Local realism ruled out? (was: Photon entanglement and )

[MaxwellsDemon]

Special Relativity is certainly local, but I would argue that General Relativity is not. In GR, the geometry is a global description, not a local one. Locally the geometry is flat, its only on a large scale that spacetime curvature comes into play. I would think that the principle of general covariance (where all “regular” derivatives in local laws are replaced with covariant derivatives when talking about large scale phenomena) is where this difference is most apparent. The covariant derivative still applies locally, but the extra term added in is dependent on the overall geometry. The curvature is something extra that requires a knowledge of the energy-momentum distribution in a region that goes beyond simply knowing the distribution in the here and now. The fact that we have to change our calculations in GR depending on the global geometric features of a region suggests to me that it is locality that needs to be abandoned. To me, abandoning realism is far more distasteful anyway. I prefer to think that concepts like position and momentum aren’t just ideas I have about nature, or biases from my human way of thinking, but that they have some objective foundation in reality. Even if they don’t exist exactly as I conceive of them, I’d like to think that a concrete objective phenomenon can be related to my ideas in some way. Color and temperature don’t exist as I perceive them, but there are still well defined objective things like wavelengths of light and atomic vibrations that can be related to my sensory experiences.

 

[Demystifier]

and partial differential equations, which are all-pervading in physics, also favor locality.

Schrodinger equation for two particles is a partial differential equation, so it is local but in the (6+1)-dimensional CONFIGURATION space, not in the ordinary (3+1)-dimensional space. This is exactly why QM is nonlocal (or nonseparable to be more precise) in the ordinary space, even though it is described by a partial differential equation. You may say that the world is still local, but then you must also say that the world contains a huge number of dimensions (3 new space dimensions for each particle). Does such a multi-dimensional local world makes you more happy?

 

[Demystifier]

And indeed, it is a loophole for all physical theories, not just quantum mechanics. Relativity, evolution, big bang... all can be equally well explained by superdeterminism. With a mere wave of the hand, at that!

Exactly.

 

[akhmeteli]

Schrodinger equation for two particles is a partial differential equation, so it is local but in the (6+1)-dimensional CONFIGURATION space, not in the ordinary (3+1)-dimensional space. This is exactly why QM is nonlocal (or nonseparable to be more precise) in the ordinary space, even though it is described by a partial differential equation. You may say that the world is still local, but then you must also say that the world contains a huge number of dimensions (3 new space dimensions for each particle). Does such a multi-dimensional local world makes you more happy?

First, I said PDE favor locality, not dictate it.

Second, we don't know what the final theory will look like: according to your papers and our previous discussions, you don't even believe all predictions of quantum theory will be confirmed experimentally.

Third, for pretty much any system A of (nonlinear) PDE in 3+1 dimensions one can construct a system of linear differential equations in the Fock space, which is equivalent to A on the set of solutions of A (see the outline of this result by Kowalski/Steeb in my post https://www.physicsforums.com/showpost.php?p=1825523&postcount=90 - some time ago I read about this result in nightlight's posts). That means that if quantum unitary evolution is successfully described by a linear system of equations in the Fock space (which is broader than any configuration space), you cannot be sure that system cannot be successfully replaced by a system of nonlinear equations in 3+1 dimensions. Therefore, you cannot be sure the system in the Fock space describes nonlocal reality.

And I would very much appreciate your answer to my question: everything els being equal, would you prefer a local theory, or a nonlocal one?

 

[yoda jedi]

Can you be more specific?

have not a unified dynamics for microscopic and macroscopic systems.
its physically incomplete.

 

[RUTA]

Special Relativity is certainly local, but I would argue that General Relativity is not. In GR, the geometry is a global description, not a local one. Locally the geometry is flat, its only on a large scale that spacetime curvature comes into play. I would think that the principle of general covariance (where all “regular” derivatives in local laws are replaced with covariant derivatives when talking about large scale phenomena) is where this difference is most apparent. The covariant derivative still applies locally, but the extra term added in is dependent on the overall geometry. The curvature is something extra that requires a knowledge of the energy-momentum distribution in a region that goes beyond simply knowing the distribution in the here and now. The fact that we have to change our calculations in GR depending on the global geometric features of a region suggests to me that it is locality that needs to be abandoned. To me, abandoning realism is far more distasteful anyway. I prefer to think that concepts like position and momentum aren’t just ideas I have about nature, or biases from my human way of thinking, but that they have some objective foundation in reality. Even if they don’t exist exactly as I conceive of them, I’d like to think that a concrete objective phenomenon can be related to my ideas in some way. Color and temperature don’t exist as I perceive them, but there are still well defined objective things like wavelengths of light and atomic vibrations that can be related to my sensory experiences.

