Parodite wrote:Typhoon wrote: QM is a strictly linear theory with the all important principle of superposition.
I think the video tries to make possible
physical sense of superposition beyond the mathematical formalism. Superposition and collapse of the wave function are mathematical descriptions, what they mean/represent physically is open for debate and a controversy still.
The Trouble with Quantum Mechanics - Steven Weinberg
Lots of very bright people are uncomfortable with QM.
None as yet have come up with a viable testable alternative.
Parodite wrote:I like the Feynman approach to safely remain agnostic about the physical reality of things before a quantum measurement. Is a "wave-particle in a superposition when all possible states (outcomes) exist at the same time?" Makes no linguistic sense.
That is a limit of language, not of nature.
Parodite wrote:Claims about the un-observed are not helpful it seems to me. I prefer terms like "unknown" "undecided" and leave it at that. So a legit phrase would be: the mathematical formalisms and their proven reliability to predict and be applied in technology, suggest that before a quantum measurement (mathematically: the collapse of the wave function), it is as-if a wave-particle exists in a superposition of all possible outcomes "at the same time". With the emphasis on as-if. Same with non-locality claims: as-if a particle can be at two different places at the same time.
I don't worry much about the linguistics, as mathematics is the language of nature.
Parodite wrote:
The experiment is governed by non-linear equations.
You mean the experiment in the video?
Yes.
Parodite wrote:
Not sure this is relevant: harmonic oscillations in classical physics yield linearity.
No. The solution of the
linear Schrodinger equation with a quadratic restoring potential yields a quantized harmonic oscillator.
Parodite wrote:
In the video the wave that goes with the bouncing particle is a standing wave.
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Lovely. Except that no one has come up with a underlying medium, such as water, that would act as a "pilot wave" to "guide" an electron.
Reminds one of the
luminiferous aether hypothesis of the late 19th century that was thought to be necessary for the propagation of light.
Analogies can only take one so far.
There are further issues. QM based on the Schrodinger equation is only an approximation and is incomplete.
One has to reconcile QM with the constraints of special relativity:
The consequences of relativistic QM [RQM], the Dirac equation, are the existence of antimatter and the spin of the electron [and positron].
As far as I'm aware, no one has successfully written down a RQM for the de Broglie-Bohm pilot wave hypothesis.
However, this is not the end of the story, by any means.
For example, RQM comes close to predicting the correct difference between the 2S 1/2 and 2P 1/2 energy levels of the hydrogen atom and the magnetic moment of the electron, but not close enough. RQM it turns out, is only another higher level of approximation.
To achieve agreement between theory and experiment required the development of quantum field theory [QFT for the EM field, quantum electrodynamics - QED, by Schwinger, Tomonaga, Feynman, and Dyson].
[Aside. The history of this heroic intellectual effort is documented here:
https://www.amazon.com/Selected-Papers- ... +schwinger ]
QFT is required to described the fundamental EM and weak and strong nuclear forces in nature.
As far as I'm aware, no one has successfully written down a QFT for the de Broglie-Bohm pilot wave hypothesis.
QFT is the required description of fundamental quantum processes in nature.
If you wish to learn QM, then I can suggest no better source than
QM; Vols 1 and 2
by Cohen-Tannoudji, Diu, and Laloe
https://www.amazon.com/Quantum-Mechanic ... 047116433X
The chapter on the quantization of the harmonic oscillator is classic.
Although the MIT OpenCourse is also certainly worth viewing.
Btw, the quantum harmonic oscillator (QHO) and the ladder operator formalism of Dirac
are fundamental to the development of quantum field theory.
For example, the excitations of the EM field correspond to the energy levels of the QHO.
The ladder operators become the field creation - annihilation operators.