Is wave function a real physical thing?

[atyy]

Its exactly the same ensemble used in probability. I think you would get a strange look from a probability professor if you claimed such a pictorial aid was a hidden variable.

At any rate, what you have done here is to introduce something beyond unitary time evolution. So given that one uses this pictorial aid in setting up the wave function, couldn't one argue that the wave function is at least partly epistemic?

Atty I think we need to be precise what is meant by collapse. Can you describe in your own words what you think collapse is?

My view is its the idea observation instantaneously changes a quantum state in opposition to unitary evolution. Certainly it changes in filtering type observations - but instantaneously - to me that's the rub. It changed because you have prepared the system differently but not by some mystical non local instantaneous 'collapse' - if you have states - you have different preparations - its that easy.

Yes, it is the immediate change of state after a measurement. So for example, if we have an EPR experiment with a Bell state |uu>+|dd>, then immediately after A measures and obtains an up outcome, the state collapses to |uu>, and if A obtains a down outcome, the state collapses to |dd>. How immediate does it have to be? If there is a frame in which the measurements of A and B are simultaneous, then there is a frame in which B measures slightly after A, and so far all data is consistent with quantum mechanics with collapse, and with relativity.

One cannot simply say that one has a different preparation. The reason is that the the preparation of the state |uu> or |dd> following the measurement is linked to whether A gets the outcome up or down. So the preparation of an |uu> or |dd> state is identified with the measurement outcome, and has the same probabilities as the Born rule.

Added Later:
As the Wikipedia artice says:
On the other hand, the collapse is considered a redundant or optional approximation in:
the Consistent histories approach, self-dubbed "Copenhagen done right"
the Bohm interpretation
the Many-worlds interpretation
the Ensemble Interpretation

IMHO it's redundant in the above.

I agree that collapse is not required in consistent histories, Bohmian Mechanics and Many-Worlds. I don't agree that the Ensemble interpretation does away with it, unless one adds another postulate to the interpretation that is equivalent to collapse.

 

[atyy]

No, they are disentangled due to the (local!) interaction of A's photon with the polarizer and photon detector. Usually it gets absorbed by the latter, and there's only B's photon left as long as his is not absorbed by his detector either.

So if I understand you correctly, you are saying that if we have a Bell state |uu>+|dd>, after A measures and gets an up result the state is |uu>, and after A gets a down result, the state is |dd>. This is the collapse postulate. (Let's assume non-destructive measurements for simplicity.)

 

[vanhees71]

FAPP yes. In reality it's of course way more complicated. You have a system consisting of the BaO crystal, a laser, the entangled two-photon Fock state (wave packets!) as well as polarization foils and photon detectors at Alice's and Bob's place. I guess that should roughly be the relevant setup.

The time evolution of this whole setup is described by the unitary time evolution of quantum theory. Now for our experiment we only look at the polarization states of the two photons. One should however also include the spatial part of the two-photon state, because this enables us to effectively distinguish A's and B's photon which are defined by local interactions with the respective photo detectors. FAPP you can use the "collapse postulate" to understand the outcome of correlated measurements on the photon's polarization state when the polarizers are set in the same or perpendicular directions at A's and B's place. This "collapse" should however really only be seen as an effective description of the entire quantum dynamics through the local interactions of the photons with the equipment around them, but not as a process happening "really in nature". This would lead to the very serious problems brought up by EPR.

My interpretation of the EPR paper is that they have not critizized quantum theory as such but only the Copenhagen flavor with the collpase of it.

The only interpretation that bhobba lists I've not yet studied enough to have an opinion on is the consistent history approach. How is the "collapse" seen there?

 

[bohm2]

My interpretation of the EPR paper is that they have not critizized quantum theory as such but only the Copenhagen flavor with the collpase of it.

The shortest summary of the EPR paper that I've read and makes sense to me can be summarized in 2 sentences:
1. Either QM is incomplete or if it's complete, it must be nonlocal.
2. Nonlocality is unreasonable, therefore it is incomplete.

