## Is QM non-local?

This question is a means of preventing automated form submissions by spambots.

BBCode is ON
[img] is ON
[flash] is OFF
[url] is ON
Smilies are OFF
Topic review

### Re: Is QM non-local?

FrediFizzx wrote:
Joy Christian wrote:
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.

It is probably not so clear cut as to how your hidden variables connect to the Shrodinger equation but there may be a more easily seen connection to the Dirac equation via the Pauli matrix algebra. The Dirac equation can actually be written two different ways.

$i\hbar\gamma^{\mu}\partial_{\mu}\psi - mc\psi = 0$

$i\hbar\gamma^{\mu}\partial_{\mu}\psi + mc\psi = 0$

So again, we have the sign ambiguity showing up. Can this be traced back to your hidden variable for the sign ambiguity via the Pauli algebra? I think we would have to actually re-arrange like so,

$mc\psi - i\hbar\gamma^{\mu}\partial_{\mu}\psi = 0$

$mc\psi + i\hbar\gamma^{\mu}\partial_{\mu}\psi = 0$

I am not sure whether this sign ambiguity is the same as the one in the orientation of the 3-sphere I have used in my framework.

In any case, neither Schrodinger equation nor Dirac equation can be connected directly to my local-realistic framework, because both of them describe evolutions of the amplitudes of the probabilities of obtaining measurement results, not the evolutions of the probabilities themselves. Since my framework is about expectation values of obtaining joint measurement results without relying on the amplitudes like $\psi$, the best way to approach the problem is through the Ehrenfest theorem:

$\frac{d\;}{dt}\left\langle{\cal O} \right\rangle=\frac{1}{i\hbar}\left\langle\left[ {\cal O},\,H\right]\right\rangle+\left\langle{\frac{\partial{\cal O}}{\partial t}}\right\rangle,$

where ${\cal O}$ is a time-dependent operator to be "observed", $H$ is the corresponding Hamiltonion, and $\left\langle{\cal O}\right\rangle$ is the expectation value of ${\cal O}.$

http://libertesphilosophica.info/blog/

### Re: Is QM non-local?

Joy Christian wrote:
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.

It is probably not so clear cut as to how your hidden variables connect to the Shrodinger equation but there may be a more easily seen connection to the Dirac equation via the Pauli matrix algebra. The Dirac equation can actually be written two different ways.

$i\hbar\gamma^{\mu}\partial_{\mu}\psi - mc\psi = 0$

$i\hbar\gamma^{\mu}\partial_{\mu}\psi + mc\psi = 0$

So again, we have the sign ambiguity showing up. Can this be traced back to your hidden variable for the sign ambiguity via the Pauli algebra? I think we would have to actually re-arrange like so,

$mc\psi - i\hbar\gamma^{\mu}\partial_{\mu}\psi = 0$

$mc\psi + i\hbar\gamma^{\mu}\partial_{\mu}\psi = 0$

### Re: Is QM non-local?

Joy Christian wrote:The overall picture you are presenting is ontologically quite poor.

That's your opinion, but needless to say I disagree with it.
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.

True, that is a problem for those who deny ontology. But not relevant for what I'm saying. I don't even know what you mean by "ontologically significant". I distinguish "information about nature" from "nature itself". Information about nature is certainly ontologically significant, but it is not ontology by itself. What you describe may apply to those who believe "there is no nature other that information". I'll use the Fermat example again to clarify what I'm saying. There are two possibilities:
a) Fermat's principle is ontological, ie photons in nature actually choose where to go based on now long it will take to get there.
b) Fermat's principle is epistemic, ie we know from observation that the path light takes happens to be the one that takes the shortest time, even though we do not know how nature accomplishes it.

The equations from both cases are identical and will result in the same accurate predictions every time. However, case (a) does not admit any other possible ontology that could account for the observation, it states categorically that there is no other ontology than the one stated -- photons some how query all possible paths, calculate how long it will take and then take the shortest one.
Case (b) on the other hand, simply uses the principle as a way to get the correct answer. In fact, case (b) does not rule out case (a). If nature was in fact doing it as stated in case (a), case (b) would still be a reasonable position to take. But it is not correct to suggest that case (b) is denying ontology or that case (b) is ontologically poor.

But I suppose these issues are now sufficiently removed from the original question posed in this thread to be called "off-topic."

On the contrary, it is very relevant. It is at the core of the Non-locality discussion. We've seen how such things can result in non-locality even in a classical principle like Fermat's. The interpretation of the Shrodinger's equation or the wavefunction is not any different and similar problems arise in the interpretation of the path-integral or pilot waves in the Bohmian interpretation, or even Huygens principle (from which Shrodinger drew inspiration). Of couse anyone is free to interpret them ontologically but paradoxes are bound to result. This is what Ed Jaynes termed the Mind Projection Fallacy.

### Re: Is QM non-local?

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."

### Re: Is QM non-local?

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?

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 Schrödinger 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?

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 Schrödinger 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?

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?

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?

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?

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?

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?

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?

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?

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?

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?

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?

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?

As Unruh says, "It's the interpretation that stinks".

### Re: Is QM non-local?

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).

Top