Is wave-matter duality a proven theory?

[PVT_RV]

TL;DR 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.

 

[anuttarasammyak]

Summary:: 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.

I am not well aware of experiments. Could you show some examples not fitting to the theories you mentioned ?

 

[PVT_RV]

Hi Anuttarasammyak

The following are two experiments where there were problems fitting optics theory to experimental results.

Page 323 of AJP Vol 71 No 4, 2003
https://aapt.scitation.org/doi/10.1119/1.1531580
The paragraph beginning " In principle, the diffraction patterns can be understood
quantitatively within the Fraunhofer approximation of Kirchhoff’s
diffraction theory as it can be found in any optics
textbook.38 However, Fraunhofer’s diffraction theory in the
context of optics misses an important point that becomes
evident in our experiments with matter waves"
It goes on to describe the problems of fitting optics diffraction to experimental results.
In the end they use "fits of our data to this modified Kirchhoff–Fresnel theory" without providing any formalisms / equations of the "modified Kirchhoff-Fresnel theory"

and again in
PHYSICAL REVIEW A, VOLUME 61, 033608 - Feb 2000
He-atom diffraction from nanostructure transmission gratings: The role of imperfections
Page 12 of the above article
"Both the transmission and the diffraction measurements
show the decrease of the effective slit width with increasing
angle of inclination, but consistently for both gratings the
effective slit widths determined from the transmission data
decrease faster with increasing angle of inclination than
those determined from the diffraction intensities. The large
discrepancy especially at large angles of inclination is
surprising.1 Possibly, it is due to an increased deviation of
the diffraction intensities from Eq. ~31!, which is based on
Kirchhoff’s extinction boundary conditions,"

Hope this helps in identifying the problems associated with fitting diffraction by optics theory to observed results.

Can anyone provide a better explanation of these diffraction patterns?

 

[atyy]

If you read further, they say
"In principle, the diffraction patterns can be understood quantitatively within the Fraunhofer approximation of Kirchhoff’s diffraction theory as it can be found in any optics textbook. However, Fraunhofer’s diffraction theory in the context of optics misses an important point that becomes evident in our experiments with matter waves and material gratings: the attractive interaction between molecule and wall results in an additional phase of the molecular wave function after the passage of the molecule through the slits. Although the details of the calculations are somewhat involved, it suffices here to say that the qualitative effect of this attractive force can be understood as a narrowing of the real slit width toward an effective slit width."

And footnote 40
"The van der Waals interaction scales with $r^{-3}$ with the distance $r$ between molecule and grating walls. For C₆₀ the scaling even starts to change into a $r^{-4}$ behavior at distances beyond 20 nm, due to the finite (retarded) signaling time between the molecule and its mirror image; see also H. B. G. Casimir and D. Polder, ‘‘The influence of retardation on the London-van der Waals forces,’’ Phys. Rev. 73, 360–372 (1948)."

 

[anuttarasammyak]

the attractive interaction between molecule and wall results in an additional phase of the molecular wave function after the passage of the molecule through the slits.

Just to confirm my understanding, say we choose electron beam and add charge on rim of slit, the behind screen pattern of electrons suffer from electromagnetic interaction between passing electron and charge on the rim and show difference from the case of uncharged rim. Though not explicitly charged, $C_{60}$ and slit materials do electromagnetic interaction which disturbs a theoretical pattern.

 

[weirdoguy]

The observed diffraction patterns in slit experiments are held up as proof of wave-particle duality.

It's important to note that wave-particle duality is not a full-blown theory but just set of outdated heuristic ideas that are important historicly-wise but do not constitue a part of modern quantum theory. A lot of modern textbooks on quantum physics do not even mention those ideas. This issue has been discussed here multiple times since pop-sci authors do often mention w-p duality beacuse it is quite easy to present it in non-technical terms. It's sad they do not tell the full story...

 

[phinds]

Summary:: Wave-particle Duality

Best reply on "wave particle duality":

There isn't a "wave" part of the electron and "particle" part of the electron. There's a single quantum object which is neither a wave nor a particle, but has some properties that we naturally associate with particles and other properties that we naturally associate with waves.

Although it's a popular metaphor and an OK visualization tool, "wave/particle duality" isn't a solid enough idea to build new theories on top of - it's more a user-friendly approximation of what quantum mechanics really says. Pillows are fuzzy, and tables have four legs, but when you encounter a sheep (which is fuzzy like a pillow and has four legs like a table) you aren't going to find the concept of "table/pillow duality" very helpful.

