A An argument against Bohmian mechanics?

[vanhees71]

It's not a collapse in the sense of Copenhagen. It's due to a local interaction between the measured object and the device but not an instantaneous interaction at a distance violating causality!

 

[rubi]

"$S_x=+1\wedge S_y=-1$ (at the same time)" is an invalid statement in BM. It is also an invalid statement in the standard Copenhagen interpretation. And more importantly, there is no experiment which gives $S_x=+1\wedge S_y=-1$ (at the same time). So how can this be dictated by experiments?

This is exactly what CH says. It is logically invalid to form the conjunction $A\wedge B$, if $A$ is $S_x=+1$ and $B$ is $S_y=-1$, i.e. you cannot apply the rules of classical logic to propositions about quantum systems. BM of course (like every other interpretation) doesn't get around this. The CH rules tell you, which propsitions are logically meaningful and can be combined into a single framework. My example about $S_x$ and $S_y$ is one such meaningless proposition. It's not meaningful in CH, Copenhagen and BM. CH doesn't violate the rules of classical logic more than BM does. In classical logic, you can always form conjunctions like $A\wedge B$. If you give me two meaningful propositions $A$ and $B$ and I'm not allowed to take their conjunction $A\wedge B$, then I'm not dealing with classical logic.

I think you're arguing something different than vanhees is. I am not arguing against the possibility of a stochastic description of physics.

Okay, I see.

when the system is in a superposition of those two states, then the composite wave function makes a transition to a superposition of those macroscopic states (or mixture, if you like, but I'm using superposition because I'm including the environment in the wave function)

Maybe in vanhees POV, these superpositions will cancel each other, leaving only one macroscopic possibility (with $P>\epsilon$). I don't think this is impossible, but one needs a big enough Hilbert space and there will of course always remain some variables (concerning the whole system), which will be completely non-classical.

 

[stevendaryl]

It's not a collapse in the sense of Copenhagen. It's due to a local interaction between the measured object and the device but not an instantaneous interaction at a distance violating causality!

This is the point that I have been making: I don't have a philosophical problem with what you're saying; I have a technical problem with it. It's factually incorrect. You seem to be saying that local interactions are sufficient to explain the occurrence of definite results for quantum measurements. That's provably false. Bell proved it to be false.

 

[Demystifier]

This is exactly what CH says. It is logically invalid to form the conjunction $A\wedge B$, if $A$ is $S_x=+1$ and $B$ is $S_y=-1$, i.e. you cannot apply the rules of classical logic to propositions about quantum systems. BM of course (like every other interpretation) doesn't get around this. The CH rules tell you, which propsitions are logically meaningful and can be combined into a single framework. My example about $S_x$ and $S_y$ is one such meaningless proposition. It's not meaningful in CH, Copenhagen and BM. CH doesn't violate the rules of classical logic more than BM does. In classical logic, you can always form conjunctions like $A\wedge B$. If you give me two meaningful propositions $A$ and $B$ and I'm not allowed to take their conjunction $A\wedge B$, then I'm not dealing with classical logic.

So physical impossibility in other interpretations is promoted to a logical nonsense in CH interpretation. But one could do that even in classical physics. For example, let
A = there are two free massive particles at distance r
B = these two particles are not attracted by a force
Due to gravitational force, it is never the case that both A and B are true. In a CH interpretation of Newtonian mechanics, one would say that $A\wedge B$ is a logical nonsense. But that's not a good approach, because science must be testable. One must consider the statement $A\wedge B$ as a logical possibility, and then make experiments to see whether $A\wedge B$ is true. (The experiments show that it isn't).

 

[stevendaryl]

This is the point that I have been making: I don't have a philosophical problem with what you're saying; I have a technical problem with it. It's factually incorrect. You seem to be saying that local interactions are sufficient to explain the occurrence of definite results for quantum measurements. That's provably false. Bell proved it to be false.

Let's go through this for the EPR experiment.

