Wave-Particle Duality Theory: Explaining Electron Properties

[rlduncan]

There seems to be a need for a theory that explains both the particle and wave properties of the electron. Neils Bohr treated the proton and electron as point-charges and successfully calculated the energy levels. He attempted to explain the stability of the h-atom by suggesting the planetary model and circular orbits that do not radiate energy. However, he did not account for the wave properties of the electron. On the other hand, quantum mechanics uses the wave properties to explain hydrogen's spectral lines, yet fails to address the stability of the h-atom or its particle properties. Just my observation. Could some comment on a unified theory incorporating both properties.

 

[ttn]

There seems to be a need for a theory that explains both the particle and wave properties of the electron. Neils Bohr treated the proton and electron as point-charges and successfully calculated the energy levels. He attempted to explain the stability of the h-atom by suggesting the planetary model and circular orbits that do not radiate energy. However, he did not account for the wave properties of the electron. On the other hand, quantum mechanics uses the wave properties to explain hydrogen's spectral lines, yet fails to address the stability of the h-atom or its particle properties. Just my observation. Could some comment on a unified theory incorporating both properties.

J.S. Bell once wrote about the two-slit experiment (where the "dual" nature of the electron is most manifest): "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? DeBroglie showed in detail how the motion of a particle, passing through just one of two holes in the 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 completely ignored."

You can find out more about this "natural and simple" (but unfortunately still largely ignored) theory here:

http://plato.stanford.edu/entries/qm-bohm

 

[Rach3]

QM does describe both wave-like and particle-like behavior of the same particle. Classical descriptions are ultimately insufficient; it will not work to describe an electron as a classical point particle, nor a classical wave. QM is very different.

Neils Bohr treated the proton and electron as point-charges and successfully calculated the energy levels.

So? Schrodinger's wave mechanics can do that also. Keep in mind Bohr's model was the very first of its kind back then, it has many shortcomings - for example, it doesn't know how to deal with two electrons and so it can't get the spectrum of Helium.

On the other hand, quantum mechanics uses the wave properties to explain hydrogen's spectral lines, yet fails to address the stability of the h-atom or its particle properties.

You've got it backwards - QM was the first to succeed in explaining the stability of atoms - it was the earlier, primitive models like Bohr atom which failed at this.

 

[Rach3]

You can find out more about this "natural and simple" (but unfortunately still largely ignored) theory here:

http://plato.stanford.edu/entries/qm-bohm

Why would a new student hasn't even studied QM, be interested in foundational issues like the Bohm interpretation?

 

[DrChinese]

Why would a new student hasn't even studied QM, be interested in foundational issues like the Bohm interpretation?

I thought I was the only one who noticed this. For ttn, oQM is simply "wrong" while Bohmian Mechanics is "right". I wish I could see things in such black and while terms.

 

[masudr]

...wave-particle dilemma...

What dilemma?

 

[rlduncan]

Quantum mechanics does not explain the stability of the ground state electron of the h-atom where it is postulated that the angular momentum is zero. If there is no circular motion why doen't the electron fall into the nucleus of the atom? At least Bohr attempted to expalin the stability of the atom by proposing a dynamic equilibrium between the proton and electron, that is, the planetary model.

 

[masudr]

Have you solved the energy eigenvalue problem for the Hydrogen atom?

There are a number of energy eigenstates that come out; and the state of lowest energy is at -13.6eV. The Rules of Quantum Mechanics don't allow there to be any lower state. Applying the angular momentum operator on that state gives an angular momentum of zero. That perfectly explains everything.

Whoever said anything about circular motion? Does it even make sense to say such a thing? Motion requires position and momentum at every instant to specify it's path. Quantum mechanics prohibits a system being in state of definite position and momentum at the same time, so one's notions of classical motion do not apply to electrons in the H atom.

Bohr's ideas were good for the time, but are a poor model compared to what we have now.

 

[rlduncan]

Yes I have calcuated the eigenstated which are purely mathematical. Where is the connection to the h-atom? In physics you start with a model and then write the mathematics to explain the model. Quantum mechanic avoids explaining the stability of the h-atom based on basic principles of physics. To say circular motion does not make sense or classical physics does not apply is avoiding the physical basis for hydrogen's spectral lines. Are you saying the h-atom is not real and therefore no physical basis is needed?

