Lorentz force (atomic)

[swansont]

Quantum means "particle". Quantization is naturally a part of classical physics as in Q1*Q2/r^2 or M1*M2/r^2, Qs and Ms are quanta and classical physics already have them as particles. Quantization is something you need to mess around when you are dealing with statistics and wave functions.

 

Quantum means "discrete," as in "not a continuum. There's nothing inherently discrete in either of those equations — any value of Q or M will do.

[gre]

Right. Not in those equations, but I've seen (apparent) discrete values come out of classical equations wrt ground state hydrogen.

 

How about the following:

 

Magnetic flux of ground state hydrogen:

 

(f * m * (2*pi*r)^2 ) / e or B * (2 * pi * r^2)

 

where, f = 6.57e15 hz , m=electron_rest_mass, r =5.29e-11 m , e = 1.602e-19 C , B = (13.605 eV)/Bohr_Magneton

 

The result is (2 * magnetic_flux_quantum)

Edited February 2, 2009 by gre

[swansont]

The quantum of magnetic moment is not derived from classical theory, though. The Bohr magneton is dependent on Planck's constant, which is the quantum of angular momentum.

[gre]

Does the result make sense, though?

How many magnetic flux quanta exist in the ground state of hydrogen (according to QM)?

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B * (2 * pi * r^2)

 

Seems strange to me .. and would be a (magnetic field strength) * (area of half a sphere). Could this represent the geometry of an electron in a spin up or down state?

[swansont]

Does the result make sense, though?

How many magnetic flux quanta exist in the ground state of hydrogen (according to QM)?

 

Make sense to whom? Nature is under no obligation to be understandable to us.

 

The proton is about 2.8 nuclear magnetons, and the electron is about one Bohr magneton

 

B * (2 * pi * r^2)

 

Seems strange to me .. and would be a (magnetic field strength) * (area of half a sphere). Could this represent the geometry of an electron in a spin up or down state?

 

Where did you get that equation?

[gre]

Make sense to whom? Nature is under no obligation to be understandable to us.

 

I was referring to my assumption that ground state hydrogen contains 2 magnetic flux quanta (particles). Then I was asking .. if that agreed with the standard model / quantum mechanics.

 

 

The proton is about 2.8 nuclear magnetons, and the electron is about one Bohr magneton

 

This is where I'm getting confused. I'm working with magnetic flux measured in webers J/A and magnetic field strength measured in T.

 

The magnetic moment is measured in units J/T. How do you convert the magnetic moment to field strength in Teslas. I'm assuming my previous method is correct?

Where did you get that equation?

 

magnetic flux = field_strength * area

 

So I came up it in an attempt to make geometric sense out of the other equation. I understand this doesn't make it correct, but it seemed to work.

Edited February 3, 2009 by gre

[swansont]

This is where I'm getting confused. I'm working with magnetic flux measured in webers J/A and magnetic field strength measured in T.

 

The magnetic moment is measured in units J/T. How do you convert the magnetic moment to field strength in Teslas. I'm assuming my previous method is correct?

 

On axis, the field will be [math]\frac{\mu_0 \mu}{4\pi r^3}[/math]

 

[math]\frac{\mu_0}{4\pi}[/math] is 10^-7 N/A^2

 

 

magnetic flux = field_strength * area

 

So I came up it in an attempt to make geometric sense out of the other equation. I understand this doesn't make it correct, but it seemed to work.

 

Plugging in terms just to make the units consistent is a quick way to get into trouble

[gre]

 

 

Plugging in terms just to make the units consistent is a quick way to get into trouble

 

Observing that a result could actually be half the area of a sphere * a magnetic field strength, could make sense, I think... no?

 

 

Anyone know the answer to this?

How many magnetic flux quanta exist in the ground state of hydrogen (according to QM)?

