Von Neumann QM Rules Equivalent to Bohm?

[vanhees71]

Neutrino masses are just very difficult to measure, as is to figure out whether they are Majorana or Dirac particles. Of course, the models for neutrino oscillations are predictions, which may be falsified by experiment. So it's a feature not a bug, because that's after all what defines a scientific theory or model.

Hm, maybe I end up becoming a Bohmian, but for this I'd need a convincing formulation for the standard relativistic QFTs.

 

[Demystifier]

Hm, maybe I end up becoming a Bohmian, but for this I'd need a convincing formulation for the standard relativistic QFTs.

Fair enough!

You can try with my own proposal
http://lanl.arxiv.org/abs/0904.2287 [Int.J.Mod.Phys.A25:1477-1505,2010]
http://lanl.arxiv.org/abs/1205.1992 [Chapter 8. of the book "Applied Bohmian Mechanics: From Nanoscale Systems to Cosmology"]

 

[rubi]

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?

One could for example write down a photon-phonon interaction Hamiltonian that absorbs photons into phonons (of the polarizer material) and adjust the selection rules so that only horizontal photons are absorbed and vertical photons pass through. One can keep phonon number degrees of freedom for both the polarizers of Alice and Bob. So the basis states would look like this: $|$(Alice photon number horizontal)$>\otimes|$(Alice photon number vertical)$>\otimes|$(Alice phonon number)$>\otimes|$(Bob PNH)$>\otimes|$(Bob PNV)$>\otimes|$(Bob PN)$>$
We would start with $|1>\otimes|0>\otimes|0>\otimes|0>\otimes|1>\otimes|0>-|0>\otimes|1>\otimes|0>\otimes|1>\otimes|0>\otimes|0>$ and end up with $|0>\otimes|0>\otimes|1>\otimes|0>\otimes|1>\otimes|0>-|0>\otimes|1>\otimes|0>\otimes|0>\otimes|0>\otimes|1>$ (if both Alice and Bob had oriented their polarizers so that horizontal photons are absorbed). Now both Alice and Bob either have a photon left or they don't and if they do, it's not correlated with anything that can be measured (assuming they don't have access to the phonon degrees of freedom).

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.

Yes, that's essentially the idea.

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.

I would argue that this is not the right thing to do. QM is a statistical theory and it doesn't make sense to speak about individual measurements within its framework. If you want to compare experimental results to the theory, you first need to translate them into the language of statistics, i.e. you must have performed several measurements and computed the statistical mean and so on. You can of course collect your data in a spacetime diagram, but it tells you nothing about what the quantum state on the corresponding hypersurface was. If you are interested in the quantum state, you basically need to perform something like a quantum tomography, where measure position or momentum a thousand times, but everytime start with a newly prepared state and then find a quantum state that is consistent with the statistics.

 

[stevendaryl]

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.

No, it's not analogous.

Shoe case: With left and right shoes: Alice knows that Bob's box either contains a right shoe or a left shoe. She just doesn't know which. Opening her box tells her which is the case.

EPR twin-pair case: With EPR twin-pairs, the analogous claim would be: Alice knows that Bob's box is either polarized horizontally, or it's polarized vertically. She just doesn't know which. Opening her box tells her which is the case.

Bell's theorem (together with the assumption of locality) shows that the analogous claim for EPR twin-pairs is wrong. Alice's measurement tells her with certainty what the state of Bob's photon is (or at least, as much as is possible to know): she knows that it's horizontally polarized. But unlike the classical case, it isn't consistent for her to assume that that was the case all along.

So do you see the difference:

• Classically, Alice discovers that Bob's box contains a right shoe. She concludes that it was a right shoe all along.
• Quantum-mechanically, Alice discovers that Bob's photon is horizontally polarized. She CAN'T conclude that it was horizontally polarized all along.

 

[stevendaryl]

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.

Well, it seems to me that the "spilling over into atoms of the measurement device" is exactly what leads to the Many Worlds Interpretation.

The collapse interpretation is only relevant if we assume that measurements have unique outcomes.

 

[stevendaryl]

@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 doesn't imply causation and therefore it wouldn't be a good definition of causality in the first place.

Einstein causality doesn't really have to do with "causation", it can be expressed as purely a claim about correlations. Bell actually worked out a more general claim about correlations in his "theory of local beables" (where "beables" is pronounced BEE-able in an analogy with OBSERV-able).

