tag:blogger.com,1999:blog-6461076876392084102017-07-15T11:25:38.931-07:00The Quantum SkepticQuantum Skeptichttp://www.blogger.com/profile/17540964211124616979noreply@blogger.comBlogger63125tag:blogger.com,1999:blog-646107687639208410.post-52800913615863267972017-07-15T11:25:00.000-07:002017-07-15T11:25:38.955-07:00My photon paper is publicly viewableI extracted from my longer paper on arxiv all the parts about the massive composite photon, and how it leads to a correction to the Planck-Einstein relation and explains the spin-orbit coupling anomaly without invoking Thomas precession, and put it together into a short paper. I submitted the paper to Foundations of Physics a couple of days ago. Now I have posted it on Researchgate: <a href="https://www.researchgate.net/publication/318440358_Composite_Photon_Energy-Frequency_Relation" target="_blank">Composite Photon Energy-Frequency Relation</a>.Quantum Skeptichttp://www.blogger.com/profile/17540964211124616979noreply@blogger.com0tag:blogger.com,1999:blog-646107687639208410.post-59282237285195666682017-06-25T15:52:00.001-07:002017-06-25T23:06:19.707-07:00One Photon Does Not Make a Standing Wave I have finally figured out how to reconcile the composite massive photon model, that gives E equals h nu over 2, with the Planck-Einstein law, E equals h nu. It's a very simple reconcilation that requires no modification of Planck's blackbody spectrum, or of the value of the Planck constant h.<br><br>When Einstein realized that quantization of light explained the photoelectric effect, he assumed that the light quanta carried energy in accordance with Planck's assumption that the standing wave electromagnetic modes inside a cavity had energy quantized as integer multiples of h nu, where h is as found by Planck (and to within a few percent by Planck himself). However, a photon must necessarily carry momentum E/c, where c is the speed of light, while electromagnetic standing waves in a cavity and at therrmodynamic equilibrium cannot possess net linear momentum. Therefore the quantized energy value of a standing wave mode in multiples of h nu and the number of photons in the cavity at frequency nu cannot be directly equated. Rather, since a standing wave can be regarded as a superposition of two oppositely-traveling waves of equal amplitude, the expected number of photons is twice the number of energy multiples of h nu. This is in agreement, to within all measurements of the speed of light to date, with the frequency-to-energy relationship for the composite photon, which is easily derivable based on the relativistic Doppler effect.<br><br>After having thought about the possible ways that a photon of half the currently-accepted energy can be reconciled with established physics, if at all, this seems best to me. In particular, it does not require revision of the value of h, which would lead to changes in the size of atoms (as far as I can see), in addition to many other problems. On the other hand, retaining the Planck blackbody spectrum while reducing the photon energy by half, and retaining that the angular momentum of a photon is h-bar=h/(2 pi), requires only an energy recalibration. To begin with energy levels on emission spectra can be divided by two. This leads immediately to a resolution of the spin-orbit coupling anomaly that does not need to invoke the Thomas precession. It is also straightforward to modify the Schroedinger equation to be in agreement with the photon carrying half the energy. <br><br>A new version of my paper is slated to appear at midnight GMT tonight, that will reflect my new point of view. It will be version 7 here: <a href="https://arxiv.org/abs/1609.04446" target="_blank">https://arxiv.org/abs/1609.04446</a><br><br><br><a href="http://quantumskeptic.blogspot.com/2017/06/one-photon-does-not-standing-wave-make.html#more">Read more »</a>Quantum Skeptichttp://www.blogger.com/profile/17540964211124616979noreply@blogger.com0tag:blogger.com,1999:blog-646107687639208410.post-86567293894450690172017-05-23T23:00:00.000-07:002017-05-24T22:42:27.729-07:00A possible alternative explanation for the spin-orbit coupling anomalyI've been considering my hypothesis that Planck's constant is really twice the accepted value, based on that the photon energy is related to its frequency by half the accepted amount, for the composite photon, as I proposed two posts ago. The hypothesis fails in an obvious way. Since it implies the electron g-factor is actually unity, it is inconsistent with the Zeeman effect, where it is essential that the electron g-factor be (close to) two, in order to agree with observation.<br /><br />I now have an alternative hypothesis about the photon energy being half the accepted amount in relation to its frequency. That hypothesis is that it explains the spin-orbit coupling anomaly as well or better than the Thomas precession does, while also not otherwise differing noticeably from observation.