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Is QM non-local?

Posted: Mon Aug 18, 2014 11:08 pm

For anyone still on the fence, this is an interesting video presenting a different take. Interesting discussion about path integrals at the end.

Re: Is QM non-local?

Posted: Mon Aug 18, 2014 11:51 pm

For anyone still on the fence, this is an interesting video presenting a different take. Interesting discussion about path integrals at the end.

Despite what Unruh says (and I am familiar with his argument going back many years), the answer to the question posed by him is: Yes.

There are two incontrovertible arguments for the "Yes" answer, which do not involve the controversial counterfactual considerations that Stapp's argument relies on (and which Unruh is criticising).

The first argument is the EPR argument. They discovered in 1935 that QM is not a locally causal theory. Their argument is logically impeccable (I have reviewed it in Section II of this paper, for example).

The second argument is much more straightforward. It is a clear-cut mathematical fact that an entangled quantum state, such as (for example) the singlet state

$|\Psi\rangle = \frac{1}{\sqrt{2}}\left\{ |{\bf n}, +\rangle_1\otimes|{\bf n}, -\rangle_2 -|{\bf n}, -\rangle_1\otimes|{\bf n}, +\rangle_2\right\},$

cannot be factorized into an un-entangled state made up of a product of the constituent states. Path integral formalism obscures this clear-cut fact.

But the good news is that QM can be completed into a locally causal theory, as explained here: http://libertesphilosophica.info/blog/o ... lations-2/.

Re: Is QM non-local?

Posted: Tue Aug 19, 2014 5:06 am
Joy Christian wrote:The first argument is the EPR argument. They discovered in 1935 that QM is not a locally causal theory.

My recollection is that their argument was something like "either QM is incomplete or if it is complete, it must be nonlocal, but nonlocality is unreasonable, therefore it is incomplete".

The second argument is much more straightforward. It is a clear-cut mathematical fact that an entangled quantum state, such as (for example) the singlet state

$|\Psi\rangle = \frac{1}{\sqrt{2}}\left\{ |{\bf n}, +\rangle_1\otimes|{\bf n}, -\rangle_2 -|{\bf n}, -\rangle_1\otimes|{\bf n}, +\rangle_2\right\},$

cannot be factorized into an un-entangled state made up of a product of the constituent states. Path integral formalism obscures this clear-cut fact.

The second argument does not imply nonlocality either, unless you have assumed nonseparability = nonlocality. Unruh's argument is that the non separability is due to non commutativity and not nonlocality. It is a valid argument which Bell used himself against von Neumann.

Re: Is QM non-local?

Posted: Tue Aug 19, 2014 9:05 am
minkwe wrote:My recollection is that their argument was something like "either QM is incomplete or if it is complete, it must be nonlocal, but nonlocality is unreasonable, therefore it is incomplete".

Your recollection is correct, of course.

However, completeness of QM is implicit in the question "Is QM non-local." The question wouldn't have much significance if we start out with the assumption that QM is an incomplete theory of Nature. Most practicing physicists assume (at least implicitly) that QM is a complete theory of Nature. Given that fact, by a simple trade-off between the premises of completeness and locality, the logic of EPR implies that QM is a non-local theory of Nature (provided we accept the EPR criterion of reality).

minkwe wrote:
The second argument is much more straightforward. It is a clear-cut mathematical fact that an entangled quantum state, such as (for example) the singlet state

$|\Psi\rangle = \frac{1}{\sqrt{2}}\left\{ |{\bf n}, +\rangle_1\otimes|{\bf n}, -\rangle_2 -|{\bf n}, -\rangle_1\otimes|{\bf n}, +\rangle_2\right\},$

cannot be factorized into an un-entangled state made up of a product of the constituent states. Path integral formalism obscures this clear-cut fact.

The second argument does not imply nonlocality either, unless you have assumed nonseparability = nonlocality. Unruh's argument is that the non separability is due to non commutativity and not nonlocality. It is a valid argument which Bell used himself against von Neumann.

