @vanhees71 is referring to MWI and Everett did not "solve" the measurement problem as he assumes a massive amount structure first and his derivation of the statistical rules, even as improved by DeWitt has gaps and the limits don't work. Hence the work of Wallace, Zurek and others.

That is open to debate. Everett gave derivation of the Born rule that mirrors Gleason's. Good enough for the physicist in me.

 

[DarMM]

That is open to debate. Everett gave derivation of the Born rule that mirror Gleason's. Good enough for me.

It's not. Even MWI people today don't believe Everett's derivation is valid. Literally his analysis isn't mathematically valid. See the lectures of Matt Leifer where he discusses this. I've done a long analysis of the proofs of Born's rule in MWI in another thread. I'll discuss this in another thread.

 

[A. Neumaier]

I call simply blocking a partial beam of silver atoms blocking this partial beam, and the partial beam defines indeed a subensemble of silver atoms with definite $S_x$ which have been prepared to have a definite $S_z=+1/2$.

Nothing in quantum theory without collapse allows you to conclude this!

 

[vanhees71]

I doubt @vanhees71 is referring to MWI and Everett did not "solve" the measurement problem as he assumes a massive amount structure first and his derivation of the statistical rules, even as improved by DeWitt has gaps and the limits don't work. Hence the work of Wallace, Zurek and others.

I don't understand the MWI argument, because it just says there are an overcountable set of new universes popping up just when I look at something to determine its location. All these universes are unobservable and thus the entire thing looks to me as empty concerning the physical content.

All I'm saying is, that one has to take QT as it is, and Born's rule is one of the independent postulates. That is, because QT is so amazingly successful in describing all observations so far, and it's very accurately tested. Nobody has come up with a deterministic theory that is as successful as QT, and as long there is no clear evidence that the world is somehow deterministic, I don't see a reason to look for such deterministic theories to begin with. For the time being, I just accept that nature is inherently random but at the same time following very accurate rules concerning the corresponding probabilities.

 

[DarMM]

Here is a nice paper:

https://arxiv.org/abs/quant-ph/0409206

It is a nice paper, but there we do not see the emergence of a definitive $S_x$ state from the unitary dynamics. Even the graphics in the paper show this.