First, it looks like you’ve conflated causal and constitutive locality. Your argument for the “nonlocality” of the covariant derivative is of the constitutive variety. See Howard, D., “Spacetime and Separability: Problems of Identity and Individuation in Fundamental Physics” in Potentiality, Entanglement and Passion-at-a-Distance, edited by R.S. Cohen et al., Kluwer Academic, Great Britain, 1997, pp. 113-141. Then you argue to keep “realism,” but realism in this sense is associated with constitutive locality, i.e., that entanglement violates causal locality and/or realism per EPR --> causal and/or constitutive nonlocality per Healey and Howard, for example. See also Healey, R.: Holism and Nonseparability in Physics: In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy (Spring 2009 Edition), http://plato.stanford.edu/archives/spr2009/entries/physics-holism. For the term “constitutive locality” see Healey, R.: Gauging What’s Real: The Conceptual Foundations of Gauge Theories. Oxford University Press, Oxford (2007).

Essentially, EPR said there are quantum “objects” which possesses definite properties in and of themselves (realism) that are revealed by measurements independent of what’s being done to entangled partners at space-like separated events (causal locality). If you keep the causality requirement, you can explain the entangled outcomes by saying the quantum objects’ properties are not possessed in and of themselves, but they are “co-possessed” by entangled partners. That’s constitutive nonlocality/nonseparability.

Second, I don't agree that your argument establishes the constitutive nonlocality of the covariant derivative. As a differential geometry prof once emphasized, despite being definable via parallel transport, the covariant derivative is a local object independent of the choice of curve along which you parallel transport at a point on the manifold. You do need to input a vector in the tangent space of said point if by "covariant derivative" you mean the exterior derivative so restricted, but it's still local. See Misner, C.W., Thorne, K.S., Wheeler, J.A.: Gravitation. W.H. Freeman, San Francisco (1973).

So, while the measurement devices and outcomes are separated (constitutively local), the properties of the objects being measured are not per constitutive nonlocality. It’s hard to imagine (for most people, anyway) how nonseparability would be modeled, as the rest of your post indicates. If you’d like to see how we model constitutive nonlocality via discrete path integrals over graphs, see arXiv 0908.4348. It’s in the “revise and resubmit” mode at Foundations of Physics, but substantively it’s sound (at least the referees and editors had no complaints about its substance—if you find a mistake, please let us know).

 

[Demystifier]

And I would very much appreciate your answer to my question: everything els being equal, would you prefer a local theory, or a nonlocal one?

I don't understand what do you mean by "everything else".

 

[akhmeteli]

I don't understand what do you mean by "everything else".

That means just that - "everything else" :-), but since you insist:-), let me define it as follows. Let us imagine for a moment that in ten or twenty years from now, as a result of progress both in theory and experiment or just because some god told us the ultimate truth:-), we have a final quantum theory, which is fully self-consistent and perfectly agrees with all experiments. Would you prefer this theory to be local or nonlocal, provided that your own well-being and success of your own research does not depend on whether it is local or nonlocal?

You may wonder why I am persistently asking this question - because I would like to save some time:-) If you answer "yes", it'll be easier for me to answer or for you to understand why some people prefer locality, if you answer "no", maybe you'll be able to explain to me why you personally prefer nonlocality. So I am just trying to understand if your current preference for nonlocality can be explained by your personal preferences or you just believe that the current case for nonlocality is too strong to even think about a possibility of a local theory.

 

[Demystifier]

Akhmeteli, I would prefer nonlocality. The reasons are simple. First, because the Bell theorem strongly suggests (I will not say proves) that the quantum world is nonlocal, while experiments confirm the predictions of quantum mechanics. Second, because the wave function is a single mathematical object describing all particles at once, and nobody knows a reformulation of quantum mechanics in which this fact can be avoided. See also
http://xxx.lanl.gov/abs/quant-ph/0703071

 

[jambaugh]

Akhmeteli, I would prefer nonlocality. The reasons are simple. First, because the Bell theorem strongly suggests (I will not say proves) that the quantum world is nonlocal, while experiments confirm the predictions of quantum mechanics.

