Lorentz and Poincare

[sol invictus]

I think Raju provides links and quotes to what Atiyah wrote.

Nope, not that I could find. The link he gives is to an article written by two other people describing a public lecture Atiyah gave in commemoration of Einstein. In that lecture he spent a few minutes speculating on what the next revolution in physics might be. From the account it's extremely vague, but the idea is that physics might have to abandon the notion the conditions at one time suffice to determine the future. That would mean no more locality in time - in other words, instead of differential equations with finite order, differential equations of infinite order, or finite difference equations, or functional differential equations.

At that level of vagueness that's a very old idea that's been explored in many arenas probably for centuries. It's certainly not unique to Raju, and to accuse Atiyah of plagiarism on the basis that he mentioned functional differential equations applied to physics is utterly ridiculous - it's about as clear a sign of insane crackpottery as you could ask for.

 

[Eggs Ackley]

It does, unless I'm completely misunderstanding it.

Look - one solution to the classical equations is an electron orbiting in a would-be perfect circle, radiating, and therefore spiraling in. There are also elliptical orbits (or rather orbits that would be ellipses if it weren't for the radiation). This guy claims that there are two modes of perturbations to the circular orbit where the electron oscillates or wiggles back and forth around the circular trajectory by exchanging radiation with the proton, that those two modes have slightly different frequencies, and that when you put everything together, you can find one particular solution where the radiation all cancels (a claim I suspect isn't even correct, for the reasons above, but let's go on).

This solution obviously isn't general, because it works (according to him) only because the two modes beat against each other (which he says they happen to do at just the correct frequency) - which means each mode must have to have precisely the correct amplitude to cancel the radiation from the circular acceleration (because for example if the amplitude is zero, there's no cancellation).

So at best there's ONE solution (or perhaps a one-parameter family), and you have to require - by hand - that you only consider those (a la Bohr). What happens when you perturb that solution? The system radiates. And it can lower its energy arbitrarily by the electron spiraling in closer to the proton - and so it will do so.

Thanks for the more detailed explanation. That one I can take your meaning from.

I should probably just leave it until I have time to look the paper over, but my understanding of it is that one supposes a circular orbit and then searches over all orbit radii and then finds at certain radii there are resonances such that the system becomes nonradiative. That there are unique orbits that can be nonradiative seems significant and important to me and all the more so if they just happen to be close to multiples of h-bar in angular momentum.

I don't think he intends to claim the issue of stability is not important and I think it is too much to expect that one guy develop an entire new theory in one paper. What is there seems significant in its own right and prior to that paper I think no one had any quantitative basis for saying there could be nonradiative orbits let alone close to the right ones although as I mention I think Hestenes suggested something similar maybe 15 years ago.

De Luca's newer paper on arxiv, which is mostly far beyond my ability to follow it, seems to get at stability issues more directly.

 

[Eggs Ackley]

Nope, not that I could find. The link he gives is to an article written by two other people describing a public lecture Atiyah gave in commemoration of Einstein. In that lecture he spent a few minutes speculating on what the next revolution in physics might be. From the account it's extremely vague, but the idea is that physics might have to abandon the notion the conditions at one time suffice to determine the future. That would mean no more locality in time - in other words, instead of differential equations with finite order, differential equations of infinite order, or finite difference equations, or functional differential equations.

At that level of vagueness that's a very old idea that's been explored in many arenas probably for centuries. It's certainly not unique to Raju, and to accuse Atiyah of plagiarism on the basis that he mentioned functional differential equations applied to physics is utterly ridiculous - it's about as clear a sign of insane crackpottery as you could ask for.

All I know about it is what I read on Raju's site and on wikipedia (and on the discussion pages not just the articles (Raju's and Atiyah's)).

Without taking a position about whether it is well-justified or not, I am not sure either that it is a worthwhile exercise on Raju's part to attack Atiyah. The one who gets remembered is the one who builds the working theory, not the one who speculates something might be possible. I only mentioned it because I think it's interesting if a well respected mathematician like Atiyah is arguing this same case as Raju that quantum physics is really just classical physics done with proper accounting of delay. I was taking Raju's interpretation of Atiyah's words at face value, I suppose, and it's possible that's not what Atiyah meant at all, I also suppose. Me I'm already convinced there's more classical basis for quantum behavior than is heretofore generally recognized, so it's not much concern to me if Atiyah didn't mean what Raju says or thinks he does.

