Wave-Particle Duality Theory: Explaining Electron Properties

[Careful]

If the electron did radiate energy I would not ask why because of Maxwell's equations. It is because they do not radiate energy is the reason I am asking why.

If all my "whys" have been answered I guess I missed them. Unless saying "don't think in classical terms because Nature does not follow classical physics" is somehow adequate. It reminds me of my quantum physics professor saying that you must except Schrödinger's equation on faith because it is not a derived equation but it works.

You are thinking about the Coulomb *approximation* in which of course radiation back coupling has been ignored. In QFT you add photon by photon and let it interact with the Coulomb states, which results in things such as the Lamb shift and spontaneous emission.

Really, all your why's have been dealt with - but these issues are much more involved than most people know/believe they are. Check for Elliott Lieb on the web !

Cheers,

Careful

 

[masudr]

Euhh, electrons do radiate in the full QFT treatment - spontaneous transitions between different Coulomb states do occur, but there is no radiation *catastrophe* (as is proven in most cases) - the latter does not occur either in a correct classical treatment.

Euhh, even more

I was commenting on the QM model of the standard fine-structure hydrogen atom, NOT the QFT treatment. I would have thought this was so obvious from context that I wouldn't have to specify it, but here we are anyway.

Remember, QFT model of hydrogen atom is still just that, a model, and it was not that model that I was referring to.

 

[Careful]

Euhh, even more

I was commenting on the QM model of the standard fine-structure hydrogen atom, NOT the QFT treatment. I would have thought this was so obvious from context that I wouldn't have to specify it, but here we are anyway.

Remember, QFT model of hydrogen atom is still just that, a model, and it was not that model that I was referring to.

If so, then I guess you missed the worry expressed by rlduncan who obviously knows QM at such an elementary level. The QM Coulomb atomic model is entirely meaningless and even misleading (what the radiation problem is concerned), it is only good to teach to kids. It does not address the radiation issue at a satisfactory level (as is oversold in most QM textbooks even before stability of the full theory was proven), which was the reason why we got stuck with it in the first place.

Careful

 

[vanesch]

It is indeed true that many basic claims of successes of QM made in intro textbooks of quantum theory are based upon wrong reasoning. This is not done to "blind the crowds" or something, because at a certain point, historically, people thought that they were correct arguments (and only later, flaws were found in them). The fun thing is that the *conclusions* still seem to be right, but not the arguments.

One such argument is the famous radiation problem of atoms. When dealing with *the full electromagnetic field* in classical physics, and looking at a classical electron orbiting around a classical nucleus, one has the problem of the radiation reaction which would make the electron spin inward and have atoms radiate continuously.
Bohr's first atom model "solved" the issue by *postulating* non-radiating orbits (the "old quantum theory"), but it was recognized that that was putting things in by hand. What was nice was that out of it, came correct spectral values for the hydrogen lines. But it was a very ugly theory (and broke down for more complicated systems). Usually, when confronted with a problem, you cannot consider it solved by postulating that it goes away.

And then Schroedinger's non-relativistic QM could produce the same spectral results with "modern" wave mechanics...
However, Schroedinger's non-relativistic hydrogen atom (as found in all intro books on QM) ONLY DEALS WITH A COULOMB FORCE.
Now, if we're allowed to introduce classically only a coulomb force, then there's no problem for the classical radiating atom either ! The electrostatic solution to a classical atom has stable orbits too. It was only when the FULL electrodynamical interaction was taken into account that this radiatioin stuff reared its ugly head, not for the coulomb interaction.
So is it a surprise that *purely coulombic* quantum theory also provides us with stable orbits ? Not really.

The problem is that we do not have anything else but a perturbative treatment of the full EM field (which is QFT). So it is difficult to make sure that this perturbative treatment gives us the correct solution.
But QM has in it the seeds for the resolution of the issue: one should demonstrate that the full EM system in the hydrogen atom has on the lower side, a discrete spectrum which is bounded from underneath.
*THEN* the stability of the hydrogen atom will be demonstrated in QM (and apparently this has been done, and you "can feel in your bones that this can be the case").