 

[stevendaryl]

Its exactly the same ensemble used in probability. I think you would get a strange look from a probability professor if you claimed such a pictorial aid was a hidden variable.

That comparison is not fair, in my opinion. In classical probability, the assumption is that your actual system is in some actual state. But all you know about that state is that it is one of a virtual (or actual, maybe) ensemble of systems. So it certainly is the case that classical probability involves "hidden variables", namely the actual state of your system (or the one you pick to examine, if there is an actual ensemble).

 

[vanhees71]

That's a bit too short for me. What do you mean by "complete" and "nonlocal"?

Well, I don't think that any physical theory can be proven to be complete. So I don't bother about this question very much. So far we have no hint that quantum theory is incomplete, but that doesn't imply that it is complete.

Now, the most comprehensive QT we have is relativistic quantum field theory (let's ignore the substantial mathematical problems in its foundations and let's take the physicist's practical point of view to define it in a perturbative sense). By construction the interactions within this theory are strictly local. Nobody could construct a consistent QFT with non-local interactions so far.

On the other hand, there is entanglement, implying the possibility of correlations between far-distant observations, as is demonstrated by the Aspect-Zeilinger like experiments with entangled photons. In principle you could detect the two photons at places as far from each other as you like and still find the correlations described by the entangled two-photon states. These I'd call non-local correlations, but these do not violate the relativistic causality structure, as long as you don't consider the collapse as a real process and stick, e.g., to the minimal statistical interpretation (some time ago we had a debate along these lines when discussing the quantum-eraser experiment by Scully et al). Thus, I think EPR rightfully criticized the Kopenhagen collapse doctrine rather than quantum theory itself.

Whether one can "quantum theory consider complete" depends on the definition of "complete". As stressed above, I don't think that we can ever be sure of any physical theory to be complete. I'd consider a theory as complete as long as there are no phenomena that contradict this theory. This can change. For quite a long time the physicists considered Newtonian mechanics as complete, but with the discovery of Faraday-Maxwell electromagnetism it turned out that it cannot be complete, because its very basic foundation doesn't hold for electromagnetic processes. This puzzle was finally solved by Einstein in his famous 1905 paper about what we call Special Relativity Theory today. Then one could have thought that relativistic mechanics + electrodynamics is complete. This idea hold for at most 2 years, when Einstein discovered that he couldn't make easy sense of gravity, which lead to the development of the General Relativity Theory, which was finished by Einstein (and at the same time also Hilbert) in 1915 (big anniversary next year :-)).

The entire classical picture of physics, which was completed (at least from our present knowledge) with General Relativity, was found to be incomplete in 1911, when Rutherford discovered the true (to our present knowledge) structure of atoms as consisting of a pointlike (to the accuracy available at his time) nucleus surrounded by electrons, held together by the electromagnetic interaction. The very simple experience of the stability and rigidity of matter around has, however, leads to a contradiction of this picture. The solution finally was quantum theory, discovered in 1925/26 by Heisenberg, Born, Jordan, Pauli, and Schrödinger, and Dirac.

Even today we know that in a certain sense our theoretical edifice of physical models is not complete, but it's not an observation contradicting relativistic quantum field theory (to the contrary the Standard Modell is too successful to get it finally ruled out with the necessary hint for the theorists to move on with a better model) but intrinsic problems, among the most fundamental is the lack of a satisfactory quantum description of the gravitational interaction. In this sense we already today know that our models are not the final word of a "theory of everything", and at the moment there's no help in sight from any observations in HEP or astrophysics/cosmology, and both fields are very closely connected in those days!

 

[DrChinese]

The shortest summary of the EPR paper that I've read and makes sense to me can be summarized in 2 sentences:
1. Either QM is incomplete or if it's complete, it must be nonlocal.
2. Nonlocality is unreasonable, therefore it is incomplete.

EPR only refers to non-locality somewhat indirectly - via the idea that a measurement on one part of a system does not affect another part of that system. What they refer to as unreasonable is a particular form of realism, also see below. If you want to make your statements consonant with what EPR said, I might suggest replacing "nonlocality" with "Observer Dependent Reality". I believe that would get pretty close to what you want.