In this and all cases however I will strive to judge Raju's (or anyone's) arguments on their own individual merits, and not on his position on issues not directly related. I think there are probably lots of examples of people doing perfectly good science while holding views that are questionable on their face. And I still tend to think that Raju might at least have a fair point in that Atiyah should cite him and acknowledge his prior work. It's true this is based on taking Raju's interpretation and chronology as correct, so if that were refuted I would no longer be sympathetic to Raju.

 

[sol invictus]

I should probably just leave it until I have time to look the paper over, but my understanding of it is that one supposes a circular orbit and then searches over all orbit radii and then finds at certain radii there are resonances such that the system becomes nonradiative.

Yeah, I think that's more or less the idea - but it's not just the radius, you also need precisely the right amplitude for these extra oscillations. And as I said, it's completely impossible for such a solution to be stable, because for any finite radius there always exist solutions to classical EM with lower energy and vastly greater entropy.

That there are unique orbits that can be nonradiative seems significant and important to me and all the more so if they just happen to be close to multiples of h-bar in angular momentum.

If true, I agree it's mildly interesting. But I strongly suspect it's not.

I don't think he intends to claim the issue of stability is not important and I think it is too much to expect that one guy develop an entire new theory in one paper.

Sure - he doesn't have to develop the entire theory. But he does have to argue convincingly that further work might yield something interesting. Considering the fundamental and obvious problems I've raised after a few minutes consideration - which he never even mentions, other than mumbling something about not addressing "Lyapunov stability" - he utterly fails to do so.

De Luca's newer paper on arxiv, which is mostly far beyond my ability to follow it, seems to get at stability issues more directly.

I looked through his arxiv papers. I don't see anything that addresses the issue.

 

[sol invictus]

I only mentioned it because I think it's interesting if a well respected mathematician like Atiyah is arguing this same case as Raju that quantum physics is really just classical physics done with proper accounting of delay.

According to Raju's link - the article about Atiyah's lecture - Atiyah didn't say anything even remotely close to that. What's your source?

I was taking Raju's interpretation of Atiyah's words at face value, I suppose, and it's possible that's not what Atiyah meant at all, I also suppose.

If your only source is Raju, I'd be veeeeeery cautious about giving it any credence.

 

[Perpetual Student]

I will say, however, that Einstein deserves all the credit he gets in a general sense. Not specifically for SR, but he made so many contributions to physics, way beyond SR and GR.

No doubt! I do a great deal of recreational reading about science and the history of science (especially physics). The more I explore, the more I am struck by Einstein's breadth and his profound contributions. Newton is probably the only figure in history who may have made greater contributions to physics.

 

[Eggs Ackley]

I looked through his arxiv papers. I don't see anything that addresses the issue.

It was this bit from the abstract of the latest one:

http://arxiv.org/abs/0901.1077

"We prove that our functional has a local minimum at circular orbits of large enough radii, at variance with the limiting Kepler action that has a minimum at circular orbits of arbitrary radii."

I take this to mean that unlike the Kepler action, orbits under the WF action with delay can't decay below some radius.

 

[sol invictus]

It was this bit from the abstract of the latest one:

http://arxiv.org/abs/0901.1077

"We prove that our functional has a local minimum at circular orbits of large enough radii, at variance with the limiting Kepler action that has a minimum at circular orbits of arbitrary radii."

I take this to mean that unlike the Kepler action, orbits under the WF action with delay can't decay below some radius.

It means almost precisely the opposite, as is clear from the very next sentence: "Our results suggest a bifurcation at some O(1) radius below which the circular orbits become saddle-point extrema."

In other words, the circular orbits are stable to perturbative (small) fluctuations above some radius (a claim I'm very dubious of, by the way), but below that size they are unstable. And even above the radius, those orbits cannot be better than meta-stable - which isn't good enough (the ground state has to be absolutely stable).

 

[Eggs Ackley]

It means almost precisely the opposite, as is clear from the very next sentence: "Our results suggest a bifurcation at some O(1) radius below which the circular orbits become saddle-point extrema."

In other words, the circular orbits are stable to perturbative (small) fluctuations above some radius (a claim I'm very dubious of, by the way), but below that size they are unstable. And even above the radius, those orbits cannot be better than meta-stable - which isn't good enough (the ground state has to be absolutely stable).

I can see you are right. I guess I was reading it optimistically. But it does at least appear that the paper is getting at the issue of stability, and reporting the situation as the analysis obtains.