Alice has a device that has two pointer states: S_u and S_d. If an electron that is spin-up along the z-axis interacts with her device, then the device will almost certainly make a transition to having the pointer state S_u. If an electron is spin-down, the device will almost certainly make a transition to having the pointer state S_d. If an electron is in a superposition or mixed state of spin-up and spin-down, then the device will make a nondeterministic transition to either the state S_u or S_d (depending on the coefficients of the superposition or mixture). So far, it seems that everything is perfectly well described by local interactions. But now, we add one more constraint on Alice's device:

• If, far far away, Bob's device, interacting with the electron's twin, already made the transition to the state pointer state S_u, then Alice's device will definitely make the transition to S_d

You can't account for this additional fact with only local interactions.

 

[rubi]

So physical impossibility in other interpretations is promoted to a logical nonsense in CH interpretation.

If the problem were only physical impossibility, then the statement $S_x=+1\wedge S_y=-1$ would be completely unproblematic. We would just assign $P=0$ to it and be happy. However, no possible assignment of probabilities to such a proposition is consistent with QM, so it must be the case that taking this conjunction is an invalid operation. (I know the $d=2$ loophole. Let's stick to $d=2$ for simplicity.) This is all CH says. You must restrict yourself to a single framework if you want to apply classical logic. If your framework includes $S_x=+1$, then it can't include $S_y=-1$. Nothing more and nothing less. Bohmians should agree with this.

But one could do that even in classical physics. For example, let
A = there are two free massive particles at distance r
B = these two particles are not attracted by a force
Due to gravitational force, it is never the case that both A and B are true. In a CH interpretation of Newtonian mechanics, one would say that $A\wedge B$ is a logical nonsense.

No, CH has nothing to say about this example. The CH rules apply to propositions that are modeled as projectors in a Hilbert space. The problem with your propositions is that they are self-referential. This is not possible in classical logic either. You are dealing with an unformalized problem in natural language here. Translate it into formalized logic and the problem should vanish.

But that's not a good approach, because science must be testable. One must consider the statement $A\wedge B$ as a logical possibility, and then make experiments to see whether $A\wedge B$ is true. (The experiments show that it isn't).

Whether $S_x=+1\wedge S_y=-1$ is a valid proposition can be tested experimentally and the experiment says that it isn't (again, let's not harp on about the $d=2$ loophole).

 

[stevendaryl]

It's not a collapse in the sense of Copenhagen. It's due to a local interaction between the measured object and the device but not an instantaneous interaction at a distance violating causality!

Just so we're clear: You are agreeing that after a measurement, the measurement device has a definite pointer state. Is that correct? If so, I don't understand how that is not a "collapse". Whether or not it is mediated by local interactions, the result is that a single outcome is selected out of a set of possible outcomes. That's what people mean by "collapse".

 

[vanhees71]

Let's go through this for the EPR experiment.

Alice has a device that has two pointer states: S_u and S_d. If an electron that is spin-up along the z-axis interacts with her device, then the device will almost certainly make a transition to having the pointer state S_u. If an electron is spin-down, the device will almost certainly make a transition to having the pointer state S_d. If an electron is in a superposition or mixed state of spin-up and spin-down, then the device will make a nondeterministic transition to either the state S_u or S_d (depending on the coefficients of the superposition or mixture). So far, it seems that everything is perfectly well described by local interactions. But now, we add one more constraint on Alice's device:

• If, far far away, Bob's device, interacting with the electron's twin, already made the transition to the state pointer state S_u, then Alice's device will definitely make the transition to S_d

You can't account for this additional fact with only local interactions.

Yes, we can! The answer is relativistic QFT. The correlations are not due to non-local interactions but due to the preparation in an entangled state at the very beginning, and it's indeed incompatible with local deterministic models a la Bell.

 

[PeterDonis]

Whether or not it is mediated by local interactions, the result is that a single outcome is selected out of a set of possible outcomes. That's what people mean by "collapse".

Perhaps it would help to state a concrete example. Suppose we put an electron through a Stern-Gerlach device oriented in the $z$ direction. The spin eigenstates of this measurement are $\vert z+ \rangle$ and $\vert z- \rangle$. The "pointer variable" here is the direction in which the electron is moving; it starts out moving horizontally, which we will call pointer state $\vert R \rangle$ (for "ready"), and ends up moving either up or down, which we will call pointer states $\vert U \rangle$ and $\vert D \rangle$.

