Quantum state: Reality or mere probability?

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What I don't understand is the no crossing rule obeyed in Bohmian trajectories. Since the non-crossing is with respect to configuration space why do some authors (e.g. Sanz) argue that the no-crossing offers insights that the more orthodox interpration does not. This appears to suggest that, in some ways, the bohemian trajectories are less "hidden" than the wave function:
In that sense, even though the trajectories reconstructed from the experiment cannot be associated with the paths followed by individual photons, but with electromagnetic energy streamlines, the experiment constitutes an important milestone in modern physics. The fact that the trajectories do not cross means that, at the level of the average electromagnetic field (or the wave function, in the case of material particles, in general), full which-way information can still be inferred without destroying the interference pattern. That is, rather than complementarity, the experiment seem to suggest that superposition has a tangible (measurable) physical reality [14], in agreement with a recent theorem on the realistic nature of the wave function [15].
How does light move? - Determining the flow of light without destroying interference
http://www.europhysicsnews.org/articles/epn/pdf/2013/06/epn2013446p33.pdf

A trajectory-based understanding of quantum interference
http://arxiv.org/pdf/0806.2105v2.pdf

Particles, waves and trajectories: 210 years after Young's experiment
http://arxiv.org/pdf/1402.3877.pdf

Quantum phase analysis with quantum trajectories: A step towards the creation of a Bohmian thinking
http://arxiv.org/pdf/1104.1296.pdf

Quantumness beyond quantum mechanics
http://arxiv.org/pdf/1202.5181.pdf

Any insights would be appreciated as I might be misinterpreting this.
 

atyy

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What I don't understand is the no crossing rule obeyed in Bohmian trajectories. Since the non-crossing is with respect to configuration space why do some authors (e.g. Sanz) argue that the no-crossing offers insights that the more orthodox interpration does not. This appears to suggest that, in some ways, the bohemian trajectories are less "hidden" than the wave function:

How does light move? - Determining the flow of light without destroying interference
http://www.europhysicsnews.org/articles/epn/pdf/2013/06/epn2013446p33.pdf

A trajectory-based understanding of quantum interference
http://arxiv.org/pdf/0806.2105v2.pdf

Particles, waves and trajectories: 210 years after Young's experiment
http://arxiv.org/pdf/1402.3877.pdf

Quantum phase analysis with quantum trajectories: A step towards the creation of a Bohmian thinking
http://arxiv.org/pdf/1104.1296.pdf

Quantumness beyond quantum mechanics
http://arxiv.org/pdf/1202.5181.pdf

Any insights would be appreciated as I might be misinterpreting this.
In this view, Bohmian trajectories are not any more real than virtual particles, which are just intermediate steps in a calculation. Just as the virtual particles picture made things easier for Feynman, the Bohmian trajectories make things easier for some people. Everything calculated by Bohmian trajectories can be calculated by standard Copenhagen quantum mechanics. (This is completely tangential to the real problem solved by Bohm - that there is at least one interpretation of quantum mechanics without observers.)

Also, the first link asks http://www.europhysicsnews.org/articles/epn/pdf/2013/06/epn2013446p33.pdf "According to the complementarity principle, complementary aspects of quantum systems cannot be measured at the same time by the same experiment. This has been a long debate in quantum mechanics since its inception. But is this a true constraint?" The answer to that is yes, it is a true constraint: http://arxiv.org/abs/1304.2071.
 
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Thanks, atyy. That was what I understood but why does A. S. Sanz et al. claim the following (and note the hi-lited part (e.g. from a theoretical point of view" on p. 7. I didn't understand how they can make that claim. Are their arguments just plainly wrong?
As seen above, quantum coherence and its Bohmian effect, namely the non-crossing property, allow us to discern the slit traversed by a particle without disturbing it in two-slit experiments, at least from a theoretical point of view.
Quantum phase analysis with quantum trajectories: A step towards the creation of a Bohmian thinking
http://arxiv.org/pdf/1104.1296.pdf
 
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The two systems are initially prepared in a classical non-entangled state, but the meassurement is performed in a non-classical entangled basis. In other words, the measurement makes them entangled. This should not be surprising, because measurement in a specific basis can often be viewed as a preparation.
How is "entangled" state accounted for in cos^2(theta), wouldn't that equation predict the same coincidence rate for both entangled and non-entangled systems?
 

atyy

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Thanks, atyy. That was what I understood but why does A. S. Sanz et al. claim the following (and note the hi-lited part (e.g. from a theoretical point of view" on p. 7. I didn't understand how they can make that claim. Are their arguments just plainly wrong?

