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C. Bernard
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Does entanglement means that space-time is not a continuum after all?
Does entanglement means that space-time is not a continuum after all?
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?
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?
Does entanglement means that space-time is not a continuum after all?
Does entanglement means that space-time is not a continuum after all?
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"
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.
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Feynman showed that you can dispense complex numbers to describe quantum phenomena, if you wish
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?
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.
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:
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.'
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 [6], 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.
algebraic, matrix, real pairs.
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I think this is what Bohr had always argued for.
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?
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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