Von Neumann QM Rules Equivalent to Bohm?

[rubi]

I think vanhees' point is that the statistical information about the 100% correlation is already contained in the quantum state $\left|\Psi\right>=\left|HV\right>-\left|HV\right>$ and one doesn't need to collapse it to extract that information. $\left<HH|\Psi\right>=\left<VV|\Psi\right>=0$ (and so on). We just prepare the state $\left|\Psi\right>$ and repeat the experiment a thousand times and the statistics will agree with the QM predictions.

Also, I think we should be careful with the words correlation and causation. QM predicts non-local correlation. That's different from non-local causation. Correlation doesn't imply causation, even in the case of 100% correlation. This is just a logical leap that cannot be made. It is also true that "the sun will rise tomorrow" will be 100% correlated with "humans have two legs" for example, but that doesn't mean that one causes the other or that there is a common cause.

 

[atyy]

I think vanhees' point is that the statistical information about the 100% correlation is already contained in the quantum state $\left|\Psi\right>=\left|HV\right>-\left|HV\right>$ and one doesn't need to collapse it to extract that information. $\left<HH|\Psi\right>=\left<VV|\Psi\right>=0$ (and so on). We just prepare the state $\left|\Psi\right>$ and repeat the experiment a thousand times and the statistics will agree with the QM predictions.

Also, I think we should be careful with the words correlation and causation. QM predicts non-local correlation. That's different from non-local causation. Correlation doesn't imply causation, even in the case of 100% correlation. This is just a logical leap that cannot be made. It is also true that "the sun will rise tomorrow" will be 100% correlated with "humans have two legs" for example, but that doesn't mean that one causes the other or that there is a common cause.

The part about vanhees71's point that is wrong is that he is using the EPR objection to collapse. EPR's version of causality is not consistent with quantum field theory.

Furthermore, as long as we use the Schroedinger picture, the collapse is how we extract the information that is contained in the wave function in order to predict the nonlocal correlations.

Of course, one doesn't have to accept the wave function or the collapse as real, so one may say that Einstein causality is empty in quantum field theory. If one accepts the wave function and collapse as real, then Einstein causality is violated. There is no choice of saying that quantum field theory fulfills Einstein causality.

 

[Ilja]

Whether or not there are non-local deterministic theories (which I think is what's meant by "realistic theories" by philosophers) which are as successful as standard QFT, I don't know.

First, no, classical stochastic theories are also realistic, and Nelsonian stochastics is an example. Then, the first example of a local deterministic theory for the EM field was given already in Bohm's original paper. And, given that such theories are, as interpretations of QT in the particular domain, equivalent to QT in this domain, there is no difference in success betwenn a QFT and a QFT in a realistic interpretation.

 

[vanhees71]

[1)]The part about vanhees71's point that is wrong is that he is using the EPR objection to collapse. EPR's version of causality is not consistent with quantum field theory.

[2)] Furthermore, as long as we use the Schroedinger picture, the collapse is how we extract the information that is contained in the wave function in order to predict the nonlocal correlations.

[3)] Of course, one doesn't have to accept the wave function or the collapse as real, so one may say that Einstein causality is empty in quantum field theory. If one accepts the wave function and collapse as real, then Einstein causality is violated. There is no choice of saying that quantum field theory fulfills Einstein causality.

Ad 1) What's wrong?

Ad 2) You cannot argue with a specific picture of time evolution, because all are equivalent (modulo mathematical quibbles a la Haag's theorem ;-)).

Ad 3) This I don't understand. The usual local microcausal QFTs are precisely constructed such that they fulfill Einstein causality (among other things it makes the S-matrix with its time-ordered products of field operators manifestly covariant wrt. special orthochronous Poincare transformations). Last but not least, if the collapse isn't considered real, it's just a sloppy abbreviation for what the minimal interpretation states more carefully, and there's nothing to argue about it anymore. Then all our debates are pretty empty ;-).

