Where does non-locality originate in dBB theory?

[LukeD]

Where does non-locality come from in dBB?

I've heard that when dealing with multiple particles, dBB is a non-local theory.
The standard knowledge from studying Bell's inequalities is that any hidden-variable theory must be either non-local or non-realist. I'm ok with non-realist theories, but non-local theories weird me out when I'm trying to describe physics that I think should be completely local.

So I'm wondering: What is dBB's description of a situation where non-locality shows up (I've heard that EPR is a good example)? In what sense is dBB "non-local"? Is there any way of interpreting non-locality in dBB as being due to local, but non-realist, effects?
Links to articles would be appreciated in lieu of or in addition to explanations.

--Sorry if this is answered clearly in another thread. I've been searching for the past few hours and haven't found a treatment of this.

 

[unusualname]

dBB type theories are an alternative to "non-realist" explanations. The whole point is that they are non-local by design.

The modern consensus is that some form of non-locality exists in nature at least at Planck-scale geometry, and for macroscopic non-local correlations in EPR etc the Holographic Principle is a possible mechanism.

But I don't think there's an accepted explanation for how the non-locality mechanism works in dBB theories, probably best for now to interpret the pilot wave as a descriptive idea rather than a "physical" non-local field.

 

[LukeD]

Ok, I did some more research.
It seems to me that the non-locality shows up when you try to make a 2nd order differential equation for the trajectories. The 1st order equation, however, seems to be completely local.
So the dynamics of dBB are completely local, but concepts like "force" do not seem to be.

 

[Galap]

Ok, I did some more research.
It seems to me that the non-locality shows up when you try to make a 2nd order differential equation for the trajectories. The 1st order equation, however, seems to be completely local.
So the dynamics of dBB are completely local, but concepts like "force" do not seem to be.

Yes. Exactly.

And as for nonlocality weirding you out, as humbling as it may seem, we must always remember that the way the universe is isn't based on what human beings do or to not find sensible or intuitive. in fact, it CAN'T be sensible or intuitive to us; our brains are extremely tiny compared to the entire system. If part of the universe could emulate perfectly the whole thing, information constraints would be violated and the rest of the universe would be redundant.

 

[Demystifier]

The 1st order equation, however, seems to be completely local.

That is wrong. In the 1st order form, the velocity of one particle depends on the instantaneous positions of all other particles. This is not local. And indeed, it must be nonlocal according to the Bell theorem, because it is a realist theory.

 

[Demystifier]

I'm ok with non-realist theories, but non-local theories weird me out when I'm trying to describe physics that I think should be completely local.

I never understood people who find non-realism less weird than non-locality.

After all, the good old high-school Newtonian gravity is nonlocal. When you learned about this theory the first time, did it really look so weird to you?

See also
http://xxx.lanl.gov/abs/quant-ph/0607057 [Foundations of Physics, Vol. 37 No. 3, 311-340 (March 2007)]

 

[LukeD]

Edit: Actually, I guess to summarize my question: Doesn't the velocity only depend on the local wavefunction? I thought non-localities only showed up when you tried to take the wave away. The wave propagates so you clearly can't take it away without non-locality. Is there another reason for non-locality though?
Below is a method of... i guess bringing the wave back into dBB? I don't know that it's local though.

-----

I never understood people who find non-realism less weird than non-locality.

Well.. standard Quantum Mechanics is already pretty "non-realistic", and it's local. To me adding more non-realistic elements is just like adding an unobservable field or wave to your theory, and these exist all over the place in Physics, so I have no problem with it.
Non-Locality, on the other hand, just doesn't seem useful. You have many more options for calculating a local law than a non-local law (for instance, it is easier to parallelize the calculations)

That is wrong. In the 1st order form, the velocity of one particle depends on the instantaneous positions of all other particles. This is not local. And indeed, it must be nonlocal according to the Bell theorem, because it is a realist theory.