The idea is this: If two events A and B are correlated (whether 100% or otherwise), then there is some fact C in the common backwards lightcones of A and B such that the correlation between A and B are explaining by sharing the common past C.

Let's go through some examples. Suppose that Alice and Bob each have a device that produces a sequence of random digits. When they compare notes, they find that their devices produce the SAME sequence. Then this principle would tell you that there is some unknown common explanation.

Maybe the two devices are using the same, deterministic algorithm. That would explain the correlation.

Maybe the two devices are receiving signals from a common source. That would explain the correlation.

I don't think that there is any logical necessity that there be a common explanation. But it's what people usually assume. An apparent correlation can be a coincidence, but a sustained correlation indicates some common explanation.

 

[vanhees71]

No, it's not analogous.

Shoe case: With left and right shoes: Alice knows that Bob's box either contains a right shoe or a left shoe. She just doesn't know which. Opening her box tells her which is the case.

EPR twin-pair case: With EPR twin-pairs, the analogous claim would be: Alice knows that Bob's box is either polarized horizontally, or it's polarized vertically. She just doesn't know which. Opening her box tells her which is the case.

Bell's theorem (together with the assumption of locality) shows that the analogous claim for EPR twin-pairs is wrong. Alice's measurement tells her with certainty what the state of Bob's photon is (or at least, as much as is possible to know): she knows that it's horizontally polarized. But unlike the classical case, it isn't consistent for her to assume that that was the case all along.

So do you see the difference:

• Classically, Alice discovers that Bob's box contains a right shoe. She concludes that it was a right shoe all along.
• Quantum-mechanically, Alice discovers that Bob's photon is horizontally polarized. She CAN'T conclude that it was horizontally polarized all along.

But in the EPR-Twin case it's the same. The only qualification is that you have to say "Bob's photon is either H or V polarized, IF he chooses to measure the polarization in that direction." For the classical case you don't need the "IF". That's the only difference. Of course you are right in saying that Bob's photon had no definite polarization before A made her measurement. Caught in a classical worldview you then could conclude that then there must be a mechanism (called "collapse") that makes Bob's photon polarized horizontally through the measurement. But this is not a compulsary conclusion, because you can as well interpret it in the minimal way, according to which there are simply these non-classical correlations described by the quantum formalism and that's the cause why, if A measures a V-polarized photon, then B must find a H-polarized photon (supposed B measures the same polarization direction).

 

[martinbn]

The idea is this: If two events A and B are correlated (whether 100% or otherwise), then there is some fact C in the common backwards lightcones of A and B such that the correlation between A and B are explaining by sharing the common past C.

What does it mean for two events to be correlated? Don't you need sequences of events?

 

[stevendaryl]

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.)

The importance of collapse is that Bell's inequality as applied to EPR is proved under the assumption that there are no nonlocal influences affecting the two measurements. If there is a nonlocal collapse, then the assumptions behind Bell's proof are not satisfied, and so you shouldn't expect Bell's inequality to hold, necessarily.

That's really the issue: Does the violation of Bell's inequality imply that something nonlocal is happening? The unitary evolution of the wave function is local (although there's a little confusion about that in my mind, because the wave function is a function on configuration space, not physical space, so it's a little tricky to say what "local evolution" means). But the selection of one alternative out of a set of possible alternatives seems to be a nonlocal event. It seems as if this selection process happens at Alice's device and Bob's device simultaneously.

 

[stevendaryl]

What does it mean for two events to be correlated? Don't you need sequences of events?

I'm sloppily using the word "correlated" to mean dependent probabilities. That is,

P(A\ \&\ B) \neq P(A) \cdot P(B)

Bell's theory of local beables says that if A and B are statements about localized conditions at spacelike separations, then there must be some fact C that is a statement about the common past (the intersection of the backward lightcones) such that:

P(A\ \&\ B | C) = P(A | C) \cdot P(B | C)

 

[rubi]

No, it's not analogous.

Shoe case: With left and right shoes: Alice knows that Bob's box either contains a right shoe or a left shoe. She just doesn't know which. Opening her box tells her which is the case.

EPR twin-pair case: With EPR twin-pairs, the analogous claim would be: Alice knows that Bob's box is either polarized horizontally, or it's polarized vertically. She just doesn't know which. Opening her box tells her which is the case.