There is more to quantum entanglement than just non-separability. There is also a superposition between the two product states. Moreover, there is a projection, or reduction of the state vector in the orthodox quantum mechanics (without which there would be no measurement result to begin with). Thus superposition, plus non-separability, plus the reduction of the state $|\Psi\rangle$ inevitably leads to the non-locality of QM (unless of course we assume that QM is an incomplete theory of Nature).

Re: Is QM non-local?

Posted: Tue Aug 19, 2014 1:22 pm
As Unruh says, "It's the interpretation that stinks".

Re: Is QM non-local?

Posted: Tue Aug 19, 2014 4:43 pm
Joy Christian wrote:However, completeness of QM is implicit in the question "Is QM non-local." The question wouldn't have much significance if we start out with the assumption that QM is an incomplete theory of Nature.

That is true. Though a better answer to the question at least from the EPR perspective could be. "No, it is local and incomplete, rather than complete and non-local". We don't have to accept a priori that it is non-local. In the example of two halves of a dollar bill sent off to two people. We do not suggest that non-locality is at play when one person opens the envelope.

Most practicing physicists assume (at least implicitly) that QM is a complete theory of Nature.

Sure. Most practicing physicists also believe QM is non-local, and many other strange ideas. But they are wrong. QM is both local and incomplete.

There is more to quantum entanglement than just non-separability. There is also a superposition between the two product states. Moreover, there is a projection, or reduction of the state vector in the orthodox quantum mechanics (without which there would be no measurement result to begin with). Thus superposition, plus non-separability, plus the reduction of the state $|\Psi\rangle$ inevitably leads to the non-locality of QM.

Classically, you also have superposition of "possible" states in the dollar bill case prior to opening of the envelopes, an reduction of the state when one person opens the envelope but we do not invoke non-locality in that case. Besides, we nave hon-separability of classical joint probabilities too. P(AB) = P(A)P(B|A) is not separable but does not imply non-locality. So why would we assume that QM is non-local based only on those features which are already present in classical mechanics/probability? Unruh explains that quite well I think.

Re: Is QM non-local?

Posted: Tue Aug 19, 2014 4:48 pm
Joy Christian wrote:(unless of course we assume that QM is an incomplete theory of Nature)

I think it is more than that even. You'd need to add in the assumption that $|\Psi\rangle$ is ontological to arrive at non-locality. Just like in the dollar bill case, you'd have to assume that probabilities are ontological to arrive at non-locality, since before A opens her envelope, the probabilities of head are 0.5, 0.5 on both ends but the instant she opens her envelop and observes head, the probability of head on B's end instantaneously changes to 0. If we assume probabilities are ontological, then we interpret the superposition of 0.5/0.5 on both ends to not simply be superpositions of various possibilities, but actual ontological superposition, and therefore the reduction on opening one envelope must also then be interpreted as an actual ontological non-local effect. Why don't we also believe that classical probability is non-local?

We may even ask the question: Is QM even a theory of Nature? Or let me ask this first. Is classical probability a theory of Nature, or is it a theory for consistently reasoning about nature?

Re: Is QM non-local?

Posted: Tue Aug 19, 2014 5:08 pm
FrediFizzx wrote:As Unruh says, "It's the interpretation that stinks".

The interpretation stinks indeed. In the path-integral case, you can already see it in the statement that "the particle takes all possible paths". Here again ascribing ontological status to alternate possibilities. I think understanding the distinction between "possibilities" and "actualities" is a good antidote for the stench.

Re: Is QM non-local?

Posted: Tue Aug 19, 2014 5:19 pm
minkwe wrote:
Joy Christian wrote:However, completeness of QM is implicit in the question "Is QM non-local." The question wouldn't have much significance if we start out with the assumption that QM is an incomplete theory of Nature.

That is true. Though a better answer to the question at least from the EPR perspective could be. "No, it is local and incomplete, rather than complete and non-local". We don't have to accept a priori that it is non-local. In the example of two halves of a dollar bill sent off to two people. We do not suggest that non-locality is at play when one person opens the envelope.