 

[vanhees71]

First, no, classical stochastic theories are also realistic, and Nelsonian stochastics is an example. Then, the first example of a local deterministic theory for the EM field was given already in Bohm's original paper. And, given that such theories are, as interpretations of QT in the particular domain, equivalent to QT in this domain, there is no difference in success betwenn a QFT and a QFT in a realistic interpretation.

Ok, as you well know, I don't understand what philosophers mean by "realistic", particularly as it seems as if there are as many notions of this word as there are philosophers. Then, if everything is "solved" with Bohm's original paper, why is then always stated, also by followers of the Bohmian interpretation, that there are problems with Bohm and relativistic QFT?

 

[vanhees71]

No, it's not the same. In classical probability, there is a distinction between what is true and what my knowledge of the truth is. Someone randomly puts a left shoe into one box and a right shoe into the other box. One box is sent to Alice, and the other box is sent to Bob. When Alice opens her box, she finds a left shoe. She updates her epistemic probabilities for Bob's box to be 100% chance of a right shoe. There's clearly no nonlocal influence going on. HOWEVER, Alice knows that Bob actually had a right shoe BEFORE she opened the box. She just didn't know it until she opened her box.

But in the quantum case A also knew beforehand that the two photons in the entangled state are in this entangled state. That is as good as in the classical example. The only difference is that in classical physics you can't have such correlations. It's clear that the single-photon polarizations are completely indetermined before A's measurement according to standard QT, while the single-shoe states in the classical example are always definite, but there's no difference concerning a collapse between the two ensembles. In both cases the probabilities describe the knowledge of the observers about the sytem, and that's adapted after new information is gained.

 

[rubi]

The part about vanhees71's point that is wrong is that he is using the EPR objection to collapse. EPR's version of causality is not consistent with quantum field theory.

Furthermore, as long as we use the Schroedinger picture, the collapse is how we extract the information that is contained in the wave function in order to predict the nonlocal correlations.

Of course, one doesn't have to accept the wave function or the collapse as real, so one may say that Einstein causality is empty in quantum field theory. If one accepts the wave function and collapse as real, then Einstein causality is violated. There is no choice of saying that quantum field theory fulfills Einstein causality.

As I see it, the problem is the following: We have a state $\left|\Psi\right> = \left|HV\right>-\left|VH\right>$. This state contains all information that is obtained in an EPR experiment, so a collapse is not necessary. The collapse is not needed to explain the results of an EPR experiment. However, we also know that if we measure any of the same photons again, we will not get the same correlations again. Therefore, after the measurement, the state cannot be $\left|\Psi\right>$ anymore, but needs to be something different. This is the real reason for why we usually assume that the system has collapsed into $\left|HV\right>$ or $\left|VH\right>$ and this would indeed be a non-local interaction. However, it doesn't need to be so. There is another option that is only available if we are willing to include the measurement devices into the description: The local interaction with the measurement device could have made the correlations spill over into some atoms of the measurement device, so the correlations are still there, but not easily accessible. One only needs local interactions for this to happen. I'm convinced that if we could ever control all the degrees of freedom of the measurement apparata, we could recover the information about correlations. It's basically analogous to the quantum eraser.

 

[Ilja]

The usual local microcausal QFTs are precisely constructed such that they fulfill Einstein causality (among other things it makes the S-matrix with its time-ordered products of field operators manifestly covariant wrt. special orthochronous Poincare transformations).

No, it does not care at all about Einstein causality - this would require to care about the EPR argument - it cares only about correlations.

Last but not least, if the collapse isn't considered real, it's just a sloppy abbreviation for what the minimal interpretation states more carefully, and there's nothing to argue about it anymore. Then all our debates are pretty empty ;-).

"The collapse" is, of course, not the point, the point which proves nonlocality is the violation of Bell's inequality. And this violation exists in QFT too, and that means, QFT is not compatible with the EPR criterion of reality, thus, with Einstein's understanding of causality.