1. Either QM is incomplete or if it's complete, it must be observer dependent.
2. An observer dependent reality is unreasonable, therefore QM is incomplete.EPR Locality assumption/definition according to EPR:

“On the other hand, since at the time of measurement the two systems no longer interact, no real change can take place in the second system in consequence of anything that may be done to the first system. This is, of course, merely a statement of what is meant by the absence of an interaction between the two systems. Thus, it is possible to assign two different wave functions … to the same reality (the second system after the interaction with the first).”

Comment: the Bohr view of the EPR example was: there is one system consisting of 2 particles, not 2 systems of one particle as EPR suppose. Therefore, saying “the two systems no longer interact” is not accurate at some unspecified level (in that view).

EPR Realism assumption/definition according to EPR:

“The elements of the physical reality cannot be determined by a priori philosophical considerations, but must be found by an appeal to results of experiments and measurements. A comprehensive definition of reality is, however, unnecessary for our purpose. We shall be satisfied with the following criterion, which we regard as reasonable.If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity. It seems to us that this criterion, while far from exhausting all possible ways of recognizing a physical reality, at least provides us with one such way, whenever the conditions set down in it occur. Regarded not as necessary, but merely as a sufficient, condition of reality, this criterion is in agreement with classical as well as quantum-mechanical ideas of reality.”

Comment: Later, they make clear that their “reasonable” definition also assumes as follows. Any single element of reality that passes the test (i.e. predictable with probability of 100%) is simultaneously real along with all other elements that also individually pass the same test. Therefore, a collection of elements of reality constitute what is usually called “realism” in the EPR context. That would include elements of reality that do not commute with each other. Specifically: "Indeed, one would not arrive at our conclusion if one insisted that two or more physical quantities can be regarded as simultaneous elements of reality only when they can be simultaneously measured or predicted. On this point of view, since either one or the other, but not both simultaneously, of the quantities P and Q can be predicted, they are not simultaneously real.” EPR stated such requirement was unreasonable (“No reasonable definition of reality could be expected to permit this.”).

 

[DrChinese]

PS If discussion of my post above is desired, we can always move it to another thread to avoid getting off topic.

 

[atyy]

FAPP yes. In reality it's of course way more complicated. You have a system consisting of the BaO crystal, a laser, the entangled two-photon Fock state (wave packets!) as well as polarization foils and photon detectors at Alice's and Bob's place. I guess that should roughly be the relevant setup.

The time evolution of this whole setup is described by the unitary time evolution of quantum theory.

Yes, so I think we really disagree. My view is that the whole minimal interpretation is FAPP, and requires the cut and collapse which are also FAPP.

On the other hand, you believe that collapse can be derived from unitary evolution alone, and so the cut and collapse are not required. I don't agree with this because to derive collapse from unitary evolution requires additional assumptions usually considered non-minimal, for example hidden variables or many-worlds. So collapse, which is FAPP, or an equivalent postulate is required in a minimal interpretation.

 

[vanhees71]

Not from unitary evolution alone. You always need coarse graining to derive the classical behavior of measurement/preparation devices.

I can live with any interpretation without collapse as a real process, becausevit violates causality.

 

[atyy]

Not from unitary evolution alone. You always need coarse graining to derive the classical behavior of measurement/preparation devices.

Sure, introducing coarse graining as an additional postulate is equivalent to introducing a cut and collapse as postulates. Then the measurement problem is that the coarse grained theory makes sense, but the fine grained theory (without hidden variables or MWI) does not, whereas in classical physics both the fine-grained or more fundamental theory and the coarse-grained or emergent theory make sense. It is in this sense that I consider the cut and collapse essential: if you remove it, in a minimal interpretation you must reintroduce the measurement problem by introducing an additional FAPP postulate beyond unitary evolution.

I can live with any interpretation without collapse as a real process, becausevit violates causality.

In the minimal interpretation, the cut and collapse are not necessarily real, they are FAPP. So we have collapse or coarse graining, both of which are FAPP. So here are the questions: Is collapse ontic or epistemic? Is coarse graining ontic or epistemic? Is FAPP ontic or epistemic?