(If I may hum yet another chorus of the CI song...)

It is hard to say an RAA argument "suggests" which of the prior assumptions should be considered false. It rather points that the assumptions as a whole are mutually inconsistent. However to my mind we can't have "reality" if we sacrifice local causality if one is to accept special relativity.

SR + violation of local causality implies future actions can affect past states of reality. What then is the meaning of "reality" if it is not objectively defined and immutable once in the past?

I think it no more strange to reject absolute reality in QM than to reject absolute time in SR. It just takes some getting used to. The alternative is not nihilism or illusory mind created phenomena. It is a relative actuality of observed phenomena without the underlying assumption of a clockwork objective mechanism. We don't assume, we don't deny we simply pay attention only to the scientifically meaningful observations and observables without painting our own prejudices about what must lie beneath.

Alternative "interpretations" always remind me of the epicycles invented to hold onto the Platonic perfection of circular motion in spite of the evidence to the contrary in observed planetary behavior. I think the "absolute objective reality" hypothesis is similar to the Platonism of old in this sense.

 

[Demystifier]

SR + violation of local causality implies future actions can affect past states of reality. What then is the meaning of "reality" if it is not objectively defined and immutable once in the past?

There is a way out of this problem. Due to violation of local causality, some properties of the system in the past are determined by some properties of the system in the future. However, it does not mean that the past can be changed. Since there is only one future (the one that will actually happen), there is only one past as well (the one that has actually happened). Once the past is known, the future cannot be changed in a way that would contradict the known past.

See also the attachment in
https://www.physicsforums.com/showpost.php?p=2455753&postcount=109

 

[jambaugh]

There is a way out of this problem. Due to violation of local causality, some properties of the system in the past are determined by some properties of the system in the future. However, it does not mean that the past can be changed. Since there is only one future (the one that will actually happen), there is only one past as well (the one that has actually happened). Once the past is known, the future cannot be changed in a way that would contradict the known past.

See also the attachment in
https://www.physicsforums.com/showpost.php?p=2455753&postcount=109

I understand that. But that just boils it all down to "known" past i.e. observables instead of states. As a philosophical foundation, the "reality" of the "unobserved past" is meaningless in this context so why continue to work with it? The reason for invoking the "reality hypothesis" is no less invalid given this "way out".

If you are going to work with "tentative reality" then call it what it is, classes of possible observations. My point is that one can still reject the absolute reality of what is not observed (past, present, and future) while retaining the desired local causality. The reverse just isn't possible, your comments not withstanding.

Either you have violation of local causality with its implied invalidation of (unobserved) reality or you have local causality with QM+Bell invalidation of unobserved reality.

So reality being lost, we can still retain local causality if it, by itself, is consistent with observation. We know it to be consistent with predicted observations in QM, via the "no Bell telephones" theorem.

 

[Demystifier]

I understand that. But that just boils it all down to "known" past i.e. observables instead of states. As a philosophical foundation, the "reality" of the "unobserved past" is meaningless in this context so why continue to work with it? The reason for invoking the "reality hypothesis" is no less invalid given this "way out".

Well, this way out works even if you replace the word "known" by the word "real". I am not saying here that reality is necessary or needed or desirable (nor I'm saying that it is not), but I AM saying that reality may be compatible with SR and nonlocality. Maybe there is no reality, but SR+nonlocality are not a valid argument against reality.

 

[yoda jedi]

Well, this way out works even if you replace the word "known" by the word "real". I am not saying here that reality is necessary or needed or desirable (nor I'm saying that it is not), but I AM saying that reality may be compatible with SR and nonlocality. Maybe there is no reality, but SR+nonlocality are not a valid argument against reality.

and in any case, the fact, that if there is no CFD, does not mean that there is no reality,
cos we can ask, what do you observe ? (or measure) its something, and then, something its reality.

 

[Peter Morgan]

Well, this way out works even if you replace the word "known" by the word "real". I am not saying here that reality is necessary or needed or desirable (nor I'm saying that it is not), but I AM saying that reality may be compatible with SR and nonlocality. Maybe there is no reality, but SR+nonlocality are not a valid argument against reality.

