@Patrice Ayme

*Not so. The claim is that quantum physics is the application of (noncommutative) probability theory¹ to physics. As (Copenhagenist) Ray Streater says, “It took some time before it was understood that quantum theory is a generalisation of probability, rather than a modification of the laws of mechanics.”²
*

Well, this is your opinion and that of Mr. Streater. Actually interpretations of the Copenhagen Interpretation vary considerably. You can consider:

https://en.wikipedia.org/wiki/Copenhagen_interpretation

As engineers are trying to make functional Quantum computers and Quantum simulators, they have to figure out exactly what causes “decoherence” or “wave function collapse”. “Interpreting” Quantum Physics has become an experimental subject.

Quantum Physics has even been interpreted as a change of logic (with no less than Birkhoff and Von Neumann as the original authors):

https://en.wikipedia.org/wiki/Quantum_logic

As you can see therein, the subject is not closed. It involves now supersymmetry, supergeometry and thus non-commutative mathematics.

Waves: first, there is no general definition of “wave”. That’s, precisely the force of the concept (whereas there is a strict definition of eigenstate, that’s a weakness). If a Quantum state has not (yet!) be demonstrated to be caused by waves, that does not mean it’s not. It just mean we don’t know. To be sure why something does not happen, one has to be sure why it does not happen. In this particular case, one would have to know more than what the Copenhagen Interpretation says. “Copenhagist” who claim to know more than Copenhagen, are not really Copenhagists. That’s rather ironical.

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]]>Magnema says

Patrice Ayme: Entanglement gets un-entangled (it’s called decoherence) NON-LOCALLY. Occasionally Free Will will even be involved (say choosing the direction of polarization measurement, or a magnetic field in a Stern-Gerlach device, etc.). Without evoking Free Will, decoherence will involve a large macroscopic object, thus a large space, like a gravitational field, but with a life of its own, so to speak, thus irreversible. As Bohr would say, the Quantum System cannot be isolated when “measured” (or made to decohere).

Non-Locality does not look reversible to me: it involves non topologically trivial “inner” geometry (see below).

Magnema: *“Your assumption that things are not entangled before interaction is simply not necessarily true, generically, unless you specify that the two particles have never, through any chain of effects looking backwards in time, interacted (and even then, it is questionable).”
*

PA: The entanglement is caused by an interaction. In general. Always.

Could the particles have been entangled before, without suspecting it? This is the last loophole in the proof of the Bell Inequality. This is the subject of present research, but many in the know do not doubt what will be found. The question has been asked in the case of Einstein-Podolski-Rosen (type) experiments (“EPR”). These involve making a measurement on an element of a pair of “particles” A and B which are entangled, yet “separated” by what I would call a “CLASSICAL DISTANCE”.

Starting with Alain Aspect (who got the Wolf Prize in Physics for it), it has been shown that spin measurement can be made in flight, where the direction of the polarization is changed haphazardly in flight, and the measurement on A “immediately” changes B (“immediately” meaning out of the light cone of A).

The suggestion has been made that A and B could be actually within the same much larger, much older light cone, and thus causally related in the classical relativistic sense. An esteemed team of American experimenters will thus run a version of the Aspect experiment, where the polarization direction are obtained by signals from quasars so distant from each other that they cannot plausibly be causally related.

It seems extremely unlikely that the experiment will reveal that, after all all correlations observed and predicted (by the Quantum axiomatics) were the fruit on long set hidden causality.

As far as I know, (Quantum) entanglement arises only from interaction. Thus picking two particles haphazardly, they should NOT have, generically, a common entanglement (albeit we don’t know what they are entangled with, some could end entangled with each other).

Because of its non-local character, Quantum entanglement is impossible to reverse. Why? It has a non-trivial geometry and topology. It’s not the (simple) one of relativistic spacetime, it is the geometry of what happened before: not the sum of all histories, just the (geometrical and topological) nature of a particular history. Once again, not the geometry of spacetime, but a subset with a non trivial topology of the geometry of much higher dimensional manifold in which spacetime is embedded (see Nash embedding theorem).

Now for waves. I remember Dirac, initially an engineer, saying he was looking for the simplest relativistic wave (simpler that a solution of the Klein-Gordon equation, a second order PDE). it struck him that that the simplest wave had to be a first order PDE (waves on a string like sines answer to second order PDEs; other waves, such as the KdV solitons, answer to nonlinear SE PDEs: waves don’t have to be just trigonometric functions!).

Angular momentum in its simplest form arises from spinor geometry, not linear algebra (it was discovered by Elie Cartan before World War One, in a purely geometrical setting). It’s a square root of the Riemannian metric.

http://mathoverflow.net/questions/66681/classical-geometric-interpretation-of-spinors

Dirac rediscovered it by postulating the simplest relativistic wave, a solution to the simplest, thus first order, Partial Differential Equation giving what can be called a wave. It’s equivalent to taking the square root of the relativistic WAVE operator (the usual Laplacian).

https://en.wikipedia.org/wiki/Dirac_equation

However, Michael Atiyah said:

“No one fully understands spinors. Their algebra is formally understood but their general significance is mysterious. In some sense they describe the “square root” of geometry and, just as understanding the square root of −1 took centuries, the same might be true of spinors.”

May I suggest the same is true of the geometry of entanglement?… With the caveat that it is irreversible?

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]]>January 18, 2016 at 10:57 am

@Patrice Ayme

“What is Quantum Physics about? Some, mostly the “Copenhagen Interpretation” followers, claim Quantum Physics is a subset of functional analysis”

Not so. The claim is that quantum physics is the application of (noncommutative) probability theory¹ to physics. As (Copenhagenist) Ray Streater says, “It took some time before it was understood that quantum theory is a generalisation of probability, rather than a modification of the laws of mechanics.”²

1) Does physics need probability theory? Yes.³

2) Does it have noncommuting observables? Yes.³

3) P̶r̶o̶f̶i̶t̶!!! Quantum theory.

“The notion of wave is more general than the notion of eigenstate ”

Depending on context / definition of eigenstate it might be. It certainly isn’t more general than the notion of state and wave function states are not enough for physics (cf. Chris Isham’s Lectures on QT: “there are many examples of quantum-mechanical systems whose states cannot be represented as wave functions”).

“The classical system evolves, from a given order, to one, more disordered. The Quantum system does not evolve through increasing disorder. ”

Neither the quantum entropy ( https://en.wikipedia.org/wiki/Von_Neumann_entropy ) nor its classical counterpart (Gibbs entropy) increase: http://www.ucl.ac.uk/~ucesjph/reality/entropy/text.html

¹ https://terrytao.wordpress.com/2010/02/10/245a-notes-5-free-probability/

² http://arxiv.org/abs/math-ph/0002049

³ http://www.nobelprize.org/nobel_prizes/physics/laureates/1954/born-lecture.html

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