For those who like the pilot wave theories: — Agustino
This one touches upon an important issue. When we say there is a unique ket for each physical state, we are saying that the relation between physical states and kets is a 'function', as that word is technically understood in mathematics. That means that any physical state can only have one associated ket. It does not, however mean that two different physical states cannot have the same ket, and that's where your point about complete descriptions comes in. For any two different states to necessarily have different kets would imply that the ket is a complete description of the physical state. The postulates of QM do not claim that the ket is a complete description. Claims of completeness or otherwise of the kets are either interpretations of QM, or part of theories that seek to extend QM. They are not part of core QM. — andrewk
I didn't completely grasp all of your question, but I answered it as best I could. Let me know if I left anything out. — andrewk
Actually, that video was pretty amazing! Maybe there really is something to pilot waves. I didn't know there was a classical system that produced similar results for the double slit experiment. And you can see it happening! Definitely helps visualize de Broglie's interpretation.
I guess the bouncing silicon oil drops creating the standing waves is a classical pilot wave system. — Marchesk
What is Hilbert space, and what makes it any more real than probability waves? And I don't mean what is the math, I mean what does the math represent? — Marchesk
Quite right, they are not the same uncertainty and, as far as I know, Heisenberg had nothing to do with the time-energy relation. The explanation of the relation in Shankar is just a hand wave, not a mathematical derivation. When I looked it up in my hard copy I found some scathing comments I had written about it at the time I read it, which is probably why I dismissed it from my mind and didn't remember it.The other issue I was trying to bring to your attention is the nature of the time-energy uncertainty relation. Some may say that this uncertainty relation is just a form of expression of the Heisenberg uncertainty, but it is impossible that these are the same uncertainty because time and energy are not canonically conjugate variables. — Metaphysician Undercover
According to wikipedia, those are the people that invented that relation, and published it in that paper. One would have to read the paper to find out what assumptions it uses, and I have not read it.So the question is what is the relationship between these two distinct uncertainties, the time-energy uncertainty, and the Heisenberg uncertainty. .......... There's a Soviet paper, by Mandelshtam and Tamm, (Journal of Physics, vol. 9 no. 4, 1945), entitled "The uncertainty relation between energy and time in non relativistic quantum mechanics" which is quite descriptive. — Metaphysician Undercover
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