Main Question or Discussion Point
Does entanglement means that space-time is not a continuum after all?
In the quantum world, there is what is often referred to as Quantum Non-locality.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?
Entanglement outcomes are independent of time ordering, so you would see no difference.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?
This leads to questions such as:Does entanglement means that space-time is not a continuum after all?
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?
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"
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?
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.
A reference for that would be most interesting.Feynman showed that you can dispense complex numbers to describe quantum phenomena, if you wish
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?
Its got nothing to do with it.Does entanglement means that space-time is not a continuum after all?
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...
Brownian Entanglement.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.
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
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:
'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.'
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 a global (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 , which discusses similarities between quantum entanglement and certain correlations in classical optics.
A no-go theorem for the composition of quantum systemsWhile 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.
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.
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?
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.