All through this thread, I find no distinction made between dynamical nonlocality and nonlocality of initial conditions (not that the distinction is much made in the literature). Dynamical locality is essentially preferred by classical physics. Initial conditions of a classical dynamics, however, are essentially always nonlocal, whether the dynamics are Newtonian or Lorentz invariant, because at a given time we have to specify the position and momentum of all particles, everywhere on a space-like hyperplane. Furthermore, classically, if we observe some phenomenon that requires a weird set of initial conditions, then that just means that the initial conditions in the past were also weird. This is all that superdeterminism is --- if what we observe now is weird, the setup must have been weird too. It makes no difference whether we introduce local or nonlocal dynamics. All of which is to say, Demystifier, that I say with you that "reality may be compatible with SR and nonlocality".

The only superdeterminism that is required to model the Bell-EPR situation, however, is superdeterminism of the evolution of probability densities. That is, if the probability density now is weird, then the probability density in the past must also have been weird. Superdeterminism of the state of a classical deterministic dynamics is not necessary. Amongst other consequences, it's therefore not necessary to impinge much on free will, unless, I suppose, one wants to deny that probability can be applied to model people's microbehaviour.

Another distinction not introduced here, in my look through, is contextuality. It's well-established that noncontextuality alone is enough to derive Bell inequalities. The distinction can also be put in terms of whether we regard settings of an instrument as parameters of a model or as observables in the model. Noncontextuality is rather against the spirit of classical particle modeling, and arguably can be thought of as anti-realist relative to particle properties, but it is not against the spirit of classical field models. Indeed, for field systems at thermal equilibrium the global configuration of an experimental apparatus condition the thermal equilibrium state, just as the Copenhagen interpretation insists it should. Think heat equation in contact with various heat reservoirs. I include a sketch of an experiment that gives more detail (which is of course needed) in a recent preprint, http://arxiv.org/abs/1001.4993" (this says nothing against any of the sophisticated interpretations that are out there, each of which gives its own interesting way of thinking about QM, and each of which a person may reasonably find more-or-less in tune with their own intuitive preferences).

Happy hunting!

 

[DrChinese]

All through this thread, I find no distinction made between dynamical nonlocality and nonlocality of initial conditions (not that the distinction is much made in the literature). Dynamical locality is essentially preferred by classical physics. Initial conditions of a classical dynamics, however, are essentially always nonlocal, whether the dynamics are Newtonian or Lorentz invariant, because at a given time we have to specify the position and momentum of all particles, everywhere on a space-like hyperplane. Furthermore, classically, if we observe some phenomenon that requires a weird set of initial conditions, then that just means that the initial conditions in the past were also weird. This is all that superdeterminism is --- if what we observe now is weird, the setup must have been weird too. It makes no difference whether we introduce local or nonlocal dynamics. All of which is to say, Demystifier, that I say with you that "reality may be compatible with SR and nonlocality".

The only superdeterminism that is required to model the Bell-EPR situation, however, is superdeterminism of the evolution of probability densities. That is, if the probability density now is weird, then the probability density in the past must also have been weird. Superdeterminism of the state of a classical deterministic dynamics is not necessary. Amongst other consequences, it's therefore not necessary to impinge much on free will, unless, I suppose, one wants to deny that probability can be applied to model people's microbehaviour.

Another distinction not introduced here, in my look through, is contextuality. It's well-established that noncontextuality alone is enough to derive Bell inequalities. The distinction can also be put in terms of whether we regard settings of an instrument as parameters of a model or as observables in the model. Noncontextuality is rather against the spirit of classical particle modeling, and arguably can be thought of as anti-realist relative to particle properties, but it is not against the spirit of classical field models. Indeed, for field systems at thermal equilibrium the global configuration of an experimental apparatus condition the thermal equilibrium state, just as the Copenhagen interpretation insists it should. Think heat equation in contact with various heat reservoirs. I include a sketch of an experiment that gives more detail (which is of course needed) in a recent preprint, http://arxiv.org/abs/1001.4993" (this says nothing against any of the sophisticated interpretations that are out there, each of which gives its own interesting way of thinking about QM, and each of which a person may reasonably find more-or-less in tune with their own intuitive preferences).

Happy hunting!

I saw that a few days ago on the arxiv and just starting reading it. For those interested, it comments on a paper by Navascues and Wunderlich regarding classic-quantum correspondence. It also has some good references.