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On axis, the field will be [math]\frac{\mu_0 \mu}{4\pi r^3}[/math]

 

[math]\frac{\mu_0}{4\pi}[/math] is 10^-7 N/A^2

 

 

It looks like I replaced the electron mass with relativistic mass of the ground state kinetic energy (13.605 ev)

 

If,

[math]{\mu}[/math] = (( - e / (2 * (( -13.605 eV) / c^2 )) ) * h-bar)

 

The result is 235051 T on the orbital radius.

Edited February 4, 2009 by gre
Consecutive posts merged.

[swansont]

It looks like I replaced the electron mass with relativistic mass of the ground state kinetic energy (13.605 ev)

 

If,

[math]{\mu}[/math] = (( - e / (2 * (( -13.605 eV) / c^2 )) ) * h-bar)

 

The result is 235051 T on the orbital radius.

 

Why would you do this, though? Of what significance is it?

[gre]

Why would you do this, though? Of what significance is it?

 

I don't know. Could it have any significance?

[gre]

If I had to guess. I would assume the kinetic mass-energy of an orbital electron was the actual (massless) wave aspect of the electron.

Edited February 8, 2009 by gre

[swansont]

Momentum, not energy. The deBroglie wavelength is h/p

[gre]

The magnetic moment of the proton is well-known.

 

If you want to try and take the tactic of inferring the magnetic field from the "shell curvature" (by which I assume you mean the Bohr orbit) then you need to reconcile this with the Hyperfine splitting of Hydrogen — the energy difference between the two orientations of the electron magnetic moment in that field — being h * 1420 MHz. (or ~10^-24 J)

 

Since the Bohr magneton is ~ 10^-23 J/T, that implies about 0.1 T

 

 

I think I've tied the hyperfine splitting/structure into this "model".

[gre]

This is probably a flawed view ... But here is what I was thinking/wondering ... Could ground state hydrogen have two different frequencies within its ground state? One that represents the electric field / electron ... and another which represents the magnetic field / magnetic flux quanta.

 

 

The De Broglie ("matter wave") frequency, is one, which can be determined with:

f_matter = (m * v^2) / h = (electron_mass * (a*c)^2) / h

 

f_matter = (9.10938188e-31 kg * (2.1876912640028e6 m/s)^2) / 6.6260689633e-34 = 6.579683785380655e15 hz

 

 

The Zitterbewegung angular frequency, is the second, which can be determined with:

f_zitter = (2*m*c^2) / h-bar

 

using the kinetic mass-energy of hydrogen's ground state:

 

kinetic_mass-energy = ((1/2)*me*(a*c)^2) / c^2 = 2.42543e-35 kg

 

Plug this into the Zitterbewegung equation:

 

f_zitter = (2 * 2.42543e-35 kg * c^2) / hbar = 4.134137e16 rad/sec

 

Convert to hz: 4.134137e16 / (2*pi) = 6.579684741937312436e15 hz

 

Subtract the De Broglie frequency from the trembling frequency:

f_zitter - f_matter = 6.579684741937312436e15 - 6.57968378538066519742e15 = 9.565564e8 Hz

 

Which is (2/3) of the hydrogen 21-cm line frequency of 1.42040575e9 Hz

(3/2) * 9.565564e8 Hz = 1.42e9 Hz

Strange?

Edited February 14, 2009 by gre

[swansont]

Strange?

 

Numerology

[dclush]

Llewellyn Thomas, at the dawn of modern quantum theory, delved into the classical electrodynamics of a point charge electron with spin. Thomas found that there was nothing interesting going on in terms of quantization of atomic orbits, but through this analysis he famously accounted for the "anomalous" factor of a half in the Zeeman effect. This is all in his 1927 paper that is cited in Jackson. Thomas was only a graduate student at the time, and his paper was submitted on his behalf by Niels Bohr.

 

It turns out though that Thomas's conclusion about secular angular momentum conservation would not be considered supported by modern electrodynamics that includes the "hidden momentum" of a magnetic dipole in an electric field. When I do what he did based on the force on a magnetic dipole in the Jackson third edition (not the same as the previous editions!) I get the opposite result of what he got. He got that the secular total angular momentum is a constant of the motion independent of the details of the orbit and the relative orientations of the electron axis and the orbital normal. I get that it cannot be a constant of the motion unless the spin axis and the orbit normal are parallel.

