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## Main Question or Discussion Point

Does entanglement means that space-time is not a continuum after all?

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Does entanglement means that space-time is not a continuum after all?

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I'd say that any possible spacetime implication is at best an interpretational issue, bordering on speculation (as far as I know). I have read some papers discussing such things, but I am not sure of the status of these papers - that is, if they are suitable by the PF forum standards/rules. I leave such a discussion to others who hopefully know more about this than me.

Anyway, here is a recent PF thread (in the subforum Beyond The Standard Model) that touches similar issues:

https://www.physicsforums.com/showthread.php?t=707439

(see "Maldacena/Susskind ("ER=EPR") conjecture" in the first post)

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DrChinese

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Entanglement itself tells us little about that.Does entanglement means that space-time is not a continuum after all?

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Indeed, in itself it does not. However, I understand that Entanglement operates outside of time and space paradigms and therefore it may suggest that, so to speak, there is a void in the space-time continuum where it can do its tricks.

A void in space being tantamount to a space in space or a break in time involving stopping time, the whole thing makes no sense to me, can you shed some light?

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DrChinese

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In the quantum world, there is what is often referred to as Quantum Non-locality.

Indeed, in itself it does not. However, I understand that Entanglement operates outside of time and space paradigms and therefore it may suggest that, so to speak, there is a void in the space-time continuum where it can do its tricks.

A void in space being tantamount to a space in space or a break in time involving stopping time, the whole thing makes no sense to me, can you shed some light?

Generally, this same thing can be said to exist in situations in which entanglement does not come into play. A single free electron in open space, for example, can be said to have its wave state occupy all of the Milky Way at once. When localized, that wave state now collapses to nearly a point instantaneously. That is quantum non-locality at work with no entanglement.

Also, it is possible to entangle photons which have never existed at the same time. That is also an example of quantum non-locality, but the emphasis in this case is on the temporal side.

Ultimately, no one actually can demonstrate that the physical space-time metric does or does not come into play to allow the above. At least, not yet. So in the meantime, scientists work on hypotheses as to how the rules might operate. Of course, these ideas must make predictions in close agreement with existing experiments.

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What is the state of the research on explaining the phenomenon?

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DrChinese

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Entanglement outcomes are independent of time ordering, so you would see no difference.

What is the state of the research on explaining the phenomenon?

Currently more research effort is going into experimenting and exploring entanglement along QM theoretical lines. There isn't strictly a need to explain things that are predicted by existing theory. The existing theory is the explanation.

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This leads to questions such as:Does entanglement means that space-time is not a continuum after all?

which is more fundamental or apriori -

The science/dimensions behind entanglement or time-space?

This would be bordering on speculation, however you are right - the entanglement phenomena does open up our minds to possibilities "beyond/outside" (or in addition to) time-space.

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or conected epr pairs on space time continuum, epr pairs conected by einstein rosen bridges.Does entanglement means that space-time is not a continuum after all?

Suskind, Maldacena.

http://arxiv.org/abs/1306.0533

Ramsdonck.

http://arxiv.org/abs/0907.2939

Jensen, Karch.

http://arxiv.org/abs/1307.1132

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and locality re-established.

"Einstein-Podolsky-Rosen pair is a string with a wormhole on its world sheet. We suggest that this constitutes a holographically dual realization of the creation of a Wheeler wormhole."

Sonner.

http://prl.aps.org/abstract/PRL/v111/i21/e211603

http://arxiv.org/abs/1307.6850

http://news.sciencemag.org/physics/2013/12/link-between-wormholes-and-quantum-entanglement

"gives a concrete realization of the idea that wormhole geometry and entanglement can be different manifestations of the same physical reality"

"Einstein-Podolsky-Rosen pair is a string with a wormhole on its world sheet. We suggest that this constitutes a holographically dual realization of the creation of a Wheeler wormhole."

Sonner.

http://prl.aps.org/abstract/PRL/v111/i21/e211603

http://arxiv.org/abs/1307.6850

http://news.sciencemag.org/physics/2013/12/link-between-wormholes-and-quantum-entanglement

"gives a concrete realization of the idea that wormhole geometry and entanglement can be different manifestations of the same physical reality"

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Oooh, I just got goose-bumps! I was wondered why the fuss about holograms but now I can see where it was coming from. Our reality is the hologram of a 4-d space. Is this why we need complex numbers in the wavefunction?http://news.sciencemag.org/physics/2013/12/link-between-wormholes-and-quantum-entanglement

"gives a concrete realization of the idea that wormhole geometry and entanglement can be different manifestations of the same physical reality"

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Feynman showed that you can dispense complex numbers to describe quantum phenomena, if you wish.Is this why we need complex numbers in the wavefunction?

are not strictly required.

complex numbers is just a tool that so far works pretty well, an effective computing device.