 

[nikman]

FWIW in "Quantum nonlocality vs. Einstein locality" Dieter Zeh makes a distinction between "dynamic" and "kinematic" (quote):

Quantum theory is kinematically nonlocal, while the theory of relativity (including relativistic quantum field theory) requires dynamical locality ("Einstein locality"). How can these two elements of the theory (well based on experimental results) be simultaneously meaningful and compatible? How can dynamical locality even be defined in terms of kinematically nonlocal concepts?

http://www.rzuser.uni-heidelberg.de/~as3/nonlocality.html

 

[Peter Morgan]

I saw that a few days ago on the arxiv and just starting reading it. For those interested, it comments on a paper by Navascues and Wunderlich regarding classic-quantum correspondence. It also has some good references.

Thanks, DrC, and I'd be glad of your comments as always, here or by e-mail. There's an after-thought to this Comment, which is that a friend pointed out that the arXiv version of the paper it comments on does not includes the word "field" at all. To appreciate the details of the argument therefore requires the Proc.Roy.Soc.A paper. I'm somewhat curious whether the published version only introduces the classical field concept because a referee introduced the question (which might slightly improve the chances of the Comment being accepted, because the Proc.Roy.Soc.A editorial procedure for Comments includes the original paper's referee if the editors decided to send it to referees).

Fortunately, I believe the published version is freely available at http://rspa.royalsocietypublishing.org/content/466/2115/881" because of the Proc.Roy.Soc.A anniversary celebrations.

The chance of this Comment being accepted by Proc.Roy.Soc.A is small. The editorial board will presumably understand that discontent would be expressed in some quarters if they were to accept it, so I presume they will only accept it if it touches something of their own interests in the question.

 

[yoda jedi]

"A glance beyond the quantum model"

Happy hunting!

http://arxiv.org/PS_cache/arxiv/pdf/0907/0907.0372v1.pdf

...Here we propose a fundamental axiom that we believe any reasonable post-quantum theory should satisfy, namely, that such a theory should recover classical physics in the macroscopic limit...

coincidence (a correlation, or better yet a metaphysical corelation), i am reading:


On the Classical Limit of Quantum Mechanics
http://www.springerlink.com/content/p57117239x631547/fulltext.pdf


...In spite of many results of the standard approach, it is not yet clear how to explain within standard quantum mechanics the classical motion of macroscopic bodies.....


but suffers the same problems that standard quantum theory, is a patchwork proto-theory.

 

[Peter Morgan]

FWIW in "Quantum nonlocality vs. Einstein locality" Dieter Zeh makes a distinction between "dynamic" and "kinematic" (quote):

Quantum theory is kinematically nonlocal, while the theory of relativity (including relativistic quantum field theory) requires dynamical locality ("Einstein locality"). How can these two elements of the theory (well based on experimental results) be simultaneously meaningful and compatible? How can dynamical locality even be defined in terms of kinematically nonlocal concepts?

http://www.rzuser.uni-heidelberg.de/~as3/nonlocality.html

Thanks for this. Definitely worthwhile. I'm not as familiar with Zeh's thinking on environmental decoherence as I should be.

As an aside, I went to Foundations of Physics for Zeh's most recently mentioned paper on his web-site, "Quantum discreteness is an illusion", which is not yet published but is available as an "online first" paper. The quality of the (69!) papers in the "online first" queue (that's probably 6 months ahead) shows signs of 't Hooft's tenure as editor starting to make a very big difference. The list of authors who have decided to publish at FoP is close to stellar.

 

[ThomasT]

Akhmeteli, I would prefer nonlocality. The reasons are simple. First, because the Bell theorem strongly suggests (I will not say proves) that the quantum world is nonlocal ...

Is Bell's theorem about the way the quantum world is, or is it about limitations on the formalization of entangled states?

 

[nikman]

As an aside, I went to Foundations of Physics for Zeh's most recently mentioned paper on his web-site, "Quantum discreteness is an illusion", which is not yet published but is available as an "online first" paper. The quality of the (69!) papers in the "online first" queue (that's probably 6 months ahead) shows signs of 't Hooft's tenure as editor starting to make a very big difference. The list of authors who have decided to publish at FoP is close to stellar.