If collapse is not physical, then it is presumably at least partly epistemic. So my point against your argument that the wave function is ontic is that collapse is part of the time evolution of the wave function. Consequently, if one considers collapse to be epistemic, it isn't obvious how the wave function can be purely ontic.

 

[vanhees71]

Sure, introducing coarse graining as an additional postulate is equivalent to introducing a cut and collapse as postulates. Then the measurement problem is that the coarse grained theory makes sense, but the fine grained theory (without hidden variables or MWI) does not, whereas in classical physics both the fine-grained or more fundamental theory and the coarse-grained or emergent theory make sense. It is in this sense that I consider the cut and collapse essential: if you remove it, in a minimal interpretation you must reintroduce the measurement problem by introducing an additional FAPP postulate beyond unitary evolution.

NO! There's a big difference in this approach: It's showing that there are no instantaneous interactions at a distance as claimed with collapse postulates but only local interactions as postulated in all successful relativistic-QFT models (including the standard model).

See also the very nice paper, somebody brought up in one of our "interpretation discussions". I don't like some subtleties like using the word "collapse" and "wave functions" for photons, but the overall conclusion is right. Note that Fig. 1 does not provide the correct interpretation of measurements according to Sect. 3.

Of course, he misses the point somewhat by oversimplifying the math with the entangled states somewhat. I plead guilty for myself in this respect, when I discussed the Scully quantum eraser experiment in this forum. The oversimplification is in leaving out the spatial part of the two-photon state. Here a "wave-packet formulation" is mandatory to make the issue utmost clear, and this also leads to the correction of Fig. 1 described in words at the end of Sect. 3. Of course "wave packet" should not be understood as introducing a "wave function for photons". There cannot be such an object, because the photon hasn't even a position operator in the usual sense. You have locations of detection events, which are well-defined by the fact that photons are detected with devices consisting of massive particles and not because the asymptotic free photon states have a position.

 

[atyy]

NO! There's a big difference in this approach: It's showing that there are no instantaneous interactions at a distance as claimed with collapse postulates but only local interactions as postulated in all successful relativistic-QFT models (including the standard model)

Can you show that the coarse-graining is local and preserves relativistic causality? Peres talks about coarse-graining such that the Wigner function becomes entirely positive, which means that the theory resulting from the coarse-graining is a classical probabilistic theory and therefore realistic. If the coarse-graining is local, the resulting theory is presumably a local realistic theory. However, the Bell theorem forbids local realistic theories, so the theory that results from local coarse-graining presumably cannot explain violations of the Bell inequalities at spacelike separation.

See also the very nice paper, somebody brought up in one of our "interpretation discussions". I don't like some subtleties like using the word "collapse" and "wave functions" for photons, but the overall conclusion is right. Note that Fig. 1 does not provide the correct interpretation of measurements according to Sect. 3.

Of course, he misses the point somewhat by oversimplifying the math with the entangled states somewhat. I plead guilty for myself in this respect, when I discussed the Scully quantum eraser experiment in this forum. The oversimplification is in leaving out the spatial part of the two-photon state. Here a "wave-packet formulation" is mandatory to make the issue utmost clear, and this also leads to the correction of Fig. 1 described in words at the end of Sect. 3. Of course "wave packet" should not be understood as introducing a "wave function for photons". There cannot be such an object, because the photon hasn't even a position operator in the usual sense. You have locations of detection events, which are well-defined by the fact that photons are detected with devices consisting of massive particles and not because the asymptotic free photon states have a position.

I think the paper you are thinking about is Braam Gaasbeek's "Demystifying the Delayed Choice Experiments" http://arxiv.org/abs/1007.3977. I agree with this paper completely. Section 3 does not correct Figure 1. Section 3 says Figure 1 is correct, but that collapse is not necessarily physical (not an frame-invariant event). Quantum mechanics in the minimal interpretation is an FAPP theory, and the predictions of FAPP collapse are thus far completely successful and consistent with special relativity. So this paper does not support your point (unless we are agreeing, but using different language). Rather it supports my point that collapse is part of the standard postulates of quantum mechanics, and is not in conflict with relativity.