 

[vanhees71]

It's important to note that wave-particle duality is not a full-blown theory but just set of outdated heuristic ideas that are important historicly-wise but do not constitue a part of modern quantum theory. A lot of modern textbooks on quantum physics do not even mention those ideas. This issue has been discussed here multiple times since pop-sci authors do often mention w-p duality beacuse it is quite easy to present it in non-technical terms. It's sad they do not tell the full story...

Indeed! I would say it even more clearly: Modern quantum theory abandoned the inconsistent ideas of the "old quantum theory" completely. There is no wave-particle dualism but, according to todays understanding, only quantum fields.

 

[PVT_RV]

It's important to note that wave-particle duality is not a full-blown theory but just set of outdated heuristic ideas that are important historicly-wise but do not constitue a part of modern quantum theory. A lot of modern textbooks on quantum physics do not even mention those ideas. This issue has been discussed here multiple times since pop-sci authors do often mention w-p duality beacuse it is quite easy to present it in non-technical terms. It's sad they do not tell the full story...

The question is not so much about the name given to the theory and its history. The real question is whether the scientific community accepts that wave theory (borrowed from optics - Kirchhoff, Fresnel, Fraunhofer) satisfactorily describes the diffraction patterns quantitatively.
Or is there a more satisfying diffraction theory, with its origins in field theory, that offers a better quantitative description.
Can anyone shed light on this new 'diffraction by field theory' approach.
The new theory, I believe, originates from quantum field entanglement and the clear connection between geometry and energy.

 

[PeroK]

The question is not so much about the name given to the theory and its history. The real question is whether the scientific community accepts that wave theory (borrowed from optics - Kirchhoff, Fresnel, Fraunhofer) satisfactorily describes the diffraction patterns quantitatively.
Or is there a more satisfying diffraction theory, with its origins in field theory, that offers a better quantitative description.
Can anyone shed light on this new 'diffraction by field theory' approach.
The new theory, I believe, originates from quantum field entanglement and the clear connection between geometry and energy.

Despite this being an A level thread, Here's my simplistic analysis.

Wave-particle duality is a description of certain experimental results where light or massive particles behave like classical waves in some respects and like classical point particles in others respects.

Wave-particle duality is not a theory.

QM explains Wave-particle duality directly from the single quantum mechanical description of a particle.

The diffraction pattern predicted in single and double slit experiments assumes a perfect slit, with no interaction between the slit and the particle.

An added complexity, however, is that there is an interaction between the slit and the particle. There is no new theory here, as such, but the inclusion of a further level of detail in an otherwise idealised experiment.

A crude analogy would be including the influence of Jupiter in calculations of Earth's orbit does not change or challenge the theory of gravitation.

 

[weirdoguy]

Can anyone shed light on this new 'diffraction by field theory' approach.

Can you give any reference? Of course one that is written by physicist, because the one you gave in another thread was not. And if you can't find one, then that tells all about validity of that approach

 

[hutchphd]

PHYSICAL REVIEW A, VOLUME 61, 033608 - Feb 2000

I actually know a couple of these guys and here is the abstract

Good agreement between calculated and measured peak intensities, up to the sixth order, is obtained by accounting for random deviations in the slit positions, and averaging over the velocity spread of the incident beam as well as the spatial extent of the nozzle beam source. It is demonstrated that He atom beam diffraction together with simple transmission measurements is an excellent means of characterizing such gratings including a detailed determination of the slit width, the bar shape, and random as well as periodic disorder

So I don't know what you are talking about...incidentally this was very similar to my PhD thesis.

 

[PVT_RV]

I actually know a couple of these guys and here is the abstract

So I don't know what you are talking about...incidentally this was very similar to my PhD thesis.