Ok.. but now let's add a non-realistic element ala the Quantum Trajectory Method.
In QTM, we do our calculations with the whole set of Bohmian Trajectories at once. We use |\psi|^2 as a distribution of particle positions (rather than having just 1 point), and we have a velocity field. The velocity field is derived from an action field S that follows the usual differential equation from dBB:
\frac{\partial S(\mathbf{x},t)}{\partial t} = -\left[ V + \frac{1}{2m}(\nabla S(\mathbf{x},t))^2 -\frac{\hbar ^2}{2m} \frac{\nabla ^2R(\mathbf{x},t)}{R(\mathbf{x},t)} \right]
where R is |\psi| (square root of the distribution of positions)

The velocity field is then calculated as \nabla S /m, and the distribution of particle positions updates via the velocity field.
The wave function is then R*e^(iS/hbar)

--

This seems completely local. Am I wrong that QTM is a local, non-realistic formulation of dBB? I know that the velocity in dBB is supposedly non-local in the multi-particle case, but I just don't see where any non-locality would come into these formulas.

 

[LukeD]

Oh, I just remembered:

Newtonian Gravity is local. Poisson's Equation is local and it contains the full dynamics of gravity. The Newtonian field can even be quantized with spin-0 (Schroedinger) particles! I don't think that could be done if its dynamics weren't local (but the particles are massless and travel at infinite speed, so I might be wrong about that)

 

[Demystifier]

Doesn't the velocity only depend on the local wavefunction?

No!
If you know ONLY the wave function and the position of ONE particle, you CANNOT calculate the velocity of that particle. Instead, you must also know the positions of all other particles.

 

[Demystifier]

Newtonian Gravity is local. Poisson's Equation is local and it contains the full dynamics of gravity.

No!
Poisson equation is local, but acceleration of ONE particle CANNOT be calculated by knowing ONLY the solution of the of the Poisson equation and position of that particle. Instead, you must also know the positions of all other particles.

 

[Demystifier]

LukeD, perhaps you are confused by the difference between 1-particle case and many-particle case. The 1-particle Bohmian mechanics is indeed local. However, the many-particle Bohmian mechanics is not local, provided that the wave function is such that there is entanglement between the particles. Similarly, Newtonian gravity is local for the 1-particle case, but not for the many-particle case.

 

[unusualname]

If Newtonian Gravity was local it wouldn't even predict the stability of planetary orbits. Newtonian Gravity is (in)famous for being precisely non-local.

Gravity in General Relativity however is local, and propagates at c, you need quite difficult calculations to explain why this (hardly) effects the planetary orbits.

http://math.ucr.edu/home/baez/physics/Relativity/GR/grav_speed.html

(QFT is local by design, so a graviton inspired field theory of gravity will also be local)

 

[Demystifier]

The simplest answer to the question above is:
From the fact that the many-particle wave function depends on many particle positions at the same time.

This means that QM is, in a certain formal sense, intrinsically nonlocal even without dBB. See also
http://xxx.lanl.gov/abs/quant-ph/0703071
for an elaboration of that view.

 

[Demystifier]

(QFT is local by design, so a graviton inspired field theory of gravity will also be local)

Here you (like many others) are failing to distinguish field operators from quantum states. The field operators are indeed local in QFT, but nonlocality (more precisely, nonlocal correlations) is a property of quantum states. The nonlocality of many-particle states is related to the fact that QFT contains also NONLOCAL OPERATORS, which are certain PRODUCTS of many local field operators.

Or loosely speaking:
(LOCAL X LOCAL) + (LOCAL X LOCAL) = NONLOCAL
That's how nonlocal entanglement emerges from otherwise local quantum theory, such as QFT.

 

[unusualname]

Here you (like many others) are failing to distinguish field operators from quantum states. The field operators are indeed local in QFT, but nonlocality (more precisely, nonlocal correlations) is a property of quantum states. The nonlocality of many-particle states is related to the fact that QFT contains also NONLOCAL OPERATORS, which are certain PRODUCTS of many local field operators.

Or loosely speaking:
(LOCAL X LOCAL) + (LOCAL X LOCAL) = NONLOCAL
That's how nonlocal entanglement emerges from otherwise local quantum theory, such as QFT.

correlation functions in QFT are purely mathematical devices, they don't imply any physical non-locality. In a QFT of gravity, gravity will propagate at speed c.

 

[Demystifier]

correlation functions in QFT are purely mathematical devices, they don't imply any physical non-locality.

They DO imply (or are related to) nonlocal EPR correlations, which, by the way, are MEASURED. If it is not physical for you, then you have a very unusual definition of the word "physical".