 

It is interesting, however, that one can equate the spin and orbit precession frequencies, in the modern quasiclassical model, only for orbits with angular momentum equal to h-bar. In Thomas's analysis they equate for all orbits regardless of angular momentum or energy. They must equate in order for the total angular momentum to be constant. It turns out, though, that in spite of that they equate only for orbits with angular momentum of h-bar, the total angular momentum is still not constant.

 

This is a very interesting situation, seems to me.

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Now that I've had time to review the thread more carefully I want to make a few more comments.

 

I think that the detailed electrodynamics of a point-charge atomic model with intrinsic spin have yet to be explored very carefully, and yet are very promising to yield new insight into quantum behavior. I can talk further about exactly how much they have been explored later if anyone is interested as I have spent quite a lot of time over the last year and more looking into just that (and I have access to both American Journal of Physics and American Physical Society online archives, as well as to arxiv.org, of course). For now I want to argue for why this is a more interesting dynamic than seems to be getting recognized upthread.

 

First, there is a hardly-explored dynamic due to the motion of the electron intrinsic magnetic moment. Even in s states, the electron has an expected speed that is quite high and this will induce an electrical force on the nucleus. There is also a back-force on the electron (although it is not easy to see where it comes from!) and so with these the classical atom with spin is a little oscillator that already wants to be unstable, apart from classical radiative decay. In fact, it wants to fly apart and if you start studying this dynamic the question that arises is why doesn't it fly apart, not why doesn't it decay. I guess radiation reaction will actually stop it from flying apart, ultimately, but it is a much richer dynamic than the usual classical hydrogen atom electron spiraling in due to radiation reaction. The forces due to the motion of the electron magnetic moment, in, say, hydrogen in the ground state of the Bohr model, are much larger than the radiation reaction force due to electric dipole radiation in the circular orbit, about a million times stronger if I recall.

 

The second reason this dynamic is particularly interesting is that the equations of motion that result come with Planck's constant attached due to it being associated with the intrinsic spin. So, Planck's constant is not intrdoduced ad hoc as it is in conventional quantum theory, it comes in simply as a property of the particles, no more (or less!) interesting than that there is a fundamental charge. This is a truly beautiful idea seems to me and it puzzled me for a while after I first had it that it seemed to never have occurred to anyone else. Then eventually I discovered that David Hestenes has been writing about this since at least the early 1970s. But he did not ever try to directly address the electrodynamics in the way that I have been attmepting. What he has done though with it is truly very remarkable and I have to suspect that most of the participants on this thread are not aware of his work nor that of Jayme De Luca or C. K. Raju, or certain others that are working on this from a rigorous electrodynamcs point of view.

 

My "electrodynamics", where I treat the spin as a fundamental property of particles, is merely an ad hoc electrodynamics, since there are only point charges in Maxwell/Lorentz/Dirac (classical) electrodynamics. For this reason it may have been overlooked by mainstream physics. But it seems to have something to contribute, I think, because it is much easier to work with than full rigorous electrodynamics of point charges where at close range delay cannot be neglected. It seems that the existence of spin itself emerges from point-charge electrodynamics including delay and the self-force. (It may seem paradoxical, but at close range, delay effects become more important, not less. This is why the full electrodynamic two-body problem has yet to be solved.)

[dclush]

I want to volunteer what is my current conjecture of how a quasiclassical atomic model could handle the issue of hyperfine splitting where it's clear that the electron has to spend some time within the nucleus in the ground s state, whereas in a Bohr model the electron in the ground state orbit will never be near there, being always separated by many electron Compton wavelengths. I'm going to get there in a somewhat roundabout way, though.