Thank you for your insightful reply. I am indeed pleased to communicate with someone close to the work. In my opinion, the experimental physicists involved in these experiments deserve all respect and thorough congratulations for their creative and innovate skills in producing such accurate results. As part of their team those congratulations are extended to you also.
The words quoted in my OP came from the article. Those are not my words.
The problem is that, presently, the only mathematical tool available to physicists to explain the diffraction patterns quantitively is wave optics.
As someone close to the work, can you explain if effective slit widths, effective grating periods and other approximations are used in the calculations to get peak intensities to agree with experimental results. Are there equations that give the effective widths or is it that values are chosen that match results.
One of my concerns is that when you choose wave optics as your mathematical tool, then you give up on the position of the particle in the slit; you effectively make the choice that the particle-wave occupies the entire slit.
So until another quantitative explanation is offered, we have to live with the inaccurate solutions offered by wave optics theory.

 

[hutchphd]

When you do the calculation, you use some form of Schrodinger's eqn. (or equivalent) at some reasonable approximation to make the problem solvable. One does not wring hands and worry about particle wave duality. The theory works really well to describe atoms scattering from a periodic surface.

One of my concerns is that when you choose wave optics as your mathematical tool, then you give up on the position of the particle in the slit; you effectively make the choice that the particle-wave occupies the entire slit.
So until another quantitative explanation is offered, we have to live with the inaccurate solutions offered by wave optics theory.

You choose Quantum Mechanics because it works to explain all the data. I made no other choice about the "particle-wave".
Again there is no other theory required.

 

[Vanadium 50]

You choose Quantum Mechanics because it works to explain all the data. I made no other choice about the "particle-wave".

The history is de Broglie came up with wave-particle duality in 1925 and it was put to rest with the Schroedinger Equation in...later in 1925.

 

[PeroK]

The history is de Broglie came up with wave-particle duality in 1925 and it was put to rest with the Schroedinger Equation in...later in 1925.

As long ago as that?

 

[vanhees71]

When you do the calculation, you use some form of Schrodinger's eqn. (or equivalent) at some reasonable approximation to make the problem solvable. One does not wring hands and worry about particle wave duality. The theory works really well to describe atoms scattering from a periodic surface.You choose Quantum Mechanics because it works to explain all the data. I made no other choice about the "particle-wave".
Again there is no other theory required.

Of course, since 1925 there is no more wave-particle duality but quantum theory as discovered independently by (at least) three colaborations (Born, Jordan, Heisenberg) and single physicists (Schrödinger and Dirac). An electron or other "particles" is not adequately described completely by classical physics, neither with classical point-particle theory (which is anyway ill-defined in the relativistic context) nor classical field theory but very successfully with quantum theory.

Of course, what's presented in theoretical textbooks about diffraction is either in classical electrodynamics using Kirchhoff's scalar diffraction theory, usually also approximated to Fraunhofer or Fresnel diffraction. In classical electrodynamics the exact diffraction theory goes back to Sommerfeld and can be solved only for the most simple cases analytically (e.g., for the half space). The same holds true for the solution of the Schrödinger equation in non-relativistic QM.

These idealized analytical solutions of the diffraction problem are sufficient to get a pretty good qualitative picture for the diffraction patterns observed but it's of course not accurate when comparing to quantitative measurements. You have to take into account various things concerning the sources (particularly the finite coherence lengths and times, linewidth etc) and sometimes also more detailed descriptions of the interaction between the material making up the slits/gratings than just the simple boundary conditions used in standard diffraction theory. AFAIK there is no case of unexplained discrepancy between Q(F)T and observations concerning diffraction phenomena.

 

[rude man]

Best reply on "wave particle duality":

Electrons are particles, pure & simple.

They can behave as though they were waves but this is due to fundamental QM behavior in ANY particle, even cannon balls. The fact that electrons are charges plays an inconsequential role, at least to 1st order, in the dual-slit experiment..

The connection between wave ($\lambda$) and particle (momentum $p$) is a postulate of QM: $\psi(x) _p = exp(ipx/\hbar) \rightarrow\psi(x)_{\lambda} = exp(i2\pi x/\lambda)$ i.e. the deBroglie relation $\lambda \cdot p = 2\pi \hbar$ .

(Unnormalized, 2-dimensional in x.) The above $\psi(x)$ are the factors in the Fourier expansion of the fundamental particle wave equation $\psi(x)$. in momentum/wave space.

 

[PVT_RV]

These idealized analytical solutions of the diffraction problem are sufficient to get a pretty good qualitative picture for the diffraction patterns observed but it's of course not accurate when comparing to quantitative measurements.

