Is the concept of "wave function collapse" obsolete?

[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.

 

[DarMM]

I don't see a reason to look for such deterministic theories to begin with

Well I'm not arguing for determinism or that QM is wrong, I'm just flummoxed as to how one removes the collapse postulate.

 

[vanhees71]

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

The solution of the Schrödinger equation allows it very well. It tells you that I simply have to pick a silver atom from one of the partial beams prepared by running the silver atoms through the magnetic field. Due to the position-spin-component-entanglement I've a silver atom in a pure $S_z=1/2$ state.

 

[vanhees71]

Well I'm not arguing for determinism or that QM is wrong, I'm just flummoxed as to how one removes the collapse postulate.

Just tell me, where in the argument that I simply have to select a silver atom from one of the partial beams prepared by running the silver atoms through the magnetic field to have silver atom prepared in a pure $S_z=1/2$ state I need a the collapse postulate. Nowhere is instantanteous actions at a distance, just the quite local choice, which silver atom to work with after it has run through a magnetic field.

 

[Michael Price]

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.

There are three independent proofs of Born.
1) Everett's Gleason-style proof.
2) Dewitt's frequentist proof (in Physics and Reality)
3) Zurek's symmetry based proof.

 

[DarMM]

Nowhere is instantanteous actions at a distance, just the quite local choice, which silver atom to work with after it has run through a magnetic field

I'm not talking about instantaneous action at a distance. I'm just talking about the collapse postulate.

Just tell me, where in the argument that I simply have to select a silver atom from one of the partial beams prepared by running the silver atoms through the magnetic field to have silver atom prepared in a pure $S_z=1/2$ state I need a the collapse postulate.

QM will not tell you which beam a given atom will be in. So the formalism will just say it has a 50% chance to be in one beam, 50% chance to be in the other. Then when you find it to be in a given beam or take an atom from one beam you can then ignore the "50%" term related to the other beam.

Collapse is just a generalisation of conditioning in probability. That's why I don't get this, it even occurs in basic probability theory with conditional updating of probabilities.

 

[vanhees71]

I think that's a debate about what you call a "derivation of Born's rule", i.e., which assumptions you are accepting as "sufficiently independent" of Born's rule. I think, from a physics point of view, it doesn't make much difference, whether you can derive Born's rule from some other assumptions. A good thing of such proofs might be to understand certain aspects of QT better, but I think after all we have to accept it as a property of nature, as we have to accept that electromagnetic waves are described by Maxwell's equations or the standard model by local gauge symmetries. It's just a result of many careful investigations of nature in terms of observations/experiments and mathematical analysis towards their systematic quantitative description.

 

[DarMM]

There are three independent proofs of Born.
1) Everett's Gleason-style proof.
2) Dewitt's frequentist proof (in Physics and Reality)
3) Zurek's symmetry based proof.

There is also the Oxford Decision theoretic derivation and Vaidman and Carroll's self-locating derivation. I know all of them. As I said I've discussed them in other threads.

 

[Michael Price]

There is also the Oxford Decision theoretic derivation and Vaidman and Carroll's self-locating derivation. I know all of them. As I said I've discussed them in other threads.

Oxford/Deutsch is just too complex, and Carroll's is basically Zurek (but more complex). People that don't get these derivations fall into two camps.
1) those infected by philosophy
2) those that recoil from MWI.

 

[DarMM]

Oxford/Deutsch is just too complex, and Carroll's is basically Zurek (but more complex). People that don't get these derivations fall into two camps.
1) those infected by philosophy
2) those that recoil from MWI.

Carroll and Zurek have quite different assumptions, i.e. quite different postulates about the quantum states of subsystems have to be true. They're not the basically the same.

I'm not sure what you mean by the last part.

 

[vanhees71]

QM will not tell you which beam a given atom will be in. So the formalism will just say it has a 50% chance to be in one beam, 50% chance to be in the other. Then when you find it to be in a given beam or take an atom from one beam you can then ignore the "50%" term related to the other beam.

