Wave-particle duality at Macro scale?

[liquidspacetime]

I'm not trying to refute anything. I'm interested in understanding how close of a quantum analogue, the walking droplet model is. I was under the impression (maybe wrongly) that if trajectories cross-over, then that model isn't a good quantum analogue.

In Bohmian mechanics, if trajectories cross-over, then that model isn't a good quantum analogue. We are discussing walking droplets which have nothing to do with Bohmian mechanics. Walking droplets have to do with de Broglie's wave mechanics and double solution theory. The physical wave of de Broglie's wave mechanics and double solution theory is allowed to cross-over.

Why is Bohmian mechanics fundamentally flawed?

In Bohmian mechanics the wavefunction wave is considered to be physically real and exist over all of configuration space. de Broglie disagreed with this. That is why there are two waves in de Broglie's wave mechanics and double solution theory. In de Broglie's wave mechanics and double solution theory there is the physical wave which guides the particle, which is the physical wave of walking droplets. There is also a wavefunction wave in de Broglie's wave mechanics and double solution theory. The wavefunction wave of de Broglie's wave mechanics and double solution theory is statistical only. It doesn't physically exist. It only exists in order to determine the probabilistic results of experiments.

'NON-LINEAR WAVE MECHANICS
A CAUSAL INTERPRETATION
by
LOUIS DE BROGLIE'

"The Wave Mechanics of systems of particles as we have just set forth, following Schrodinger, is an essentially non-relativistic theory because it assumes that the interactions can be represented at every instant by functions of the actual separation distances of the particles, whereas in a relativistic theory of interactions, these interactions are propagated at a finite velocity, which introduces retardation of one sort or another. A relativistic Wave Mechanics of the systems cannot be developed along the lines we have indicated, and only recently has there been any attempt to construct such a Mechanics within the framework of Quantum Field Theory (works by Tomonaga, Schwinger, Feynman, etc.). Let us simply emphasize the fact that the theory set forth above is valid only for the Newtonian approximation.
Schrodinger's idea of identifying the W wave of a system in configuration space at first shocked me very greatly, because, configuration space being a pure fiction, this conception deprives the W wave of all physical reality. For me the wave of Wave Mechanics should have evolved in three-dimensional physical space. The numerous and brilliant successes that resulted from adopting Schrodinger's point of view obliged me to recognize its value; but for a long time I remained convinced that the propagation of the W wave in configuration space was a purely imaginary way of representing wave phenomena which, in point of fact, take place in physical space. We will see in the second part of the present work (Chapter XII) how, from 1927 on, I had sought to develop this approach within the framework of the theory of the Double Solution."

The wave in walking droplets physically exists. It is real. The wave of Bohmian mechanics is a wave in configuration space, which deprives the wave of all physical reality.

Walking droplet wave: Physically real.
Wave which guides the particle of de Broglie's wave mechanics and double solution theory: Physically real.
Wavefunction wave of Bohmian mechanics: Fictitious, "a purely imaginary way of representing wave phenomena".

 

[vanhees71]

The only thing that's save to say is that there is nothing like wave-particle duality in modern quantum theory. Ironically with "modern" we label a theory which was completed nearly 90 years ago. The only problem is that didactics is behind by 100 years, unfortunately particularly high-school didactics (at least here in Germany). They still teach "old quantum mechanics", including Einstein's outdated photon picture and the Bohr-Sommerfeld model of the hydrogen atom. The result are wrong (and even qualitatively wrong) pictures about weird things as "wave-particle duality" or photons as if they were little minature billard balls. The abuse of the word "photon" is the worst of all of this didactical sins, as you can see in this forum. Most of what's called "photon" in the public media and in high-school physics (and unfortunately sometimes even at university) is in fact well described by the semiclassical approximation, where the electromagnetic field is described as classical background field, interacting with quantized matter particles. This is particularly true for Einstein's famous formula on the photoelectric effect. It's somwhat ironic that Einstein got his Nobel prize for the only piece of his great work that's totally outdated today and not for that part that must be counted to the most important achievements in physics for centuries, namely general relativity and statistical physics.

Bohm mechanics is just one more of many metaphysical interpretations of the quantum-theoretical formalism. It does not predict more than minimally interpreted quantum theory but is liked by some people who think it would be nice to have the idea of particle trajectories from classical mechanics translated into the quantum world. Unfortunately they are forced to complicated non-local dynamics which confuses the subject more than it helps to understand it, and this, as stressed above, without any additional merit in the sense of the physical core of the theory, which is the quantum-theoretical formalism with Born's probabilistic interpretation of the quantum state, not more and not less.

On a fundamental level our contemporary understanding of matter and its interactions (except gravity, which is not yet understood in terms of quantum theory) is a quantized relativistic-field picture anyway. One should say, however, that also this is with quite some probability only an effective theory and not the last word, as is general relativity for the description of the gravitational field, which is purely classical.