I think that is exactly right. For those that think QM is a complete theory of Nature, then it is non-local. For those (like us) that think QM is incomplete, then it is a local theory. So I guess Unruh agrees that QM is an incomplete theory of Nature?

Re: Is QM non-local?

Posted: Tue Aug 19, 2014 5:39 pm
FrediFizzx wrote:
minkwe wrote:
Joy Christian wrote:However, completeness of QM is implicit in the question "Is QM non-local." The question wouldn't have much significance if we start out with the assumption that QM is an incomplete theory of Nature.

That is true. Though a better answer to the question at least from the EPR perspective could be. "No, it is local and incomplete, rather than complete and non-local". We don't have to accept a priori that it is non-local. In the example of two halves of a dollar bill sent off to two people. We do not suggest that non-locality is at play when one person opens the envelope.

I think that is exactly right. For those that think QM is a complete theory of Nature, then it is non-local. For those (like us) that think QM is incomplete, then it is a local theory. So I guess Unruh agrees that QM is an incomplete theory of Nature?

I think he primarily argues that the wavefunction is not ontological but encapsulates contextual information, which may mean the same thing as incomplete. Here is the paper on which his talk is based.

http://arxiv.org/abs/quant-ph/9710032v2

Re: Is QM non-local?

Posted: Wed Aug 20, 2014 5:38 am
minkwe wrote:QM is both local and incomplete.

minkwe wrote:You'd need to add in the assumption that $|\Psi\rangle$ is ontological to arrive at non-locality.

FrediFizzx wrote:
minkwe wrote:Though a better answer to the question at least from the EPR perspective could be. "No, it is local and incomplete, rather than complete and non-local". We don't have to accept a priori that it is non-local. In the example of two halves of a dollar bill sent off to two people. We do not suggest that non-locality is at play when one person opens the envelope.

I think that is exactly right. For those that think QM is a complete theory of Nature, then it is non-local. For those (like us) that think QM is incomplete, then it is a local theory.

We are in overall agreement here, but using different emphases to express some of the same things.

The point is that if we assume QM to be a complete theory of Nature (in the EPR sense), or equivalently interpret $|\Psi\rangle$ ontologically, then non-locality of QM cannot be averted.

On the other hand, if we assume QM to be an incomplete theory of Nature, or equivalently interpret $|\Psi\rangle$ epistemically, then the question of non-locality (or any other voodoo) does not even arise.

But here is a conceptual puzzle:

If we do interpret $|\Psi\rangle$ epistemically and view it as merely encapsulating contextual information as Unruh does, then why such a contextual (read "subjective") information $|\Psi\rangle$ is governed by a precise, unique, and non-contextual (read "objective") dynamical equation like the time-dependent Schrodinger equation?

Re: Is QM non-local?

Posted: Wed Aug 20, 2014 1:02 pm
Joy Christian wrote:But here is a conceptual puzzle:

If we do interpret $|\Psi\rangle$ epistemically and view it as merely encapsulating contextual information as Unruh does, then why such a contextual (read "subjective") information $|\Psi\rangle$ is governed by a precise, unique, and non-contextual (read "objective") dynamical equation like the time-dependent Schrodinger equation?

How do your hidden variables "connect" to the Schrodinger equation?

Re: Is QM non-local?

Posted: Wed Aug 20, 2014 1:26 pm
FrediFizzx wrote:How do your hidden variables "connect" to the Schrodinger equation?

As yet they don't, but I have some ideas about a possible connection. It is a profound problem, and I have a profound solution in mind.

Re: Is QM non-local?

Posted: Wed Aug 20, 2014 2:59 pm
Joy Christian wrote:The point is that if we assume QM to be a complete theory of Nature (in the EPR sense), or equivalently interpret $|\Psi\rangle$ ontologically, then non-locality of QM cannot be averted.

On the other hand, if we assume QM to be an incomplete theory of Nature, or equivalently interpret $|\Psi\rangle$ epistemically, then the question of non-locality (or any other voodoo) does not even arise.

