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1:37 AM

Q: interpretation of the wavefunction in terms of classical harmonic oscillators

the following paragraph from the book The Meaning of Quantum Theory, Jim Baggott, Oxford University Press, 1992 p26 leads me to this question. consider N ("independently interacting") particles with 3N coordinates x,y,z in space. the quantum wavefunction is expressed in terms of (a superposition ...

11 hours later…

Jarek Duda

12:43 PM

Q: Quantum measurenment for incomplete basis?

Standard view of quantum measurement requires a complete basis of possibilities, however some of them might make no sense - can we just normalize probability without these possibilities? To better express this question, let me describe the situation where I got it. In page 9 of this Preskill lec...

quantum-mechanics measurement-problem bells-inequality

@vzn, regarding your last question, MERW ( en.wikipedia.org/wiki/Maximal_Entropy_Random_Walk ) brings natural interpretation for the absolute value of amplitude, including multiple particle situations.

However, it doesn't have the phase - my intuition is that quantum phase describes averaged phase difference of internal clock of particle (de Broglie's/ziterbewegung) between different points in space.

vzn

1:20 PM

Zitterbewegung

Zitterbewegung ("trembling motion" in German) is a hypothetical rapid motion of elementary particles, in particular electrons, that obey the Dirac equation. The existence of such motion was first proposed by Erwin Schrödinger in 1930 as a result of his analysis of the wave packet solutions of the Dirac equation for relativistic electrons in free space, in which an interference between positive and negative energy states produces what appears to be a fluctuation (at the speed of light) of the position of an electron around the median, with an angular frequency of 2mc2/h, or approximately 1.6×1021...

yes have been contemplating QM "phase freedom" and think its a big part of the puzzle. believe ψ is the (unrecognized) "hidden variable" staring us right in the face...

vzn

1:46 PM

That paragraph means that to describe $N$ particles you need wavefunction $\psi(x_1,y_1,z_1,x_2,y_2,z_2,x_3,y_3,z_3,... x_N,y_N,z_N)$. There's no superposition in any standard sense and no offense, but your question sounds like a gibberish to me. — OON 12 hours ago

vzn

1:56 PM

:( maybe the copenhagen interpretation rejects mere asking the question. roughly, alternative statement, am maybe asking about occurrences in classical mechanics of a wavefn as product of wavefns (in the Hamiltonian) similarly to noninteracting distinguishable particles case in QM en.wikipedia.org/wiki/…. also just noticed the Baggott quote is quite similar to Ballentine quoted on wikipedia en.wikipedia.org/wiki/… — vzn 4 mins ago

Jarek Duda

@vzn, here is a paper with experimental confirmation of such de Broglie's clock for electron: link.springer.com/article/10.1007/s10701-008-9225-1

"A Search for the de Broglie Particle Internal Clock by Means of Electron Channeling" - they shoot electrons into silicon lattice, and got increased absorption when synchronizing electron's clock with constant of the lattice

vzn

!!! wow yeah fascinating, think that "recent" experimental finesse incl weak measurements is finally starting to push the bounds/ boundaries of the theory. is the idea that "electron clock" is related to ψ?

Jarek Duda

MERW (just Boltzmann distribution among paths) brings very natural intuition about absolute value of amplitude: as probability at the end of past or future half-paths from this moment

To randomly get some value, we need to multiply probabilities from both directions (amplitudes), getting the Born rule

vzn

have studied random walks some, MERW looks intriguing but it seems like its connected to emergent behavior of multiparticle systems eg as in superconductors

yes have been looking into Born-rule like phenomena in classical physics, have seen it in systems that relate to wave density... scattered refs over yrs need to try to collect them...

Jarek Duda

in interference, e.g. Mach-Zehnder, phase of amplitude literally describes relative phase of internal clock

However, the interpretation becomes more difficult for general systems like atomic orbital

But the general intuition is that phase of amplitude describes phase different of the internal clock of particle - probably after some averaging

vzn

2:06 PM

maybe am trying to figure out some "different" superposition where product of waves is "like" a superposition eg e^x * e^y = e^(x + y)...

Jarek Duda

MERW is just properly made diffusion - accordingly to the maximum entropy principle, which is required by statistical physics models, and is only approximated in standard (GRW-based) diffusion

MERW doesn't have interference by generally ignoring clock

MERW and QM are kind of complementing perspectives on the reality - QM focuses on the wave nature of particles (clock), MERW on their corpuscular nature

vzn

ok brainstorming maybe a collection of particles with (same frequency) internal clocks has a MERW-like emergent behavior...?

Jarek Duda

What is crucial that their predictions agree in intersection of their fields of applications - like the electron conductance, where both predict stationary probability of the quantum ground state

MERW ignores internal clock - it is just properly made diffusion

However, surprisingly it still sees excited states - but they are not stable (vanish exponentially), while in pure QM (no perturbation) they are stable

vzn

ok have looked into fractal random walks over the years wrt financial data... have interesting book on it...

Jarek Duda

2:28 PM

MERW has nothing to do with some exotic concepts like fractal random walk, it is just diffusion made accordingly to the maximum entropy principle - which is required by statistical physics models, but standard (GRW-based) diffusion often turns out only approximating it

vzn

maybe there is some theory linking MERW to local random walks...? not familiar with this area

seems to relate to distinguishable vs indistinguishable particles...

Jarek Duda

MERW is Boltzmann distribution among paths - which depend on the entire space ... making it a nonlocal theory

vzn

yeah ok

Jarek Duda

but the particle doesn't use these probabilities - they are only used by us to get the most likely behavior, like in other thermodynamical models

vzn

2:56 PM

einstein got a nobel for studying brownian motion which proved atomic hypothesis :)