Bell's theorem (together with the assumption of locality) shows that the analogous claim for EPR twin-pairs is wrong. Alice's measurement tells her with certainty what the state of Bob's photon is (or at least, as much as is possible to know): she knows that it's horizontally polarized. But unlike the classical case, it isn't consistent for her to assume that that was the case all along.

So do you see the difference:

• Classically, Alice discovers that Bob's box contains a right shoe. She concludes that it was a right shoe all along.
• Quantum-mechanically, Alice discovers that Bob's photon is horizontally polarized. She CAN'T conclude that it was horizontally polarized all along.

I think you are applying classical reasoning to the quantum mechanical world. In a classical world, it would be reasonable to assume Bell's locality criterion, since all relativistically covariant classical theories automatically satisfy it. We can however have perfectly relativistically covariant quantum theories that don't satisfy the principle and therefore, we can't assume that it is generally valid. In the quantum world, there are objects like left/right shoes and right/left shoes and if Alice discovers that she got the box with the left/right shoe, then she automatically knows that Bob must have gotten the Box with the right/left shoe. I think we just have to accept the peculiar feature of QM that there can be objects that are in superposition.

Well, it seems to me that the "spilling over into atoms of the measurement device" is exactly what leads to the Many Worlds Interpretation.

I wouldn't say that leads to many world, since we only get many worlds if we include the observer into the picture. It suffices however to include enough quantum degrees of freedom to effectively hide the correlation from the observer.

The collapse interpretation is only relevant if we assume that measurements have unique outcomes.

Does the collapse lead to unique outcomes? I would say no, because even if the quantum state collapses to one of the states in a superposition, this state can still be expanded in another basis and looks like a superposition there. Just by looking at a state, we can never tell whether it is the state of a collapsed system and encodes the fact that there is something with a definite outcome or it is an unmeasured state in a superposition of possible outcomes of the conjugate variable. I think we can never interpret the state consistenly as a representation of a physical outcome. Instead, it only tells us about the statistical features that we will observe if we conduct an experiment with an identical preparation procedure a thousand times.

 

[atyy]

I would argue that this is not the right thing to do. QM is a statistical theory and it doesn't make sense to speak about individual measurements within its framework. If you want to compare experimental results to the theory, you first need to translate them into the language of statistics, i.e. you must have performed several measurements and computed the statistical mean and so on. You can of course collect your data in a spacetime diagram, but it tells you nothing about what the quantum state on the corresponding hypersurface was. If you are interested in the quantum state, you basically need to perform something like a quantum tomography, where measure position or momentum a thousand times, but everytime start with a newly prepared state and then find a quantum state that is consistent with the statistics.

I agree that one can do without collapse if one is using the philosophy that one should not have sequential measurements, and kith and I have agreed on this in another discussion here some time ago (in fact, I think Feynman says this somewhere). I would argue that it's a matter of taste whether one rejects sequential measurements or not the predictions of sequential measurements and collapse can reproduce all the predictions of the view with no sequential measurements and no collapse.

However, I don't think there can be any violation of the Bell inequalities at spacelike separation in the no collapse view. The reason is that spacelike-separated measurements that are simultaneous in one frame will be sequential in another frame. To fix this problem, instead of Bob saying that Alice made a simultaneous measurement at location x and obtained spin up at time t, he has to say that he only measured what Alice reported to him locally. This is fine, and a standard way to get rid of nonlocality in quantum mechanics.

 

[stevendaryl]

But in the EPR-Twin case it's the same. The only qualification is that you have to say "Bob's photon is either H or V polarized, IF he chooses to measure the polarization in that direction."'

Let's assume for simplicity that Alice and Bob are using the same filter orientation. That is agreed-upon ahead of time. Then after Alice measures her photon to have polarization H, Alice knows something definite about Bob's future measurement: that he will measure the polarization to be H.

Classically, if Alice learns something definite about a future measurement performed by Bob, she can assume that that means that that result was pre-determined. If Alice learns that Bob will find a right shoe when he opens the box, she assumes that it was a right shoe before he opened the box.

In EPR, Alice learns that Bob will measure polarization H. But she can't assume that it had polarization H before he measured it.

That's a pretty stark difference between the two cases.

For the classical case you don't need the "IF". That's the only difference.

You don't need an "if" in the EPR case, if Bob agrees ahead of time to use a pre-arranged filter orientation.

Of course you are right in saying that Bob's photon had no definite polarization before A made her measurement. Caught in a classical worldview you then could conclude that then there must be a mechanism (called "collapse") that makes Bob's photon polarized horizontally through the measurement.