I agree with almost everything that you have stated. I would like to pose a related but different question.
If one had never heard of the de Broglie equation and therefore unable to use that relation, is it possible to arrive at an accurate quantitative description of slit diffraction patterns?
In my opinion the answer is 'definitely yes'. The solution would involve EFE, QFT and some original thought. An accurate, quantitative description of slit diffraction patterns does not necessarily involve Kirchhoff, Fraunhofer, Fresnel or de Broglie. This is not to say that there is a challenge to Q(F)T but rather that there is another approach to the quantitative solution of slit diffraction which uses QT in a different way.. Unfortunately I am not allowed to post a link as the article does not appear in a peer reviewed journal as yet.

 

[PeroK]

I agree with almost everything that you have stated. I would like to pose a related but different question.
If one had never heard of the de Broglie equation and therefore unable to use that relation, is it possible to arrive at an accurate quantitative description of slit diffraction patterns?

A purely QM description for electron diffraction could use the infinite square well potential for the single or double slits. That, I assume, would get complicated!

Perhaps you could find something online.

 

[hutchphd]

Many approximation methods can be applied to a Feynman path integral formulation of the Scattering Amplitude. Nowhere does that formulation explicitly invoke wavelength yet the principles that allow the optical problems to solve pop right up. In particular use of stationary phase on the action integral leads pretty directly to wavelengths and diffraction. Very Useful all over the place...I have had very good teachers.

What does not seem useful to me is to worry about which "pigeonhole" a description belongs in. Having never heard of de Broglie would not matter to me because I have heard of Feynman. If Feynman had not heard of de Broglie begs a very different question...

 

[PVT_RV]

@hutchphd Thank you again for your insightful comments. From memory (which is definitely not the best source) Feynman's path integral formulation of scattering theory is about scattering of free plane waves from a local potential. While wavelength may not be explicitly invoked, the path integral formulation usually begins with a T-matrix of a free plane wave with an initial momentum. If its not too much trouble, could you post a link to the papers that you refer to "In particular use of stationary phase on the action integral leads pretty directly to wavelengths and diffraction".

 

[hutchphd]

https://en.wikipedia.org/wiki/Path_integral_formulation

 

[vanhees71]

One of the best sources for the path integral is still the famous book by Feynman and Hibbs. Then there's

H. Kleinert, Path Integrals in Quantum Mechanics, Statistics and Polymer Physics, World Scientific

You can get a (I guess legal copy) from the author's homepage

http://users.physik.fu-berlin.de/~kleinert/b5/psfiles/pi.pdf

 

[bhobba]

As long ago as that?

Yes. And at the end of 1926, Dirac extended it again with his transformation theory that is basically what goes by the name QM today. Interestingly Dirac, despite his many accomplishments in physics, always thought it was one of his most important contributions:
http://www.lajpe.org/may08/09_Carlos_Madrid.pdf

It took the efforts of some of the greatest 20th-century mathematicians (Gelfand, Schwartz and Grothendieck, plus others) to put Dirac's formulation on firm mathematical footing. Its culmination is the so-called Nuclear Spectral Theorem you can investigate yourself if it piques your interest. It was not that easy - very few mathematical things defeated the great Von-Neumann - this one did.

Thanks
Bill

 

[bhobba]

I agree with almost everything that you have stated. I would like to pose a related but different question.
If one had never heard of the de Broglie equation and therefore unable to use that relation, is it possible to arrive at an accurate quantitative description of slit diffraction patterns?

Yes.

See:
https://arxiv.org/pdf/quant-ph/0703126]

Note, as Vanhees will correctly point out, even that approach has issues - it is just 'better' than what is usually found in textbooks using the outdated idea of wave-particle duality:
https://arxiv.org/pdf/1009.2408.pdf

Physics is a bit strange like that. You start at the beginning learning one thing, then find it actually is 'wrong'. Feynman knew of it, and being the master teacher he was, did not like it. But never could figure out how to do away with it. His QED book, using path integrals at the layman level, can be looked at as one attempt.

Thanks
Bill

 

[hutchphd]

Is wave-matter duality a proven theory?​

I would also like to express displeasure at the question as posed.
No theory is ever "proven" and this causes more bad public relations for science among the naysayers than any other aspect All theories are continuously tested and we simply gain confidence in their adequacy. We should be careful here...ask Anthony Fauci.

 

[Delta2]

According to modern quantum field theory all particles arise from quantization of some underlying field and because fields usually obey some wave equation, they are waves, so all particles are waves in some sense.

