• MJA
    21
    Man is the measure of a nature that is truly immeasurable. =
  • Marchesk
    617
    For those who like the pilot wave theories:Agustino

    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.
  • Agustino
    3k
    Yes, that guy has a lot of intriguing science oriented information - you should have a look at his channel, it's quite cool. He's one of the few smart people around on youtube in my opinion.
  • Metaphysician Undercover
    973
    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 think I understand what you say here, the ket describes the state of the system in such a way which allows that two distinct states have the very same ket. Therefore the ket cannot be a complete description of the state. To make an example in a very general way, the apple and the orange may both be represented by the same mathematical symbol (1), but this does not mean that these two things are the same, it means that the mathematical way of describing them, as each being one, is an incomplete description.

    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

    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.

    Time cannot be brought into the ket in the same way as the other variables, so it becomes a parameter. I believe that this is because time, t, is not an observable, and any relation between t and an observable is the relation of a function. I understand that Von Neumann wanted to make time an operator, most likely to maintain consistency with relativity. Apparently he tried having a t for each particle of the system, and also tried a designated t particle, to no avail. Consequently, field mathematics was utilized instead, to account for this difficulty with t. But field theory produces what I believe to be absurd conclusions, such as symmetries and anti-matter.

    So the question is what is the relationship between these two distinct uncertainties, the time-energy uncertainty, and the Heisenberg uncertainty. Where exactly do these uncertainties lie, concealed within the mathematics, and what happens when they are brought to bear upon each other? The Heisenberg uncertainty is well documented and I assume the best expression of it is found in the Schrodinger equation. I assume that the time-energy uncertainty must be concealed within field theory. 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. Also, there's a paper I haven't yet read, by D. A. Arbatsky (2006) entitled "The certainty principle". If you have the time, see if you can evaluate the mathematics of this "certainty principle". Intuitively, I feel that there is a mistake in Arbatsky's claim that the Heisenberg uncertainty is more fundamental than the time-energy uncertainty, and this might result in the falsification of Arbatsky's claim that the certainty principle is more fundamental than the uncertainty principle. but this may depend on one's approach (one's prior assumptions).
  • Rich
    82
    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

    I believe that it was Bohm in one of his writings who suggested that there really wasn't a particle in the De Broglie-Bohm Interpretation, but rather what we witnessing is a wave perturbation. This would make the theories realistic properties quite straightforward to understand from a realistic, conceptual point of view. The impulse behind this wave perturbation is something to ponder which is why Bohm suggested that his model leaves open the possibility for creative impulses in his Implicate Order. The video was quite interesting.

    quantum_potential_1.jpg
  • Rich
    82
    Yes, that guy has a lot of intriguing science oriented information - you should have a look at his channel, it's quite cool. He's one of the few smart people around on youtube in my opinion.Agustino

    Really like what he is doing on YouTube.
  • tom
    557
    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

    Would it surprise you to learn that classical mechanics can also be formulated in terms of wavefunctions on Hilbert space?

    No one thinks there are probability waves flying around in classical physics. What exists are rocks, chairs, planets ... and they aren't in Hilbert space either.
  • andrewk
    310
    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
    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.

    I have not studied the time-energy relation and so do not know whether it can be deduced from the bare postulates. My pencilled comments on the text indicate a suspicion that other, non-core, assumptions are being used. But because the Shankar presentation is so lacking in detail, one cannot be sure of that.
    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
    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.

    I suspect the time-energy uncertainty relation is not very important anyway since (1) it only appears in a short appendix to the Shankar chapter on uncertainty relations and (2) while the wiki article on Heisenberg highlights his uncertainty principle (for complementary observables) as the discovery for which he is best known, the energy-time relation is not directly mentioned in the articles on its discoverers, Mandelshtam and Tamm.
  • Metaphysician Undercover
    973
    I wouldn't be so quick to dismiss the importance of the time-energy uncertainty relation. It is not well understood, and perhaps that's why Shankar does a bad job covering it. But it is derived directly from the Fourier transform due to the nature of the frequency - time conjugate variables. It was not discovered or invented by Mandelshtam and Tamm, as it was already understood by people like Heisenberg, Von Neumann, and Pauli. Dirac apparently had produced a formal representation in 1926.

    As I understand it, the time-energy uncertainty is closely related to the local/non-local dichotomy. Von Neumann could not bring time into the QM equations as he desired, as an operator, a conjugate variable of the Hamiltonian operator for energy. Others, like Pauli saw this right away as an impossibility, time is not observable, and they were willing to accept the consequences So time became a parameter, it is therefore outside the system. This leaves an uncertainty relation between the quantum system and its environment which determines time. That allows for relations between the internal and the external of the system which are not constrained by the laws of physics.
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