 

[DrChinese]

Of course "wave packet" should not be understood as introducing a "wave function for photons". There cannot be such an object, because the photon hasn't even a position operator in the usual sense. You have locations of detection events, which are well-defined by the fact that photons are detected with devices consisting of massive particles and not because the asymptotic free photon states have a position.

Are you in the school of thought that free photons don't exist because they are excitations of the EM field?

 

[vanhees71]

No, there are free-photon states within QED and thus they exist within this framework. However, photons cannot be interpreted as particles like massive quanta, because massless particles with spin $s \geq 1$ have no position observable (at least not one in the strict sense). See Arnold Neumaier's FAQ:

http://arnold-neumaier.at/physfaq/topics/position.html

 

[vanhees71]

Can you show that the coarse-graining is local and preserves relativistic causality? Peres talks about coarse-graining such that the Wigner function becomes entirely positive, which means that the theory resulting from the coarse-graining is a classical probabilistic theory and therefore realistic. If the coarse-graining is local, the resulting theory is presumably a local realistic theory. However, the Bell theorem forbids local realistic theories, so the theory that results from local coarse-graining presumably cannot explain violations of the Bell inequalities at spacelike separation.

I've the kinetic approach in mind. There the "coarse-graining" is done via gradient expansion. I've to think harder, whether this leads to a violation of Bell's theorem. Maybe this is a loophole in my argument!

I think the paper you are thinking about is Braam Gaasbeek's "Demystifying the Delayed Choice Experiments" http://arxiv.org/abs/1007.3977. I agree with this paper completely. Section 3 does not correct Figure 1. Section 3 says Figure 1 is correct, but that collapse is not necessarily physical (not an frame-invariant event). Quantum mechanics in the minimal interpretation is an FAPP theory, and the predictions of FAPP collapse are thus far completely successful and consistent with special relativity. So this paper does not support your point (unless we are agreeing, but using different language). Rather it supports my point that collapse is part of the standard postulates of quantum mechanics, and is not in conflict with relativity.

Yes, that's the paper. Sorry, I forgot to cite it properly again. Here's the crucial point (at the end of Sect. 3):

B. Gaasbek:
We can now solve the problem we started with in the
introduction. If the measurement is nothing but an iso-
lated event in space time, there is no point whatsoever in
trying to associate a spatial slice to it. So the horizontal
and tilted lines in Figure 2 actually have no meaning at
all! Nothing happens along these slices - the only place
where something physical happens is the place of the
measurement, and the implications on conditional prob-
abilities hold for other measurements throughout the en-
tire spacetime, present and past.

If "nothing happens along these slices" in Fig. 2 then the instantaneous collapse proposed in Fig. 1 doesn't happen, or did I get this wrong?

 

[atyy]

If "nothing happens along these slices" in Fig. 2 then the instantaneous collapse proposed in Fig. 1 doesn't happen, or did I get this wrong?

Yes, I agree with that. Let me use my flavour of Copenhagen. I will take a classical/quantum cut (don't take the term "classical" too literally), by which I mean that only things on the classical side are real or physical, while things on the quantum side are not (necessarily) real or physical. As shorthand, I will simply say that things on the quantum side are not real or not physical. So yes, in Copenhagen the instantaneous collapse is not physical and does not really happen. Only the measurement choice and the measurement outcome are real, and these are local classical events.

 

[DrChinese]

No, there are free-photon states within QED and thus they exist within this framework. However, photons cannot be interpreted as particles like massive quanta, because massless particles with spin $s \geq 1$ have no position observable (at least not one in the strict sense). See Arnold Neumaier's FAQ:

http://arnold-neumaier.at/physfaq/topics/position.html

Thanks, that's a treasure trove of his material. :-)

 

[vanhees71]

Yes, I agree with that. Let me use my flavour of Copenhagen. I will take a classical/quantum cut (don't take the term "classical" too literally), by which I mean that only things on the classical side are real or physical, while things on the quantum side are not (necessarily) real or physical. As shorthand, I will simply say that things on the quantum side are not real or not physical. So yes, in Copenhagen the instantaneous collapse is not physical and does not really happen. Only the measurement choice and the measurement outcome are real, and these are local classical events.