 

[Ilja]

Ok, as you well know, I don't understand what philosophers mean by "realistic", particularly as it seems as if there are as many notions of this word as there are philosophers. Then, if everything is "solved" with Bohm's original paper, why is then always stated, also by followers of the Bohmian interpretation, that there are problems with Bohm and relativistic QFT?

I said EM theory is presented in Bohm's original paper, not that everything is solved in that paper.

Then, the problem is, of course, that dBB theory requires a preferred frame. The interpretation of relativity we are forbidden to talk about does not have a problem with this, but to talk about it is forbidden not only here, so some people indeed think this is a problem.

The first proposal for fermion fields I know about is from Bell, in my paper http://arxiv.org/abs/0908.0591 I obtain equations for a pair of Dirac fermions from those of a scalar field with broken symmetry, which reduces Bohmian versions of fermions (as long as they appear in pairs) to the unproblematic case of scalar fields, which can use the same scheme used by Bohm for the EM field. For gauge fields, one should not use the Gupta-Bleuer approach with an indefinite Hilbert space, but the older Fermi-Dirac one, what remains is unproblematic too. And, even if some part of it would be problematic, there is a less beautiful but possible variant where only for a part of the degrees of freedom one has a dBB trajectory.

 

[atyy]

Ad 1) What's wrong?

Ad 2) You cannot argue with a specific picture of time evolution, because all are equivalent (modulo mathematical quibbles a la Haag's theorem ;-)).

Ad 3) This I don't understand. The usual local microcausal QFTs are precisely constructed such that they fulfill Einstein causality (among other things it makes the S-matrix with its time-ordered products of field operators manifestly covariant wrt. special orthochronous Poincare transformations). Last but not least, if the collapse isn't considered real, it's just a sloppy abbreviation for what the minimal interpretation states more carefully, and there's nothing to argue about it anymore. Then all our debates are pretty empty ;-).

Yes, of course one does not privilege a particular picture of time evolution. However, one also cannot disallow it. So if one allows the Schroedinger picture, there is collapse.

The place I think you are wrong is that Einstein causality is not the causality that is fulfilled by explicit construction in quantum field theory. Here by Einstein causality, I mean the causality in EPR and in classical special relativity, in which the cause of an event is in its past light cone - I am using this definition of Einstein causality because I think this is what you are using by bringing up EPR. The "causality" in quantum field theory is a different thing from Einstein causality - it forbids faster-than-light transfer of classical information. So your mistake is that you are confusing two types of causality - signal causality (which is present in relativistic QFT) and Einstein causality (like EPR, which is not present in relativistic QFT).

 

[rubi]

@atyy: Can you explain what you mean by Einstein causality and how Bell tests violate it?

If Einstein causality says that non-local 100% correlations should not be allowed if there is no common cause, then I would reply that correlation does't imply causation and therefore it wouldn't be a good definition of causality in the first place.

 

[atyy]

@atyy: Can you explain what you mean by Einstein causality and how Bell tests violate it?

If Einstein causality says that non-local 100% correlations should not be allowed if there is no common cause, then I would reply that correlation does't imply causation and therefore it wouldn't be a good definition of causality in the first place.

Einstein causality says that each event in a nonlocal correlation has causes that are entirely in its past light cone. So let's say we have a variable representing the source of the entangled photons $\lambda$, and we have Alice's measurement setting $S$ and measurement outcome $A$, and Bob's measurement setting $T$ and measurement outcome $B$. We also assume that Alice and Bob can choose their settings independently of how the source is prepared, and independently of each other and the measurement results. Assuming Einstein causality, Alice's outcome $A$ depends only on $\lambda$ and $S$, since these are in the past light cone of A. Similarly, assuming Einstein causality, Bob's outcome $B$ depends only on $\lambda$ and $T$, since these are in the past light cone of B. The assumption of Einstein causality can be given pictorially (from http://arxiv.org/abs/1208.4119):

Hence:

$P(A,B|S,T,\lambda) = P(A|S,\lambda)P(B|T,\lambda)$ ["separability"]

However, assuming quantum mechanics, the Bell argument shows that separability cannot be fulfilled. Regarding this not being a good definition of causality, that is fine, which is why I said that in quantum mechanics Einstein causality is either empty or violated.