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I sort of got the impression that you needed them so the evolution of the wavefunction was unitary with no discontinuous classical jumps. In what way can one dispense with them? Is it to do with the Path Integral formulation of QM?Feynman showed that you can dispense complex numbers to describe quantum phenomena, if you wish.

are not strictly required.

complex numbers is just a tool that so far works pretty well, an effective computing device.

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bhobba

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A reference for that would be most interesting.Feynman showed that you can dispense complex numbers to describe quantum phenomena, if you wish

What he did show 100% for sure is it can be described by particles taking all paths with little twirling arrows in his QED - Strange Theory Of Light And Matter - but it's utterly obvious that's complex numbers in more visual language.

Thanks

Bill

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bhobba

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I am as sure as I am of just about anything you can't do away with complex numbers especially in the path integral formalism (its required for phase cancellation to get rid of all but the paths of stationary action) - but await the detail.I sort of got the impression that you needed them so the evolution of the wavefunction was unitary with no discontinuous classical jumps. In what way can one dispense with them? Is it to do with the Path Integral formulation of QM?

I suspect its likely a misunderstanding of what Feynman says in his QED book.

Thanks

Bill

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bhobba

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Its got nothing to do with it.Does entanglement means that space-time is not a continuum after all?

Entanglement is a phenomena associated with the vector space formalism of QM.

Given two particles, a and b, with states |a> and |b> its combined state is |a>|b> which introduces linear combinations different to each separately eg superpositions of |a1>|b1> and |a2>|b2> where |a1> |a2> are possible states of particle a and similarly for particle b. They have become entangled with each other.

It is thought by some, including me, entanglement is the rock bottom essence of QM:

http://arxiv.org/abs/0911.0695

Thanks

Bill

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What's your opinion about entanglement in classical Brownian motion, an effect of coarse-graining, disappearing for finer resolutions of timescales and an effect of contextuality:It is thought by some, including me, entanglement is the rock bottom essence of QM...

We show that for two classical brownian particles there exists an analog of continuous-variable quantum entanglement: The common probability distribution of the two coordinates and the corresponding coarse-grained velocities cannot be prepared via mixing of any factorized distributions referring to the two particles in separate. This is possible for particles which interacted in the past, but do not interact in the present. Three factors are crucial for the effect: 1) separation of timescales of coordinate and momentum which motivates the definition of coarse-grained velocities; 2)the resulting uncertainty relations between the coordinate of the brownian particle and the change of its coarse-grained velocity; 3) the fact that the coarse-grained velocity, though pertaining to a single brownian particle, is defined on a common context of two particles. The brownian entanglement is a consequence of a coarse-grained description and disappears for a finer resolution of the Brownian motion.

http://arxiv.org/pdf/quant-ph/0412132v1.pdf

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bhobba

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Off the top of my head I would say the key word here is ANALOG. Entanglement is a QM effect pure and simple and is not in principle derivable in a classical system based on classical probabilities.What's your opinion about entanglement in classical Brownian motion, an effect of coarse-graining, disappearing for finer resolutions of timescales and an effect of contextuality

Indeed the link I gave proves its simply not possible. Only two choices are possible if you impose a few reasonableness assumptions - classical probability theory and QM.

That being the case the paper you linked almost certainly contains some kind of error if its proposing a classical Brownian motion. But like proofs of 1=0 where the division by 0 is so cunningly hidden it requires great effort to spot it, even though you know it must be there, I don't relish going through such.

Added Later:

One thing that needs to be emphasized is that interpretations of QM exist based on classical stochastic processes such as primary state diffusion and Nelson stochastic's. The out they have is QM emerges from a realm that is classical and that is only possible because deviations from QM exist eg:

http://arxiv.org/pdf/quant-ph/9508021.pdf

'The theory is falsiﬁable in the laboratory, and critical matter interferometry experiments to distinguish it from ordinary quantum mechanics may be feasible within the next decade.'