I don't recall a clear answer on whether you now would agree that Planck's constant is not put in by hand in the De Luca 2006 PRE paper. Seems like since you agreed with my basic interpretation, and if all orbits are checked equally for the resonance, and it pops up only for L multiples of h-bar, then that is not putting it in by hand. I continue to think that is a great achievement if not in error. I wouldn't fault anyone for doubting it, but it seems more than mildly interesting if true, to me. And that it's in Physical Review ought to mean something. What is more mainstream than that?

Now I want to return to the question of the stability of circular orbits. It turns out that in this objective of obtaining a stable non-radiative dynamics from relativistic classical ED but respecting delay, the motions to be expected are not close to circular orbits, in any case. Rather, they are close to the Sommerfeld ellipses and in the rehabilitated Sommerfeld model by Bucher, circular orbits are disallowed to make room for the "Coulomb oscillator" states that have L=0. With this modification, the Bucher-Sommerfeld model matches modern quantum theory perfectly as far as it will go. That is, unlike the Bohr model or the original Sommerfeld model, it has the proper (i.e., none at all) angular momentum in the ground state, and it can also give the proper hyperfine splitting, even. This one cannot get with a circular orbit because as you know the electron has to spend some time in the nucleus. Here is the place to start:

http://arxiv.org/abs/0802.1366

When I discovered Bucher's work I realized it was just exactly what is needed to make it plausible to make a quasiclassical atomic model that reproduces quantum mechanics. So since then I have been trying to develop quasiclassical physical bases for the three Sommerfeld quantum rules. One of them I have quantitatively, although it is still not well motivated, in that equality of the spin and orbit mutual precession frequencies only occurs for L = h-bar. When I first found this I was doing circular orbits (they're easier!) and so got the Bohr radius, but since reading Bucher I did the elliptical orbit case and found that it is really the angular momentum that is constrained by this. There is no basis for assuming the orbit is circular based on this alone.

A couple of years ago though when I was still trying to get a stable circular orbit, and I actually did find a way to cancel the decay (not that it would be stable necessarily). There is a force that can cancel the radiative decay force, believe it or don't, if you consider the motion of the electron intrinsic magnetic moment and the resulting non-Coulomb electric field at the proton, and what happens to that due to propagation delay, and if the spin is aligned properly relative to the orbit, this force will counter the radiation reaction exactly in a circular orbit of radius equal to 9/16 of the Bohr radius.

I got that result about two years ago and I wrote this paper that I have never put on arxiv because it over reaches mightly in its original form:

http://home.comcast.net/~d.lush/Basis_of_Atomic_Stability.pdf

There are other things wrong with it including that I didn't know about the "hidden momentum" then, which obtains an equal and opposite reaction on the electron, and also the magnetic electron acquires relativistically an electric dipole moment which has to be included as well. But it turns out when these are included it is still true that if the spin is pointed correctly relative to the sense of the orbit then there is a nonradial force that exactly cancels the radiation reaction at 9/16ths of a Bohr radius.

It is a strange thing it's true because it doesn't stop the atom from radiating, so it doesn't sit well with energy conservation. So I don't believe it is a real thing, but rather that it shows the wrongness of doing electrodynamics in a non-time-symmetric fashion. If you include the advanced action as in Wheeler-Feynman ED it is cancelled out. But I think it is still interesting because it shows there is a powerful added dynamic due to motion of the electron with its magnetic moment, that is so much stronger (about a million times) than the radiation reaction that its nonradial component due to delay is the same size as the radiation reaction, at just about the right scale to be interesting. This is something that so far as I have been about to tell, hardly anybody has looked at before me, except Alfred Schild, who considered a semiclassical dynamical model in 1963 where he gave the electron a magnetic moment and also assumed a time-symmetric electrodynamics, explicitly.

I am wondering about the Russians, though. I think I mentioned on the other thread that I read a translated Malykin review article about Thomas precession and that he cites a Bagrov monograph where it is claimed Thomas precession never causes radiation. I had been thinking it had to but then I calculated the magnetic dipole radiation intensity in the Thomas model where I am getting the total angular momentum moves and so thought it had to radiate, but it doesn't. I couldn't post the link to my paper where this is done previously but now I can: http://arxiv.org/find/grp_physics/1/au:+lush/0/1/0/all/0/1 (that is to both my arxiv papers). When I got that result I got pretty excited and put the update up in about 10 hours, so fast that I overlooked putting in a reference to Malykin but I will fix that with the next update. His review paper was very helpful and has over 250 references in it. I would like to know if that Bagrov monograph he refers to has any commonality with my paper on Thomas's paper.