Whether there will ever be a better more comprehensive theory, future will perhaps tell. Thinking to have the final answer to all physics questions was always wrong in the past. It's a quite well-known story about Planck's try to figure out, what to do after finishing high school. He asked a renowned physics professor about physics, and this guy told him, it would be a waste of such a brillant mind as Planck to study this subject, because everything is in principle known, and the only task is to measure things to ever higher accuracy to confirm the known laws. The "little clouds" on the horizon of theoretical physics (mostly in statistical physics at the time) will be solved simply by measuring things more accurate. So the professor adviced Planck to better study ancient Latin and Greek rather than physics. Fortunately Planck hasn't followed this advice and later opened the window to the quantum world, leading to the resolution of all the "little clouds" on the horizon of theoretical physics.

 

[liquidspacetime]

The only thing that's save to say is that there is nothing like wave-particle duality in modern quantum theory. Ironically with "modern" we label a theory which was completed nearly 90 years ago. The only problem is that didactics is behind by 100 years, unfortunately particularly high-school didactics (at least here in Germany). They still teach "old quantum mechanics", including Einstein's outdated photon picture and the Bohr-Sommerfeld model of the hydrogen atom. The result are wrong (and even qualitatively wrong) pictures about weird things as "wave-particle duality" or photons as if they were little minature billard balls. The abuse of the word "photon" is the worst of all of this didactical sins, as you can see in this forum. Most of what's called "photon" in the public media and in high-school physics (and unfortunately sometimes even at university) is in fact well described by the semiclassical approximation, where the electromagnetic field is described as classical background field, interacting with quantized matter particles. This is particularly true for Einstein's famous formula on the photoelectric effect. It's somwhat ironic that Einstein got his Nobel prize for the only piece of his great work that's totally outdated today and not for that part that must be counted to the most important achievements in physics for centuries, namely general relativity and statistical physics.

Bohm mechanics is just one more of many metaphysical interpretations of the quantum-theoretical formalism. It does not predict more than minimally interpreted quantum theory but is liked by some people who think it would be nice to have the idea of particle trajectories from classical mechanics translated into the quantum world. Unfortunately they are forced to complicated non-local dynamics which confuses the subject more than it helps to understand it, and this, as stressed above, without any additional merit in the sense of the physical core of the theory, which is the quantum-theoretical formalism with Born's probabilistic interpretation of the quantum state, not more and not less.

On a fundamental level our contemporary understanding of matter and its interactions (except gravity, which is not yet understood in terms of quantum theory) is a quantized relativistic-field picture anyway. One should say, however, that also this is with quite some probability only an effective theory and not the last word, as is general relativity for the description of the gravitational field, which is purely classical.

Whether there will ever be a better more comprehensive theory, future will perhaps tell. Thinking to have the final answer to all physics questions was always wrong in the past. It's a quite well-known story about Planck's try to figure out, what to do after finishing high school. He asked a renowned physics professor about physics, and this guy told him, it would be a waste of such a brillant mind as Planck to study this subject, because everything is in principle known, and the only task is to measure things to ever higher accuracy to confirm the known laws. The "little clouds" on the horizon of theoretical physics (mostly in statistical physics at the time) will be solved simply by measuring things more accurate. So the professor adviced Planck to better study ancient Latin and Greek rather than physics. Fortunately Planck hasn't followed this advice and later opened the window to the quantum world, leading to the resolution of all the "little clouds" on the horizon of theoretical physics.

'Interpretation of quantum mechanics by the double solution theory - Louis de BROGLIE'
http://aflb.ensmp.fr/AFLB-classiques/aflb124p001.pdf

“When in 1923-1924 I had my first ideas about Wave Mechanics I was looking for a truly concrete physical image, valid for all particles, of the wave and particle coexistence discovered by Albert Einstein in his "Theory of light quanta". I had no doubt whatsoever about the physical reality of waves and particles.”

“any particle, even isolated, has to be imagined as in continuous “energetic contact” with a hidden medium”

"For me, the particle, precisely located in space at every instant, forms on the v wave a small region of high energy concentration, which may be likened in a first approximation, to a moving singularity."

A particle may be likened in a first approximation to a moving singularity which has an associated physical wave in a hidden medium.

"the particle is defined as a very small region of the wave"

In a double slit experiment the photon particle is a moving singularity which travels through a single slit. It is the associated physical wave in the hidden medium which passes through both.

"While the founding fathers agonized over the question 'particle' or 'wave', de Broglie in 1925 proposed the obvious answer 'particle' and 'wave'. Is it not clear from the smallness of the scintillation on the screen that we have to do with a particle? And is it not clear, from the diffraction and interference patterns, that the motion of the particle is directed by a wave? De Broglie showed in detail how the motion of a particle, passing through just one of two holes in screen, could be influenced by waves propagating through both holes. And so influenced that the particle does not go where the waves cancel out, but is attracted to where they cooperate. This idea seems to me so natural and simple, to resolve the wave-particle dilemma in such a clear and ordinary way, that it is a great mystery to me that it was so generally ignored." - John Bell

And so influenced that the particle does not go where the waves cancel out, but is [guided] to where they cooperate.

 

[Nugatory]

This thread has drifted well away from the original topic. As always, PM me if you feel that it should be reopened for any reason.