 

[Ilja]

Can you explain what you mean by Einstein causality and how Bell tests violate it?
If Einstein causality says that non-local 100% correlations should not be allowed if there is no common cause, then I would reply that correlation does't imply causation and therefore it wouldn't be a good definition of causality in the first place.

Causality is something we cannot observe - only correlations are observable. Thus, we always need some theoretical principles to make conclusions about causality.

One such theoretical principle is Reichenbach's principle of common cause: Every observable correlation has to have some causal explanation, and for causal explanations we have the following possibilities: Or one of the thing which are correlated is the cause of the other, or above have some common cause. A principle of this type is necessary, because we need some ways to conclude that some causal relation exists. If you reject the common cause principle, you can forget about causality completely, it is no longer a meaningful notion.

But Reichenbach's principle is sufficient to prove Bell's inequality - it is, in this sense, strong enough to give EPR, because Reichenbach's principle tells us common cause or one is cause of the other, and these last two possibilities are excluded by Einstein causality (but not by the interpretation of relativity we are forbidden to talk about, SCNR).

So, even if in general correlation does not imply causation, we have a method to imply causation - Reichenbach's principle. And we need it, else causation would be meaningless.

 

[Ilja]

Can you explain what you mean by Einstein causality and how Bell tests violate it?
If Einstein causality says that non-local 100% correlations should not be allowed if there is no common cause, then I would reply that correlation does't imply causation and therefore it wouldn't be a good definition of causality in the first place.

Causality is something we cannot observe - only correlations are observable. Thus, we always need some theoretical principles to make conclusions about causality.

One such theoretical principle is Reichenbach's principle of common cause: Every observable correlation has to have some causal explanation, and for causal explanations we have the following possibilities: Or one of the thing which are correlated is the cause of the other, or above have some common cause. A principle of this type is necessary, because we need some ways to conclude that some causal relation exists. If you reject the common cause principle, you can forget about causality completely, it is no longer a meaningful notion.

But Reichenbach's principle is sufficient to prove Bell's inequality - it is, in this sense, strong enough to give EPR, because Reichenbach's principle tells us common cause or one is cause of the other, and these last two possibilities are excluded by Einstein causality (but not by the interpretation of relativity we are forbidden to talk about, SCNR).

So, even if in general correlation does not imply causation, we have a method to imply causation - Reichenbach's principle. And we need it, else causation would be meaningless.

 

[rubi]

Einstein causality says that each event in a nonlocal correlation has a cause that is entirely in its past light cone. So let's say we have a variable representing the source of the entangled photons $\lambda$, and we have Alice's measurement setting $a$ and measurement outcome $A$, and Bob's measurement setting $b$ and measurement outcome $B$. We also assume that Alice and Bob can choose their settings independently of how the source is prepared, and independently of each other and the measurement results. Assuming Einstein causality, Alice's outcome $A$ depends only on $\lambda$ and $a$, since these are in the past light cone of A. Similarly, assuming Einstein causality, Alice's outcome $B$ depends only on $\lambda$ and $b$, since these are in the past light cone of B. Hence:

$P(A,B|a,b,\lambda) = P(A|a,\lambda)P(B|b,\lambda)$ ["separability"]

However, assuming quantum mechanics, the Bell argument shows that separability cannot be fulfilled.

Ok, I would have called that Bell's criterion, though. It's of course true that QM and QFT violate Bell's inequalities, but I don't see how that is relevant to the question whether there is a collapse or not. (After all, you can't cure the violation by introduction of a collapse either.)

Causality is something we cannot observe - only correlations are observable. Thus, we always need some theoretical principles to make conclusions about causality.

[...]

So, even if in general correlation does not imply causation, we have a method to imply causation - Reichenbach's principle. And we need it, else causation would be meaningless.