 

[sol invictus]

I don't recall a clear answer on whether you now would agree that Planck's constant is not put in by hand in the De Luca 2006 PRE paper.

It is put in by hand. Even if it's true that there are some special orbits that don't radiate, there is no physical reason to focus on them and disallow all others. So if for some random reason you insist that only those orbits are allowed - whatever that actually means - you've put the quantization in by hand, just as Bohr did.

And as I said, I'm very skeptical of the claim that these orbits emit no radiation. The method looks simply invalid, although I haven't studied it closely enough to be sure.

 

[sol invictus]

Look - there's a very simple way to think about this. Quantum mechanics tells us that ALL angular momenta are quantized in units of Planck's constant. That's an incredibly general and profound statement, and it's one which really cannot be reproduced by classical physics. To see that, one only needs to think about dimensional analysis.

Consider the hydrogen atom. Using CGS units, the only quantities entering the classical equations for it are e^2 (e is the electron/proton charge), c (the speed of light), and the masses of the electron and proton. That's it.

Now, QM tells us there's a minimum orbital angular momentum gap for this system. If that minimum is going to come out of classical physics, it has to be some combination of those constants. The only combination with the correct units is e^2/c multiplied by any function of the ratio of the masses. It turns out that Planck's constant h is very roughly (1/2)(m_p)/(m_e)e^2/c. So suppose you managed to produce that combination (or a more accurate one) from classical physics, AND that you managed to argue that for some reason that combination should be the minimum angular momentum difference allowed in any transition. Then you'd have to reproduce the correct spectrum for all the rest of the states, the right selection rules, decay rates, etc. etc. etc. That's a very tall order.

But you wouldn't be done - far from it, because you'd have to do the same for helium, for individual electrons, for photons, for gluons.... but all of those systems have different masses, different charges, etc. So for each system, a completely DIFFERENT combination of those parameters would have to emerge from your classical equations - a combination that, in every case, precisely equals Planck's constant, and which you could argue represented the quantization of the angular momentum.

And in many cases - photons are an excellent example - there is NO combination of the parameters that appear in classical physics that even has the dimensions and angular momentum. How are you going to argue that there's a minimum quantum of angular momentum in electromagnetic radiation, when there's no constant with dimensions of mass appearing in any of the classical equations for it? It's literally impossible.

 

[orange31]

the media simplifies it all to mostly one person, AE.
But most library biographies/histories give detailed credit, etc to the others.

Here's a link to this general issue given as a Nobel Prize speech a few years ago by David Politzer


http://www.theory.caltech.edu/~politzer/NOBEL_LECTURE.pdf

 

[Eggs Ackley]

It is put in by hand. Even if it's true that there are some special orbits that don't radiate, there is no physical reason to focus on them and disallow all others. So if for some random reason you insist that only those orbits are allowed - whatever that actually means - you've put the quantization in by hand, just as Bohr did.

And as I said, I'm very skeptical of the claim that these orbits emit no radiation. The method looks simply invalid, although I haven't studied it closely enough to be sure.

I don't see how you can maintain De Luca puts in Planck's constant by hand. What you say after your claim that he does is no support for that it's true. I understand that being nonradiative is not alone a substitute for quantum theory but it's not insignificant. It is a physical reason to focus on them, and it distinguishes them from other, radiative, orbits in a very significant fashion. It remains to be seen whether they are stable or local energy minima or whatever criteria they would have to satisfy in addition to being nonradiative in order to reproduce quantum mechanics, but that does not obviate the significance they have in their own right by virtue of being nonradiative.

When Bohr puts in Planck's constant by hand, there is no doubt about it. He says, ok let's assume that allowed orbits must have angular momentum in multiples of h-bar. Sommerfeld does the same thing separately with the azimuthal and radial actions. These have no resemblence to what De Luca does unless you can find where h or h-bar are introduced.

