Is wave-matter duality a proven theory?

[sysprog]

With all due respect, what is the sense of your remark in an exchange of views about the meaning of the "wave-particle duality".
Matter and light ‘by themselves’ are neither particles nor waves.
Weizsäcker simply states what physics can say up to now in a nutshell!

I think that @vanhees71 was partly just being a bit humorous.

 

[vanhees71]

I don't like the style of those physicists. I'm more inclined to the "no-nonsense approach" of people like Born, Jordan, Pauli, Sommerfeld, and (particularly) Dirac. It's of course a personal opinion.

 

[Jarek 31]

Some experiments claiming to use simultaneously both wave and particle nature:
https://en.wikipedia.org/wiki/Afshar_experiment using simultaneously both destructive interference and lens-based optics in double-slit experiment
"Simultaneous observation of the quantization and the interference pattern" https://www.nature.com/articles/ncomms7407

For slits it is worth to remember that diffraction pattern is already there for single slit: https://en.wikipedia.org/wiki/Double-slit_experiment

ps. For the source of wave nature of e.g. electron, there is often considered its intrinsic periodic process called de Broglie' clock or zitterbewegung ( https://en.wikipedia.org/wiki/Zitterbewegung ) - which was confirmed experimentally for electron: https://link.springer.com/article/10.1007/s10701-008-9225-1

 

[PeroK]

Matter and light ‘by themselves’ are neither particles nor waves. Yet if we wish to visualize them we must use both pictures.

Let's assume we do have wave-particle duality in some theoretical sense.

1) Describe the theoretical framework that supports the wave picture.

2) Describe the theoretical framework that supports the particle picture.

3) Compare and contrast the two frameworks.

 

[vanhees71]

I'd formulate it much simpler: The only way to "visualize" matter and the em. field is Q(F)T. It's not an intuitive classical picture (neither in the sense of point-particle theory which in full glory only really works in the non-relativistic approximation nor in the sense of classical field theory). The only "image" we have that describes all phenomena in a satisfactory way (as far as we know the phenomena today, of course) is Q(F)T.

Wave-particle duality was notoriously known to be self-contradictory and it was made obsolete with the discovery of modern Q(F)T. It still survives in the (pseudo-)historical narrative of textbooks introducing quantum theory, because to build an intuition of this very abstract formalism one seems to need this narrative. The danger is that we take this narrative too literally and keep the long overcome inconsistent pictures as the only picture we have.

 

[Jarek 31]

Nice and thought provoking way to visualize wave-particle duality are the hydrodynamical walking droplets experiments started by Couder, e.g. slits ( https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.97.154101 ):



Gathered materials about lots of hydrodynamical QM analogs: https://www.dropbox.com/s/kxvvhj0cnl1iqxr/Couder.pdf

 

[vanhees71]

This is also utterly misleading. The only analog is that both the time-independent Schrödinger equation and the linear approximation of hydro take the same mathematical form of a Helmholtz equation. The meaning of the described quantity ("wave function" of quantum mechanics and pressure, densities, etc. of hydro) is completely different ("wave function" = probability amplitude, hydro quantities=classical observables described by continuum-mechanical fields).

 

[gentzen]

Gathered materials about lots of hydrodynamical QM analogs

I don't want to dispute that you gathered nice material. However, the experiments by Couder are not helpful for better understanding quantum phenomena. Perhaps they are helpful for better understanding how to apply mathematics developed in the context of QM to other domains. Fine, but it doesn't help with respect to wave-matter duality.

 

[Jarek 31]

Sure, hydrodynamical analogs use a bit different equations, but recreate impressive number of QM-like effects, like Casimir, Aharonov-Bohm, double-slits, interference, quantum statistics, orbit quantization - including Zeeman effect and double quantization in analogy to (n,l) ( https://www.nature.com/articles/ncomms4219 ).

The big question is how appropriate these analogs are?