Quantum phase analysis with quantum trajectories: A step towards the creation of a Bohmian thinking
http://arxiv.org/pdf/1104.1296.pdf
I think they just mean that because the trajectories are non-crossing, particles detected in the left side of the screen must come from the left slit, and particle detected from the right side of the screen must come from the right slit, which seems to me correct if non-crossing in ordinary space holds.
 
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This quote from Einstein presents his views on the issue more clearly than the presetation attempts to:
Einstein said:
Consider a mechanical system consisting of two partial systems A and B which interact with each other only during a limited time. ψ is the wavefunction before their interaction. One performs measurements on A and determines A's state. Then B's ψ function of the partial system B is determined from the measurement made, and from the ψ function of the total system. This determination gives a result which depends upon which of the observables of A have been measured (coordinates or momenta). That is, depending upon the choice of observables of A to be measured, according to quantum mechanics we have to assign different quantum states ψB and ψB' to B. These quantum states are different from one another. After the collision, the real state of (AB) consists precisely of the real state A and the real state of B, which two states have nothing to do with one another. The real state of B thus cannot depend upon the kind of measurement I carry out on A. But then for the same state of B there are two (in general arbitrarily many) equally justified ψB, which contradicts the hypothesis of a one-to-one or complete description of the real state.
Since there can be only one physical state of B after the interaction which cannot reasonably be considered to depend on the particular measurement we perform on the system A separated from B it may be concluded that the ψ function is not unambiguously coordinated to the physical state.
This coordination of several ψ functions to the same physical state of system B shows again that the ψ function cannot be interpreted as a (complete) description of a physical state of a single system. Here also the coordination of the ψ function to an ensemble of systems eliminates every difficulty.
 
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I think they just mean that because the trajectories are non-crossing, particles detected in the left side of the screen must come from the left slit, and particle detected from the right side of the screen must come from the right slit, which seems to me correct if non-crossing in ordinary space holds.
But, if that is the case, then it appears to provide us with more information than the orthodox view. In the orthodox view we cannot have such information, because the diffraction is lost if we look. So in a sense (if their arguments are correct) this appears to suggest that, in some ways, the bohmian trajectories are less "hidden" than the wave function. But I don't see how no-crossing over on configuration space allows one to claim that in fact, there is no-crossing over in ordinary space and infer "which slit" the particle went through without looking. I would think that this would be a pretty major finding.
 
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The bugbear is while photons can be made to interact at a point, it is always destroyed by such, so you cant say it had such and such position.
I won't even say it has to do with the longevity of photons after they are measured. I think we sometimes mystify the situation more than is necessary. Momentum, like velocity is a vector. It is mathematically undefined at a single point, let alone being able to measure it at a single point. It's like trying to determine a person's behavior from a photograph.

But coming back to PBR, the two possibilities given in the presentation, are:
1- knowledge of lambda determines p(head) and p(tail) uniquely (ontic)
2- knowledge of lambda not enough to determine p(head) and p(tail) uniquely (epistemic)
appear to be criteria for completeness rather than definitions ontic/epistemic. In the second case, lambda is incomplete as far as the prediction of p(head) and p(tail). In the first p(head)/p(tail) is limited to the coin only, in second p(head)/p(tail) is describing the coin and the tossing mechanism.
 

atyy

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But, if that is the case, then it appears to provide us with more information than the orthodox view. In the orthodox view we cannot have such information, because the diffraction is lost if we look. So in a sense (if their arguments are correct) this appears to suggest that, in some ways, the bohmian trajectories are less "hidden" than the wave function. But I don't see how no-crossing over on configuration space allows one to claim that in fact, there is no-crossing over in ordinary space and infer "which slit" the particle went through without looking. I would think that this would be a pretty major finding.
I think ordinary space is a type of configuration space, where the dimensions are just labelled by coordinates. In contrast, phase space or state space in classical mechanics has dimensions labelled by positions and momenta.

I looked at the trajectories in http://scienceblogs.com/principles/2011/06/03/watching-photons-interfere-obs/ and it seems correct that one can get an interference pattern, and from the interference pattern know which slit a particle has come from.