De Luca's contention is clearly that it is not to be considered put in by hand, as evidenced in this bit from page 11: "(ii) The angular momenta of the resonant orbits turn out to be approximate integer multiples of Planck’s constant." (emphasis added)

If you want to argue it is no more interesting than your formula, which I have seen previously BTW, then I could understand that a lot better. However I would argue here that while I don't fault you for being skeptical of the significance or accuracy of the finding, if correct it is more significant than that formula because the condition of being nonradiative is much more obviously connected to the problem of stable atoms than such a formula which is thrown together without any justification or physical basis. It is hardly surprising one can write a formula for Planck's constant to within 7%, when you can choose from many available physical constants and put in whatever exponents and multiplies or divides you like. That is vastly different than working a really complicated dynamical problem and having it exhibit this feature of nonradiativeness (which is remarkable to begin with, if correct) at approximate multiples of h-bar.

I don't see that De Luca is claiming only these orbits are allowed, and I don't think I said that either. It's fair enough to say that for the whole thing to pan out they would have to be stable or metastable, but identifying a new mechanism for nonradiativeness where for 100 years it has been claimed in every physics textbook that the classical atom simply must radiate in every orbit continues to astonish me on its own. That it happens in multiples of about h-bar is simply icing on the cake.

 

[sol invictus]

When Bohr puts in Planck's constant by hand, there is no doubt about it. He says, ok let's assume that allowed orbits must have angular momentum in multiples of h-bar.

"OK, let's assume the allowed orbits are these non-radiative ones, even though they're unstable and all the other orbits are allowed by classical physics". See what I mean?

But I agree that it would be interesting if it works the way he claims. But I don't think it does.

I don't see that De Luca is claiming only these orbits are allowed, and I don't think I said that either.

Then the theory is wrong.

It's fair enough to say that for the whole thing to pan out they would have to be stable or metastable,

Why would that make it "pan out"? In QM no other values for the angular momentum are allowed, period. It's impossible to have other values. There is nothing in between. In this theory that cannot possibly be the case - not unless you put something in by hand.

but identifying a new mechanism for nonradiativeness where for 100 years it has been claimed in every physics textbook that the classical atom simply must radiate in every orbit continues to astonish me on its own.

If it were true, it would be quite surprising. But I'd be willing to bet it's not.

Now tell me - how are you going to argue that the electromagnetic field in vacuum must have quantized momentum? The only parameter in the theory is c - so it's impossible to even construct something with dimensions of angular momentum.

 

[Eggs Ackley]

"OK, let's assume the allowed orbits are these non-radiative ones, even though they're unstable and all the other orbits are allowed by classical physics". See what I mean?.

That seems a strawman argument to me. There's a big difference between an implication that these orbits may somehow be stable or related to stable ones, and a claim that they are. That they are nonradiative (if so) marks them of interest for further investigation.

Anyhow the classical physics you're referring to is a fiction. The kind of motions you get from the Kepler problem don't apply to the properly-formulated (i.e. with delay, self-force, and radiation reaction) two-body electrodynamic problem of point charges. The two-body electrodynamic problem is unsolved and so the detailed nature of its solutions remains unknown.

But I agree that it would be interesting if it works the way he claims. But I don't think it does.

That's nice that we can agree on at least this. And again, I don't fault you for holding your opinion, and frankly I don't hold a strong opinion it has to be right, or feel half qualified to judge, but this is a paper in a prestigious journal. At the least it is not crackpotism as you stated initially.

Then the theory is wrong.

I hope you don't think it is right or wrong based on somebody's (especially my) claims about it. If you mean, it must be wrong if these orbits are not the only allowed ones, then I disagree. I don't know what is De Luca's concept, but in mine circular orbits are disallowed, generally. I'm happy to have the circular orbit decay radiatively due to dipole radiation. I just can't have it go all the way to the nucleus. If we quantize the angular momentum, but give up the Bohr assumption of circular orbits, then orbital energy is no longer quantized. There is a continuum of energy for each alllowed angular momentum. When the circular orbit assumption of the Bohr model is replaced by Sommerfeld's quantization of the radial action, then atomic energy quantization is recovered. I already have an observation from my model with spin about why orbital angular momentum of h-bar is unique: only then is the total mechanical angular momentum a constant of the motion. This also doesn't say why it would be stable dynamically but it's interesting enough to make me want to try to find a dynamical reason it would be. Both De Luca's and my model have a lot of dynamics beyond the Kepler model, that hasn't been explored yet. I think they'd be worthy of exploration in their own right, regardless, but I certainly wouldn't be doing it as an amateur but for the fact that it has already yielded such an interesting connection to quantum theory. And in my model, I get not only exactly h-bar, I get that the total L must be exactly h-bar, not just the electron part. That is, I get the proper reduced-mass Bohr radius. This is fully in accord with observation, and I don't have to put in the reduced mass by hand as is done in quantum theory.

