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Many thing in quantum mechanics point to an underlying reality. And I'm not talking about bohmian mechanics and hidden classical variables. I believe that is ob

Many thing in quantum mechanics point to an underlying reality. And I'm not talking about bohmian mechanics and hidden classical variables. I believe that is obviously wrong, since "location" and "momentum" are obviously emergent properties, as you can easily see when you play around with a wave packet and derive the uncertainty relation. There are so many equivalences between quantum theory and probability theory, beyond "QM is an extension of probability to complex numbers" and "square the amplitude to get the probability". For example, look at Feynman's path integral - where you sum up all possible ways to go from A to B, to get the transition amplitude. You can do a wick rotation (t -> it) and get a new expression related to a classical random walk. I hear you can even use a version of it in finance mathematics. Another example is superluminal signaling. It would seem like something superluminal is going on with entanglement. But nature conspires just so that we cannot use it for transmitting information. A beginner would try to explain it classically - imagine you have two boxes, and put a marble in one. Now find the marble in one box, and obviously it will not be in the second. But classical analogies cannot give the same statistics as QM. (Sorry, it's been a while, I have difficulties recalling the argument :-).) Anyway it seems like there must be an underlying reality that is "non-local" (in that it is not concerned with x, p, t, because these are emergent), and of which QM emerges as a statistical limit. There is an interesing idea from Gerard 't Hooft that this is a cellular automaton - the math seems to work out, but personally I feel that it should be a field theory (without any great justification as I'm just an armchair theorist).

continuational 6y ago
> imagine you have two boxes, and put a marble in one. Now find the marble in one box, and obviously it will not be in the second. But classical analogies cannot give the same statistics as QM. (Sorry, it's been a while, I have difficulties recalling the argument :-).) This nicely sums up every explanation on this topic I've ever encountered.
typicalset 6y ago
I'm not sure we have the same understanding of emergence, here (and I'm not going to insist on being precise). I would think being emergent has something to do with a structure being present in a system which is not a fundamental part of the description. Something like thought being emergent from connecting a group of neurons. Calling x, p, t, emergent, when they are co-ordinates in the conventional formulation of QM, is not this. I wouldn't call time emergent in the description of a simple harmonic oscillator, and I wouldn't call frequency emergent either. Could you elaborate on what you meant?
- captainmuon 6y ago
  I mean that the underlying "real" theory would be for example just a manifold that obeys certain equations. There is no mention of particles, space, or time. Then you'd have a procedure to get from this manifold to the observables of this universe. One point in the manifold does not map to one point in physical space. Rather, for example, the state of the manifold at many different points collectively determines a certain physical thing in spacetime. So the fundamental description of the world would be some strange configuration space, which is neither classical nor quantum. And the physical world would sit "on top". If the universe was like this, and you'd try to form a hidden variables QM theory using the wrong, i.e. physical variables x, p, t, you'd automatically get either nonlocality + infinitely many variables, or very convoluted dynamics (like Bohmian mechanics). Which is exactly what you see. Another reason for me to believe that a description below QM and spacetime is possible, is because QM looks like a statistical limit of something. I find it very odd to identify that QM is the extension of probability theory to imaginary numbers, and then not ask: Probability theory of what?

continuational 6y ago

> imagine you have two boxes, and put a marble in one. Now find the marble in one box, and obviously it will not be in the second. But classical analogies cannot give the same statistics as QM. (Sorry, it's been a while, I have difficulties recalling the argument :-).) This nicely sums up every explanation on this topic I've ever encountered.

typicalset 6y ago

I'm not sure we have the same understanding of emergence, here (and I'm not going to insist on being precise). I would think being emergent has something to do with a structure being present in a system which is not a fundamental part of the description. Something like thought being emergent from connecting a group of neurons. Calling x, p, t, emergent, when they are co-ordinates in the conventional formulation of QM, is not this. I wouldn't call time emergent in the description of a simple harmonic oscillator, and I wouldn't call frequency emergent either. Could you elaborate on what you meant?

captainmuon 6y ago
I mean that the underlying "real" theory would be for example just a manifold that obeys certain equations. There is no mention of particles, space, or time. Then you'd have a procedure to get from this manifold to the observables of this universe. One point in the manifold does not map to one point in physical space. Rather, for example, the state of the manifold at many different points collectively determines a certain physical thing in spacetime. So the fundamental description of the world would be some strange configuration space, which is neither classical nor quantum. And the physical world would sit "on top". If the universe was like this, and you'd try to form a hidden variables QM theory using the wrong, i.e. physical variables x, p, t, you'd automatically get either nonlocality + infinitely many variables, or very convoluted dynamics (like Bohmian mechanics). Which is exactly what you see. Another reason for me to believe that a description below QM and spacetime is possible, is because QM looks like a statistical limit of something. I find it very odd to identify that QM is the extension of probability theory to imaginary numbers, and then not ask: Probability theory of what?