Ok, then that's just other wording for the minimal interpretation. I can live with this understanding of "collapse".

Then you would you also call the result of tossing a die and finding it showing "6" a collapse (before you'd have asserted $P("6")=1/6$, if you've known nothing about the specific die before)?

 

[TrickyDicky]

Then you would you also call the result of tossing a die and finding it showing "6" a collapse (before you'd have asserted $P("6")=1/6$, if you've known nothing about the specific die before)?

Well, if all the information about observables you had in classical physics was in this form, I bet you'd call it collapse too, or maybe would use like previously the fancier expression "coarse graining" ;), but it amounts to the same thing: sneaking irreversibility into the reversible Schrodinger equation picture, or into reversible Newtonian laws thru entropy(Boltzmann variety).

 

[atyy]

Ok, then that's just other wording for the minimal interpretation. I can live with this understanding of "collapse".

Then you would you also call the result of tossing a die and finding it showing "6" a collapse (before you'd have asserted $P("6")=1/6$, if you've known nothing about the specific die before)?

Within my flavour of Copenhagen, I cannot answer whether the wave function is ontic or epistemic. The wave function is not necessarily real or ontic because I do take a classical/quantum cut. I like the die analogy, but the analogy between collapse and Bayesian updating is not exact, so I don't know whether collapse is epistemic.

Here's the question I've been trying to ask you: Since you support the die analogy, it seems that collapse is epistemic in the minimal interpretation. However, earlier you argued that the wave function is ontic in the minimal interpretation. Collapse (measurement and selection of a sub-ensemble) is a method of preparing a wave function. If one method of preparing a wave function is epistemic, how can the wave function be ontic?

 

[stevendaryl]

Ok, then that's just other wording for the minimal interpretation. I can live with this understanding of "collapse".

Then you would you also call the result of tossing a die and finding it showing "6" a collapse (before you'd have asserted $P("6")=1/6$, if you've known nothing about the specific die before)?

If the wave function simply reflects the knowledge (or lack thereof) of the observer, then there is nothing weird about a "collapse". When you observe something, you're just discovering a pre-existing value. But that interpretation is difficult to maintain for quantum mechanics, because in some circumstances (for example, EPR), there is no way to interpret the results of a measurement in terms of pre-existing values.

 

[bohm2]

EPR stated such requirement was unreasonable (“No reasonable definition of reality could be expected to permit this.”).

Here's the exact quote from the EPR paper:

This makes the reality of P and Q depend upon the process of measurement carried out on the first system, which does, not disturb the second system in any way. No reasonable definition of reality could be expected to permit this.

Can Quantum-Mechanical Description of Physical Reality Be Considered Complete' ?
http://journals.aps.org/pr/pdf/10.1103/PhysRev.47.777

I take this as just point 2. ("Nonlocality is unreasonable..") mentioned above; that is, the "unreasonableness" that elements of reality could depend on nonlocal effects. Blaylock and Fine agree on this point:

Regarding the possibility that elements of reality could depend on nonlocal effects, they concluded: “No reasonable definition of reality could be expected to permit this.”

The EPR paradox, Bell’s inequality, and the question of locality
http://www.stat.physik.uni-potsdam.de/~pikovsky/teaching/stud_seminar/Bell_EPR-1.pdf

The unreasonableness to which EPR allude in making “the reality [on the second system] depend upon the process of measurement carried out on the first system, which does not in any way disturb the second system” is just the unreasonableness that would be involved in renouncing locality understood as above.

