Comments by "Lepi Doptera" (@lepidoptera9337) on "What did Einstein mean by “Spooky Action at a Distance"?" video.
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I have managed to sort it out nicely in my own mind over the years, mostly by trying to explain it to other people over and over, again. The first few hundred times I was talking complete nonsense, of course, just like everybody else. Eventually it clicked and now I have a number of actually workable analogies and examples, but yeah, it took a decade or two to get there.
Feynman really didn't do the the world a service with that statement, if it is by him, that is. Of course he was joking, but most people seem to take it at face value, which is a pity because then it becomes an anti-intellectual statement that defends intellectual laziness.
I learned that quantum mechanics can not be treated with logic when I saw that the operator algebras in quantum mechanics are non-commutative while Boolean logic is a commutative algebra. So that's really a hard mathematical fact. We should be teaching these non-commutative structures much sooner, preferably at the middle school level when we teach children "ordinary" algebra. I think it would make student's minds much more open to "unusual" and "unintuitive" ideas if we would show them examples of "what else is out there" early and often.
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@xiupsilon876 Yes, there has been a lot of theoretical research in that area and even Sabine Hossenfelder has recently published an article about a different type of "hidden variable" approach if I am not mistaken.
There are a couple of problems with a phrase like "quantum mechanics is incomplete". What do we mean by that?
Incomplete because we can not know position and momentum with arbitrary precision at the same time? That's not a quantum mechanical property to begin with. It's a general mathematical property of functions with L2-norm (that's what the mathematicians call "energy"). It's just as valid for water waves as it is for classical electromagnetic waves as it is for quark and gluon quantum fields. Wifi routers have a protocol that uses time-energy uncertainty to shape radio-wave packets in a certain way. Our engineers are using this principle in mechanical, electrical and information systems daily. This can never be "undone" because it runs into a fundamental mathematical property of continuous functions. If Einstein would have wanted that, then he didn't even realize that the classical world had exactly the same limitations as soon as continua were involved.
Incomplete because photons, electrons etc. do not behave like classical particles? Absolutely nothing in the universe behaves like a classical particle. A classical particle in physics was always an abstraction to simplify problems like the Kepler problem to the level where it can be (almost) solved in closed mathematical form. All it ever meant was that we reduce the dynamics of an extended classical body to the dynamics of its center of mass, i.e. we neglect rotations and internal degrees of freedom. As it turns out, there are approx. one dozen single particle Hamiltonians that are integrable (that have general closed form solutions) and some of them (like the three dimensional Kepler problem and the four dimensional harmonic oscillator) are mathematically equivalent. Every other "particle problem" does not have a closed form solution and we can not predict its motion for arbitrary long times. If we connect three or four masses with rigid sticks and ask what the general rotation of these masses are, then it takes about a thousand pages of mathematics and physical discussion to sort out the possible modes of rotation of such systems under symmetry conditions and there is no solution for a completely asymmetric rotator, at all. That system is already completely chaotic.
So what, exactly, are we losing in quantum mechanics compared to classical systems? If anything, the hydrogen atom is a much better behaved system than a general Newtonian rotator ever was.
Finally, quantum mechanics the way Einstein saw it was not a physical theory. It was more like thermodynamics, a framework that connects different types of physical properties with each other but that does not say anything, at all, about a specific physical system. The physical theory that makes solid statements about nature is quantum field theory. It builds on what Einstein knew, but it goes far beyond it. Even Heisenberg mentions in that paper I just read that he does not believe (this is in 1925, I believe) that a quantum mechanical theory of the electromagnetic field is even possible. Feynman and others gave us such a theory in the 1948 to mid 1950's time frame, i.e. we went from knowing nothing about quantum fields to a complete (if unexplored) theory in another 30 years. That theory happens to be the one that has the best numerical match between theoretical prediction and experiment of all of our theories, to date. It's better than Newtonian mechanics/general relativity in the solar system by a factor of 100 or so, if I am not mistaken.
So, then what does it take to make quantum theory complete? A predictive formula of when the next photon will appear in a photon detector? Do we have such a formula for the lottery numbers? The roulette wheels in Las Vegas? When two cars will collide the next time at any given intersection? Whether it will rain at 3:12pm next Thursday? If we do not have those predictors, then why does it bother us so much that they also do not exist for photons? Just my two cents.
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Not a bad article, as far as the mathematical implications of the formalism are concerned, but it still misses the actual physical ontology, which is not surprising. It was written by a capable theoretical physicist. He thinks in terms of formalisms, rather than the physical systems that the formalism stands for. He gets a lot of things right, including the time scale separation in Schroedinger's cat, but that already happened at the level of the nuclear decay that drives the experiment, so he misses that the "cat is alive" criterion is a mere garnish on the actual physics that has already happened long before we ever get to that level. That's the same physics that Schroedinger missed to understand because he was not a nuclear physicist. It is also obvious that he still can't distance himself from the particle picture, which causes most of the confusion among laymen. It is, in some sense, useful among high energy physicists like himself, because detectors are measuring high energy quanta with weak measurements, which leads to particle-like effects, but it is completely wrong in e.g. quantum optics experiments with optical photons, which comprise the large majority of "mystical" experiments.
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