<br /><br />If the photon energy for a given atomic transition is half that currently assigned (that is, if the current energy assigned is twice the correct value), then the measure of the spin-orbit coupling energy from emission spectra will appear to be doubled as well. So, correcting the transition energy to be half the accepted value will recover the spin-orbit coupling energy consistent with the original prediction. There will be no need to apply the Thomas factor of one-half in order to find agreement with observation. <br /><br />As I think I have stated previously, and various people have been pointing out for many decades, it makes no sense that the Thomas precession, a purely kinematical effect, can alter the interaction energy. <br /><br />Halving the energy per photon has another consequence of halving the expected magnitude of the Zeeman effect generally. I'm not sure if this would be noticeable or not.<br /><br /><br /><br /><br />Quantum Skeptichttp://www.blogger.com/profile/17540964211124616979noreply@blogger.com0tag:blogger.com,1999:blog-646107687639208410.post-73714437497978362092017-03-11T13:14:00.000-08:002017-03-11T13:14:33.026-08:00More extensions to my paper on ArXivThis version (v5) obtains that the modulating factor on the inverse-square radial magnetic force between equal mass and parallel-spin zitter particles satisfies the three-dimensional time-dependent Schroedinger equation, except that hbar multiplying the partial derivative with respect to time is replaced by hbar/2. This equation implies an angular momentum spectrum in terms of integer multiples of hbar, but an energy spectrum in terms of integer multiples of hbar/2. This is consistent both with the energy per photon as derived in the same paper for a composite photon to be h/2 times the photon frequency, and so that the accepted value of Planck's constant (h) is only half the correct value. This also implies that the electron g-factor is approximately unity, rather than approximately 2 as currently thought.<br /><br /><a href="https://arxiv.org/abs/1609.04446v5" target="_blank">Spin-Spin Interaction as Quantum Phase Measurement and the Mechanism of Atom Formation</a><br /><br />Next I will go over everything in it again and try to shorten it, and then submit it to a journal. Since Foundations of Physics published my earlier paper from which this one derives, I plan to submit there.<br /><br />There is much more I would like to do on it, in particular to try to derive the same result using Hamilton-Jacobi theory, but I have no idea if I can succeed at that or how long it might take, so I think it is a good enough time to submit. I hope at least they will review it. Quantum Skeptichttp://www.blogger.com/profile/17540964211124616979noreply@blogger.com0tag:blogger.com,1999:blog-646107687639208410.post-22671636294909762042017-01-12T21:10:00.000-08:002017-05-23T21:54:30.143-07:00Why the electron g-factor is 2It's because the generally accepted value of Planck's constant is only half the correct value.<br /><br />The quantity h-bar in the Schroedinger equation is actually h-bar/2. That's because it represents the spin of the electron, not of the photon, as implicitly assumed by de Broglie and carried forward by Schroedinger, and everyone else.<br /><br />This fact has been overlooked because it was not recognized that the photon frequency is related to its energy not as E = h nu, but as E = h nu /(1 + v_l/c), where c is the limiting velocity of relativity theory, and v_l is the velocity of the photon, which is only very slightly less than c. <br /><br />Although I derived that the energy of a composite photon is half the accepted value several months ago, and posted it about here previously, I didn't realize the implications until a few days ago, when I realized that the modulating factor on the Coulomb-like magnetic force between zitter particles satisfies the Schroedinger equation for a free particle in one spatial dimension. Except, the hbar must be replaced by hbar/2. This makes the energy difference between atomic energy levels half as large as previously thought, consistent with the photon energy being half the accepted value. However, simply replacing the hbar in the SE by hbar/2 leads obviously also to an angular momentum spectrum in multiples of hbar/2 rather than hbar. This cannot be, and the photon energy being hbar/2 can only be correct if, in addition to hbar being twice the currently-accepted value, hbar remains the quantum unit of angular momentum. So, the form of the SE has to change from its current form. <br /><br />The modulation factor that I derived is equivalent to the Schroedinger wavefunction in one dimension, but not in three dimensions. There is a preferred dimension defined by the null four-displacement between the zitter particles. It is essentially the relativistic Doppler effect along the radial direction that gives rise to the modulating factor that can be equated with the de Broglie wave if hbar is replaced by hbar/2. (De Broglie was reasoning by analogy with the photon without knowing of the intrinsic angular momentum difference of the electron. Had he known of the difference, he would have expected the hbar/2.) In the cross-radial direction, though, the modulation goes over to a de Broglie wavelength (rather than half it for radial motion), as I showed in my FOOP paper. So it seems plausible that the Schroedinger-like equation based on the magnetic force modulation could lead to an energy spectrum in terms of multiples of hbar/2 but an angular momentum spectrum that agrees with observation, but that is work to do at the moment.