But concluding from the *coulombic* treatment of the hydrogen atom that the radiation problem is solved, which gave a problem in classical theory if we were not allowed to make the coulombic approximation there, is a wrong reasoning: in the coulombic atom, the very element of potential instability which screwed the classical atom, has been left out (namely the radiation reaction).

 

[Careful]

***
One such argument is the famous radiation problem of atoms. When dealing with *the full electromagnetic field* in classical physics, and looking at a classical electron orbiting around a classical nucleus, one has the problem of the radiation reaction which would make the electron spin inward and have atoms radiate continuously. ***

How, how, what I said is that this treatment is incorrect, it originates from the misunderstanding that all classical radiation in the universe is thermal and that no classical motion at T=0 exists (+ a bunch of other mistakes).

**
The problem is that we do not have anything else but a perturbative treatment of the full EM field (which is QFT). **

Na, na, Barut self field is entirely well defined non-perturbatively and is shown to agree (on these issues) up to fifth order in e^2.

With the rest of your post I agree

 

[vanesch]

How, how, what I said is that this treatment is incorrect, it originates from the misunderstanding that all classical radiation in the universe is thermal and that no classical motion at T=0 exists (+ a bunch of other mistakes).

Yes, of course, in the idealized situation of JUST one single proton, one single electron, and a classical, empty EM field.

**
The problem is that we do not have anything else but a perturbative treatment of the full EM field (which is QFT). **

Na, na, Barut self field is entirely well defined non-perturbatively and is shown to agree (on these issues) up to fifth order in e^2.

Yes, but that's not QFT. It is *another* theory. You cannot use Barut self field theory to prove the hydrogen atom stability in QUANTUM theory.

 

[Careful]

**
Yes, but that's not QFT. It is *another* theory. You cannot use Barut self field theory to prove the hydrogen atom stability in QUANTUM theory.**

It is not QFT, but it is first quantized Dirac-Maxwell theory, hence you can use it to prove hydrogen stability in quantum theory (and it is used like that, you still start from the usual Coulomb wavefunctions ... ).

 

[rlduncan]

Yes many of the principles of physics I accept without proof, but I have a special interest in the basic h-atom and the other atoms of the Periodic Table. My approach to the formation and structure of these atoms is somewhat different than most. The Electronic Configuration Pattern can be found in Pascal's Triangle ( see Journal of Chemical Education, Vol. 73, Page 742-743, August 1996) where I reveal two quantum numbers and make the sugguestion that this find may help in understanding of quantum theory. The article shows that Fibonacci Numbers are related to the Electronic Configuration Pattern. This pattern shows up in the macroscopic world in plants and animals, a direct connection between the microscopic level to the macroscopic level. In knowing this I was looking for other theories to explore the possibility of bridging the gap between classical physics and quantum mechanics.

 

[ZapperZ]

Yes many of the principles of physics I accept without proof, but I have a special interest in the basic h-atom and the other atoms of the Periodic Table. My approach to the formation and structure of these atoms is somewhat different than most. The Electronic Configuration Pattern can be found in Pascal's Triangle ( see Journal of Chemical Education, Vol. 73, Page 742-743, August 1996) where I reveal two quantum numbers and make the sugguestion that this find may help in understanding of quantum theory. The article shows that Fibonacci Numbers are related to the Electronic Configuration Pattern. This pattern shows up in the macroscopic world in plants and animals, a direct connection between the microscopic level to the macroscopic level. In knowing this I was looking for other theories to explore the possibility of bridging the gap between classical physics and quantum mechanics.

Then you are trying to formulate your own personal theory. Please do this in the IR forum, not here.

Zz.