Collapse is just a generalisation of conditioning in probability. That's why I don't get this, it even occurs in basic probability theory with conditional updating of probabilities.

Of course, QM will not tell me which beam a given atom will be in. But that's not a problem, because indeed as you say, I can just decide to use the 50% of the atoms I want to have (with determined spin component).

That's the point: You don't need the collapse. It's just precisely what you say, the "conditional updating of probabilities". Nowhere is something needed that (a) outside of quantum dynamical laws (in other words, you don't need a "Heisenberg cut") nor do I need (b) spooky actions at a distance (which follows from (a), because in relativistic QFTs you envoke the microcausality constraint in building your models to begin with).

In our example, I just select 50% of the "right atoms" and through the other 50% of the "bad atoms" away and then precisely know the probabilities for the "right atoms". The selection is just guaranteed by blocking out the "bad atoms", which is a local interaction of them with a piece of matter, following the dynamics of local interactions of relativistic QFT.

 

[DarMM]

That's the point: You don't need the collapse. It's just precisely what you say, the "conditional updating of probabilities"

That's what "collapse" refers to in the basic formalism. Conditioning the state upon observations. So when you say you reject collapse, you mean you reject thinking of updating the quantum state in terms of some instantaneous physical process. That's fine, but it's very confusing as that's not what "collapse" refers to.

 

[vanhees71]

Well, then you have a different understanding of the word "collapse" than I have. Of course, I don't deny the "collapse" in this sense. To apply probability theory to the real world (aka statistics) that's what you have to do. In this sense also the outcome of the Saturday's drawing of the lotery numbers in Germany is a "collapse".

The problem is that collapse in the context of QT usually means that

(a) it's according to some (unspecific) classical dynamical laws outside of the QT formalism. The claim is that such a "Heisenberg cut" is necessary.

(b) it's working non-locally, i.e., the collapse violates Einstein causality.

I think (a) is unncessary and also not justified by observations. There's no evidence for the invalidity of QT but a quite well understood explanation for the fact that macroscopic systems usually behave according to classical physics concerning the "relevant macroscopic observables". (b) is simply wrong, because it contradicts the very fundamental construction of relativistic QT in terms of microcausal (aka local) QFT.

 

[DarMM]

In this sense also the outcome of the Saturday's drawing of the lotery numbers in Germany is a "collapse"

Yes indeed. Then we just have different terminology.

The only thing I'll say is that the "cut" isn't really about collapse needing classical laws. It's a separate thing, but not suited to this thread.

 

[Lord Jestocost]

Of course, QM will not tell me which beam a given atom will be in. But that's not a problem, because indeed as you say, I can just decide to use the 50% of the atoms I want to have (with determined spin component).

That's the point: You don't need the collapse.

What the heck do you want to tell?

When you partially block the beam in a say z-oriented Stern-Gerlach apparatus which is fed with a beam of say |+x> polarized particles, you simply acquire a “which path information”. That’s at the end a measurement leading to a “state reduction” to say |+z> or |-z>. There exist no subensembles in the Stern-Gerlach apparatus. As long as nothing is blocked, every particle is in its |+x> state.

 

[vanhees71]

I know which beam to block to get the one I want. I simply put a piece of matter in the way of the other beam.

If you have a $|+x \rangle$ polarized particle and let it run through a SG-magnetic field in $z$ direction, it's state is involving in a state where the spin-z component is entangled with the position of the particle, and thus I know, whether the particle has $\sigma_z=1/2$ or $\sigma_z=-1/2$. I just need to check, where it is located.

Of course running through the magnetic field, now $\sigma_x$ got maximally randomized again, no matter whether or not I block particles or not.

 

[Lord Jestocost]

Of course running through the magnetic field, now σx\sigma_x got maximally randomized again, no matter whether or not I block particles or not.

In case you would recombine "both beams", you would find every particle in the pure |+x> state again. Nothing is randomnized.

 

[PeterDonis]

Thread closed for moderation.

 

[fresh_42]

It seems the discussion came to a kind of end. As we already have many threads with this topic or similar, this one will remain closed.