 

[ZapperZ]

Yes I have calcuated the eigenstated which are purely mathematical. Where is the connection to the h-atom?

Er... look at the energy eigeinvalues that you get. It doesn't match experimental observations?

In physics you start with a model and then write the mathematics to explain the model. Quantum mechanic avoids explaining the stability of the h-atom based on basic principles of physics.

Er... it doesn't?

So what other physics do you wish to invoke to explain the stability of H atom? Classical E&M?

To say circular motion does not make sense or classical physics does not apply is avoiding the physical basis for hydrogen's spectral lines.

I would like to see you use classical physics to "explain" the bonding H-atom makes, or even to derive accurately H-spectra especially when you apply a magnetic field to it. Or what about we stick in the Stark effect? If you can show such derivation that fits the experimental observation, I'll help you write a paper to AJP.

Are you saying the h-atom is not real and therefore no physical basis is needed?

What is a "physical basis"? What can be more physical than when it agrees QUANTITATIVELY with experimental observation?

Zz.

 

[masudr]

When you say electrons have circular motion in the H atom, what you mean is, you have a model of the H atom where the electrons move in circular orbits. From that model, you can extract some consquences, like how much EM radiation will be emitted and the path of the electron as a function of time etc.

When you compare that with reality via experiments, what you find is utter disagreement between the two.

So you come up with another model. In this model, we have operators, and eigenstates, and Schrodinger's equation (among other things), and we call it QM. Using that model, we derive consequences, like there is a ground state, no radiation is emitted unless the electron jumps between energy levels etc. etc.

We now compare this model with the reality, and find good agreement, but not perfect. We refine our model: add the relativistic K.E. correction, account for spin-orbit coupling etc. We get better agreement and so on.

By doing this, we can say that QM provides a better model of reality, at the microscopic scale, than classical mechanics.

Quantum mechanic avoids explaining the stability of the h-atom based on basic principles of physics

What could be more basic than the principles of conservation of energy, momentum and angular momentum?

 

[rlduncan]

Yes the energy eigeinvalues match the experimental values (and yes quantum mechanics agrees quantitatively with experimental observation) but so do the Bohr values. What physics would I use? I would obey the laws and principles of classical physics, Maxwell's equations, and conservation of angular momentum. Predicting the energy levels in itself does not equate to a physical basis. Any complete theory must not simply postulate nonradiating states but supply a physical basis for non-radiating states in an electric field.

 

[Rach3]

What physics would I use? I would obey the laws and principles of classical physics, Maxwell's equations, and conservation of angular momentum.

But nature doesn't obey classical physics and Maxwell's equations, isn't that enough? You've taken a QM course, it should have been obvious throughout.

As for why the 94-year old Bohr model is inferior to actual QM, do we really need to go through this?
-Doesn't explain anything other than spectra of hydrogen-like atoms; fails at helium, everything else
-Cannot explain molecular bonding or any multiatomic physics
-Cannot explain Stark or Zeeman shifts quantitively
-Cannot explain interactions of light (photons) with matter (atoms)
-It doesn't even fit into classical physics - it requires violation of Maxwell's equations by posulating that electrons do not radiate in atoms!

 

[Rach3]

You've got to realize that you're requiring physical law to a priori take a given physical form - classical mechanics and EM - and that is not science.

 

[rlduncan]

Of course the Bohr model fails and as you stated it violates Maxwell's equations. So your conclusion is that the electron can't be explain by classical physics or that classical physics fails. It seems to me the only conclusion is that the Bohr model failed. I am not ready to accept the other. What is not science is a mathematical model incapable of any conceptual model of the h-atom.

 

[Rach3]

Of course the Bohr model fails and as you stated it violates Maxwell's equations. So your conclusion is that the electron can't be explain by classical physics or that classical physics fails. It seems to me the only conclusion is that the Bohr model failed. I am not ready to accept the other. What is not science is a mathematical model incapable of any conceptual model of the h-atom.

By 'conceptual', do you mean anything stronger than "it satisfies everyday physical intutition?" That kind of criterea is quite irrelevant to science.