To be honest, I have never understood the traditional formulation in which obtaining "which way" information prevents the interference pattern from forming. Is it a heuristic, or is there an equation that one can actually derive from quantum mechanics to show it? To me, when you do a different experiment and place a detector in front of one slit, then you block the slit, so it becomes a single slit interference. We had a long discussion in https://www.physicsforums.com/showthread.php?t=762601, and I don't think anyone pointed me to an exact mathematical formulation of the principle. Here is an interesting related thread started by RUTA https://www.physicsforums.com/showthread.php?t=765772.
 
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1- knowledge of lambda determines p(head) and p(tail) uniquely (ontic)
2- knowledge of lambda not enough to determine p(head) and p(tail) uniquely (epistemic)
Why are we unable to experimentally confirm whether knowledge of lambda determines p(head) and p(tail) uniquely, or not?
 

atyy

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But coming back to PBR, the two possibilities given in the presentation, are:
1- knowledge of lambda determines p(head) and p(tail) uniquely (ontic)
2- knowledge of lambda not enough to determine p(head) and p(tail) uniquely (epistemic)
appear to be criteria for completeness rather than definitions ontic/epistemic. In the second case, lambda is incomplete as far as the prediction of p(head) and p(tail). In the first p(head)/p(tail) is limited to the coin only, in second p(head)/p(tail) is describing the coin and the tossing mechanism.
Yes, some people don't like this terminology, because one can say that both cases assume reality simply by assuming hidden variables. That's fine, and this is widely acknowledged. But given the underlying ontic framework, this is I think a nice definition that allows one to distinguish subclasses of hidden variable theories. The definition comes from Harrigan and Spekkens http://arxiv.org/abs/0706.2661 (see their fig 2, not fig 1).

Since then, explicit ψ-epistemic constructions for the Born rule have been given.
http://arxiv.org/abs/1201.6554
http://arxiv.org/abs/1303.2834

And there is a no-go theorem against "maximally ψ-epistemic" theories
http://arxiv.org/abs/1207.6906
http://arxiv.org/abs/1208.5132
 
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The most obvious thing about determinism is that every quantum outcome appears completely random (and has no known cause). So the data is against you.
Random? Would you say flipping a coin or rolling a dice produces random outcome, or that it has no known cause? What experiment and what data are you talking about?
 

DrChinese

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Random? Would you say flipping a coin or rolling a dice produces random outcome, or that it has no known cause? What experiment and what data are you talking about?
No one has been able to point to a root cause for any quantum outcome. That is a far cry different from a coin flip or a die toss, which cause of outcome could be determined precisely in principle. The key here is that one thing has an explanation, the other doesn't.

Of course, no one is disputing that the cause for an random quantum outcome could be discovered next week. Then you would have some evidence. But currently there is none. Otherwise: If it walks like a duck, and quacks like a duck, it's random. :smile:
 
808
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Why are we unable to experimentally confirm whether knowledge of lambda determines p(head) and p(tail) uniquely, or not?
Because we can't know that we know everything knowable about lambda. And even if we could, we won't be interested in *probabilities*, everything will be certain. That is why I'm not sure the idea of "real probability distributions" makes sense. There is a modal contradiction in there somewhere.
 
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Actually, there's an interesting way the Bohmian view explains a traditional short-cut in which the particle is assumed to have a classical trajectory. After a particle has passed through a slit (single or double), its momentum just after it has passed through the slit can be measured by detecting its position at a distant screen, and calculating as if the particle had a classical trajectory.
It has always seemed to me that the fact that the Bohmian trajectories are not straight is evidence they are not real. Otherwise there is a momentum conservation elephant in the room. Photons and electrons spontaneously changing direction? How do the Bohmians address this issue.
 

atyy

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It has always seemed to me that the fact that the Bohmian trajectories are not straight is evidence they are not real. Otherwise there is a momentum conservation elephant in the room. Photons and electrons spontaneously changing direction? How do the Bohmians address this issue.
Ooops, sorry, I deleted my post before you replied. Anyway, the Bohmian laws are not the same as the classical laws. Bohmian trajectories do not have a classical momentum. Anyway, I wouldn't worry too much about how unnatural it is. The point is it works. No one is saying this particular law is correct - for a given choice of hidden variables, the dynamical law isn't even unique. Furthermore, the choice of hidden variables is also not unique. The point is that it solves the measurement problem, and we can conceive as quantum theory as just an effective theory with a common sense reality, just like all of classical physics.
 

naima

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As a Bohmian, I agree fully with Fuchs! If degrees of freedom can be emergent, then so can ontology:)

Maybe a more serious question to which I don't know the answer - can we take the Bohmian quantum equilibrium distribution in the sense of subjective probability, say de Finetti? If so, then can we make Bohmian mechanics subjective too?