<br /><br />Sorry there are some typos I'll fix in the next revision. Current is v4: <a href="https://arxiv.org/abs/1609.04446" target="_blank">https://arxiv.org/abs/1609.04446</a><br /> <br /><br /> Quantum Skeptichttp://www.blogger.com/profile/17540964211124616979noreply@blogger.com0tag:blogger.com,1999:blog-646107687639208410.post-69408462141316967212016-11-05T10:25:00.000-07:002016-11-18T21:02:46.846-08:00Full Version of My New Paper on ArXivThis is the complete sequel to my previously published paper in Foundations of Physics. The first two versions on arxiv only concerned the similarities of time-symmetric zitterbewegung radiation to the de Broglie wave. The new version (v3) continues on, and at least triples the length.<br /><br /><a href="https://arxiv.org/abs/1609.04446" target="_blank">https://arxiv.org/abs/1609.04446</a><br /><br /><br />I still plan to rewrite the abstract and add some bits to the introduction, and generally go over all of the narrative and citations, and then submit it to Foundations of Physics, hopefully within the next few weeks.<br /><br />The new version incorporates all of the extensions of my previous paper that were posted on arxiv as new versions beyond what was in Found Phys. I will therefore soon be updating that paper on arxiv as well, reverting to the published version with corrections. I posted that previously as v11 (v10 is the version in Found Phys, except for formatting). v12 is extended and has some considerable material that is now in the paper linked above. When I post v13, it will be the corrected version that was v11, but I will add the erratum I have written but not yet posted or provided to Foundations of Physics. I plan to submit the erratum and the new paper to Foundations of Physics at about the same time, although as separate submittals. Here is to the latest:<br /><br /><br /><a href="https://arxiv.org/abs/1409.8271" target="_blank">https://arxiv.org/abs/1409.8271</a><br /><br /><br />Quantum Skeptichttp://www.blogger.com/profile/17540964211124616979noreply@blogger.com0tag:blogger.com,1999:blog-646107687639208410.post-31763342663838020572016-09-10T18:32:00.000-07:002016-09-10T18:32:15.288-07:00My new paper is publicly viewable<div>I have just uploaded it to arxiv, so it won't be public there for a few days. But I anticipate they may flag it and question me about my lack of an institution, as they did with my previous paper (although they approved it eventually), so I have also uploaded it already to Researchgate. It's linkable here:</div><div><br /></div><a href="https://www.researchgate.net/publication/307970519_Similarity_of_the_de_Broglie_matter_wave_to_the_Doppler-shifted_time-symmetric_electromagnetic_field_of_a_Dirac_particle" target="_blank">Similarity_of_the_de_Broglie_matter_wave_to_the_Doppler-shifted_time-symmetric_electromagnetic_field_of_a_Dirac_particle</a><div><br /></div><div>I will be looking it over and very likely making some tweaks in the next day or so, since it won't get posted to arxiv until probably Tuesday midnight GMT at the earliest.</div><div><br /></div><div>It's still a bit rough but I've been eager to post something since about a week ago when I was successful in obtaining the de Broglie wave correct superluminal phase velocity, as well as the correct group velocity and wavelength.</div><div><br /></div><div>It is actually the beginning of a longer paper I've been writing as a sequel to my previous paper, that was published in Foundations of Physics. Figuring this new bit out has changed my understanding (for the better I believe) and so I now want to revise the rest of it to reflect the better understanding. Then I will replace the current version with the expanded version, and I plan to submit the full version to Found. Phys. Also, I made an erratum to offer them. But the (full version of the) new paper notes the problem (as mentioned in previous blogger posts and already fixed on the arxiv version) in any case. </div><div><br /><br /></div>Quantum Skeptichttp://www.blogger.com/profile/17540964211124616979noreply@blogger.com0tag:blogger.com,1999:blog-646107687639208410.post-32906328833399648462016-05-16T21:24:00.000-07:002016-06-04T09:38:31.035-07:00An extended version of my paper deriving the de Broglie wavelength<br />In the last week or so I believe I've made real progress in understanding the meaning of my finding the de Broglie wavelength associated with the modulation of the magnetic force between zitter particles; that is, particles consisting point charges going in Compton-wavelength diameter circles at the speed of light.