We know that the Hamiltonian is such that the spin eigenstates will induce evolution as follows:

$$
\vert z+ \rangle \vert R \rangle \rightarrow \vert z+ \rangle \vert U \rangle
$$

$$
\vert z- \rangle \vert R \rangle \rightarrow \vert z- \rangle \vert D \rangle
$$

Therefore, a superposition of spin eigenstates $\vert \psi \rangle = a \vert z+ \rangle + b \vert z- \rangle$, where $\vert a \vert^2 + \vert b \vert^2 = 1$, will induce evolution as follows:

$$
\vert \psi \rangle \vert R \rangle \rightarrow a \vert z+ \rangle \vert U \rangle + b \vert z- \rangle \vert D \rangle
$$

This state does not describe "a single outcome"; it describes a superposition of "outcomes". But this state is what unitary evolution predicts. So if in fact the final state is not the above, but either

$$
\vert z+ \rangle \vert U \rangle
$$

or

$$
\vert z- \rangle \vert D \rangle
$$

with probabilities $\vert a \vert^2$ and $\vert b \vert^2$ respectively, then some other process besides unitary evolution must be involved, and this other process is what is referred to by the term "collapse". Decoherence doesn't change this; all decoherence does is ensure that there are no "cross terms" of the form $\vert z+ \rangle \vert D \rangle$ or $\vert z- \rangle \vert U \rangle$ in the superposition.

 

[Mentz114]

''
''

• when the system is in a superposition of those two states, then the composite wave function makes a transition to a superposition of those macroscopic states (or mixture, if you like, but I'm using superposition because I'm including the environment in the wave function)

That follows from the linearity of the evolution equations for quantum mechanics. Coarse graining is a mathematical tool for extracting a macroscopic state from a microscopic state. It isn't going to produce a single outcome if the underlying microscopic state reflects a superposition of macroscopically different outcomes.

You can certainly have an additional, stochastic step in which one coarse-grained macroscopic state is selected from the superposition or mixture, but that is an additional step.

Looking at the third point, "... the composite wave function makes a transition to a superposition of those macroscopic states ... or mixture ... ".

If you mean a statistical mixture then that implies that on every run of the experiment ( ensemble member ) a definite outcome was achieved, and no further step is required. Nor any explanation of how the state was selected. But you probably don't mean that, do you ?

 

[kith]

But in QM, the difference is not simply a matter of what to choose to ignore. Different rules apply to measurements than to other types of interactions.

This may be only a minor point but I don't like the distinction of "ordinary interactions" and "measurement interactions". The Heisenberg cut can be shifted. So whether a specific interaction is of the first or of the second type depends on the person which does the analysis. Measurements are not merely physical.

In what I would consider a coherent formalism, you would describe how the world works, independently of observers, and then add physical-phenomenal axioms saying that such-and-such a condition of such-and-such subsystem counts as a measurement of such-and-such a property. There would be no additional physics to the measurement process, since it would just be an ordinary process.

I agree that this sounds desireable but the chain of logic doesn't reflect how science is done. Our theories are distilled from observations so it isn't a priori clear that we can take the observer out of the picture. Sure, it did work for classical physics but it doesn't for theories with entanglement-like properties.

So given that we have a theory with entanglement, we should ask what a possible alteration of the Born rule could look like in order that we wouldn't consider it ad hoc. If separating the observer from the system changes the system in a non-trivial way, there doesn't seem to be n easy way for this. So for me, the weird thing about QM is that I cannot imagine how a non-weird version of it would look like and I take that as a sign that I don't understand what exactly is weird well enough.

 

[kith]

But why can we ignore part of the universe? Is it because of locality? Why is the universe operationally local, even though reality is nonlocal (or retrocausal etc ...)?

I'm not sure how this relates to what I wrote.

Your starting point seems to be that out of all possible theories, we got one which is demonstrably nonlocal on a fundmental level but at the same time, everything we as humans can think of to exploit this nonlocality is equally demonstrably impossible. How strange! (Please correct me if I'm wrong)

The starting point of my post #281 was us doing experiments. From this point of view, your first question doesn't make sense. We cannot not ignore part of the universe because in order to observe something, we have to exclude at least the part of ourselves which experiences the observation.

(Also, more fundamental theories must include the older ones as limiting cases. So shouldn't you condition your second question on the fact that classical physics is local? But here I see even less connection to my post)

 

[Jilang]

Let's go through this for the EPR experiment.