I don't think it's a matter of assuming a mechanism. Collapse is just a description of the situation, it seems to me. Assuming once again that Bob has agreed ahead of time to use the same pre-arranged filter orientation as Alice, Alice knows before Bob does what his measurement will be. She learns a fact about Bob's photon + filter + detector remotely. Under the assumption that Alice and Bob are using the same orientation, and that Alice observes a horizontally-polarized photon before Bob does his measurement, let X be the claim: "Bob will observe a horizontally-polarized photon".

It seems to me that there are only three possibilities:

1. X was a fact before Alice observed her photon.
2. X only became a fact after Alice observed her photon.
3. X is not really a fact at all (the MWI tactic of rejecting unique outcomes)

By "fact" I mean something that is objectively true, independent of any observer. If you assume definite outcomes, then it seems to me that "Bob will observe a horizontally-polarized photon" is a fact, in this sense.

 

[rubi]

Einstein causality doesn't really have to do with "causation", it can be expressed as purely a claim about correlations. Bell actually worked out a more general claim about correlations in his "theory of local beables" (where "beables" is pronounced BEE-able in an analogy with OBSERV-able).

[...]

I don't think that there is any logical necessity that there be a common explanation. But it's what people usually assume. An apparent correlation can be a coincidence, but a sustained correlation indicates some common explanation.

I think the logical reasoning is as follows:
1. All classical relativistically covariant theories satisfy Einstein causality.
2. All theories that satisfy Einstein causality satisfy Bell's inequality.
3. Quantum mechanics doesn't satisfy Bell's inequality.
4. Therefore quantum mechanics can't be a classical relativistically covariant theory.

So the point of Einstein causality is not the be a physical principle that must necessarily be true, but rather to be a tool that allows us to prove that QM can't be a classical relativistically covariant theory. This is not a problem though, since QM can still be a quantum mechanical relativistically covariant theory and it needs to be interpreted differently.

The importance of collapse is that Bell's inequality as applied to EPR is proved under the assumption that there are no nonlocal influences affecting the two measurements. If there is a nonlocal collapse, then the assumptions behind Bell's proof are not satisfied, and so you shouldn't expect Bell's inequality to hold, necessarily.

That's really the issue: Does the violation of Bell's inequality imply that something nonlocal is happening? The unitary evolution of the wave function is local (although there's a little confusion about that in my mind, because the wave function is a function on configuration space, not physical space, so it's a little tricky to say what "local evolution" means). But the selection of one alternative out of a set of possible alternatives seems to be a nonlocal event. It seems as if this selection process happens at Alice's device and Bob's device simultaneously.

I would just say that Einstein causality is a too strong requirement. It is certainly true for classical theories, but it's not in the spirit of quantum mechanics and shouldn't be applied there. Of course, it's legitimate to look for deeper reasons for the 100% correlations, but in my opinion, nobody has really come up with a convincing theory so far.

 

[stevendaryl]

I would just say that Einstein causality is a too strong requirement. It is certainly true for classical theories, but it's not in the spirit of quantum mechanics and shouldn't be applied there. Of course, it's legitimate to look for deeper reasons for the 100% correlations, but in my opinion, nobody has really come up with a convincing theory so far.

As I said, it seems to me that the selection of a single outcome out of a set of possible outcomes is a nonlocal event (or substitute some other word than "event", since Einstein used "event" to mean something local). The fact that quantum field theory is local in a certain sense (spacelike separated field operators commute, or anticommute) doesn't imply that the whole shebang is local, because the equations governing the evolution of the field operators does not include a selection of one outcome out of many possible outcomes. That's an addition needed to apply QFT to experiment. I don't see how there is any possibility of making that step local.

Or here's another way to talk about it. Ultimately, what we observe is not quantum fields. What we observe are macroscopic histories---histories of outcomes of measurements. So quantum mechanics can be thought of simply as a computational tool for computing probabilities of these macroscopic histories.

So what quantum mechanics gives us is a way of computing P(h), the probability for a particular macroscopic history h. Mathematically, you can turn a probability distribution on histories into a stochastic process. We can define for such a process what it means to be "Einstein-separable". Roughly speaking, it means that we can split space up into small regions, and give an independent transition probability for each region that depends only neighboring regions. A failure of Einstein-separability means that the transition probabilities for distant regions are not independent.