But perhaps it should not be surprising that someone who calls himself unusualname uses unusualmeanings of the words. :-)

 

[unusualname]

They DO imply (or are related to) nonlocal EPR correlations, which, by the way, are MEASURED. If it is not physical for you, then you have a very unusual definition of the word "physical".

But perhaps it should not be surprising that someone who calls himself unusualname uses unusualmeanings of the words. :-)

Yes they do imply nonlocal correlations, (by "correlation function" I mean propagator which is a mathematical device to calculate probability amplitudes) but the correlations are purely probabilistic results. I don't think many people believe a physical non-local field mechanism is responsible for the correlations, a la dBB.

But obviously, no one really knows the physical basis behind the correlations, so it is possible that the mathematics are describing a physical non-local effect. (Personally I think it's more likely that the reality we are observing is a reconstruction or projection of the simple smooth mathematical space upon which the field theory is constructed, and the non-locality results from the reconstruction or projection)

 

[Demystifier]

I don't think many people believe a physical non-local field mechanism is responsible for the correlations, a la dBB.

That is true. However, the number of people who believe that reality does not exist before we measure it - is also small. Yet, the Bell theorem shows that at least one of these two weird options (neither of which is believed by many people) should be true. So the fact that not many people believe in any of these two options is merely a consequence of their ignorance. If they were aware of the meaning of the Bell theorem, the number of supporters of both of the two options would be much larger.

 

[inflector]

That is true. However, the number of people who believe that reality does not exist before we measure it - is also small. Yet, the Bell theorem shows that at least one of these two weird options (neither of which is believed by many people) should be true. So the fact that not many people believe in any of these two options is merely a consequence of their ignorance. If they were aware of the meaning of the Bell theorem, the number of supporters of both of the two options would be much larger.

One needs to make a choice in the matter, once one understands the implications of the state of the experiments.

I too, find non-locality to be more to my liking than non-reality. That's why I believe that dBB is the way forward.

 

[zonde]

That is true. However, the number of people who believe that reality does not exist before we measure it - is also small. Yet, the Bell theorem shows that at least one of these two weird options (neither of which is believed by many people) should be true. So the fact that not many people believe in any of these two options is merely a consequence of their ignorance. If they were aware of the meaning of the Bell theorem, the number of supporters of both of the two options would be much larger.

I wanted to ask if you consider this definition as belonging to option "reality does not exist before we measure it"?
If two observables are non-commuting then at least one of them can not be unambiguously defined as property of single particle.

 

[Demystifier]

I wanted to ask if you consider this definition as belonging to option "reality does not exist before we measure it"?
If two observables are non-commuting then at least one of them can not be unambiguously defined as property of single particle.

Yes, I agree with that. This is essentially the content of the Kochen-Specker theorem. That's why Bohmian mechanics has "preferred" observables (particle positions).

 

[PhilDSP]

Non-locality may be intrinsically present even in Maxwell's Equations - especially the original ones written and interpreted by Maxwell himself. Both Fitzpatrick and Heavyside objected to Maxwell's invocation of non-locality and recast the interpretation and usage of the equations to reflect what we see today. They were apparently the original relativists. Heavyside can be quoted as saying "Maxwell was only 50% Maxwellian"

If the Maxwell Equations, in either their original form or the "modern" relativistic form are intrinsically non-local then any quantum theory based on their usage would seem to require non-local observations or measurements also, wouldn't it?

PS. The non-locality occurs in the determination of the Vector Potential.

 

[DevilsAvocado]

After all, the good old high-school Newtonian gravity is nonlocal. When you learned about this theory the first time, did it really look so weird to you?

Newtonian Gravity is local. Poisson's Equation is local and it contains the full dynamics of gravity.

No!
Poisson equation is local, but acceleration of ONE particle CANNOT be calculated by knowing ONLY the solution of the of the Poisson equation and position of that particle. Instead, you must also know the positions of all other particles.

If Newtonian Gravity was local it wouldn't even predict the stability of planetary orbits. Newtonian Gravity is (in)famous for being precisely non-local.

Gravity in General Relativity however is local, and propagates at c, you need quite difficult calculations to explain why this (hardly) effects the planetary orbits.

??