Alice has a device that has two pointer states: S_u and S_d. If an electron that is spin-up along the z-axis interacts with her device, then the device will almost certainly make a transition to having the pointer state S_u. If an electron is spin-down, the device will almost certainly make a transition to having the pointer state S_d. If an electron is in a superposition or mixed state of spin-up and spin-down, then the device will make a nondeterministic transition to either the state S_u or S_d (depending on the coefficients of the superposition or mixture). So far, it seems that everything is perfectly well described by local interactions. But now, we add one more constraint on Alice's device:

• If, far far away, Bob's device, interacting with the electron's twin, already made the transition to the state pointer state S_u, then Alice's device will definitely make the transition to S_d

You can't account for this additional fact with only local interactions.

I can't quite follow this,( but I'm trying my best). If the electron were in a superposition of u and d states wouldn't it have needed to have been prepared in a definite state of l or r to be guaranteed to produce a random result in the u/d direction? If the up coefficient were bigger than the down coefficient (so to speak) would it not be expected to migrate one way rather than the other?

 

[stevendaryl]

Looking at the third point, "... the composite wave function makes a transition to a superposition of those macroscopic states ... or mixture ... ".

If you mean a statistical mixture then that implies that on every run of the experiment ( ensemble member ) a definite outcome was achieved, and no further step is required. Nor any explanation of how the state was selected. But you probably don't mean that, do you ?

It's a little difficult to discuss without getting into endless levels of details. But the use of mixtures is not limited to the case in which a system has a definite (though unknown) state. You also get a mixture by taking a composite system and "tracing out" unobservable degrees of freedom.

This is what makes the discussion a little complicated. On the one hand, people say that realistically, you shouldn't use pure states to describe macroscopic objects, you should use mixtures. But the use of mixtures already blurs the distinction between probabilities that are inherent in the quantum formalism and probabilities that are due to lack of knowledge. Some people say that there is no distinction, but that seems wrong to me. To say that an electron is in a superposition of spin-up and spin-down is not to say that it is one state or the other, I just don't know which.

 

[stevendaryl]

Therefore, a superposition of spin eigenstates $\vert \psi \rangle = a \vert z+ \rangle + b \vert z- \rangle$, where $\vert a \vert^2 + \vert b \vert^2 = 1$, will induce evolution as follows:

$$
\vert \psi \rangle \vert R \rangle \rightarrow a \vert z+ \rangle \vert U \rangle + b \vert z- \rangle \vert D \rangle
$$

This state does not describe "a single outcome"; it describes a superposition of "outcomes". But this state is what unitary evolution predicts. So if in fact the final state is not the above, but either

$$
\vert z+ \rangle \vert U \rangle
$$

or

$$
\vert z- \rangle \vert D \rangle
$$

with probabilities $\vert a \vert^2$ and $\vert b \vert^2$ respectively, then some other process besides unitary evolution must be involved, and this other process is what is referred to by the term "collapse". Decoherence doesn't change this; all decoherence does is ensure that there are no "cross terms" of the form $\vert z+ \rangle \vert D \rangle$ or $\vert z- \rangle \vert U \rangle$ in the superposition.

Unless I'm misunderstanding you, you seem to be agreeing with me. Decoherence, or irreversibility is not going to result in a definite outcome.

So if someone says that a measurement results in either the state |U\rangle, with such-and-such probability, or the state |D\rangle, with such and such a probability, then does that imply that something nonunitary is involved?

 

[stevendaryl]

Yes, we can! The answer is relativistic QFT.

This is a misconception on your part. There are two parts to QFT, just as there are two parts to nonrelativistic quantum mechanics: (1) evolution of the quantum state, and (2) the Born rule.

QFT affects the first part, but not the second. We're only talking about the second.

 

[PeterDonis]

you seem to be agreeing with me.

Yes, I am. But I'm trying to state your point using a concrete example in the hope that it will help to make it clearer to others.

So if someone says that a measurement results in either the state $|U\rangle$, with such-and-such probability, or the state $|D\rangle$, with such and such a probability, then does that imply that something nonunitary is involved?

To me it obviously must, since unitary evolution gives the superposition. So a no collapse interpretation, like MWI, would say that the measurement results in the superposition--i.e., "measurement" is not a non-unitary collapse but simply a unitary entanglement interaction between the measured system and the "pointer" system (the one whose state becomes entangled with the measured system's state). In the Stern-Gerlach case, the measured system is the electron's spin and the pointer system is the electron's momentum.