Why would that make it "pan out"? In QM no other values for the angular momentum are allowed, period. It's impossible to have other values. There is nothing in between. In this theory that cannot possibly be the case - not unless you put something in by hand..

I didn't say it would make it pan out. I said in order to pan out that condition would need to be met. I do know how quantum theory works pretty well at least that much. I know that position and momentum wavefunctions are a Fourier transform pair and how this enforces the uncertainty relation. But that's quantum theory not what I'm doing. In either what I'm doing or De Luca is doing particles have definite position and momentum and angular momentum of any values. Also this is true in David Hestenes' Zitterbewegung interpretation of quantum mechanics. That's what I like about it. No wave-particle duality, no strange action-at-distance, or other quantum woo.

If it were true, it would be quite surprising. But I'd be willing to bet it's not..

There's no need for you especially or even me to bet anything on it. You can sit back and do nothing and other people will do the work. I'm spending a lot of time on it but I enjoy it so it's its own reward for me. It's a fun and rewarding hobby for me. Seems like it must be more of a wager for a professional physicist like De Luca, though.

Now tell me - how are you going to argue that the electromagnetic field in vacuum must have quantized momentum? The only parameter in the theory is c - so it's impossible to even construct something with dimensions of angular momentum.

I suspect I'm never going to argue the former. The necessity of it is not obvious to me. Just because one theory is successful doesn't mean no other theory can be. Where's the theorem that says QED is the unique and fundamental theory that can describe nature? Anyhow I think there are some interpretations of quantum mechanics that are taken fairly seriously by some serious people, that don't admit of second quantization. Bohmian mechanics, in particular, I'm thinking but not that sure. It doesn't matter much to me because I don't think the Bohm interpretation is right, either. I am pretty sure though that what I'm doing is incompatible with the existence of the photon as a real entity as opposed to a mathematical convenience. I also think, there need be no ultraviolet catastrophe absent the photon, if the oscillators in the walls of the cavity are quantized. Einstein said that I think in about 1905.

I don't understand the second part of your statement. Certainly EM fields can carry angular momentum, quantized or not. Its density is just r cross (E cross B), right? I mentioned earlier, I have written out the field angular momentum expression in my model very recently to try to see if it balances the mechanical angular momentum nonconservation. It looks too complicated to evaluate analytically except in the far field (but I need it everywhere) and so today at lunch I was looking at it thinking seriously of numerically integrating it.

 

[sol invictus]

If you mean, it must be wrong if these orbits are not the only allowed ones, then I disagree. I don't know what is De Luca's concept, but in mine circular orbits are disallowed, generally. I'm happy to have the circular orbit decay radiatively due to dipole radiation. I just can't have it go all the way to the nucleus. If we quantize the angular momentum, but give up the Bohr assumption of circular orbits, then orbital energy is no longer quantized.
There is a continuum of energy for each alllowed angular momentum.

But orbital energy for hydrogen IS quantized. Haven't you ever heard of emission lines? You can't just find a model in which there's a stable state and declare victory - you have to find one that agrees with experiment.

I'm not sure you appreciate the strength of the experimental support for this stuff. It's massive, because it applies to every area of atomic or nuclear physics, astrophysics, condensed matter, particle physics - essentially the entire field. Which means a large fraction of all the experiments done in the last century are tests of quantum effects like quantization of hydrogen energy levels.

So if in your model, or de Luca's model, or anyone else's model a hydrogen atom at rest can emit or absorb a photon with energy other than one of the values allowed by QM, your model is dead. But any classical model will be able to do so.

I don't understand the second part of your statement. Certainly EM fields can carry angular momentum, quantized or not. Its density is just r cross (E cross B), right?

Yes, of course - but you're not getting the point. According to experiment and QM, the angular momentum carried by an EM pulse is quantized in integer multiples of Planck's constant (I'm talking about the intrinsic angular momentum of a photon). That quantum of angular momentum should come out of the theory. In the case of hydrogen, the problem has enough parameters that one can construct a quantity with the correct dimensions. But in the case of pure EM, the only quantity at hand is c. r cross E cross B doesn't help - what are r, E, and B? If there's a fundamental quantum that applies always, it must have an expression in terms of the parameters - not in terms of the value of E on some specific solution.