But here is a conceptual puzzle:

If we do interpret $|\Psi\rangle$ epistemically and view it as merely encapsulating contextual information as Unruh does, then why such a contextual (read "subjective") information $|\Psi\rangle$ is governed by a precise, unique, and non-contextual (read "objective") dynamical equation like the time-dependent Schrodinger equation?

I don't quite agree that you should make the links contextual -- subjective , non-contextual -- objective. In classical probability, you have a precise and unique set of equations for updating information based on other information. Its all epistemology but not subjective.

Re: Is QM non-local?

Posted: Wed Aug 20, 2014 3:26 pm
minkwe wrote:I don't quite agree that you should make the links contextual -- subjective , non-contextual -- objective. In classical probability, you have a precise and unique set of equations for updating information based on other information. Its all epistemology but not subjective.

Fair enough.

But that still does not address my question. Schrodinger equation (or its relativistic or field-theory generalization) does not depend on the nature of the physical system. The question then is: Why should an epistemically interpreted $|\Psi \rangle$, which is thus a compendium of my knowledge of the physical system, be governed by the time-dependent Schrodinger equation, regardless of the nature of the physical system? Why should my knowledge of the physical system evolve under such a special dynamical equation?

Re: Is QM non-local?

Posted: Wed Aug 20, 2014 4:46 pm
Joy Christian wrote:But that still does not address my question. Schrodinger equation (or its relativistic or field-theory generalization) does not depend on the nature of the physical system. The question then is: Why should an epistemically interpreted $|\Psi \rangle$, which is thus a compendium of my knowledge of the physical system, be governed by the time-dependent Schrodinger equation, regardless of the nature of the physical system? Why should my knowledge of the physical system evolve under such a special dynamical equation?

Unless I misunderstand your question, I thought I did answer it. The Schrodinger equation encapsulates the set of rules by which the information changes over time. The uniqueness of the set of rules does not imply $|\Psi \rangle$ should be interpreted ontologicaly. It simply results from the the necessity for consistency in manipulation of information, and the fact that the equations take into account information that is certain/assumed. That's what I meant when I said you also have a consistent set of rules for manipulating classical probabilities, without any question that the probabilities themselves are epistemology.

"Your knowledge" should evolve under the same rules because you want to be consistent. But of course anyone is free to be inconsistent.

Re: Is QM non-local?

Posted: Thu Aug 21, 2014 5:55 am
minkwe wrote:
Joy Christian wrote:But that still does not address my question. Schrodinger equation (or its relativistic or field-theory generalization) does not depend on the nature of the physical system. The question then is: Why should an epistemically interpreted $|\Psi \rangle$, which is thus a compendium of my knowledge of the physical system, be governed by the time-dependent Schrodinger equation, regardless of the nature of the physical system? Why should my knowledge of the physical system evolve under such a special dynamical equation?

Unless I misunderstand your question, I thought I did answer it. The Schrodinger equation encapsulates the set of rules by which the information changes over time. The uniqueness of the set of rules does not imply $|\Psi \rangle$ should be interpreted ontologicaly. It simply results from the the necessity for consistency in manipulation of information, and the fact that the equations take into account information that is certain/assumed. That's what I meant when I said you also have a consistent set of rules for manipulating classical probabilities, without any question that the probabilities themselves are epistemology.

"Your knowledge" should evolve under the same rules because you want to be consistent. But of course anyone is free to be inconsistent.

OK, so let me spell these things out in more detail so that I can understand what you are saying.

$|\Psi\rangle$ is interpreted epistemically. So it has little or nothing to do with the structure of the world per se. It is only a representation of our incomplete information about the behaviour of the physical systems.

Now this incomplete information happens to be governed by the time-dependent SchrÃ¶dinger equation. You are saying that we can interpret Schrodinger equation as encapsulating a consistent set of rules by which this information changes over time. It results from the necessity for consistency in manipulation of information by us.

