What does the probabilistic interpretation of QM claim?

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The probabilistic interpretation of quantum mechanics (QM) asserts that the probability of observing a specific eigenvalue from a self-adjoint operator in a state psi is given by psi^* P_k psi, where P_k is the projector onto the k-th eigenspace. This interpretation does not specify which operators are observable, as that is determined by theoretical and experimental advancements. Wigner's theorem indicates that only quantities commuting with all additive conserved quantities can be precisely measured, which excludes the position operator. While many discussions emphasize the wave-mechanics interpretation of |psi(x)|^2 as a probability density, practical measurements often focus on momentum rather than position, especially in scattering experiments. Ultimately, the conversation highlights the complexities and philosophical implications surrounding the interpretation of measurements in quantum mechanics.
  • #91
strangerep said:
It's not all-or-nothing.
Maths develops/evolves partly to meet new challenges.



Perhaps, but they should probably be taken up in the philosophy forum,
since this seems to be gradually drifting away from the original intent of
this thread.

This is all pure philosophy anyway unless you are going to tell me interpretations now aren't? But yes I was not expecting a discussion on them anyway. They just highlight that mathematically we have no idea if maths even represents anything, just that it appears to inductively reproduce results. The actual maths is pretty much a philosophical representation of something we can't measure, on which we base a philosophical interpretation.
 
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  • #92
A. Neumaier said:
In my lecture http://arnold-neumaier.at/ms/optslides.pdf , I call this revision the thermal interpretation of quantum mechanics. It does not require the slightest alteration of quantum mechanics or quantum field theory. I only changed the currently accepted weird way of talking about quantum system (a long tradition introduced by many years of brainwashing) into one which matches common sense much better. So it is not a change in the foundations but only a change in the interpretation - one that is more consistent with the mathematics

A discussion forum for discussing the thermal interpretation has been approved:
https://www.physicsforums.com/showthread.php?t=490492
Please post your comments there.
 
  • #93
Calrid said:
Bit of a tangent but I read an article about them having closed all the loop holes in Bell's recently.

Calrid said:
There are only one or two left now that haven't been filled in by experiment and I suspect they will become ever more absurd as they are closed, or more bizarrely correct even! :biggrin:

Ah? Not all have been closed, clearly, since you're saying there are a few left lingering.
 

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