Actually, Wiseman had some comments on subjective probability in Bohmian mechanics, but I think along somehwat different lines: http://arxiv.org/abs/0706.2522.
You add wave functions to calculate fringes. Fuchs says that "there is no state function"
 
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Ooops, sorry, I deleted my post before you replied. Anyway, the Bohmian laws are not the same as the classical laws. Bohmian trajectories do not have a classical momentum. Anyway, I wouldn't worry too much about how unnatural it is. The point is it works. No one is saying this particular law is correct - for a given choice of hidden variables, the dynamical law isn't even unique. Furthermore, the choice of hidden variables is also not unique. The point is that it solves the measurement problem, and we can conceive as quantum theory as just an effective theory with a common sense reality, just like all of classical physics.
Surely we can. But we don't have to introduce weirdness just because we can. Bohmian "trajectories" don't have to be real to be correct. It can be epistemic and still produce the correct results, and still work very well. In which case the "trajectories" are not really trajectories but rather probability distributions for finding particles. In other words, the particles are not *really" travelling along those curvy lines (often called trajectories).
 
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Because we can't know that we know everything knowable about lambda. And even if we could, we won't be interested in *probabilities*, everything will be certain. That is why I'm not sure the idea of "real probability distributions" makes sense. There is a modal contradiction in there somewhere.
Can you draw a parallel between a coin toss or dice roll probability compared to QM randomness, and point out what does lambda correspond to in each case? Are classical and QM probability really different kinds of "randomness"?
 

atyy

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Surely we can. But we don't have to introduce weirdness just because we can. Bohmian "trajectories" don't have to be real to be correct. It can be epistemic and still produce the correct results, and still work very well. In which case the "trajectories" are not really trajectories but rather probability distributions for finding particles. In other words, the particles are not *really" travelling along those curvy lines (often called trajectories).
Do you mean "epistemic" in the sense of Harrigan and Spekkens, and the PBR paper?
 

atyy

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Can you draw a parallel between a coin toss or dice roll probability compared to QM randomness, and point out what does lambda correspond to in each case? Are classical and QM probability really different kinds of "randomness"?
Classical and QM probability are not necessarily different kinds of randomness - the Bohmian construction proves that. In fact, the entire assumption behind the distinction between ψ-ontic and ψ-epistemic theories discussed in this thread assumes that classical and QM probability are not different kinds of randomness.
 

DrChinese

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Classical and QM probability are not necessarily different kinds of randomness - the Bohmian construction proves that. In fact, the entire assumption behind the distinction between ψ-ontic and ψ-epistemic theories discussed in this thread assumes that classical and QM probability are not different kinds of randomness.
Just to be clear (since there are readers of all levels in this thread): there is absolutely no evidence that there is a Bohmian cause to any quantum event. This is strictly hypothetical.

I don't have any evidence it isn't correct either. But it is something at this point you believe in out of faith.
 
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Since there was a bit of confusion regarding interpretations ruled out when we were discussing this previously (assuming PBR is accurate), Leifer suggests that it rules out the following 3 models:

1. Einstein's
2. Spekken's
3. Ballentine's
The second type of ψ-epistemic interpretation are those that are realist, in the sense that they do posit some underlying ontology. They just deny that the wavefunction is part of that ontology. Instead, the wavefunction is to be understood as representing our knowledge of the underlying reality, in the same way that a probability distribution on phase space represents our knowledge of the true phase space point occupied by a classical particle. There is evidence that Einstein's view was of this type. Ballentine's statistical interpretation is also compatible with this view in that he leaves open the possibility that hidden variables exist and only insists that, if they do exist, the wavefunction remains statistical (as a frequentist, Ballentine uses the term "statistical" rather than "epistemic"). More recently, Spekkens has been a strong advocate of this point of view.
 

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