Classically (classically meaning physics including SR but excluding QM), the failure of a macroscopic history to be Einstein-separable indicates microscopic facts that were not taken into account. If you enrich your notion of "history" to include these microscopic facts, then Einstein-separability would be restored.

Quantum-mechanically, this is apparently not the case. There is no way to restore Einstein-separability by giving more details about the histories. It's a semantic quibble about whether you consider this failure to be about "locality" or not. It is about locality in the sense that "decisions" about distant regions have to coordinated.

 

[atyy]

Hm, maybe I end up becoming a Bohmian, but for this I'd need a convincing formulation for the standard relativistic QFTs.

But do relativistic QFTs exist? Do we have a gauge invariant and Lorentz invariant regulator for the standard model and Einstein gravity?

 

[stevendaryl]

I think you are applying classical reasoning to the quantum mechanical world.

I'm saying that you CAN'T say that the quantum situation is analogous to the classical situation, because classically, discovering some fact about a distant situation implies that the fact was already true before you made that discovery. But quantum mechanically, we can't assume that.

In a classical world, it would be reasonable to assume Bell's locality criterion, since all relativistically covariant classical theories automatically satisfy it. We can however have perfectly relativistically covariant quantum theories that don't satisfy the principle and therefore, we can't assume that it is generally valid.

You have to be a little care about what you mean. As I said in another post, the sense in which QFT is covariant is that evolution for the field operators in the Heisenberg picture are governed by covariant equations of motion. But the field operators are not the full story. In addition to the field operators, there is the state itself, which is not an entity living in spacetime, but some object in Hilbert space. Then there is the phenomenon of unique outcomes of experiments. That is not described by the equations of motion.

In the quantum world, there are objects like left/right shoes and right/left shoes and if Alice discovers that she got the box with the left/right shoe, then she automatically knows that Bob must have gotten the Box with the right/left shoe. I think we just have to accept the peculiar feature of QM that there can be objects that are in superposition.

That's not the distinction that I was bringing up. Whether or not particles can exist in superpositions of states, it is the case in EPR that if Alice and Bob choose aligned filters, and Alice measures her photon to be horizontally polarized, then she can conclude, with 100% certainty, that Bob will also measure his photon to be horizontally polarized. So the possibility of superpositions doesn't seem relevant; we're in the situation in which Alice knows exactly what Bob will measure.

Does the collapse lead to unique outcomes?

I would say that collapse IS the picking of one outcome out of several alternatives.

I would say no, because even if the quantum state collapses to one of the states in a superposition, this state can still be expanded in another basis and looks like a superposition there.

Collapse is usually talked about in terms of measurement outcomes. Before the measurement, there are a number of outcomes that are possible. After the measurement, one of those possibilities is chosen. Following the measurement, the collapse assumption is that the wave function is now in an eigenstate of whatever observable was measured. So in my understanding of collapse, it also involves selection of one outcome out of a number of possibilities.

You're certainly right, that the post-collapse wave function doesn't imply unique outcomes for future measurements.

Just by looking at a state, we can never tell whether it is the state of a collapsed system and encodes the fact that there is something with a definite outcome or it is an unmeasured state in a superposition of possible outcomes of the conjugate variable.

Right. Collapse is hypothesized to be a particular kind of transition between two states. The states themselves don't encode the fact that they were produced by a measurement.

I think we can never interpret the state consistently as a representation of a physical outcome. Instead, it only tells us about the statistical features that we will observe if we conduct an experiment with an identical preparation procedure a thousand times.

Sure, but if the state is an eigenstate of a particular observable, then we can say with certainty what the measurement of that observable will yield. So the claim "If you measure X, you will get Y" seems to be an objective fact about the world.

 

[stevendaryl]

But do relativistic QFTs exist? Do we have a gauge invariant and Lorentz invariant regulator for the standard model and Einstein gravity?

I think most people assume that relativistic QFTs are possible, even if we haven't figured out a consistent one.

It would be very strange (but certainly possible) if it turned out that the only way to make QFT consistent is to chuck out SR and assume that there is an absolute notion of time. My intuition is that the problems in understanding what's going on in EPR-type experiments is orthogonal to the problems of making a consistent QFT. But it would certainly be exciting to find out that they are connected.

 

[vanhees71]

But do relativistic QFTs exist? Do we have a gauge invariant and Lorentz invariant regulator for the standard model and Einstein gravity?