I don't agree that we need an all-encompassing criterion for causality. We should admit that there is just no way to imply causation from correlation. That would be what honest scientist should do in my opinion. Now on the other hand, we can of course formulate theories about the world in a mathematical framework. And then it makes sense to ask: "Does the theory predict X only if there previously had been Y?" This is a question that we can analyze mathematically and we could come to a definite answer. So it makes sense to talk about causality only given a particular theory.

 

[atyy]

Ok, I would have called that Bell's criterion, though. It's of course true that QM and QFT violate Bell's inequalities, but I don't see how that is relevant to the question whether there is a collapse or not. (After all, you can't cure the violation by introduction of a collapse either.)

Yes, my point is that vanhees71's argument against collapse using Einstein causality (considering Bell's criterion to formalize Einstein causality in EPR, which vanhees71 mentioned) is faulty, since the violation cannot be cured in QM, whether one uses collapse or not.

Going back to your construction of making a density matrix into a unit vector, I do see your point that it is not decoherence, and I don't know what it is. However, even at the non-rigourous level, there are simple versions of collapse in which a pure state collapses into a pure state, eg. a wave function collapses into a delta function. Referring to http://arxiv.org/abs/0810.3536, the collapse is usually either
(1) linear and trace non-preserving (Eq 6.9), or
(2) nonlinear and trace-preserving (Eq 6.12)

Is there any way to make either Eq 6.9 or Eq 6.12 unitary?

Of course, there are ways of thinking that there is nothing strange with this non-unitary evolution, since as vanhees71 likes to say, it is just choosing a sub-ensemble. That's fine, except that in quantum mechanics without hidden variables, there are no sub-ensembles until measurement. Without hidden variables, the sub-ensembles appear at the moment of measurement and are labelled by the measurement outcome. It is ok to think that collapse is choosing a sub-ensemble, but then one should admit that one is using hidden variables.

 

[rubi]

Yes, that is exactly my point - that vanhees71's argument using Einstein causality (considering Bell's criterion to formalize Einstein causality in EPR, which vanhees71 mentioned) is faulty, since the violation cannot be cured in QM, whether one uses collapse or not.

I think vanhees' motivation to get rid of the collapse isn't to fix Einstein causality, but rather to get rid of the two different ways of time evolution, if one way is enough to describe physics. (See my post #97 for that. It's not Einstein causal, but causal in the QFT sense.)

Going back to your construction of making a density matrix into a unit vector, I do see your point that it is not decoherence, and I don't know what it is. However, at least intuitively, I can feel it is right since there is a simple version of collapse which is just that we have a pure state that collapses into a pure state, eg. a wave function collapses into a delta function (to use the non-rigourous language). Referring to http://arxiv.org/abs/0810.3536, the collapse is usually either
(1) nonlinear and trace-preserving (Eq 6.9), or
(2) linear and non-trace-preserving (Eq 6.12)

Is there anyway to make the collapse unitary?

You can't make a non-linear evolution linear using my construction. The point was to make linear evolutions of pure states into density matrices unitary. That works for evolutions given by a Lindblad equation for example, which can be given by decoherence but doesn't need to.

Of course, there are ways of thinking that there is nothing strange with this non-unitary evolution, since as vanhees71 likes to say, it is just choosing a sub-ensemble. That's fine, except that in quantum mechanics without hidden variables, there are no sub-ensembles until measurement. Without hidden variables, the sub-ensembles appear at the moment of measurement and are labelled by the measurement outcome. It is ok to think that it is choosing a sub-ensemble, but then one should admit that one is using hidden variables.

I would say that taking a subensemble is just a mathematical technique that is not related to physics. It's about taking an equivalent description of the physics one is interested in. If we compare it to general relativity for example, it would correspond to looking at a local coordinate patch instead of describing physics globally. The physics stays the same, but the description is different.