One was gratified that 't Hooft published Suarez's "Nonlocal 'Realistic' Leggett Models" paper. It's hard to imagine two scientists with more starkly contrasting world-views than that pair.

http://www.springerlink.com/content/v5652005u01628h2/

or, for you members of the vast unfunded public, grab it gratis:

http://www.quantumphil.org/SuarezFOOP201R2.pdf

 

[yoda jedi]

Well, this way out works even if you replace the word "known" by the word "real". I am not saying here that reality is necessary or needed or desirable (nor I'm saying that it is not), but I AM saying that reality may be compatible with SR and nonlocality. Maybe there is no reality, but SR+nonlocality are not a valid argument against reality.

and in any case, the fact, that if there is no CFD, does not mean that there is no reality,
cos we can ask, what do you observe ? (or measure) its something, and then, something its reality.

same thing for suarez:
http://arxiv.org/PS_cache/arxiv/pdf/0705/0705.3974v1.pdf

.....Additionally, Bohm’s objective description can no longer be considered completely “realistic” since in experiments involving entangled polarized photon pairs neither of the two photons carries a definite polarization when it leaves the source....

 

[akhmeteli]

Akhmeteli, I would prefer nonlocality. The reasons are simple. First, because the Bell theorem strongly suggests (I will not say proves) that the quantum world is nonlocal, while experiments confirm the predictions of quantum mechanics. Second, because the wave function is a single mathematical object describing all particles at once, and nobody knows a reformulation of quantum mechanics in which this fact can be avoided. See also
http://xxx.lanl.gov/abs/quant-ph/0703071

Thank you for your answer. So it looks like you prefer nonlocality not because you like it more than locality, but because you think theory and experiment favor it. However, as I argued starting this thread, there are no no-go theorems or no-go experiments ruling out locality, so I don't have your reasons to favor nonlocality, and I regard it as a radical notion, and the burden of proof is very high for such radical ideas. As for the absence of a local reformulation of quantum mechanics, let me give you an example. For a quarter of a century after formulation of modern quantum mechanics, the de Broglie - Bohm interpretation, while existed (in the form offered by de Broglie), was dead, for all intents and purposes. Nevertheless, it was resuscitated by Bohm. And even now, as far as I know, there is no generally recognized relativistic form of this interpretation (actually, you told me that some time ago, and I don't think much has changed since then). But I guess you believe there will be such relativistic form in the future, and even have your own suggestions. So we don't know what can happen in the future. And I mentioned one possibility how a nonlocal theory can be a local theory in disguise.

So it started with your question: what's so special about locality. I gave you my reasons. Again, if there were some iron-clad no-go arguments, I would have to accept nonlocality. So far I see no reasons for that.

 

[Demystifier]

while the theory of relativity (including relativistic quantum field theory) requires dynamical locality ("Einstein locality").

You have a too narrow view of the concept of relativity. If by relativity one means only that the laws of physics do not depend on the choice of spacetime coordinates, then relativity does not require locality.

 

[Demystifier]

theory and experiment favor it. However, as I argued starting this thread, there are no no-go theorems or no-go experiments ruling out locality, so I don't have your reasons to favor nonlocality, and I regard it as a radical notion, and the burden of proof is very high for such radical ideas.

I still don't understand your logic. So I'll start with a question. Do you agree that theory and experiment favor nonlocality? (I'm not asking if they definitely prove it, because they don't. I'm only asking if they favor it.)

And I mentioned one possibility how a nonlocal theory can be a local theory in disguise.

If you mean your idea that a single charged particle guided by the wave function can be viewed as being guided by the electromagnetic potential (which is an interesting idea), then it has nothing to do with locality and nonlocality. To say anything about nonlocality, you must consider a system of at least two entangled particles.

 

[Maaneli]

If you mean your idea that a single charged particle guided by the wave function can be viewed as being guided by the electromagnetic potential (which is an interesting idea), then it has nothing to do with locality and nonlocality. To say anything about nonlocality, you must consider a system of at least two entangled particles.

I think Akhmeteli is referring to this claim in one of his prior posts:

... for pretty much any system A of (nonlinear) PDE in 3+1 dimensions one can construct a system of linear differential equations in the Fock space, which is equivalent to A on the set of solutions of A (see the outline of this result by Kowalski/Steeb in my post https://www.physicsforums.com/showpos...3&postcount=90 - some time ago I read about this result in nightlight's posts). That means that if quantum unitary evolution is successfully described by a linear system of equations in the Fock space (which is broader than any configuration space), you cannot be sure that system cannot be successfully replaced by a system of nonlinear equations in 3+1 dimensions. Therefore, you cannot be sure the system in the Fock space describes nonlocal reality.