 

[stevendaryl]

Yes, we can! The answer is relativistic QFT. The correlations are not due to non-local interactions but due to the preparation in an entangled state at the very beginning, and it's indeed incompatible with local deterministic models a la Bell.

No, relativistic QFT is not the answer. Look, if you described everything in EPR---the twin pair, the detectors, Bob, Alice, the environment, etc.---using QFT, what you would NOT find is that smooth unitary evolution would result in Alice's detector having a definite pointer state. What you would find is that the composite wave function of everything relevant would evolve into a superposition of different worlds with different pointer states. It doesn't matter whether you describe the detectors using QFT or nonrelativistic quantum mechanics. The evolution equations are not stochastic, they are deterministic.

So if Alice's detector ends up in a definite pointer state, that is NOT described by QFT's unitary evolution.

 

[stevendaryl]

This may be only a minor point but I don't like the distinction of "ordinary interactions" and "measurement interactions". The Heisenberg cut can be shifted. So whether a specific interaction is of the first or of the second type depends on the person which does the analysis. Measurements are not merely physical.

Okay, that's a possible answer, which is that there is nothing objective about measurement results--for one person, an object might be in a definite state, while for another person, the same object might be in a superposition.

So given that we have a theory with entanglement, we should ask what a possible alteration of the Born rule could look like in order that we wouldn't consider it ad hoc. If separating the observer from the system changes the system in a non-trivial way, there doesn't seem to be n easy way for this. So for me, the weird thing about QM is that I cannot imagine how a non-weird version of it would look like and I take that as a sign that I don't understand what exactly is weird well enough.

Fair enough. I'm not sure what a nonweird version of QM would be like, either.

 

[Mentz114]

It's a little difficult to discuss without getting into endless levels of details. But the use of mixtures is not limited to the case in which a system has a definite (though unknown) state. You also get a mixture by taking a composite system and "tracing out" unobservable degrees of freedom.

This is what makes the discussion a little complicated. On the one hand, people say that realistically, you shouldn't use pure states to describe macroscopic objects, you should use mixtures. But the use of mixtures already blurs the distinction between probabilities that are inherent in the quantum formalism and probabilities that are due to lack of knowledge. Some people say that there is no distinction, but that seems wrong to me. To say that an electron is in a superposition of spin-up and spin-down is not to say that it is one state or the other, I just don't know which.

As far as I understand this I can't see anything to disagree with. The point I've emphasized is worth exploring further, so I'll do that for a bit.

 

[kith]

Therefore, a superposition of spin eigenstates $\vert \psi \rangle = a \vert z+ \rangle + b \vert z- \rangle$, where $\vert a \vert^2 + \vert b \vert^2 = 1$, will induce evolution as follows:

$$
\vert \psi \rangle \vert R \rangle \rightarrow a \vert z+ \rangle \vert U \rangle + b \vert z- \rangle \vert D \rangle
$$

This state does not describe "a single outcome"; it describes a superposition of "outcomes". But this state is what unitary evolution predicts. So if in fact the final state is not the above, but either

$$
\vert z+ \rangle \vert U \rangle
$$

or

$$
\vert z- \rangle \vert D \rangle
$$

with probabilities $\vert a \vert^2$ and $\vert b \vert^2$ respectively, then some other process besides unitary evolution must be involved, and this other process is what is referred to by the term "collapse".

I'd like to point out two subtleties which haven't been mentioned in this thread yet. I think both might be relevant to the discussion with vanHees71.

First, proponents of the ensemble interpretation might say that the final state really is the full final state which involves a superposition of macroscopically distinct apparatus states (Ballentine does this in his textbook, see section 9.3, 1st edition). This is possible because in the ensemble interpretation, states do not refer to single systems.

