B What Is Surprising About Wave Function Collapse?

[Jimster41]

I agree with Atty.

But I would also add our much better understanding of the basis of the formalism as the most reasonable extension of probability theory that reached fruition in a paper by Hardy:
http://arxiv.org/pdf/quant-ph/0101012.pdf

Thanks
Bill

I've tried to grok that paper 3 times now, just in rough outline. Got farther this time. Next to impossible, even for the enthusiastic. I get it is a great paper. A climber's guide for the non-genius would be a wonderful thing to have for such a thing.

I think I got the idea of the signature of the probability theory this time. I can sort of see a two step space of states. eq 28.

The part I am confused about though is the Continuity Axiom (I know you have mentioned it in the past). As I understand it, it is required to derive QM from the other axioms and it differentiates QM from classical probability theory. But doesn't that just say the theory in which evolution between definite states occurs (which is axiomatically continuous) is physically not classical. I mean the justifications for the classical case sound pretty physical to me, especially the part about the impossibility of a computer with infinite resources. And yet the continuous QM theory describes where evolution between pure states occurs. Is that right? So in what location in the universe is my diet-coke getting warm. Is it in classical reality or someplace continuous? Does discontinuity define the boundary? If so where is the other reality. I honestly can't get my head around how everyone talks about the theory as this bizarre but accepted abstract thing. I believe it, but I want to feel where it is in the world?

I also found this tidbit from Prof Hardy's Perimeter Institute Page really intriquing:
"I am currently working on reformulating General Relativity as a probabilistic theory with agency. The Probabilities can be thought of as being a consequence of ignorance (the underlying theory remaining deterministic). Agency (the possibility of making different choices) is built into quantum theory (we choose which measurement to make). We can also build it into General Relativity."

- which is kind what my commutator question was about (that no-one answered). Aren't commutators real physical decisions that make a proper-time history of a thing in space-time the history it is and not something else?

 

[bhobba]

But doesn't that just say the theory in which evolution between definite states occurs (which is axiomatically continuous) is physically not classical.

No. It says it's 'not' classical probability theory in a particular way. QM is basically the simplest generalised probability model that allows continuous transformations between pure states:
http://arxiv.org/pdf/1402.6562v3.pdf

which is kind what my commutator question was about (that no-one answered). Aren't commutators real physical decisions that make a proper-time history of a thing in space-time the history it is and not something else?

To me the original question was not even understandable. But I think you have now changed it which may bring some comments.

Thanks
Bill

 

[Jean Philippe]

Yes, and that's what people are referring to when they speak of the "collapse of the wave function". Prior to passing through the device, the particle does not have a definite spin. Afterward, it does have a definite spin. That's a change. Either it's a physical change, or its an epistemological change (a change in our knowledge of the situation). You seem to be denying both alternatives, and they seem exhaustive to me.

Mathematically, the "collapse of the wave function" is a projection that introduces an abrupt change (interpreted as unphysical) in the quantum state, that otherwise evolves continuously over time (according to the Schrödinger equation). Considering a single particle, if we perform this "collapse" operation when passing through the device, we prevent the possibility to recover the initial quantum state by further passing through other devices that would recombine the beams (consider a Mach-Zehnder Interferometer). This would be in disagreement with experimental results, because we can recover the initial state by recombining the beams.

[Details : In the case of a MZI, when it is not a which-way experiment, and when no phase shift is introduced, we do recombine the beams and we do recover the initial quantum state. As well, in the Stern-Gerlach experiment, if I let you collapse the quantum state and then decide (without having informed you in advance of this change in the experimental setup) to bring around more devices to make a MZI, I can really recover the initial quantum state while you, having collapsed the quantum state without necessity, cannot anymore, so that "your" quantum state would become inconsistent with the statistics of the measurements. Consider that we have a x-up spin at the beginning, that we split it into a y-up and a y-down spin, there you collapse it onto either y-up or y-down, but I recombine it into the original x-up and measure spin along x, I then get x-up with probability 1, while you would get x-up and x-down with probabilities 1/2, whether you collapsed it onto y-up or y-down.]

[Sorry if it is not what you meant. But anyway it may be what a visitor understood.]

I mean that it is improper to consider a "collapse of the wave function" at this point, because if we actually perform the "collapse" at this point, we actually become inconsistent with experimental results. This is not a matter of interpretation; it is a matter of consistency.

We can delay performing the "collapse" operation as much as we want (stacking more and more conditional probabilities while performing more and more measurements), we may even never perform it, but we cannot perform it too early. [Roughly speaking, it is not "retroactive"].

BTW, I would like to express exactly the same remark with regard to the statement "In such an experiment there is another paradoxical aspect: we can get information about a region of space never visited by any particle" in http://arxiv.org/abs/quant-ph/9610033

If we get information about a region of space it is because it has been visited by the quantum state of the particle. Mathematically speaking, the quantum state went in that region of space, because the only possibility to deny that mathematically would be to perform the "collapse" earlier, but then we would generally get inconsistent with experimental results (consider again the MZI in its most simple embodiment). Hence, the suggested paradox is only a logical consequence of having performed the "collapse" too early. This "too early" is not a matter of taste, it is a matter of consistency with the phenomenon as we can experiment it (consider the MZI).

"According to Bohr a 'physical quantity' can be well-defined by its 'correspondence with a classical quantity' only within the context of the measurement arrangement set up to measure that quantity". [ Sentence copied from http://www.phys.tue.nl/ktn/Wim/qm2.htm ] Maybe I have infringed this rule (because I have considered the quantum state of the particule after the preparation and then I changed the experiment setup on the fly). I plead guilty but my mobile was more consistency (I describe the SG experiment and the MZI experiment in the same way, for what they have in common, in the first example) and less unnecessary paradoxical aspects (in the second example).

 

[bhobba]

I mean that it is improper to consider a "collapse of the wave function" at this point

Collapse is NOT part of QM - only some interpretations.

If you want to discuss collapse specify the interpretation you are using and exactly what you mean by collapse. In the ensemble interpretation for example states and preparation procedures are synonymous. There is no collapse - you simply prepared the particle/system differently. But some consider that just semantics. We have interpretations like MW where there is no collapse - period. We need to know exactly what you think collapse is and the interpretation you are using.

Thanks
Bill