 

[Eggs Ackley]

But orbital energy for hydrogen IS quantized. Haven't you ever heard of emission lines? You can't just find a model in which there's a stable state and declare victory - you have to find one that agrees with experiment.

I'm not sure you appreciate the strength of the experimental support for this stuff. It's massive, because it applies to every area of atomic or nuclear physics, astrophysics, condensed matter, particle physics - essentially the entire field. Which means a large fraction of all the experiments done in the last century are tests of quantum effects like quantization of hydrogen energy levels.

So if in your model, or de Luca's model, or anyone else's model a hydrogen atom at rest can emit or absorb a photon with energy other than one of the values allowed by QM, your model is dead. But any classical model will be able to do so.

There's a lot more to that paragraph but maybe it wasn't very transparent. All I was saying is that if you quantize orbital angular momentum you haven't quantized the energy; you need a second rule to get quantized energy. In Bohr's model it is an unmotivated assumption of orbit circularity, while in the Sommerfeld model it is the quantization of the radial action. As is well known and especially by me, the Bohr model does not match experiment in terms of angular momentum allowed, but it is only known to people who have read Bucher that the Sommerfeld model can admit of a hierarchy that matches. Specifically, with Bucher's reinterpretation it has orbital angular momentum of zero in the ground state and other s states. To accommodate these states it is necessary to disallow the circular orbits. Bucher doesn't really have a good reason for disallowing them, but they are already disallowed by radiative decay, classically, as you know.

The Bucher-Sommerfeld model is the one that I am trying to obtain and it definitely only allows the proper energy and angular momentum values and (as I said) even gives the hyperfine splitting properly.

To get this in my approach I need a dynamical justification through the existence of the spin, of Sommerfeld's quantization of the radial action. That is what I am working on. There are several dynamical effects due to motion of the electron with an intrinsic magnetic moment, that are maybe a million times weaker than the Coulomb force, but that is still very strong compared to the radiative reaction due to acceleration of the charge. It seems entirely plausible to me that quantization of the radial action in multiples of the electron spin magnitude could fall out as a stabiltity condition, along with the orbital angular momementum quantization.

The circular orbits are different than the elliptical ones in that there is a force component due to the moving magnetic moment that vanishes in the case of orbit circularity. I think this force component can do something to cancel out the other components that make the circular orbit unstable. These are all stronger than the radiation reaction force due to acceleration of the charge.

For the De Luca model I was hypothesizing between the lines that he will also have to abandon circular orbits for ellipses in order to find stable ones. If you had a stability requirement that was equivalent to the Sommerfeld quantization of the radial action, plus nonradiativity in multiples of h-bar, you would have a pretty good model right there because presumably if you have nonradiativity at only L= n * h-bar then you have to have some kind of radiative decay process in the other orbits.

Yes, of course - but you're not getting the point. According to experiment and QM, the angular momentum carried by an EM pulse is quantized in integer multiples of Planck's constant (I'm talking about the intrinsic angular momentum of a photon). That quantum of angular momentum should come out of the theory. In the case of hydrogen, the problem has enough parameters that one can construct a quantity with the correct dimensions. But in the case of pure EM, the only quantity at hand is c. r cross E cross B doesn't help - what are r, E, and B? If there's a fundamental quantum that applies always, it must have an expression in terms of the parameters - not in terms of the value of E on some specific solution.

I was responding to what you said, not what you meant, apparently. You said it couldn't have angular momentum and I guess we agree that is not ture. If you mean I have to get quantization of the EM field then I understand what you mean but I do not agree with it. I remain unconvinced that the photon is other than a mathematical convenience. If the atoms can only emit and absorb radiation in multiples of h-bar, then it seems to me (and some other people) that the idea of the photon is superfluous. As I mentioned it isn't needed to explain the blackbody spectrum and avoid the ultraviolet catastrophe. The trickier bit is photoemission, of course. I don't have an explanation for that without a photon but I haven't worked on it yet. I don't let not having an explanation for everything stop me from working on other bits of the problem. I work on things that are interesting that I think I can do that I think shouldn't be possible according to conventional wisdom like yours. There shouldn't be a direct link between the existence of spin and quantization of orbital angular momentum if quantum theory is fundamental, seems to me. Since there is one I'm curious of what its implications are. I thought maybe some other people might be interested as well.

 

[sol invictus]

I was responding to what you said, not what you meant, apparently. You said it couldn't have angular momentum and I guess we agree that is not ture.