Second, let's look at a very similar situation which prepares a beam of particles in state |z+ \rangle. Suppose that we modify your device such that particles which would hit the "UP"-part of the detector are transmitted and particles which would hit the "DOWN"-part are reflected back, becoming trapped in the device. The final state then is $$a|z+, \text{transmitted} \rangle \otimes |\psi_\text{Device} \rangle \,\,+\,\,\, b|z-, \text{trapped}\rangle \otimes|\phi_\text{Device} \rangle $$ If we use |z+ \rangle as the state for further measurements, it looks like a textbook example of collapse. What actually happens is that we make the choice to use only the first part of the final state because we know that the overlap of the second term wrt to the eigenstates of all subsequent observables is zero. So in this case, "collapse" is simply the redefinition of what the system of interest is.

 

[kith]

I'm not sure what a nonweird version of QM would be like, either.

What's your personal expectation: will there be a future theory which removes the weirdness of QM?

 

[stevendaryl]

First, proponents of the ensemble interpretation might say that the final state really is the full final state which involves a superposition of macroscopically distinct apparatus states (Ballentine does this in his textbook, see section 9.3, 1st edition). This is possible because in the ensemble interpretation, states do not refer to single systems.

In my opinion, saying that the QM state refers to an ensemble, rather than an individual system, doesn't seem to be of much help in the interpretational problems. You might be tempted to say that "an electron has 50% chance of being spin-up in the z-direction" means that in the ensemble, 50% of the electrons of the ensemble are spin-up in the z-direction, and 50% are spin-down. That would imply that for each element of the ensemble, the spin component in the z-direction is fixed. Probabilities arise from not knowing which element is the "actual world". That's the way ensembles work classically.

But we know that QM doesn't work that way. That would be a hidden-variable theory, saying that the spin component is definite, but we don't know what its value is, so we describe it using probability. Bell proved that that is not a viable way to interpret quantum probabilities. So I don't see how introducing ensembles does any good.

 

[stevendaryl]

Second, let's look at a very similar situation which prepares a beam of particles in state |z+ \rangle. Suppose that we modify your device such that particles which would hit the "UP"-part of the detector are transmitted and particles which would hit the "DOWN"-part are reflected back, becoming trapped in the device. The final state then is $$a|z+, \text{transmitted} \rangle \otimes |\psi_\text{Device} \rangle \,\,+\,\,\, b|z-, \text{trapped}\rangle \otimes|\phi_\text{Device} \rangle $$ If we use |z+ \rangle as the state for further measurements, it looks like a textbook example of collapse. What actually happens is that we make the choice to use only the first part of the final state because we know that the overlap of the second term wrt to the eigenstates of all subsequent observables is zero. So in this case, "collapse" is simply the redefinition of what the system of interest is.

I think that that makes sense for most experiments, but not for EPR-type experiments involving distant entangled particles. If Alice measures spin-up along one axis, we know that Bob will measure spin-down along that axis. So it's not just a matter of Alice ignoring those electrons that we spin-down. (Unless she's also somehow ignoring those "Bobs" that measured the wrong value.)

 

[atyy]

Well, there are two possibilities:
1. BM makes the same predictions as QM, which is what the Bohmians usually claim. In that case, the analogy is spot on.
2. BM makes different predictions than QM. In that case it either contradicts experiments or the different predictions concern only situations that have not been experimentally tested yet. Then, most physicist would expect the QM predictions to be right and the BM predictions to be wrong. If the QM predictions turned out to be wrong, people would be more likely to just adjust the QM model (e.g. modify the Hamiltonian) than to adopt BM (e.g. see neutrino oscillation).

My preferred analogy is that BM is really more like string theory. Heuristics suggest that we try constructing another theory that matches existing theory over a wide range of phenomena, but that (may) deviate from it in some regime. However, the heuristics do not uniquely indicate what the better theory is.

In QG, the heuristic is the nonrenormalizability of gravity, and the alternative approaches are string theory, LQG, asymptotic safety ...

In QM, the heuristic is the measurement problem, and the alternative approaches are BM, MWI, CH, ...

QM is like stat mech (nonsensical but works), equilibrium BM is like kinetic theory, non-equilibrium BM is like Newtonian mechanics or the Einstein-Maxwell equations.

 

[kith]

You might be tempted to say that "an electron has 50% chance of being spin-up in the z-direction" means that in the ensemble, 50% of the electrons of the ensemble are spin-up in the z-direction, and 50% are spin-down. That would imply that for each element of the ensemble, the spin component in the z-direction is fixed. Probabilities arise from not knowing which element is the "actual world". That's the way ensembles work classically. But we know that QM doesn't work that way.