Well, then you'd through out the baby with the bath ;-). There's no mathematically rigorous relativistic QFTs for real-world problems. On the other hand the Standard Model of Elementary Particles is even too succuessful nowadays. It's also a different question, whether you can solve these purely mathematical problems or which physical interpretation you can give established theories.

On the other hand, perhaps one day somebody finds a mathematical solution for all these mathematical problems which at the same time saves the quibbles with interpretation. Meanwhile we have to live with the effective models we have.

 

[atyy]

Well, then you'd through out the baby with the bath ;-). There's no mathematically rigorous relativistic QFTs for real-world problems. On the other hand the Standard Model of Elementary Particles is even too succuessful nowadays. It's also a different question, whether you can solve these purely mathematical problems or which physical interpretation you can give established theories.

On the other hand, perhaps one day somebody finds a mathematical solution for all these mathematical problems which at the same time saves the quibbles with interpretation. Meanwhile we have to live with the effective models we have.

Well, the other way of thinking is that all are theories are wrong anyway. But let's at least have some that are well defined. So for QED we take lattice QED with fine enough spacing and large but finite volume, and similarly we hope for a lattice construction of the standard model with finite spacing in large but finite volume. Then that means our current best theories are not truly Lorentz invariant due to the finite lattice spacing, and special relativity is only a very good approximation at low energy or long wavelength compared to the lattice spacing. So there is no true Lorentz invariance, which means there is nothing wrong with a Bohmian interpretation. This doesn't mean that a Bohmian interpretation is right, since there could be other possibilities like Many-Worlds or something else. However, from the lattice point of view and the Wilsonian point of view, this would at least make Bohmian Mechanics seem more natural.

 

[vanhees71]

Let's assume for simplicity that Alice and Bob are using the same filter orientation. That is agreed-upon ahead of time. Then after Alice measures her photon to have polarization H, Alice knows something definite about Bob's future measurement: that he will measure the polarization to be H.

Classically, if Alice learns something definite about a future measurement performed by Bob, she can assume that that means that that result was pre-determined. If Alice learns that Bob will find a right shoe when he opens the box, she assumes that it was a right shoe before he opened the box.

Sure, that's what makes QT different from classical physics, where there are no indetermined observables, because all observables of a system always have definite values, which we sometimes don't know and thus use probabilistic descriptions of classical statistical physics.

Within QT there are always some observables indetermined even if we know the complete (pure) state of the system. Usually, if you have a pure state of a composite system the parts of it are not in a pure state, as it's the case here for the polarization-entangled two-photon state.

In EPR, Alice learns that Bob will measure polarization H. But she can't assume that it had polarization H before he measured it.

That's a pretty stark difference between the two cases.

Yes, it is, but this doesn't imply necessarily a collapse, because there's nothing preventing me from taking the point of view that the corresponding correlation was inherent from the very beginning in the entangled two-photon state. Thus it's a prediction of the model that when Alice finds her photon to be V-polarized, Bob must find his H-polarized, given the engangled initial state, $|HV \rangle-|VH \rangle$.

You don't need an "if" in the EPR case, if Bob agrees ahead of time to use a pre-arranged filter orientation.

Yes, but the important point is that, if he uses and appropriate other filter orientation, you can violate Bell's inequality, showing that the polarization have not been predetermined within a local deterministic hidden-variable theory. This clearly proves that QT is really fundamentally different from classical physics, as you stressed yourself above!

I don't think it's a matter of assuming a mechanism. Collapse is just a description of the situation, it seems to me. Assuming once again that Bob has agreed ahead of time to use the same pre-arranged filter orientation as Alice, Alice knows before Bob does what his measurement will be. She learns a fact about Bob's photon + filter + detector remotely. Under the assumption that Alice and Bob are using the same orientation, and that Alice observes a horizontally-polarized photon before Bob does his measurement, let X be the claim: "Bob will observe a horizontally-polarized photon".

It seems to me that there are only three possibilities:

1. X was a fact before Alice observed her photon.
2. X only became a fact after Alice observed her photon.
3. X is not really a fact at all (the MWI tactic of rejecting unique outcomes)

By "fact" I mean something that is objectively true, independent of any observer. If you assume definite outcomes, then it seems to me that "Bob will observe a horizontally-polarized photon" is a fact, in this sense.

There's a possibility missing, namely precisely the one I follow!