 

I started doing this hydrogen atom modeling using classical electrodynamics about 10 years ago, just for fun and to use some physics and electrodynamics skills that were certainly atrophying. For the first 5 or more years, I was only working with spinless and so nonmagnetic point-charge electron and proton, with the usual masses, and working out the dynamics including the delay effects, which was the motivating idea behind the project. It seemed based on something I read at the time that perhaps quantum behavior could arise due to delay, and I suspected (wrongly, it turns out) that nobody had tried recently to do this sort of thing. This part of the story I will skip although there are some very interesting things to say about whether delay could possibly cause quantum behavior. (I concluded at that time that it couldn't, and I had what I thought was a good reason, but I also was probably entirely wrong. Here for example is somebody who argues explicitly (in a paper published in Foundations of Physics) that delay does have something to do with the origin of quantum behavior http://arxiv.org/abs/quant-ph/0511235).

 

Anyhow so I concluded that I wasn't going to get anywhere with my approach to assessing the effects of delay (which was primarily computational using Fortran and the Lienard-Wiechert retarded fields, interacting the particles along their world lines and searching to past by one delay, etc etc) and decided to try incorporating the intrinsic magnetic moments. I could see this added a lot of richness to the dynamics although it was not all that clear of how to add this into the electrodynamics and I was kind of surprised nothing like how to do it was in Jackson or any of my other old textbooks. I mostly ended up not worrying the delay part of it and just treated the problem as delayless but with the intrinsic magnetic moment of the electron doing some very interesting things. (Something I wrote about this a couple of years ago is posted here: http://home.comcast.net/~d.lush/Basis_of_Atomic_Stability.pdf . There are some things not quite right about that paper, but the basic idea of it seems to hold up, but what I didn't know then that I know now is about the "hidden" momentum of a magnetic dipole and so how to make the system conserve linear momentum. Please don't critique this paper too much - I already probably know the issues with it and I will supply other stuff of mine to critique that is more current and applicable to the current discussion. But that paper shows how a moving magnetic dipole can push around a charged particle. Also it was sent to Physical Review E but they weren't interested and I haven't pursued it further to date because I found a bigger fish to fry.)

 

So then the next thing I want to mention is that in my mind I have been working in the context of a Rutherfordian atomic model not that of Bohr. My project was not based on imposing any quantum principle, rather I was hoping to see one emerge. But then I realized in working with the spin the dynamics was already including Planck's constant, how nice. Also I was not generally restricting my analysis to circular orbits, although I usually did either consider them initially or run them initially in my computer models, just because they are much simpler than nonrelativistic ellipses, let alone a full relativistic treatment where there is a precession of the orbit perihelion in its plane. So it was a remarkable result when I discovered about two and a half years ago that when one equates the spin and orbit precession frequencies in the point-charges-with-spin hydrogen model, assuming a circular orbit, one obtains that there is a unique radius where this occurs, and it is the Bohr radius. (This is intimately related to the existence of the Thomas precession, BTW.)

 

The motivation I had for equating the spin and orbit precession frequencies was that it seemed to me that this would be a necessary condition for conservation of angular momentum. I wasn't aware at that time that Thomas in his 1927 paper had shown that angular momentum would be conserved in the presence of Thomas precession, generally. (The Thomas paper can be found online on this excellent site: http://home.tiscali.nl/physis/HistoricPaper/Historic%20Papers.html) So this is a good motivation at least for equating the spin and orbit precession frequencies but it turned out that even after equating them I did not get that the (secular) angular momentum is conserved. This has tormented me for two years now but I had an insight last night that maybe can put this whole issue to rest, maybe I will get to it in this post but if not ask me later if anyone is interested.