 

[atyy]

I think vanhees' motivation to get rid of the collapse isn't to fix Einstein causality, but rather to get rid of the two different ways of time evolution, if one way is enough to describe physics. (See my post #97 for that. It's not Einstein causal, but causal in the QFT sense.)

If one gets rid of collapse and has only unitary evolution and no hidden variables, doesn't one end up with Many-Worlds?

 

[rubi]

If one gets rid of collapse and has only unitary evolution and no hidden variables, doesn't one end up with Many-Worlds?

I don't think so. MWI includes the observer into the quantum desciption, but one doesn't need to do that. It's enough to have enough additional degrees of freedom to effectively hide the correlations from the observer. We can be agnostic with respect to the ontology and just regard the quantum state as a mathematical object that encodes the statistics of measurements. We could imagine for example that Alice and Bob don't measure their photons directly, but instead route them into their own local quantum eraser apparata instead. I would be very surprised if the results wouldn't be in agreement with what one would calculate from plain old quantum mechanics, so they would still see 100% correlation in the results after the photons have gone through the quantum erasers. The difference between a quantum eraser and an measurement apparatus that destroys the entanglement is just that the correlation can be restored in the quantum eraser case and it's lost for all practical purposes with a realistic measurement device, because we can't control all of its degrees of freedom.

 

[atyy]

I don't think so. MWI includes the observer into the quantum desciption, but one doesn't need to do that. It's enough to have enough additional degrees of freedom to effectively hide the correlations from the observer. We can be agnostic with respect to the ontology and just regard the quantum state as a mathematical object that encodes the statistics of measurements. We could imagine for example that Alice and Bob don't measure their photons directly, but instead route them into their own local quantum eraser apparata instead. I would be very surprised if the results wouldn't be in agreement with what one would calculate from plain old quantum mechanics, so they would still see 100% correlation in the results after the photons have gone through the quantum erasers. The difference between a quantum eraser and an measurement apparatus that destroys the entanglement is just that the correlation can be restored in the quantum eraser case and it's lost for all practical purposes with a realistic measurement device, because we can't control all of its degrees of freedom.

I guess I just don't see how that is going to work within quantum mechanics as long as there are sequential measurements. Is there an actual calculation one can read?

It is true that one doesn't need sequential measurements in quantum mechanics. For example, normally one has Alice and Bob take separate measurements with their own time stamps. However, I could see that one could take Alice, Bob and their clocks all as one big experiment, and then we just open the box at the end and measure their results and regard their time stamps as position measurements of the hands of the clocks. I'm willing to accept that. However, that doesn't solve the problem - or rather, it is an already solved problem, since we do regard the possibility of shifting all measurements to the end as a means of preventing collapse. I think this would be something like a super use of the principle of deferred measurement http://en.wikipedia.org/wiki/Deferred_Measurement_Principle.

However, if we regard measurements and their time stamps to indicate real spacetime events, so that there are real sequential measurements, then I don't think one includes enough of the experimental apparatus to avoid collapse in a minimal interpretation.

 

[Demystifier]

Neutrino oscillations are an observed fact

Definite outcomes in QM are also an observed fact.

and you have to introduce neutrino masses into the standard model

As far as I know, there is no strict proof that neutrino masses are the only possible way to explain neutrino oscillations.

To the contrary there's no observed fact which would force me to introduce a collapse and,

There is also no direct measurement of neutrino masses.

(Don't get me wrong! I am not against neutrino masses. I think it's a very reasonable assumption which is almost certainly right. I only emphasize that almost certainly is not the same as certainly.)

in addition, the introduction of this idea is very problematic (EPR!).

I think you misunderstood it. First, if you mean the problem of non-locality, then collapse is non-local even without EPR. Second, if you mean the type of non-locality specific for EPR, then QM is non-local in that sense even without collapse, provided that some ontology (known or unknown) exists even when it is not measured. (That's what the Bell theorem says.)

So while I'm practically forced to introduce neutrino masses to adequately describe the observed fact of mixing, there's no necessity to bother oneself is unobserved and unnecessary collapses in QT!