Yes, the ensemble can't be interpreted this way.

I think that that makes sense for most experiments, but not for EPR-type experiments involving distant entangled particles. If Alice measures spin-up along one axis, we know that Bob will measure spin-down along that axis. So it's not just a matter of Alice ignoring those electrons that we spin-down. (Unless she's also somehow ignoring those "Bobs" that measured the wrong value.)

Yes, I also don't see how what I wrote could be applied to the EPR case.

 

[atyy]

I'm not sure how this relates to what I wrote.

Your starting point seems to be that out of all possible theories, we got one which is demonstrably nonlocal on a fundmental level but at the same time, everything we as humans can think of to exploit this nonlocality is equally demonstrably impossible. How strange! (Please correct me if I'm wrong)

The starting point of my post #281 was us doing experiments. From this point of view, your first question doesn't make sense. We cannot not ignore part of the universe because in order to observe something, we have to exclude at least the part of ourselves which experiences the observation.

(Also, more fundamental theories must include the older ones as limiting cases. So shouldn't you condition your second question on the fact that classical physics is local? But here I see even less connection to my post)

RIght, we do experiments And we only do experiments on a very small part of the universe. Yet we infer laws that govern the whole universe.

Some (Weinberg, Feynman) have argued that this is due to locality or symmetry (local translation invariance). So in fact we exploit locality.

Can we have a nonlocal theory, given that we only make local observations? Or can our local observations point to nonlocality - eg. Black hole information problem, measurement problem - and can we even devise successful nonlocal theories - eg. Bohmian Mechanics, Holography?

 

[Demystifier]

If the problem were only physical impossibility, then the statement $S_x=+1\wedge S_y=-1$ would be completely unproblematic. We would just assign $P=0$ to it and be happy. However, no possible assignment of probabilities to such a proposition is consistent with QM, so it must be the case that taking this conjunction is an invalid operation.

Such a probability cannot be assigned in standard QM, but it does not imply that it cannot be assigned in any theory, perhaps some more fundamental theory (yet unknown) for which QM is only an approximation. There should exist general logical rules which can be applied to any theory of nature, not only to a particular theory (such as QM) which, after all, may not be final theory of everything. In such a general logical framework, the statement $S_x=+1\wedge S_y=-1$ must not be forbidden.

What can such a theory look like? Well, the minimal Bohmian mechanics is not such a theory, because minimal BM cannot associate a probability with $S_x=+1\wedge S_y=-1$. This is because spin is not ontological in minimal BM. However, there is a non-minimal version of BM (see the book by Holland) in which spin is ontological and $S_x=+1\wedge S_y=-1$ makes perfect sense. Nevertheless, this theory makes the same measurable predictions as standard QM. Even though you can have $S_x=+1\wedge S_y=-1$ at the level of spin hidden variables, when you measure the spin you can never measure both $S_x=+1$ and $S_y=-1$.

I am not saying that this non-minimal version of BM is how nature really works. Personally, I think it isn't. What I am saying is that there is a logical possibility that nature might work that way. Therefore it is not very wise to restrict logical rules to a form which forbids you to even think about such alternative theories.

 

[vanhees71]

Unless I'm misunderstanding you, you seem to be agreeing with me. Decoherence, or irreversibility is not going to result in a definite outcome.

So if someone says that a measurement results in either the state |U\rangle, with such-and-such probability, or the state |D\rangle, with such and such a probability, then does that imply that something nonunitary is involved?

Well, the definite outcome is the entanglement between position and spin-z component, i.e., if you find a particle at position U/D you'll have spin up/down. Then you can block one partial beam, and you have prepared particles in a definite spin-z state. The probabilities tell you the intensity of the partial beams when you filter them out (relative to the intensity of the original beam).That's all QT tells you.

 

[stevendaryl]

Well, the definite outcome is the entanglement between position and spin-z component, i.e., if you find a particle at position U/D you'll have spin up/down. Then you can block one partial beam, and you have prepared particles in a definite spin-z state. The probabilities tell you the intensity of the partial beams when you filter them out (relative to the intensity of the original beam).That's all QT tells you.

But in EPR, Alice and Bob both measure the x-component of spin of their respective spin-1/2 particles. They always get opposite results. That is not a matter of having one result blocked.