 

[Farsight]

I note a thread dating back to 2003 on that. Geometry. Interesting. While looking I bumped into this:

Erwin Schroedinger understood the requirements of particle structure when he wrote in 1937: "What we observe as material bodies and forces are nothing but shapes and variations in the structure of space. Particles are just schaumkommen. (appearances)". He believed that quantum waves were real, not probability distributions with a hidden particle wondering inside. He saw that abolishing the discrete point particle would remove the paradoxes of 'wave-particle duality' and the 'collapse of the wave function'.

Anybody: Is this true?

I note he proposed his cat in 1935.

 

[Careful]

I note a thread dating back to 2003 on that. Geometry. Interesting. While looking I bumped into this:

Erwin Schroedinger understood the requirements of particle structure when he wrote in 1937: "What we observe as material bodies and forces are nothing but shapes and variations in the structure of space. Particles are just schaumkommen. (appearances)". He believed that quantum waves were real, not probability distributions with a hidden particle wondering inside. He saw that abolishing the discrete point particle would remove the paradoxes of 'wave-particle duality' and the 'collapse of the wave function'.

Anybody: Is this true?

I note he proposed his cat in 1935.

The reason for him to say so was of course the incompatibility of the probabilistic interpretation of QM with the principles of SR and GR. Moreover, one can get particle *and* wave like behaviour out of a SINGLE equation by considering for example the coupled Dirac - Maxwell system (I have given the Barut reference before).

Careful

 

[Farsight]

Thanks Careful. I'll have a browse.

 

[selfAdjoint]

Here is a sample of Barut's work,

http://streaming.ictp.trieste.it/preprints/P/93/105.pdf

It's a calculation of vacuum polarization using his method of plugging the electron "self-field" into the Dirac equation as an alternative to quantisation and QED. No UV or IR infinities but the non-linear equations he gets are no trivial to solve. That's no reason to reject his ideas of course, but this standard calculation is a needed demonstration that he can do the work od producing the numbers.

It is tragic that he died young (68) when just hitting his stride with this.

 

[Farsight]

I bumped into the "Afshar experiment" while looking for something else, and the Waving Copenhagen Goodbye caught my eye. Does anybody have current knowledge or an expert view on it?

 

[RandallB]

I bumped into the "Afshar experiment" while looking for something else, and the Waving Copenhagen Goodbye caught my eye. Does anybody have current knowledge or an expert view on it?

Zz and other views are current enough and covered petty well in the old thread:

https://www.physicsforums.com/showthread.php?t=62460&highlight=Afshar"

Search on afshar under Quantum Forum and you will find a few more.

 

[Farsight]

Duh. Thanks Randall.

 

[rlduncan]

Thank you Farsight. Afshar experiment is the kind of articles I was looking for. Thanks again.

 

[urnchurl]

The concept of wave-particle duality exists even in classical mechanics, look at Hamilton-Jacobi theory (see Goldstein, "Classical Mechanics"). Louis de Broglie exploited this fact to conceive of matter waves, which were already conceived of by Hamilton. However, particle and wave are simply classical conceptions in our imagination taken from nature, that when you talk about the quantum "realm," do not suffice. For particles, we think of a little point or grain of sand, or billiard ball. For waves, we think of an ocean wave or string vibration. But these are merely classical concepts that shouldn't be taken literally in the context of quantum mechanics. An electron or photon is simply a quantum, something we can't visualize, and can't expect to visualize given that we live life in the macroscopic world which already consists of countless quanta, and the very objects, particles and waves, in the macroscopic world that we can visualize are of course made up of quanta. It is meaningless to worry about particle and wave in quantum theory, though in some contexts they may serve as useful tools or approximations. But think about this: the wavefunction in quantum mechanics is a distribution function and does not correspond to an actual wave propagating in space. Unfortunately, when quantum theory was first being developed, physicists at the time were used to thinking in classical terms, and much of the terminology from this has persisted in quantum theory today, which can make it confusing.
See the book "Quantum Mechanics" by Ballentine. I highly recommend this book. By letting go of classical and ultimately superficial notions as wave and particle, quantum mechanics is simple, elegant, and fun.