If you can choose not to bother with collapse or other ontological aspect of QM, and use only those aspects of QM which are directly measurable, then you can also choose not to bother with neutrino masses and describe neutrino oscillations purely phenomenologically, without ever explicitly mentioning their masses.

Since when do you need an "ontology" in physics? Physics is about the description of objective observable facts about nature and not to provide an ontology (although famous people like Einstein opposed this view vehemently).

Who determines what is physics about? Why the opinion of a large portion of physicists, including Einstein, doesn't count?

E.g., it doesn't make sense to ask, whether a "particle" (better say "quantum" here) has a "shape" at all within QT.

Again, who determines which question makes or does not make sense?

You can only describe the probability of the outcome of concrete measurements (observables), which are defined as (an equivlance class) of measurement procedures.

You can describe much more than that, but you do not have direct experimental proof that your description is correct. Just as you can describe neutrino oscillations with neutrino masses, even though you do not have direct experimental proof that the description in terms of masses is correct.

 

[vanhees71]

Well, in this point I'm more with Bohr than with Einstein. It's of course my opinion.

Concerning the neutrinos: That's an interesting statement. I have no clue, how you can have neutrino mixing if the neutrinos don't have different masses. Do you have a model, where you have neutrino mixing without neutrino masses (i.e., all three neutrino flavors massless)?

 

[Demystifier]

In our example, the local interaction of A's photon with her polarizer doesn't affect instantaneously Bob's photon.

When you say that, do you imagine, in your head, that those photons exist even before they are measured by Alice or Bob? Be very careful with your answer because:

a) If you answer that you do, then I will accuse you for inconsistency. Namely, that means that you imagine, in your head, that photons have some ontology, while in another post you strictly claimed that physics is not about ontology.

b) If you answer that you don't even imagine it (which would be hard to believe), then I will ask you the following: Why, in the sentence above, do you use a classical language which seems to suggest that you do imagine that photons exist even before measurement?

And I am not asking you to say whether photons have ontology. I only want to know do you imagine that they do, for the sake of easier thinking about them.

 

[vanhees71]

I don't understand what you mean by this. Of course, there are two photons prepared with parametric down conversion. We write down a two-photon state after all. So this state tells me that there are two photons.

Of course these photons have no definite polarization and no position at all (because there's no position operator for photons). The full analysis must of course use both the space-time information and the polarization information of the two-photon correlation function, which gives the probability for detection (!) of one photon at Alice's place (within a certain macroscopically small volume) at within a certain macroscopically small time interval and dito for the registration probability at Bob's position and time.

Photons only manifest themselves in a space-time picture as "registration events". Whether you claim that this notion of photons is ontological or epistemic, is your choice. I don't consider the answer to this question essential for physics, which is about what we can observe, and photons are observable only by (local) interaction events with massive particles in a macroscopic measurement device, which have a position observable. That's a specialty of massless particles with spin $\geq 1$.

For a detailed (effective) model, see the classical paper by Hong and Mandel:

Hong, C. K., Mandel, L.: Theory of parametric frequency down conversion of light, Phys. Rev. A 31, 2409, 1985
http://dx.doi.org/10.1103/PhysRevA.31.2409

 

[Demystifier]

Well, in this point I'm more with Bohr than with Einstein. It's of course my opinion.

Fair enough!

Concerning the neutrinos: That's an interesting statement. I have no clue, how you can have neutrino mixing if the neutrinos don't have different masses. Do you have a model, where you have neutrino mixing without neutrino masses (i.e., all three neutrino flavors massless)?

I don't have an explicit alternative model, but the point is: Do I need such a model?

What I am doing is accusing you for double standards:
- In the case of neutrino oscillations you seem to suggest that we should use some model (neutrino masses or possibly something else), even if there is no direct experimental proof that it is correct.
- In the case of quantum observables taking definite values, you suggest that we should not use any model (e.g. collapse or Bohmian trajectories) if there is no direct experimental proof that it is correct.