The Einstein-Podolsky-Rosen Argument in Quantum Theory
http://plato.stanford.edu/entries/qt-epr/

 

[DrChinese]

1. Here's the exact quote from the EPR paper:...

2. I take this as just point 2. ("Nonlocality is unreasonable..") mentioned above; that is, the "unreasonableness" that elements of reality could depend on nonlocal effects. Blaylock and Fine agree on this point:

1. Yes, I included that specific quote in my post.

2. Certainly, you must be able to see that going from "This makes the reality of P and Q depend upon the process of measurement carried out on the first system, which does, not disturb the second system in any way. No reasonable definition of reality could be expected to permit this" to "non-locality is unreasonable" is a completely circular argument. EPR says one thing, and the conclusion you reach requires making a substitution that EPR would never agree with. Whether that conclusion is warranted or not is in some ways irrelevant. It wouldn't be a conclusion of EPR, but a conclusion of someone else.

Please note that although Fine's otherwise excellent Plato article skips it, I presented the quote from EPR where realism is assumed/defined explicitly. They flat out said: if you require elements of reality to be simultaneously predictable, you won't reach our conclusion. Ergo, they assume it. It doesn't get much more explicit than that. If you then further ASSUME that non-locality is the ONLY way to have non-realism, then you get your result (as Fine does).

 

[Ross D]

Why? For example EM can be written in complex form:
file:///C:/Users/Administrator/Downloads/Complex%20Maxwell%2527s%20equations.pdf

Physics is basically a mathematical model - all sorts of things can be used to model it.

Thanks
Bill

What I mean by that statement is not that you can't use imaginary numbers in modeling, but that they are not what is actually happening in the real world. For example, you cannot have an imaginary amount of ducks, but it is possible to create a complex function that gives you the amount of ducks. The wave function itself is imaginary and as such is not a physical object, but the probability distribution that it creates is very real and carries a finite amount of energy.

 

[Ross D]

How is the wave function measured?

The wave function is not measured directly, but instead it is defined in terms of three things that can be measured directly: energy, probability, and frequency. The wave function has defined mathematical relationships to all of these, so you can use measurements of these to determine the wave function. You usually have to have some constraints to simplify the process, though.

 

[TrickyDicky]

If the wave function simply reflects the knowledge (or lack thereof) of the observer, then there is nothing weird about a "collapse". When you observe something, you're just discovering a pre-existing value. But that interpretation is difficult to maintain for quantum mechanics, because in some circumstances (for example, EPR), there is no way to interpret the results of a measurement in terms of pre-existing values.

There is no way to make the interpretation within the theory, but the whole point of the EPR paper was that the theory was incomplete, that is to come up with an example that showed clearly the incompleteness. The only possible answer to the paper from within the theory is, either in Bell's form or any other, to get immersed ever deeper in the QM nonlocal flavor of antirealism. Only some interpretations of QM like many-worlds or BM attempt to do that. QFT's locality is in some way an example of the incompleteness of QM if one considers it as realist .

 

[bhobba]

but that they are not what is actually happening in the real world.

The map is not the territory. None of our models tell us what's happening in the 'real' world - whatever that is - philosophers can't seem to agree on that one - it only describes it. Any model using anything is just as valid as any other model - the only criteria is - does it agree with experiment.

you cannot have an imaginary amount of ducks,

You can't have a negative amount of ducks either - but if you owe someone some ducks its a perfectly good way to model it.

Thanks
Bill

 

[bhobba]

The wave function is not measured directly, but instead it is defined in terms of three things that can be measured directly: energy, probability, and frequency.

Energy has nothing directly to do with measuring a wave-function. To measure it you need a large ensemble and have a positive on each observation to determine if its in that state. The only invocation of probability and frequency is determining if the ensemble is large enough so that a positive on every member means the chance of it not being in that state is for all practical purposes zero.

Thanks
Bill

 

[stevendaryl]

QFT's locality is in some way an example of the incompleteness of QM if one considers it as realist .

I'm not sure what you mean by that. QFT is nonlocal, in the same sense that QM is, and I don't see that the nonlocality shows anything about completeness.

To me, that's the lesson of Bell's theorem--the apparent nonlocality of quantum mechanics is not something that is likely to be addressed by a more complete theory, because there isn't a completion that lacks the nonlocality.