Here is some article discussing this correspondence: https://www.frontiersin.org/articles/10.3389/fphy.2020.00300/full

 

[vanhees71]

These are pure mathematical analogies. Equal equations have equal solutions (modulo intial/boundary conditions which may differ in different applications of the equations). The physical meaning is completely different in continuum mechanics as compared to quantum mechanics though.

 

[Jarek 31]

These are pure mathematical analogies

... finally providing intuitions to quantum phenomena usually operated with "shut up and calculate" approach.

So how to imagine e.g. double-slit experiment?
According to Feynman "the double-slit experiment has in it the heart of quantum mechanics. In reality, it contains the only mystery."
Just substituting psi=sqrt(rho) exp(iS/hbar) to Schrodinger equation, we get the pilot wave intuition ( https://en.wikipedia.org/wiki/Pilot_wave_theory#Mathematical_formulation_for_a_single_particle ) ... confirmed e.g. while measuring averaged trajectories of interfering photons ( https://science.sciencemag.org/content/332/6034/1170 ).
Using this intuition they also get interference in analogous hydrodynamical situation, e.g. more recent "Walking droplets interacting with single and double slits": http://thales.mit.edu/bush/wp-content/uploads/2021/04/Pucci-Slits-2017.pdf

So where exactly is the problem with such intuition e.g. for double-slits interference?
What alternatives are there (beside "shut up and calculate")?

 

[vanhees71]

There is no problem with this intuition. You can take the hydro experiment as an "analog computer" to solve the Schrödinger equation, but the meaning is completely different. An electron going through a slit can neither adequately described as a point particle nor as a continuum-mechanical classical system like a fluid. All there is are the probabilities, i.e., $|\psi(x)|^2$, i.e., the intereference pattern of the fluid distribution used for "computing" the result of the corresponding wave equation, gives you probability distributions for detecting the electron at a given location on the screen. With a single electron you never find an interference pattern but a single point. Using many (equally prepared) electrons the interference pattern builds up. That's why the meaning of the wave function is completely different from a classical continuum-mechanical wave like the density (or charge density) of a fluid. This old first interpretation of the wave function by Schrödinger lasted at most about half a year, until Born found the probability interpretation which is in accord with observations, while Schrödinger's classical-field interpretation has never been.

 

[Jarek 31]

With a single electron you never find an interference pattern but a single point. Using many (equally prepared) electrons the interference pattern builds up.

This is exactly what they do with the walking droplets as analogs for wave-particle duality objects: diffraction pattern from averaging over many single walkers, like in bottom-left diagram in my previous post.

Here with statistics of trajectories they get "Wavelike statistics from pilot-wave dynamics in a circular corral": https://journals.aps.org/pre/abstract/10.1103/PhysRevE.88.011001
What is not surprising as e.g. doing diffusion right - accordingly to the (Jaynes) maximal entropy principle required for statistical physics models, one also gets quantum statistics, starting with stationary probability distribution exactly as quantum ground state: https://en.wikipedia.org/wiki/Maximal_entropy_random_walk

 

[physika]

I wouldn't dismiss wave-particle duality so quickly. Bohr was fully aware of the 'new quantum mechanics' of Heisenberg, Schrodinger and Dirac, yet he continued to talk about the 'complementarity' between the wave and particle pictures for decades after 1930.

Indeed.

Quantitative complementarity of wave-particle duality​

https://www.science.org/doi/10.1126/sciadv.abi9268

"To test the principle of complementarity and wave-particle duality quantitatively, we need a quantum composite system that can be controlled by experimental parameters. Here, we demonstrate that a double-path interferometer consisting of two parametric downconversion crystals seeded by coherent idler fields, where the generated coherent signal photons are used for quantum interference and the conjugate idler fields are used for which-path detectors with controllable fidelity, is useful for elucidating the quantitative complementarity."

"the wave-particle duality (triality) equality, i.e., quantitative complementarity, can be tested with our ENBS system, where the wave-like and particle-like behaviors of the quanton (signal photon) are tunable quantities through the experimentally adjustable path detector fidelity F ranging from 0 to 1."