 

[jambaugh]

You have a too narrow view of the concept of relativity. If by relativity one means only that the laws of physics do not depend on the choice of spacetime coordinates, then relativity does not require locality.

Not as such, of course. (Special) Relativity however sets the stage for the argument of local causality. If SR is valid and the light-cone is not a causal horizon then we have the potential of (not certainty of) constructing causal paradoxes. So absent local causality how are such paradoxes prohibited? If we actually (in our conceptual model of how nature works) allow causal feedback, future to past, it seems to me then we must invoke a "meta-time" over which such phenomena would decay out or reinforce to a caustic threshold or stable oscillation, (the local "reality" oscillating w.r.t. this meta-time). This was an attractive idea to me once, as e.g. a model for superposition and interference phenomena. But eventually I rejected it as fanciful and meaningless.

The problem as I see it is this sort of speculation is not operationally meaningful. It's no different than supposing an invisible aether, or Everette many worlds. Sure you can speculate but you can't test within the bounds of science. Such phenomena are by their nature beyond observation. Again I see the "reality" of it as meaningless within the context of science. That isn't an argument, just the results of my many internal arguments over past years.

What in the end do we mean by "reality"? Generally it is the reality of a universe of objects with always defined (though not always observed) objective properties or states of being.
Classically that is either the particles or the field quantities at each point of space.

Quantum mechanically we work in a language of phenomena, observables and observations and interactions between systems. I think it incorrect to objectify the mathematical constructs (esp. wave function=hilbert space vector). For that matter I think we should abandon the use of the Hilbert spaces all together except in the mathematics of constructing the Lie algebras and groups where the observables and dynamics are represented.

As to causal locality, that is easily enough described within QM and QFT via the structure of the dynamics. And it is easily enough tested both conceptually via though experiments, and in the lab. The only evidence I can conceive of, for true non-local causation is a classical FTL signal, e.g. a "Bell telephone". If you can't send a classical signal then you aren't talking about observable non-locality and thus speculating beyond the scope of science.

Now having said all that, I do think that if we're ever going to succeed at merging GR and QM we'll need to start with a "pre-local" theory. That is to say a theory of interacting quantum systems out of which condenses the macroscopic classical world. In which case I envision the local causality definition to be rather reversed. Nearness is ultimately defined by causal interactions and the causal structure of interacting systems ultimately defines the light-cones, and space-time metric structure. Objects are spatially close because they look close. This means they strongly interact with our eyes and our flashlights, or our radar antennas, or our fingers or sticks in our hands.

So ultimately I think causality will by definition be local because locality is ultimately based on causal interactions. At the microscopic quantum level this may break down, but not in the causal aspect, but rather the loss of meaning to geometry (and possibly even topology) at the small scale.

 

[nikman]

You have a too narrow view of the concept of relativity. If by relativity one means only that the laws of physics do not depend on the choice of spacetime coordinates, then relativity does not require locality.

You should really take that up with Herr Professor-Doktor Heinz-Dieter Zeh. I suspect he's making a deeper distinction relating to fundamental correlation and causality. Kinematics does of course rear its head in Relativity with the Lorentz contraction.

 

[RUTA]

Objects are spatially close because they look close. This means they strongly interact with our eyes and our flashlights, or our radar antennas, or our fingers or sticks in our hands.

It's possible to have a distant object be brighter than a closer object, e.g., the Sun is much brighter than this computer screen. Likewise the angle subtended by an object doesn't discriminate relative spatial distance. How do you envision relating distance and interaction? And, how do you see your approach giving a Lorentz invariant result, since it can't give a definite spatial separation and be Lorentz invariant?

 

[akhmeteli]

I still don't understand your logic. So I'll start with a question. Do you agree that theory and experiment favor nonlocality? (I'm not asking if they definitely prove it, because they don't. I'm only asking if they favor it.)

I will try to answer your question in the evening (Central time zone:-) )

If you mean your idea that a single charged particle guided by the wave function can be viewed as being guided by the electromagnetic potential (which is an interesting idea)

Thank you very much, I highly value your opinion.