What am I missing...? I always thought that anomalies in the theory of Newtonian gravity were discovered already in 1859?? That the ellipse of Mercury’s orbit was rotating slightly faster than predicted? And this problem was finally solved by General Relativity in 1915? And in 2002 http://en.wikipedia.org/wiki/Sergei_Kopeikin" ?


@Demystifier:

If we "must also know the positions of all other particles", does this include particles outside the http://en.wikipedia.org/wiki/Observable_universe" (47 billion light-years)?

If yes: If the universe is infinite, and the dBB "gravity interaction" is instantaneous without spatial limitations, wouldn’t that mean that every particle in the universe is influenced by infinite gravitation??

How does instantaneous dBB avoid "paradoxes" of http://en.wikipedia.org/wiki/Relativity_of_simultaneity" ?

I never understood people who find non-realism less weird than non-locality.

Agree! I have 'developed' my own "Stay-Sane-Little-Layman" methodology: If one assumes that the world is crazy and non-local, one should also assume that this crazy world does not exist, i.e. non-realism... to avoid all the "fuss", so to speak... also known as the "Don't Worry, Be Happy" method.

(Bell compatible)

 

[PhilDSP]

And in 2002 http://en.wikipedia.org/wiki/Sergei_Kopeikin" ?

While the popularizing sites and magazines certainly make wonderful science fiction reading in that they pander to the sensational and conveniently skip the caveats, they've probably done a great dis-service in radically distorting the issues and certainties involved with new and even very old experimental discoveries and theory.

This sounds like a more reasonable, level-headed assessment of the situation in the experiment:

http://www.aps.org/publications/apsnews/200306/gravity.cfm

 

[Demystifier]

What am I missing...?

You are missing the fact that we are discussing intrinsic properties of one particular THEORY (Newtonian gravity), not the properties of the actual world.

The motivation for discussing such a theory is the analogy with another theory (Bohmian mechanics) which MIGHT have something to do with the actual world.

 

[Demystifier]

If the universe is infinite, and the dBB "gravity interaction" is instantaneous without spatial limitations, wouldn’t that mean that every particle in the universe is influenced by infinite gravitation??

Yes. But due to quantum equilibrium and decoherence, it cannot be observed.

How does instantaneous dBB avoid "paradoxes" of http://en.wikipedia.org/wiki/Relativity_of_simultaneity" ?

See
https://www.physicsforums.com/showpost.php?p=2784237&postcount=131
and the posts preceding it.

 

[DevilsAvocado]

While the popularizing sites and magazines certainly make wonderful science fiction reading in that they pander to the sensational and conveniently skip the caveats, they've probably done a great dis-service in radically distorting the issues and certainties involved with new and even very old experimental discoveries and theory.

This sounds like a more reasonable, level-headed assessment of the situation in the experiment:

http://www.aps.org/publications/apsn...06/gravity.cfm

Hehe, I absolutely agree, we do not want to "conveniently skip the caveats".

http://en.wikipedia.org/wiki/Speed_of_gravity#Possible_experimental_measurements"

In September 2002, Sergei Kopeikin and Edward Fomalont announced that they had made an indirect measurement of the speed of gravity, using their data from VLBI measurement of the retarded position of Jupiter on its orbit during Jupiter's transit across the line-of-sight of the bright radio source quasar QSO J0842+1835. Kopeikin and Fomalont concluded that the speed of gravity is between 0.8 and 1.2 times the speed of light, which would be fully consistent with the theoretical prediction of general relativity that the speed of gravity is exactly the same as the speed of light.

Several physicists, including Clifford M. Will and Steve Carlip, have criticized these claims on the grounds that they have allegedly misinterpreted the results of their measurements. Notably, prior to the actual transit, Hideki Asada in a paper to the Astrophysical Journal Letters theorized that the proposed experiment was essentially a roundabout confirmation of the speed of light instead of the speed of gravity.[16] Further, there has been criticism of the means by which these results were presented, in that they were announced at a meeting of the http://en.wikipedia.org/wiki/American_Astronomical_Society" instead of being submitted for peer review.[17] However, Kopeikin and Fomalont continue to vigorously argue their case and the means of presenting their result at the press-conference of AAS that was offered after the peer review of the results of the Jovian experiment had been done by the experts of the AAS scientific organizing committee. Asada's claim was found theoretically unsound and disproved in later publication by Kopeikin and Fomalont [18], which operates with a bi-metric formalism that splits the space-time null cone in two - one for gravity and another one for light. The two null cones overlap in general relativity, which makes tracking the speed-of-gravity effects difficult and requires a special mathematical technique of gravitational retarded potentials, which was worked out by Kopeikin and co-authors [19][20] but was never properly employed by Asada and/or the other critics.