I said nothing of the kind. I said "The only parameter in the theory is c - so it's impossible to even construct something with dimensions of angular momentum." I didn't add "out of the parameters of the theory" because it was obvious, particularly given the context - we'd just been discussing the case of the hydrogen atom, where you can do so.

If you mean I have to get quantization of the EM field then I understand what you mean but I do not agree with it. I remain unconvinced that the photon is other than a mathematical convenience. If the atoms can only emit and absorb radiation in multiples of h-bar, then it seems to me (and some other people) that the idea of the photon is superfluous.

But it's not only atoms that are important here. It's individual particles, like electrons - which themselves carry quantized spin angular momentum. And it's neutral particles like neutrinos and gluons, which also carry spin but no charge, so that once again it's impossible to construct such a quantity from the parameters in the theory describing them alone.

As I mentioned it isn't needed to explain the blackbody spectrum and avoid the ultraviolet catastrophe.

I actually don't think that's true. For one thing photons can interact more or less directly with other photons in various ways. What's to stop those interactions from thermally populating high frequency modes?

There shouldn't be a direct link between the existence of spin and quantization of orbital angular momentum if quantum theory is fundamental, seems to me. Since there is one I'm curious of what its implications are. I thought maybe some other people might be interested as well.

That's completely untrue. In standard quantum theory there's a profound and very well understood connection between spin and quantization of orbital angular momentum. They both follow from the same group theory; the same fundamental symmetries of nature.

 

[lenny]

hi all,

I really don't know - I almost never read anything written by historians of science, nor do I know the history itself particularly well.

i am always surprised when you say this sol, even as your offhand remarks bring it into question. einstein and poincare both cared a great deal about the meaning of the symbols their maths were manipulating, and to trace the meaning you need to see the history. i owe my interests here to bertrand russell, who you may again dismiss as a philosopher, but feynmann used to say similar things; wheeler was explicit.

but, to get back on topic, if the importance of relativity had been so obvious at the time, then it is seems likely that someone would have pointed out how einstein's approach built upon others; i expect this was clear to those who cared about relativity at the time: is it not clear in his original papers? regardless, no one was willing to risk awarding a nobel prise on this novel stuff. even in 1921, the award was "especially for the photoelectric effect". it was einstein's insight and beliefs that were fundamental to his contributions, to quote the Nobel site "He had a strategy of his own and was able to visualize the main stages on the way to his goal." http://nobelprize.org/nobel_prizes/physics/laureates/1921/einstein-bio.html

 

[Darwin123]

I was responding to what you said, not what you meant, apparently. You said it couldn't have angular momentum and I guess we agree that is not ture. If you mean I have to get quantization of the EM field then I understand what you mean but I do not agree with it. I remain unconvinced that the photon is other than a mathematical convenience.

By 'mathematical convenience' you mean abstraction, right? The whole field of physics consists of describing physical phenomena in terms of abstractions. I don't think there is any analysis in physics that is not an abstraction.

Even when visualizes something in classical physics, one ends up using an abstraction.

Take heat flow, where by heat I mean enthalpy. You do know that heat flow is an abstraction, right? I recently found out that enthalpy under isobaric conditions is a passive scalar. Passive scalar means that something that acts 'like' a fluid. Is enthalpy represented as a fluid fluid any less physical than a fluid made of molecules?

Maybe you are dissatisfied at the abstract representation that makes a photon into a 'particle'. Well, you have a right to be dissatisfied. There are other representations that are mathematical con

I read a bit about field theory. I saw a theorem somewhere showing that the idea of a particle-wave duality is equivalent to a quantized amplitude of the wave.

Photons can be represented as a particle, as Einstein showed. However, it could also be represented as a 'wave' with a discontinuous amplitude. Second quantization can be visualized by saying that the electromagnetic wave has a constraint so that the amplitude of the wave is restricted to discrete values.

This type of constraint can make low intensity light waves bunch up into wave packets. The energy gets concentrated by the quantization constraint.

Unfortunately, this is not a classical assumption. Classical physics does not allow amplitude to be quantized. So quantum mechanics will still be anti intuitive if you talk about 'quantized amplitude' rather than 'wave-particle duality'. However, you may be slightly more satisfied with 'quantized amplitude' than with 'wave particle duality'. I think the mathematical expressions of the two representations vary just by the basis used to expand solutions. I have found that 'quantized amplitude' sometimes is far more convenient mathematically than 'wave-particle duality'.

Is one any more real than the other? I doubt it !-)