, then it has nothing to do with locality and nonlocality. To say anything about nonlocality, you must consider a system of at least two entangled particles.

I agree, but Maaneli was right - I was not discussing my research, and I did have in mind my post #74 in this thread and the reference there.

 

[jambaugh]

It's possible to have a distant object be brighter than a closer object, e.g., the Sun is much brighter than this computer screen. Likewise the angle subtended by an object doesn't discriminate relative spatial distance. How do you envision relating distance and interaction? And, how do you see your approach giving a Lorentz invariant result, since it can't give a definite spatial separation and be Lorentz invariant?

It is the light which we feel and the light which is then by definition "close". Chains of propagating effect are the meter sticks (and the clocks) of our universe.

Then again the sun IS close in the frame near that of the propagating light, that is to say the events of emission and absorption are distance near zero given the single photon carrier of the propagating effect.

The sun is also intimately close on the scale of the other stars in the universe. But we can also see that on our scale it is big by how it effects so many other systems near us, the light reflecting off the moon, and the planets, their very orbits, tell us that the sun is both big and (relatively) near. Then the (also relative) distance of the sun is to an extent the ratio of its affect on us and the scale of its effect on things near and far to us. This I think is quantifiable at least to the point of ordering which gives us topological structure.

What after all is a measuring rod but a rigid solid, e.g. a condensate of strongly coupled component atoms. The lengths are essentially measured by counting blocks of those atoms and thus the number of interactional links between the ends of the rods.

As we refine our description of interacting phenomena we however (lately) replace the rigid measuring rod with light signals and clocks.

What then is a clock but a series of "tick" events each causing the next and being caused by the previous.

The nullness of space-time distance between emission-absorption events points to that as the elementary unit of measurement, the --by definition-- invariant phenomenon by which all others are given relative scale.

In formulating any operationally meaningful definitions in the context of science we start with the primaries of observations vis a vis causally interacting with one's environment. It is sensible then that all other concepts, including metric distance and time are derivative of causal connection. The mystery to be solved is rather the extent to which mutually interacting systems either accidentally or necessarily resolve themselves into the space-time-field structure we are able to perceive and map with our theories. In doing that I think causality is necessarily local in that localization is necessarily defined causally.

I cannot help but think rejecting local causality in order to preserve a notion of objective reality is backwards.

[EDIT: Ruta, I'm not sure I fully addressed your question. I haven't tried to make the idea formal and quantifiable. More heuristic as I've expressed above. Let me consider it for a bit and see if it can be given a more formal, rigorous encoding... possibly the attempt will show the idea invalid. It should be a useful exercise.]

 

[RUTA]

In formulating any operationally meaningful definitions in the context of science we start with the primaries of observations vis a vis causally interacting with one's environment. It is sensible then that all other concepts, including metric distance and time are derivative of causal connection. The mystery to be solved is rather the extent to which mutually interacting systems either accidentally or necessarily resolve themselves into the space-time-field structure we are able to perceive and map with our theories. In doing that I think causality is necessarily local in that localization is necessarily defined causally.

It seems difficult to define space and time using interacting systems because you need the concepts of space and time to make sense of what you mean by "systems" to begin the process. That is, what you mean by "a system" seems to require trans-temporal identification and to have "two systems" requires spatial separation -- what else would you use to discriminate between otherwise identical systems? That's why we chose a co-definition of space, time and sources (as understood in discrete QFT) as our fundamental operating principle. I look forward to your solution.

 

[akhmeteli]

I still don't understand your logic. So I'll start with a question. Do you agree that theory and experiment favor nonlocality? (I'm not asking if they definitely prove it, because they don't. I'm only asking if they favor it.)

I know that it is generally recognized that "theory and experiment favor nonlocality". But no, I am afraid I don't agree with that for reasons outlined in my post #1 in this thread.

 

[Demystifier]

I know that it is generally recognized that "theory and experiment favor nonlocality". But no, I am afraid I don't agree with that for reasons outlined in my post #1 in this thread.

Then my next question is: What WOULD you accept as a good argument for nonlocality? For example, if someone would make better detectors with higher efficiency such that the fair sampling loophole is avoided, and if the experiments would still violate Bell inequalities, would you accept THAT as a good evidence for nonlocality?