It is important to understand that none of the participants in this controversy are claiming that general relativity is "wrong". Rather, the debate concerns whether or not Kopeikin and Fomalont have really provided yet another verification of one of its fundamental predictions.

Ooh, I almost forgot, here are the peer reviewed papers on this "wonderful science fiction":

http://arxiv.org/abs/astro-ph/0302294"
E. B. Fomalont, S. M. Kopeikin
(Submitted on 14 Feb 2003 (v1), last revised 11 Jul 2003 (this version, v2))
Journal reference: Astrophys.J. 598 (2003) 704-711

http://arxiv.org/abs/astro-ph/0301145"
Clifford M. Will
(Submitted on 9 Jan 2003 (v1), last revised 6 Mar 2003 (this version, v2))
Journal reference: Astrophys.J. 590 (2003) 683-690

http://arxiv.org/abs/astro-ph/0308343"
Hideki Asada
(Submitted on 20 Aug 2003)

http://arxiv.org/abs/astro-ph/0311063"
Sergei M. Kopeikin (Univ. of Missouri-Columbia, USA), Edward B. Fomalont (NRAO, USA)
(Submitted on 4 Nov 2003 (v1), last revised 27 Mar 2006 (this version, v6))
Journal reference: Found.Phys. 36 (2006) 1244-1285

We describe our explicit Lorentz-invariant solution of the Einstein and null geodesic equations for the deflection experiment of 2002 September 8 when a massive moving body, Jupiter, passed within 3.7' of a line-of-sight to a distant quasar. We develop a general relativistic framework which shows that our measurement of the retarded position of a moving light-ray deflecting body (Jupiter) by making use of the gravitational time delay of quasar's radio wave is equivalent to comparison of the relativistic laws of the Lorentz transformation for gravity and light. Because, according to Einstein, the Lorentz transformation of gravity field variables must depend on a fundamental speed $c$, its measurement through the retarded position of Jupiter in the gravitational time delay allows us to study the causal nature of gravity and to set an upper limit on the speed of propagation of gravity in the near zone of the solar system as contrasted to the speed of the radio waves. We discuss the misconceptions which have inhibited the acceptance of this interpretation of the experiment. We also comment on other interpretations of this experiment by Asada, Will, Samuel, Pascual-Sanchez, and Carlip and show that their `speed of light' interpretations confuse the Lorentz transformation for gravity with that for light, and the fundamental speed of gravity with the physical speed of light from the quasar.​

 

[DevilsAvocado]

You are missing the fact that we are discussing intrinsic properties of one particular THEORY (Newtonian gravity), not the properties of the actual world.

The motivation for discussing such a theory is the analogy with another theory (Bohmian mechanics) which MIGHT have something to do with the actual world.

Okay, I understand. I just thought that stone dead "Newtonian nonlocality" was maybe a little "odd" in justifying "not so weird"...

 

[DevilsAvocado]

Yes. But due to quantum equilibrium and decoherence, it cannot be observed.

Okay, fair enough. But how do you "filter out" gravitation from the http://en.wikipedia.org/wiki/Local_Group" (10 million light-years in diameter), from gravitation from (hypothetical) galaxy group XYZ314, 1000 billion light-years from earth?

See
https://www.physicsforums.com/showpos...&postcount=131
and the posts preceding it.

Well... maybe "foliation-like structures" and "joint parametrization" are 'just' above my head...

But let’s take the classical and very simple example of a speeding train car. A is onboard and B is standing on the platform:

From the frame of reference of A, the light will reach the front and back of the train car at the same time.

From the frame of reference of B, the light will strike the back of the train car before it reaches the front.​

Is there a solution to this in dBB, that can be explained to a layman like me...??

 

[Demystifier]

Is there a solution to this in dBB, that can be explained to a layman like me...??

dBB is not very useful for this case because these are macroscopic objects on which all quantum effects (including nonlocal correlations) are negligible. Classical theory of relativity is sufficient for that purpose, but I have no intention to teach you this subject here.