You need to get acquanited with the fundamental experiments themselves, which convinced half a century of physicsts that classical physics just doesn't work. Famous experiments like
-Stern-Gerlach, non-commuting measurements
-Double-slit interference and all it's variations - including single-photon interference
-Diffraction of massive particles (electrons)
-Aspect's experiment, tests of bell's inequality violation (entangled particles)

 

[masudr]

It was a lucky coincedence that classical physics happened to be a good model of reality for macroscopic systems and and for it to be easy to visualise. But QM never claimed to be both; QM claims to be a good model of reality on the microscopic scale, and that is what it is.

If you object that QM is not easy conceptually, then fine. That's your opinion. But you cannot claim that QM is not a good model of reality on the microscopic scale; for that is what it is.

So, what is your objection? And why, as you have claimed, is QM's model of the H atom not a "conceptual model"?

 

[ZapperZ]

Yes the energy eigeinvalues match the experimental values (and yes quantum mechanics agrees quantitatively with experimental observation) but so do the Bohr values.

But it doesn't! The Bohr model failed when you put that same H atom in a magnetic field, or an electric field! Try it. It's in the DETAILS of the spectrum that shows that the the QM description works.

Besides, what makes you think that you can simply judge the validity of something based on ONE data point? Have we not gone beyond the H-atom already today? Try the Rydberg formula on heavier atoms and see to what extent you get it right and to what extent the results become ridiculously wrong. You are using the ONE instant where the Bohr model somewhat got it right under a certain condition and using it to justify its validity while ignoring a whole zoo of observations where it doesn't even come close. I fail to see the rationality in this.

Zz.

 

[Careful]

**By 'conceptual', do you mean anything stronger than "it satisfies everyday physical intutition?" That kind of criterea is quite irrelevant to science.

You need to get acquanited with the fundamental experiments themselves, which convinced half a century of physicsts that classical physics just doesn't work. Famous experiments like***


-Stern-Gerlach, non-commuting measurements

Wrong: see Barut and Zanghi (1984), Ranada and Ranada (1979), Barut (1986)

-Double-slit interference and all it's variations - including single-photon interference

Wrong: a non-linear classical field theory can account for that (Barut 1984 and next years where soliton like solutions to the self coupled Dirac Maxwell equations were developed).


-Aspect's experiment, tests of bell's inequality violation (entangled particles)

These things could be very well based upon a misunderstanding of QM (and there has never been any violation of the Bell inequalities for the bare data WHEN the former were applicable in the first place !).

Your convincing evidence is already long time refuted.

Careful

 

[rlduncan]

I agree quantum mechanics has provided additional insight to the wave properties of the electron with many applications in other areas. What is important is the wave property. This aspect of the theory is certainly correct. Does that mean the entire theory is correct?

However, what happen to the particle property. If asked to calculate the force on the electron bound to the proton you would you the classical force equation and treat the particles as point-charges. But, when asked to calculate the energy states treating the particles as point-charges with wave motion you say classical physics does not apply. Quantum mechanics claims to completely solve the h-atom based on its wave properties and yet the wave equation, psi, has no physical meaning, and quantum mechanics cannot explain the wave motion of the electron bound to the h-atom. Psi is a complex function and cannot be used to describe a real wave in any kind of orbit (circular or otherwise). I do not claim the Bohr atom is correct, but has some value. There must be a middle ground between the Bohr model and quantum mechanics in which a real wave equation is used to completely solve the h-atom mystery.

 

[ZapperZ]

I agree quantum mechanics has provided additional insight to the wave properties of the electron with many applications in other areas. What is important is the wave property. This aspect of the theory is certainly correct. Does that mean the entire theory is correct?

This is a very unethical way of questioning something. You simply cannot just end with "does that mean the theory is correct" without justification. Where EXACTLY does it fail?

However, what happen to the particle property. If asked to calculate the force on the electron bound to the proton you would you the classical force equation and treat the particles as point-charges. But, when asked to calculate the energy states treating the particles as point-charges with wave motion you say classical physics does not apply. Quantum mechanics claims to completely solve the h-atom based on its wave properties and yet the wave equation, psi, has no physical meaning, and quantum mechanics cannot explain the wave motion of the electron bound to the h-atom. Psi is a complex function and cannot be used to describe a real wave in any kind of orbit (circular or otherwise). I do not claim the Bohr atom is correct, but has some value. There must be a middle ground between the Bohr model and quantum mechanics in which a real wave equation is used to completely solve the h-atom mystery.