"we anticipate that the interpretation based on the double-path interferometry experiments with ENBS will have fundamental implications for better understanding the principle of complementarity and the wave-particle duality relation quantitatively, leading to demystifying Feynman’s mystery* for the double-slit experiment explanation based on the quantum mechanics."----

the source determines the character it adopts,
wave-ness or particle-ness.
is a continuum that can tend more towards one characterization or towards the other characterization.

-----

*. P. Feynman, R. B. Leighton, M. Sands, The Feynman Lectures on Physics, vol. III, chap. I (Addison Wesley, Reading, 1965)

.

 

[bhobba]

Ok, what is the wave nature of the orbitals of the 4th energy levels of the hydrogen atom:
https://archives.library.illinois.edu/erec/University%20Archives/1505050/Rogers/Text5/Tx53/tx53.html

Wave-particle duality, except in straightforward circumstances (a free particle), was done away with at the end of 1926 when Dirac published his transformation theory and basically is what goes under the name of QM today. Likely even before - but certainly by then. It was an essential stepping stone in the development of QM. All physicists should know something of QM history, so learning about it in a historical context is of value. But as to being a principle of modern QM, it is simply not and has been that way for many years. Bohr's idea of complementarity is very subtle. In the context of wave-particle duality, it doesn't display its particle nature when acting as a wave and conversely when displaying its particle nature it does not act like a wave. But it only acts like a wave in special circumstances such as a free particle. If you want to investigate fundamental things of this sort, such as why quantisation is so common (it does not exist for a free particle, for example), that is a profound question. The following lectures explain it - but it is far from trivial


Thanks
Bill

 

[koantum]

Summary:: Wave-particle Duality

The observed diffraction patterns in slit experiments are held up as proof of wave-particle duality. But wave theory diffraction (borrowed from optics - Kirchoff's Laws, Fresenel & Fraunhofer diffraction) don't quite fit the experimental results. There is always some tinkering to get theory to match experimental results.

So is there a better explanation of the diffraction patterns observed in slit experiments?

I have heard of a new theory - the field theory of diffraction - that is supposed to offer a fuller explanation.

Can anyone help to explain this new theory.

“Things” like electrons are neither particles nor waves, and this not merely in the sense that they behave neither like traditional particles nor like traditional waves, but in the more radical sense that they lack intrinsic behavior. Classically conceived particles or waves behave the way they do whether or not we observe them. Electrons behave the way they do only if we observe them, and the way they behave depends on the experimental apparatus by means of which we observe them. In short, their behavior is contextual. See this post.

The contextuality of the properties or behaviors of quantum systems, which was stressed by Bohr, is one of the most overlooked features of the quantum theory in contemporary discussions of its meaning. Contextuality means that the properties/behaviors of quantum systems are defined by the experimental conditions under which they are observed, and that they only exist if they are observed. The click of a counter, for instance, does not simply indicate the presence of some object inside the region monitored by the counter. Instead, the counter defines a region, and the click constitutes the presence of something inside it. Without the click, nothing is there, and without the counter, there is no there.

 

[bhobba]

The click of a counter, for instance, does not simply indicate the presence of some object inside the region monitored by the counter. Instead, the counter defines a region, and the click constitutes the presence of something inside it. Without the click, nothing is there, and without the counter, there is no there.

One can look at it that way, but you do not have to. I will leave the post as is, but really it belongs in the interpretation section. What we can say for sure is between observations, what is going on is up for grabs. But speculating on it is something we humans do, rather than what QM says, which is what this subforum is all about.

Thanks
Bill

 

[physika]

I wouldn't dismiss wave-particle duality so quickly.

I agree.

 

[PeroK]

Contextuality means that the properties/behaviors of quantum systems are defined by the experimental conditions under which they are observed, and that they only exist if they are observed.

I just wanted to confirm that the pronoun "they" refers to the properties of quantum systems and not the systems themselves.