Why is it legitimate to propose theories of neutrino oscillations, but not theories of definite outcomes of quantum observables? Because Bohr said so?

 

[Demystifier]

Of course, there are two photons prepared with parametric down conversion.

How do you know that, if you didn't yet measured them? That's what I am asking you.

 

[Demystifier]

We write down a two-photon state after all. So this state tells me that there are two photons.

Some of us also write down the two Bohmian trajectories of those two photons. Does this tell us that there are two Bohmian trajectories?

 

[vanhees71]

The neutrino oscillations are an observed fact. So I'm forced to include it into the Standard Model of elementary particle physics. There's no principle difficulty to do so. So what do I need to bother about?

On the other hand, in my opinion, there's not a single hint of something like and instantaneous collapse, and to assume one makes only trouble. So why should I bother to include one. It doesn't explain anything beyond the minimal interpretation, why you measure definite values of observables. You can always only give probabilities for measuring a definite value, no matter whether you envoke a collapse or not.

The case of Bohmian mechanics is more delicate. I don't know, what to make of it to be honest. On the one hand it seems to work for the non-relativistic case and give the same result. Some people feel better about this interpretation, because they claim it's more realistic than the minimal interpretation (or other flavors of Copenhagen). So it gives the same observable facts as QT and thus seems to be a valid interpretation of this successful theory. So I can live with it easily although I still don't see any merit of the introduction of unobservable trajectories, but that's just a matter of taste and no objective argument against it.

For the case of relativistic QFT, I'm not sure what to make of it at all. There's still the open question, whether there is a consistent formulation of Bohmian mechanics for standard relativistic QFT or not. Scully et al claim that "Bohmian trajectories for photons" are at best "surreal", others claim that's not true. What to make of the notion of "trajectories" for entities which don't have a position observable, is another answer, I've not seen answered. So I'd say, it's still an open question, whether a Bohmian approach to standard QFT makes sense or not.

 

[vanhees71]

Some of us also write down the two Bohmian trajectories of those two photons. Does this tell us that there are two Bohmian trajectories?

You are quicker than I can answer! It's however in my posting #118.

 

[Demystifier]

The neutrino oscillations are an observed fact. So I'm forced to include it into the Standard Model of elementary particle physics. There's no principle difficulty to do so. So what do I need to bother about?

True, but neutrino masses are not an observed fact. Neutrino masses are a possible interpretation (albeit a very convincing one) of neutrino oscillations.

In fact, this is not even a unique interpretation: Are neutrino masses Majorana or Dirac?

On the other hand, in my opinion, there's not a single hint of something like and instantaneous collapse, and to assume one makes only trouble. So why should I bother to include one. It doesn't explain anything beyond the minimal interpretation, why you measure definite values of observables. You can always only give probabilities for measuring a definite value, no matter whether you envoke a collapse or not.

The case of Bohmian mechanics is more delicate. I don't know, what to make of it to be honest. On the one hand it seems to work for the non-relativistic case and give the same result. Some people feel better about this interpretation, because they claim it's more realistic than the minimal interpretation (or other flavors of Copenhagen). So it gives the same observable facts as QT and thus seems to be a valid interpretation of this successful theory. So I can live with it easily although I still don't see any merit of the introduction of unobservable trajectories, but that's just a matter of taste and no objective argument against it.

For the case of relativistic QFT, I'm not sure what to make of it at all. There's still the open question, whether there is a consistent formulation of Bohmian mechanics for standard relativistic QFT or not. Scully et al claim that "Bohmian trajectories for photons" are at best "surreal", others claim that's not true. What to make of the notion of "trajectories" for entities which don't have a position observable, is another answer, I've not seen answered. So I'd say, it's still an open question, whether a Bohmian approach to standard QFT makes sense or not.

With that I actually agree. Bohmian approach seems to me much more convincing than collapse. And yes, there are still some unsolved problems with Bohmian approach, but hey, which physical theory is without any problems?