But don't you see? You are objecting something based on a matter of TASTE. Physics, especially, cannot be challenged this way. Throughout history, changes to what has been accepted were done only when there's compelling experimental evidence that the prevailing way of describing things didn't work. Period.

Yet, here, you are objecting to things simply because it doesn't sit right with you. Why? Could it be because you have been indoctrinated with the classical picture? You certainly weren't basing your objection on empirical grounds. What this boils down to is a discussion on a favorite color.

Zz.

 

[Careful]

** Throughout history, changes to what has been accepted were done only when there's compelling experimental evidence that the prevailing way of describing things didn't work. Period.**

Really, so how did QM ever got to see the daylight ?? Because Planck, Wien, Boltzmann and others were doing erroneous calculations for the radiation field and made flawed deductions from these ?
PS : do not ask me to write a rebuttal, that has been done by many people already.

Changes in history are accepted because most people prefer a pseudo explanation over the sentence ``it might be that we could account for it, but we cannot calculate it yet''.

In the same way, some people are nagging because in Barut self field, you have to put in the Pauli principle by hand (just as you do in QM ); it is of course entirely reasonable to expect a physicist to deduce it in the eighties while soliton solutions for the self interacting Dirac field were only constructed in the mid-nineties by mathematicians.

Careful

 

[rlduncan]

So now it becomes unethical to question the completeness of a theory. Yes I am questioning a theory simply because it doesn't sit well with me. I believe there is a need for a more complete and even better theory to explain hydrogen's spectral lines. My questions are simple: What is the physcial basis for this event? Why is the h-atom stable? Why don't the excited states radiate energy? What happen to the particle properties of the electron? Can quantum mechanics explain these questions or does it avoid them?

 

[Careful]

So now it becomes unethical to question the completeness of a theory. Yes I am questioning a theory simply because it doesn't sit well with me. I believe there is a need for a more complete and even better theory to explain hydrogen's spectral lines. My questions are simple: What is the physcial basis for this event? Why is the h-atom stable? Why don't the excited states radiate energy? What happen to the particle properties of the electron? Can quantum mechanics explain these questions or does it avoid them?

Euh these questions have been answered (fairly recently); I guess it was Elliott Lieb (an austrian physicist in Princeton) who has devoted 25 years of his life to the study of quantum stability of matter. Highly non trivial and way beyond standard textbook stuff. But I guess you should ask yourself the question how to find a deeper underlying theory to the statistical interpretation of QM.

 

[masudr]

So now it becomes unethical to question the completeness of a theory. Yes I am questioning a theory simply because it doesn't sit well with me. I believe there is a need for a more complete and even better theory to explain hydrogen's spectral lines. My questions are simple: What is the physcial basis for this event? Why is the h-atom stable? Why don't the excited states radiate energy? What happen to the particle properties of the electron? Can quantum mechanics explain these questions or does it avoid them?

(my emphasis)

QM is a model. It can answer all the "whys" that you have asked, and they've been answered above. If QM was wrong, and say electrons did radiate energy, then you could still ask "why?" It would boil down to the validity of Maxwell, but you could still ask "why?"

 

[DrChinese]

QM is a model...

A point worth repeating for the OP: QM is a useful model, as is any good scientific theory. It is nice to hypothesize that there is a better (more useful) model out there yet to be discovered; but at this point it is speculative.

 

[Careful]

***
If QM was wrong, and say electrons did radiate energy, then you could still ask "why?" It would boil down to the validity of Maxwell, but you could still ask "why?" **

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.

 

[Careful]

A point worth repeating for the OP: QM is a useful model, as is any good scientific theory. It is nice to hypothesize that there is a better (more useful) model out there yet to be discovered; but at this point it is speculative.

Euh no, Barut Self field *is* a well developped alternative; it could be BETTER (it would be cool to derive the Pauli exclusion principle on reasonable scales), but it is certainly not worse than QM.

 

[rlduncan]

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 Schrodinger's equation on faith because it is not a derived equation but it works.

 

[ZapperZ]

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 Schrodinger's equation on faith because it is not a derived equation but it works.

But you accept Maxwell equations, don't you? Could you derive, for example, Coulomb's law? Or did you learn it out of a textbook based on it being PHENOMENOLOGICAL?

What about conservation of momentum? Did you DERIVE that too to accept its validity?

Shall I go on?

Zz.

 

[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 Schrodinger'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 adress 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