That said, there is no reason to tie the existence of something to your classical expectations of it. Classical particles have at all times a well-defined position, say. That does not mean that a quantum particle does not exist (nor that the property of "position" for a quantum particle dos not exist) unless you measure its position.

One could argue that saying that "if something does not behave classically then it doesn't exist" reveals an extraordinary classical bias!

One could perhaps make a stronger case that quantum particles exist; whereas, their classical counterparts do not!

 

[bhobba]

Does the following remark by John von Neumann in 1932 belong to interpretations?

“Indeed experience only makes statements of this type: an observer has made a certain (subjective) observation; and never any like this: a physical quantity has a certain value.”
(“Quantum Theory and Measurement“, edited by John Archibald Wheeler and Wojciech Hubert Zurek, Princeton, New Jersey 1983, page 622):

I do not think the line is hard and fast. I would put it in either. Although not philosophical in and of itself, I think mentors like myself would keep an eye on it to ensure it does not head deeply in that direction.

I would not get too hung up on this sort of stuff. Innocent 'missteps' happen all the time. Detail what you think, and if it is in the wrong place, it will be pointed out with no infringement. Infringements are not issued for innocent mistakes.

Thanks
Bill

 

[gentzen]

But it only acts like a wave in special circumstances such as a free particle. If you want to investigate fundamental things of this sort, such as why quantisation is so common (it does not exist for a free particle, for example), that is a profound question. The following lectures explain it - but it is far from trivial

I admit that those are nice lectures, but how far will I have to watch them before the question "why quantization is so common" will be explained? Actually, in the 3rd lecture at 21:30 Carl Bender talks about "some of his current research" and claims that the potential $x^2(ix)^\epsilon$ leads to discrete positive eigenvalues for all positive real $\epsilon$ despite the fact that it is for example upside down for $\epsilon=2$. He asks: "How could it be that a potential that looks like this has bound states whose energies are up here?" and then goes on: "The answer is: it does! I am not going to explain to you why that is true".

 

[Lord Jestocost]

I do not think the line is hard and fast. I would put it in either. Although not philosophical in and of itself, I think mentors like myself would keep an eye on it to ensure it does not head deeply in that direction.

I would not get too hung up on this sort of stuff. Innocent 'missteps' happen all the time. Detail what you think, and if it is in the wrong place, it will be pointed out with no infringement. Infringements are not issued for innocent mistakes.

Thanks
Bill

Sorry, and thanks for your hint! In case I understand you rightly, I completely agree with you: My comment should have only be released in the "Quantum Interpretations and Foundations" sub-forum. Thus, I have deleted it.

 

[bhobba]

I admit that those are nice lectures, but how far will I have to watch them before the question "why quantization is so common" will be explained? Actually, in the 3rd lecture at 21:30 Carl Bender talks about "some of his current research" and claims that the potential $x^2(ix)^\epsilon$ leads to discrete positive eigenvalues for all positive real $\epsilon$ despite the fact that it is for example upside down for $\epsilon=2$. He asks: "How could it be that a potential that looks like this has bound states whose energies are up here?" and then goes on: "The answer is: it does! I am not going to explain to you why that is true".

It has been a while since I watched them all, but it is there somewhere. It has to do with the wave function reaching around and interfering with itself. I should have mentioned it in my answer. The takeaway is it is not an easy issue - that is all I was trying to get across.

And yes, those lectures are good - worthwhile watching the whole lot.

Thanks
Bill

 

[bhobba]

Sorry, and thanks for your hint! In case I understand you rightly, I completely agree with you: My comment should have only be released in the "Quantum Interpretations and Foundations" sub-forum. Thus, I have deleted it.

There is no need to be sorry. You have done nothing wrong. If you had put it in the wrong place, I would have mentioned it. As I said, it can go in either. But it may lead to replies better in the interpretation subforum - that's all. Thanks for thinking about thread content. It is appreciated.

Thanks
Bill