Entanglement Geometry: Extra-Dimensional Spacetime or Wave Nature?

[Rosen]

Has anyone considered whether particle entanglement might involve an extra-dimensional substructure of spacetime which negates the need for superluminal communication between entangled particles? If so, what characteristics would such a geometry need to instantly connect particles? Or is it more likely that the wave nature of entangled particles keeps them in contact with each other?

 

[K^2]

Bell's inequalities exclude any hidden parameters. That includes any additional spaces or degrees of freedom.

At any rate, entanglement is well enough understood. There is no super-luminal communication going on and causality is strictly preserved.

 

[atyy]

See K^2's post above for sober and correct answers: there is no superluminal signalling in quantum mechanics that conveys classical information, and Bell's inequalities show that hidden variables must be nonlocal if quantum mechanics is correct. These are some pointers to more recent and speculative current work.

Speculative work published in EPL
http://iopscience.iop.org/0295-5075/78/3/30005/fulltext/
http://arxiv.org/abs/quant-ph/0701002
http://arxiv.org/abs/quant-ph/0701106

Speculative, not peer-reviewed work
http://arxiv.org/abs/1306.0533
John Preskill blogged about it: http://quantumfrontiers.com/2013/06/07/entanglement-wormholes/

More generally, it is possible to associate geometries with some forms of entanglement, but for reasons other than what you asked about. A key idea behind these is the gauge/gravity duality which is a conjecture, for which lots of evidence has been accumulated.
http://arxiv.org/abs/hep-th/0603001
http://arxiv.org/abs/0905.1317
http://arxiv.org/abs/1106.1082

 

[Jilang]

Bell's inequalities exclude any hidden parameters. That includes any additional spaces or degrees of freedom.

At any rate, entanglement is well enough understood. There is no super-luminal communication going on and causality is strictly preserved.

Bells inequalities are in conflict with quantum theory as a whole and don't even allow for the traditional degrees of freedom. As for entanglement being well understood ... Didn't Feynman say that those that think they understand QM haven't really understood it (or something similar)?

 

[bhobba]

Interestingly it seems some pretty general considerations tell us describing physical systems by generalized probability models leads to basically two choices - bog standard probability theory and QM. The difference is QM allows entanglement and probability theory doesn't:
http://arxiv.org/pdf/0911.0695v1.pdf
http://arxiv.org/pdf/quant-ph/0101012.pdf

It would seem the rock bottom essence of quantum weirdness is entanglement, so if you succeed in having some kind of mechanism like extra dimensions for entanglement you pretty much have explained QM, which would be a rather tall order.

Thanks
Bill

 

[Demystifier]

Bell's inequalities exclude any hidden parameters. That includes any additional spaces or degrees of freedom.

This is the wrongest interpretation of Bell inequalities I ever seen.
For example, that would mean that entanglement of two spin-1/2 protons excludes the possibility that protons contain any additional degrees of freedom. Any yet we know they do - they contain quark degrees of freedom.

 

[Demystifier]

See K^2's post above for sober and correct answers

See my post above.

 

[Jilang]

Has anyone considered whether particle entanglement might involve an extra-dimensional substructure of spacetime which negates the need for superluminal communication between entangled particles? If so, what characteristics would such a geometry need to instantly connect particles? Or is it more likely that the wave nature of entangled particles keeps them in contact with each other?

The answer is yes. You can find several references on line to multiple time dimensions for example. Peer reviewed journals are thin on the ground as it would appear that whilst string theorists are free to add extra dimensions at will the quantum theorists are bound by a strict code of 3 space and 1 time. I have often wondered why this might be and can only arrive at the conclusion that when you already have an infinite number in vector space why would you need any more?

 

[bohm2]

As an aside, there are other ways to model entanglement without requiring wormholes, adding hidden dimensions, etc. For example:

A Classical Framework for Nonlocality and Entanglement
http://arxiv.org/pdf/1210.4406.pdf

"Systemic Nonlocality" from Changing Constraints on Sub-Quantum Kinematics
http://arxiv.org/pdf/1303.2867v1.pdf

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

A blog (I. T. Durham) discussing the topic in this thread with the interesting quote:

So here’s my proposal: can we construct a finite geometry, preferably in (3+1) dimensions, that is also non-local and that, via coarse-graining (or some other method), is locally curved? In other words, this geometry would be, in some limit, equivalent to the geometry of general relativity, but in some other limit, would allow for the non-locality of certain quantum states and, perhaps in the process, make entanglement less mysterious.

Entanglement and non-local, finite geometry
http://quantummoxie.wordpress.com/2012/11/08/entanglement-and-non-local-finite-geometry/

 

[Jilang]

A blog (I. T. Durham) discussing the topic in this thread with the interesting quote:

...preferably in...

I rest my case

 

[Jilang]

As an aside, there are other ways to model entanglement...

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

I like this one. You just need to translate to a random walk in vector space and you have QM!

 

[bohm2]

Another interesting paper on an experiment demonstrating classical entanglement. I'm not sure how accurate the author's conclusions are but interesting, nevertheless:

We know that a field with classically random statistics is a local real field, and we also know that Bell inequalities prevent local physics from containing correlations as strong as what quantum states provide. But the experimental results directly contradict this. The resolution of the apparent contradiction is not complicated but does mandate a shift in the conventional understanding of the role of Bell inequalities, particularly as markers of a classical-quantum border. Bell himself came close to addressing this point. He pointed out that even adding classical indeterminism still wouldn’t be enough for any type of hidden variable system to overcome the restriction imposed by his inequalities. This is correct as far as it goes but fails to engage the point that local fields can be statistically classical and exhibit entanglement at the same time...Thus one sees that Bell violation has less to do with quantum theory than previously thought, but everything to do with entanglement.

Shifting the quantum-classical boundary: theory and experiment for statistically classical optical fields
http://arxiv.org/abs/1506.01305
https://www.osapublishing.org/optica/abstract.cfm?uri=optica-2-7-611
http://www.sciencedaily.com/releases/2015/07/150721162455.htm