 

So then, this is the situation I found myself in that I wasn't really looking to do it, but I had found a quasiclassical physics justification for the Bohr model. Also although I started out with a motivation for equating the precession frequencies, on closer examination there seems to be no good motivation after all. Apart from the lack of defensible motivation, as everyone even including myself at that time and certainly all the more so now, the Bohr model only works to give a rough model of hydrogenic spectra. It doesn't agree with quantum theory or experiment (I don't doubt although I couldn't say off hand what are the experiments) for angular momentum. Yet I continued (and continue) to think that getting the Bohr radius this way is not merely a coincidence. It seems very compelling how it works out. Trying to come up with a way to accommodate both the Bohr model with L=hbar in the ground state and the quantum mechanical model, I came up with the model at the end of this paper http://arxiv.org/abs/0709.0319, where the orbit precesses such that the long-term average orbital angular momentum is zero. This model (in version 3 only) is wrong in so many obvious way and I suspect it may have no real significance, but it at least does motivate equating spin and orbit precession frequencies and yield quantized orbits, albeit at totally wrong energies.

 

Then this past year three separate good things (from my point of view) have happened related to this anda two of them were handed to me on a silver platter. The first was discovery of the Joy Christian attack on Bell's theorem. This does not affect me directly because I never let it stop me trying to build a local deterministic model to complete quantum theory, but it is nice to be able to point at Christian's work to be able to claim the matter's not fully settled. The second thing though is the point of this whole post which is the work of Manfred Bucher rehabilitating the Sommerfeld theory so that it can agree with Schroedinger quantum theory for H and the H2 ion, in terms of having L=0 in the ground state and in other ways as he describes. Here is a recent paper by him and these have been published in EJP I think: http://arxiv.org/abs/0802.1366.

 

So, my answer to how such a quasiclassical model could handle that L=0 in the ground state and the hyperfine splitting is that it is getting at the Sommerfeld model as redefined by Bucher, not the Bohr model. Bucher has also directly addressed the issue of the hyperfine splitting, although I am not sure the cite right now but can probably find it later.

 

It turns out too that equating spin and orbit precession frequencies without the assumption of orbit circularity obtains orbital angular momentum equal to hbar, I have worked it out and will try to publish it pretty soon, after I finish my paper about the Thomas 1927 paper. That was the third thing to fall my way this past year since putting my arxiv paper up. It turns out as I explained in the OP that Thomas's paper at least no longer holds up. This leads to some very paradoxical outcomes. It turns out, the strange motion of the total angular momentum as used to be shown in quantum theory textbooks (e.g. in Eisberg and Resnick) where the total angular momentum precesses in spite of no external torque, is simpy a feature of this quasiclassical system when Thomas precession is not negligible.

 

I'll have to leave further explanation of this to later but I hope this will kindle someone's interest. Thanks for reading, either way.

[dclush]

I want to mention, in case anybody is looking at my arxiv paper, it might be advisable to hold off for a few days as I am about to replace it with a new one. I'll post a new link when it's up.

 

I managed for the first time to make my model work, in the sense of obtaining stationary total angular momentum, without having to invoke a second particle spin. I had missed previously what I found today, that the angular velocity of the total angular momentum (total here being electron spin and orbital) vanishes for the circular orbit only at the Bohr radius. This I feel is excellent because it was not coming out convincingly with the proton spin as in v3, because the proton intrinsic magnetic moment is too weak, and for other reasons as well. This has prompted a fast rewrite that is almost done. The new version is only half is long as the last, will drop the whole second half, as it is no longer needed. It will make a lot more sense although it will still seem pretty far-fetched to most physicists, I guess. But no matter it is for posterity. I hope to post it NLT next weekend, maybe as soon as tomorrow if all goes well.

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There is a new version of my paper now available here:

 

http://arxiv.org/abs/0709.0319

 

I think this version is a big improvement over the last. I plan to refine it some more and I have something already done I want to add, and then I will probably resubmit it to Foundations of Physics. I sent them version one, which (I realize now) had some really bad problems, but they did send it out for review and one out of the two reviews was quite favorable. The other reviewer was even not totally opposed to publication (he said) but said he could not recommend and apparently the editor agreed. That was a year and a half ago and the new version works much better than the previous three, so I am willing to try them again. What the heck it's not like they are going to come break my legs for sending them too many versions of the same paper (I hope). After that I am not sure where to send it next, if they reject. I would take advice. Physical Review does not take this kind of stuff, I am pretty sure. Maybe Annals of Physics and after that the DeBroglie Foundation. Anyhow I am just happy to be able to put it up on arXiv and that way when people finally come around to realizing that quantum theory is not a fundamental theory it will be clear who figured out what when.