 

[PVT_RV]

Yes.

See:
https://arxiv.org/pdf/quant-ph/0703126]

Note, as Vanhees will correctly point out, even that approach has issues - it is just 'better' than what is usually found in textbooks using the outdated idea of wave-particle duality:
https://arxiv.org/pdf/1009.2408.pdf

Physics is a bit strange like that. You start at the beginning learning one thing, then find it actually is 'wrong'. Feynman knew of it, and being the master teacher he was, did not like it. But never could figure out how to do away with it. His QED book, using path integrals at the layman level, can be looked at as one attempt.

Thanks
Bill

@bhobba Thank you so much for the arxiv link 0703126
Finally, someone who points out (correctly) that presently "classical wave optics, rather than quantum mechanics, is (being) used to explain quantum interference" in slit experiments. He then goes on to frame the problem in QT. While this paper does not derive all the necessary equations to fully describe the patterns (because those equations are difficult to derive and solve), it does frame the problem correctly.
It should make interesting reading for all interested persons.

 

[dx]

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. In fact, his insight into quantum theory was so great that he intuitively came to the poisson statistics of photons, which people were able to derive only much later using the sophisticated formal methods.

 

[vanhees71]

Yes, Bohr contributed much to the impression of weirdness many physicists of his time (but obviously an amazing number of contemporary ones) have today. A lot of this weirdness goes away when avoiding unnecessary philosophical gibberish and just take it as the description of nature that it "really" (pun intended) is.

 

[Lord Jestocost]

Yes, Bohr contributed much to the impression of weirdness many physicists of his time (but obviously an amazing number of contemporary ones) have today. A lot of this weirdness goes away when avoiding unnecessary philosophical gibberish and just take it as the description of nature that it "really" (pun intended) is.

Sorry, but I have to correct this oversimplified statement.

Carl Friedrich von Weizsäcker in “The Structure of Physics” (the book is a newly arranged and revised English version of "Aufbau der Physik" by Carl Friedrich von Weizsäcker)

“In the first months of 1927 there was a technical disagreement between Bohr and Heisenberg about the conjectured correct interpretation of quantum mechanics which even led to serious personal irritations. While they were separated for a few weeks, Bohr going to Norway for a skiing trip while Heisenberg remained back in Copenhagen, each found his own solution: Heisenberg the uncertainty of position and momentum, Bohr the complementarity of wave and particle. At Bohr’s return they eventually agreed to the formulation of complementarity being the cause of the uncertainty. That is the fourth possible solution to the problem of duality. Matter and light ‘by themselves’ are neither particles nor waves. Yet if we wish to visualize them we must use both pictures. And the validity of one picture imposes limitations on the validity of the other. This is the main point of the Copenhagen interpretation.” [bold by LJ]

 

[sysprog]

I think that this (by Isaac Newton) is especially good (you can find a readable version here: https://www.gutenberg.org/files/33504/33504-h/33504-h.htm).

 

[vanhees71]

Sorry, but I have to correct this oversimplified statement.

Carl Friedrich von Weizsäcker in “The Structure of Physics” (the book is a newly arranged and revised English version of "Aufbau der Physik" by Carl Friedrich von Weizsäcker)

“In the first months of 1927 there was a technical disagreement between Bohr and Heisenberg about the conjectured correct interpretation of quantum mechanics which even led to serious personal irritations. While they were separated for a few weeks, Bohr going to Norway for a skiing trip while Heisenberg remained back in Copenhagen, each found his own solution: Heisenberg the uncertainty of position and momentum, Bohr the complementarity of wave and particle. At Bohr’s return they eventually agreed to the formulation of complementarity being the cause of the uncertainty. That is the fourth possible solution to the problem of duality. Matter and light ‘by themselves’ are neither particles nor waves. Yet if we wish to visualize them we must use both pictures. And the validity of one picture imposes limitations on the validity of the other. This is the main point of the Copenhagen interpretation.” [bold by LJ]

Sure, if you want to get totally confused about quantum theory, read Bohr, Heisenberg, and finally von Weizsäcker (in increasing order of confusion)...

 

[Lord Jestocost]

Sure, if you want to get totally confused about quantum theory, read Bohr, Heisenberg, and finally von Weizsäcker (in increasing order of confusion)...

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!