Does entanglement means that space-time is not a continuum after all?
Entanglement means that observations (i.e measurements) of certain properties of pairs of particles are correlated in some way (or anticorrelated); in quantum mechanics, the entangled particles share the same quantum state.
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:
(see "Maldacena/Susskind ("ER=EPR") conjecture" in the first post)
Entanglement itself tells us little about that.
Thank you Dr Chinese,
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?
In the quantum world, there is what is often referred to as Quantum Non-locality.
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.
Non-locality is really fascinating. What would happen if two entangled particules were subjected to Einstein's twin paradox theoretical experiment?
What is the state of the research on explaining the phenomenon?
Entanglement outcomes are independent of time ordering, so you would see no difference.
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.
This leads to questions such as:
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.
or conected epr pairs on space time continuum, epr pairs conected by einstein rosen bridges.
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."
"gives a concrete realization of the idea that wormhole geometry and entanglement can be different manifestations of the same physical reality"
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?
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.
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?
A reference for that would be most interesting.
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.
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 suspect its likely a misunderstanding of what Feynman says in his QED book.
Its got nothing to do with it.
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:
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:
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.
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.
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:
'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.'
algebraic, matrix, real pairs.
I think that's why Khrennikov and group argue for a "Non-Kolmogorovian Approach to the Context-Dependent Systems Breaking the Classical Probability Law"
I know that Khrennikov sees a lot of similarity between his work and that of Gerhard Grossing et al and Couder group:
"Systemic Nonlocality" from Changing Constraints on Sub-Quantum Kinematics
A Classical Framework for Nonlocality and Entanglement
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:
A no-go theorem for the composition of quantum systems
I think this is what Bohr had always argued for.
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