So what you seem to be saying is that neither $|\Psi\rangle$ nor the dynamical equation that governs $|\Psi\rangle$ over time has much to do with the structure of the world itself. Both $|\Psi\rangle$ and the dynamical equation that governs $|\Psi\rangle$ are just tools devised by us to manipulate our incomplete information about the physical systems consistently.

This is hard for me to believe. It seems to me that Schrodinger equation is telling us something about the structure of the world itself. It has ontological significance.

Re: Is QM non-local?

Posted: Thu Aug 21, 2014 4:43 pm
Joy Christian wrote:OK, so let me spell these things out in more detail so that I can understand what you are saying.
$|\Psi\rangle$ is interpreted epistemically. So it has little or nothing to do with the structure of the world per se. It is only a representation of our incomplete information about the behaviour of the physical systems.

That's not quite what I'm saying. $|\Psi\rangle$ is information about the world, so in a sense it has something to do with the world. The structure of the information is arbitrary. For example, let us assume a particle exists at a certain position in 3D euclidean space. I can represent the information of the particles position in terms of cartesian coordinates (x,y,z). But that is just information and not ontological because someone else can have a different consistent representation in polar coordinates, and even in each case, you can pick a different reference point and you will have different coordinates. However, the coordinates themselves are not ontological, the particle's position is. In a consistent coordinate system with consistent reference points, the information can be pretty accurate, and it can allow you to make very accurate predictions about the particle. So it can say a lot about the real world without itself being the real world.

Now this incomplete information happens to be governed by the time-dependent SchrÃ¶dinger equation. You are saying that we can interpret Schrodinger equation as encapsulating a consistent set of rules by which this information changes over time. It results from the necessity for consistency in manipulation of information by us.

Yes.

Re: Is QM non-local?

Posted: Thu Aug 21, 2014 4:44 pm
Joy Christian wrote:So what you seem to be saying is that neither $|\Psi\rangle$ nor the dynamical equation that governs $|\Psi\rangle$ over time has much to do with the structure of the world itself. Both $|\Psi\rangle$ and the dynamical equation that governs $|\Psi\rangle$ are just tools devised by us to manipulate our incomplete information about the physical systems consistently.

Not quite the same, it is information about the world afterall. So long as we are manipulating information about the world, then it has to do with the world. But we shouldn't interpret the structure of the information, or the rules we have deviced to manipulate it as ontology. I'll give you another example. Fermat's principle tells us that light takes the path with the shortest time between two points. It is a variational principle which allows us to make very accurate predictions about the world. But it would be wrong to misinterpret it as ontological. Light cannot "decide" which path takes the shortest time prior to taking the path. So fermat's principle can not be a "law of nature". But it encapsulates information about nature, the fact that light is always observed to have taken the path which has the shortest time.

This is hard for me to believe. It seems to me that Schrodinger equation is telling us something about the structure of the world itself. It has ontological significance.

We didn't discover Schrodinger equation in a mine . We devised it, using information about the world so it does encapsulate information about the world and it tells us something about the world but it is a mistake IMHO to think that the form/structure of the equation itself has ontological significance. It is was derived using variational concepts and IMHO all variational theories including path-integral, least-action, Lagrangian & Hamiltonian mechanics, are epistemic.

Re: Is QM non-local?

Posted: Fri Aug 22, 2014 7:54 am
minkwe wrote:We didn't discover Schrodinger equation in a mine . We devised it, using information about the world so it does encapsulate information about the world and it tells us something about the world but it is a mistake IMHO to think that the form/structure of the equation itself has ontological significance. It was derived using variational concepts and IMHO all variational theories including path-integral, least-action, Lagrangian & Hamiltonian mechanics, are epistemic.

The overall picture you are presenting is ontologically quite poor. In fact I wonder what remains in your picture, if anything, as ontologically significant. One well known problem with poor ontology is the question: Why do we see the patterns in the world that we do see in the first place. They become mysterious without adequate commitment to ontology. But I suppose these issues are now sufficiently removed from the original question posed in this thread to be called "off-topic."