Thanks

Bill

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I think that's why Khrennikov and group argue for a "Non-Kolmogorovian Approach to the Context-Dependent Systems Breaking the Classical Probability Law"Off the top of my head I would say the key word here is ANALOG. Entanglement is a QM effect pure and simple and is not in principle derivable in a classical system based on classical probabilities.

I know that Khrennikov sees a lot of similarity between his work and that of Gerhard Grossing et al and Couder group:One thing that needs to be emphasized is that interpretations of QM exist based on classical stochastic processes such as primary state diffusion and Nelson stochastic's. The out they have is QM emerges from a realm that is classical and that is only possible because deviations from QM exist eg:

http://arxiv.org/pdf/quant-ph/9508021.pdf

'The theory is falsiﬁable in the laboratory, and critical matter interferometry experiments to distinguish it from ordinary quantum mechanics may be feasible within the next decade.'

http://arxiv.org/pdf/1303.2867v1.pdf

http://lanl.arxiv.org/pdf/1210.4406.pdf

I'm not sure if there is any close connection with the Percival link you provided above but some in the group have also offered some suggestions for distinguishing it from QM. With respect to Brownian entanglement, one individual did do his thesis on the topic but I'm not allowed to post it. But his major conclusion of the difference was the contextuality issue:

Maybe I'm mistaken but I see similarities between this and the recent criticisms of the PBR theorem by Rob Spekkens, Maximilian Schlosshauer, Arthur Fine, etc., although I don't think they draw exactly the same conclusions:Here is finally the main conceptual difference between quantum mechanical entanglement and its Brownian analog. In quantum mechanics, the above operators ˆx1,2 and ˆp1,2 pertain to their corresponding subsystem,independently of the context of the full system. This means, that all the statistics of, e.g. ˆp1 can be obtained by local measurements on the subensemble S1, whether or not this subensemble forms a part of any larger ensemble.

In contrast, the definition of the average coarse-grained velocities (2.7), (2.8), and osmotic velocity (2.20) involves aglobal (that is, depending on the two subsystems) ensemble. If one wants to determine the average of the coarse-grained velocities via expressions (2.4) and (2.5), one have to measure the coordinates of both particles in order to construct the probability distribution, from which the average can be calculated. This probability distribution will generally not be a simple product of distributions pertaining to the particles separately, because the subsystems of the particles are correlated. As seen in appendix A, the purely local definition of coarse-grained velocities can also be given, but there will not be any entanglement for that case, for the same reason as there is no entanglement in other classical systems (see section 1.4).

This conclusion on the difference in contextuality for quantum mechanical and Brownian entanglement is close to the analogous conclusion of [6], which discusses similarities between quantum entanglement and certain correlations in classical optics.

While entanglement and “quantum nonseparability” indicate that simple rules of composition for “real states” are unlikely, one might have assumed that in the case of modeling a tensor-product state, the compositional aspect of preparation independence, PIc, should be viable. The results presented here challenge this assumption. They caution us against classical, realist intuitions about how “real states” of quantum systems ought to compose, even in the absence of entanglement. It would be interesting to investigate whether such composition rules may fail also in other classes of hidden-variables models.

http://arxiv.org/abs/1306.5805

I think this is what Bohr had always argued for.

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That's pretty cryptic, but I like crosswords! Do you mean tensors rather than vectors? Would the pair be the particle and the measuring particle?algebraic, matrix, real pairs.

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bhobba

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Even if a theorem is proven similar to what Von Neumann had in mind, it wont be the death knell for alternate theories such as Primary State Diffusion etc. While such a result would be very interesting and important, quite likely earning, and worthy of, a Nobel Prize, it only would apply to theories equivalent to QM. It would not apply to theories where QM is a limit of a deeper theory - which is what Einstein believed it was. QM would not be incorrect - just incomplete.I think this is what Bohr had always argued for.

Thanks

Bill

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like nature, cryptic,That's pretty cryptic, but I like crosswords! Do you mean tensors rather than vectors? Would the pair be the particle and the measuring particle?

but more a irascible vice, sloth of my part, my sin.

http://physics.stackexchange.com/questions/32422/qm-without-complex-numbers/83219#83219

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Nice link! The maths is somewhat beyond me, but I enjoyed it very much.I remember the first time I was told exp(i ∏) =-1 when I was 17 years old and nearly falling off my chair!like nature, cryptic,

but more a irascible vice, sloth of my part, my sin.

http://physics.stackexchange.com/questions/32422/qm-without-complex-numbers/83219#83219

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