X was not a fact before Alice's measurement (Bob's photon is unpolarized), but it was a fact that you had an entangled photon pair, so that there is this 100% correlation between A's and B's measurements. There's no problem with that point of view precisely when you don't take the collapse as a physical process (I guess, you'd call this ontological) but just an update of Alice's knowledge about the system (I guess, that you'd call epistemical). Nothing changes for Bob before his measurement, because he has not gained any information yet. From this point of view, there's no contradiction that for Bob his photon's state is still the maximum-entropy mixture $1/2 \mathbb{1}$ while for Alice's it's in the pure state $|H \rangle \langle H|$. So after A's measurement and before B's measurement X became a fact for Alice but not for Bob. That's all.

 

[vanhees71]

I think nearly any non-Crackpot interpretation is "more natural" than many worlds. What does it help anyway? It introduces simply infinitely many parallel universes for any measurement act. But what's a measurement act different that the interaction of a system and a measurement apparatus. So you cannot even say how many parallel universes are created per second, because you cannot clearly define what a measurement process distinguishes from any other kind of interaction. I don't see any merit in many worlds as compared to the standard minimal interpretation.

 

[Demystifier]

I think nearly any non-Crackpot interpretation is "more natural" than many worlds. What does it help anyway? It introduces simply infinitely many parallel universes for any measurement act. But what's a measurement act different that the interaction of a system and a measurement apparatus. So you cannot even say how many parallel universes are created per second, because you cannot clearly define what a measurement process distinguishes from any other kind of interaction. I don't see any merit in many worlds as compared to the standard minimal interpretation.

You misunderstood MWI. It does not introduce infinitely many parallel universes for any measurement act. It does not make a difference between measurement and interaction.

Due to Schrodinger evolution, almost any interaction with a system with a large number of degrees of freedom creates branching of the wave function into a finite number of new branches. These branches are mathematical objects derived from Schrodinger evolution of the wave function. Their mathematical existence does not depend on the interpretation. All what MWI adds is the claim that these branches are not only abstract mathematical objects, but also actual real worlds.

These very same branches are also essential for understanding the von Neumann theory of quantum measurements (before the collapse), Bohmian mechanics (before you calculate the trajectories), and even the mainstream theory of decoherence (before you calculate the reduced density matrix). Different interpretations of QM attribute different physical meaning to these branches (MWI takes them more seriously than any other interpretation), but all interpretations deal with these branches one way or another.

The main advantage of MWI compared to other interpretations (including the standard minimal interpretation) is the claim that it is the only interpretation for which everything can be described by the Schrodinger equation. (For instance, in the standard minimal interpretation (SMI), the existence of individual results of measurements cannot be described by Schrodinger equation alone, in the sense that the events themselves are not wave functions in SMI.)

 

[stevendaryl]

Yes, it is, but this doesn't imply necessarily a collapse, because there's nothing preventing me from taking the point of view that the corresponding correlation was inherent from the very beginning in the entangled two-photon state.

Yes, the correlation was true before Alice did her measurement. But the fact that "Bob will measure the photon to have horizontal polarization" was not true before Alice performed her measurement. So a fact about Bob's measurement becomes true as a result of Alice's actions. I don't see how it could be otherwise:

Yes, but the important point is that, if he uses and appropriate other filter orientation, you can violate Bell's inequality, showing that the polarization have not been predetermined within a local deterministic hidden-variable theory.

Let's make sure we're on the same page about the case where Alice and Bob pre-arrange to use the same orientation. Alice measures her photon to be horizontally polarized. Then, under the assumption that Bob is using the same filter orientation, would you say that the statement "Bob will measure horizontal polarization" is true after Alice's measurement? Was it true before her measurement, or not? If you say yes, you're assuming hidden variables. If you say no, then it sure seems that you are saying that something about Bob's measurement was changed by Alice's measurement.

X was not a fact before Alice's measurement (Bob's photon is unpolarized), but it was a fact that you had an entangled photon pair, so that there is this 100% correlation between A's and B's measurements.

X in this case being "Bob will measure a horizontally polarized photon". So the question is: Is X true after Alice's measurement? X is a logical consequence of the two true statements: (1) Alice and Bob's results are 100% correlated, and (2) Alice measured horizontal polarization. Normally, if something follows from true statements, then it is itself true.

 

[TrickyDicky]

But do relativistic QFTs exist? Do we have a gauge invariant and Lorentz invariant regulator for the standard model and Einstein gravity?