[gre]

How exactly is this information related to the topic? (I haven't had a chance to read it all yet, but I'm curious). You might want to start a new thread.

 

 

Greg

[dclush]

Greg, I may have read more into the OP than is really there but I thought it raised a good question of whether there is richer dynamics in the classical atom than is generally recognized. You mentioned the Bohr magneton which is of course the magnetic moment of an electron and so if you consider (as is sometimes done in textbook treatments of the spin orbit interaction) things in the reference frame where the electron is at rest, the proton is moving through the magnetic field of the electron. It turns out that the Lorentz force is a covariant quantity and so it has to have meaning in every reference frame, and there is a tangible Lorentz force on the proton in the electron rest frame that includes a nonzero v cross B force in addition to the Coulomb force. You asked if this could possibly have something to do with establishing the energy levels of the atom. I believe the dynamics of this process is in fact ultimately responsible for establishing the energy levels of the atom, and also the work I have been doing as a hobby project I think goes some ways towards indicating this may be the case. At the least I think I've uncovered that there're interesting things going on that ought to be worth pursuing further. Also it does appear that nobody has studied this carefully previously from this point of view, other than Thomas, who did so prior to the update of the textbooks to account for hidden momentum, which is critical to this issue.

 

I posted on this thread for you, Greg. I thought you might appreciate the answer to your question. It would be nice if others were interested but I'm not surprised that they aren't. I don't think I will start a separate thread here about my stuff, if no one is willing to express even the slightest interest. I have some going other places. There is remarkably little interest in this among the ostensibly physics-literate, however, generally. I think they are missing out on a great opportunity for easy discovery of something very important. When I first discovered that one could obtain the Bohr radius from the existence of spin, I was very proud and I thought many many physicists would be interested. Silly me.

[gre]

I posted on this thread for you, Greg. I thought you might appreciate the answer to your question. It would be nice if others were interested but I'm not surprised that they aren't. I don't think I will start a separate thread here about my stuff, if no one is willing to express even the slightest interest. I have some going other places. There is remarkably little interest in this among the ostensibly physics-literate, however, generally. I think they are missing out on a great opportunity for easy discovery of something very important. When I first discovered that one could obtain the Bohr radius from the existence of spin, I was very proud and I thought many many physicists would be interested. Silly me.

 

Dave,

 

Thanks for posting. It is hard to find a forum where people are open to discussing new ideas, and theoretical concepts. From what I've seen, physicists don't see value in finding a classical-like representation of Quantum physics.

 

In my previous "what if" posts in this thread, In a nutshell I was curious if there is a magnetic-type force (Lorentz, maybe) which dictates the energy levels, shape, size, and maybe 0 point energy, of an atom.. perhaps an "internal" magnetic force which is not seen (completely) from an outside reference frame, like quark charge... In my calculations this might be shown mathematically w/o any rigor .. But it is still probably just speculation or not possible (which would explain the little feedback) ... Most of my calculations also involve numerology, which is pretty much an immediate turn off to most physicists.

 

 

What I'm curious about now: What would have to be shown to mathematically to get interest in these concepts? Would an alternative perceptive be useful?

Edited March 30, 2009 by gre

[swansont]

It is hard to find a forum where people are open to discussing new ideas, and theoretical concepts. From what I've seen, physicists don't see any value in finding a classical-like representation of Quantum physics.

 

I think that physicists don't see value in physics that doesn't hold at the scales under scrutiny. The deviations from classical physics at the atomic scale are well-documented. It's a tough sell to ask someone to read a bunch of papers to play "find the flaw"

 

After you've done it a few times, you find that a large fraction of "players" don't actually respond well to the critiques.