We don't, I guess the question was rhetorical.

I think most people assume that relativistic QFTs are possible, even if we haven't figured out a consistent one.

It would be very strange (but certainly possible) if it turned out that the only way to make QFT consistent is to chuck out SR and assume that there is an absolute notion of time. My intuition is that the problems in understanding what's going on in EPR-type experiments is orthogonal to the problems of making a consistent QFT. But it would certainly be exciting to find out that they are connected.

If discarding SR was the only way of making QFT consistent(I doubt that'd come to be the case), why should assuming absolute time be the only alternative? I think the choice is broader.
Regarding a connection between measurement problem and not having a consistent QFT I do believe they are connected. This can be seen clearer if one uses Penrose's RTR description of the issue in terms of the U and R processes. The non-unitary R process slips in the step from the asymptotic perturbative series to a finite terms( a valid calculation) series, preventing from keeping Poincare invariance.

 

[stevendaryl]

I think nearly any non-Crackpot interpretation is "more natural" than many worlds. What does it help anyway

To me, the issue is just one of logical consistency. The two claims

1. Only one outcome occurs.
2. There are no nonlocal effects.

seem to contradict the predictions of QM in the EPR case. You disagree because somehow you don't think that Bob's result going from "50/50 chance of being H or V" to "100% chance of H" is a physical change. I don't see how it could be otherwise. Saying that Bob will definitely measure H sure seems to be an objective fact about Bob's situation. If it wasn't true before Alice's measurement, I don't see how you can say that Alice's measurement didn't change the facts about Bob's situation.

If the two claims above are inconsistent with the predictions of QM, then one or the other (or both) is false. MWI rejects 1. Bohm rejects 2.

 

[vanhees71]

Yes, the correlation was true before Alice did her measurement. But the fact that "Bob will measure the photon to have horizontal polarization" was not true before Alice performed her measurement. So a fact about Bob's measurement becomes true as a result of Alice's actions. I don't see how it could be otherwise:
Let's make sure we're on the same page about the case where Alice and Bob pre-arrange to use the same orientation. Alice measures her photon to be horizontally polarized. Then, under the assumption that Bob is using the same filter orientation, would you say that the statement "Bob will measure horizontal polarization" is true after Alice's measurement? Was it true before her measurement, or not? If you say yes, you're assuming hidden variables. If you say no, then it sure seems that you are saying that something about Bob's measurement was changed by Alice's measurement.

After Alice finds V for her photon, she knows that Bob finds H for his for sure, and there is no hidden variable. Why should there be one?

X in this case being "Bob will measure a horizontally polarized photon". So the question is: Is X true after Alice's measurement? X is a logical consequence of the two true statements: (1) Alice and Bob's results are 100% correlated, and (2) Alice measured horizontal polarization. Normally, if something follows from true statements, then it is itself true.

After A's measurement, finding V, for sure B will measure H. That's due to the entangled initial state. This follows directly from the usual assumptions of QT.

 

[vanhees71]

To me, the issue is just one of logical consistency. The two claims

1. Only one outcome occurs.
2. There are no nonlocal effects.

seem to contradict the predictions of QM in the EPR case. You disagree because somehow you don't think that Bob's result going from "50/50 chance of being H or V" to "100% chance of H" is a physical change. I don't see how it could be otherwise. Saying that Bob will definitely measure H sure seems to be an objective fact about Bob's situation. If it wasn't true before Alice's measurement, I don't see how you can say that Alice's measurement didn't change the facts about Bob's situation.

If the two claims above are inconsistent with the predictions of QM, then one or the other (or both) is false. MWI rejects 1. Bohm rejects 2.

I don't know what you mean by "effects" under 2.

According to standard QFT (here QED for our photon case) there are no non-local interactions but there can be "non-local" correlations as described by entangled states. It's important to distinguish this. Concerning the Bohmian point of view, I've to study it for relativistic QFT, before I can say anything about it.

 

[atyy]

@vanhees71, just a comment: I don't think your intepretation is the most minimal, by saying collapse is epistemic.

Usually in a truly minimal interpretation, we say we don't know whether collapse is physical or epistemic or some unknown mixture of both. For example, Cohen-Tannoudj, Diu and Laloe (at least in the English translation of their textbook) are very careful not to exclude either possibility.

 

[vanhees71]

Good hint to look at this book!