<br /><br />The version of my paper published by Foundations of Physics obtained the de Broglie wavelength only in the low velocity limit, as a modulation of the magnetic force acting on a moving zitter particle due to another stationary zitter particle. I've known since last fall that it's possible to associate the modulation of the magnetic force on a stationary particle due to a moving field-source zitter particle with half the de Broglie wavelength, in the limit of large velocity. But, it seemed strange because the force isn't acting on the particle that is moving, and so can be associated with the de Broglie wavelength.<br /><br />The de Broglie wavelength had mostly unexpectedly appeared in the middle of a re-write I was doing trying to respond to reviewer comments, and I was then unfamiliar with the details of de Broglie's reasoning. In particular, I wasn't aware he published a note about it in the journal Comtes Rendus, prior to his different derivation in his PhD thesis. In his Comtes Rendus note de Broglie hypothesizes that particles of matter have an internal frequency that he obtains by combining the Plank-Einstein law with the Einstein mass-energy equivalency E=mc^2. This way of thinking seemed more representative of the situation of the moving field-source zitter particle, in that (as has been pointed out by Hestenes) the zitterwebegung frequency is twice the frequency de Broglie frequency. <br /><br />De Broglie was troubled that a stationary observer sees the internal motion of a moving particle as slowed down due to relativistic time dilation, which is opposite to the behavior of photons according to the Planck-Einstein relation (where the frequency increases proportionally to the energy), but he was able to show how the time dilation causes a modulation of the moving particle internal phase with a wavelength that decreases with particle energy consistent with the Planck-Einstein relation. But, this argument was apparently not entirely compelling, and by the time of his PhD thesis he replaced it with a more direct analogy with the photon wavelength, that didn't refer to a particle hypothetical internal oscillation. However, I had that if the particle has an internal charge motion, then the frequency of the resulting electromagnetic field would be seen to be shifted similarly to Planck-Einstein, due simply to the relativistic Doppler shift. Then I started to wonder if the relativistic doppler shift could also provide a basis for the Planck-Einstein formula. I was thinking of the preon model of the photon as a bound state of a + and a - preon, with the preons circulating at the zitterbewegung frequency, with a non-zero but very small rest mass, such that when photons have measurable energy their speed is indistinguishable from c.<br /><br />When I wrote out the zitterbewegung frequency for the massive photon, I realized I'd accounted for the seemingly-extraneous factor of a half in my modulation wavelength compared to de Broglie's: it comes directly from the electron intrinsic spin compared to the photon's. De Broglie reasoned by analogy from the photon to the electron. Since the electron intrinsic angular momentum wasn't appreciated in 1923 (let alone the zitterwebegung), he couldn't have taken it into account in his generalization of wave character from the photon to matter. But it needs to be, and so my factor of a half isn't extraneous at all. <br /><br />As for reproducing the Planck-Einstein relation as the relativistic Doppler shifted signal from the massive photon, it comes close. Instead of E = h nu, it obtains E = (h nu)/(1 + beta), where beta is the photon velocity divided by c. So, it predicts essentially half as much energy per photon, and a very slight deviation from linear proportionality between energy and frequency of light, compared to Planck-Einstein.<br /><br />Here's the new version on arxiv: <a href="http://arxiv.org/abs/1409.8271v12" target="_blank">http://arxiv.org/abs/1409.8271v12</a><br /><br /><br /> <script> (function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){ (i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o), m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m) })(window,document,'script','https://www.google-analytics.com/analytics.js','ga'); ga('create', 'UA-52589872-1', 'auto'); ga('send', 'pageview'); </script> Quantum Skeptichttp://www.blogger.com/profile/17540964211124616979noreply@blogger.com0tag:blogger.com,1999:blog-646107687639208410.post-40011333187717513302016-03-13T18:07:00.001-07:002016-06-04T09:39:45.451-07:00More on the relationship between the de Broglie wavelength and the Zitterbewegung <br>In my recent paper, and in <a href="http://quantumskeptic.blogspot.com/2016/02/a-short-description-of-how.html" target="_blank">my previous post</a>, I failed to point out that my derivation of the de Broglie wavelength only holds up in the limit of small relative velocities. In fact it is pretty easy to see that the quantity I identified as the de Broglie wavelength is actually different from it by a factor of (<i>L</i>+1)/2, where <i>L</i> here is the Lorentz factor, i.e., <i>L</i> = (1 - (<i>v</i>/<i>c</i>)^2)^(-1/2), where <i>v</i> is the relative velocity and <i>c</i> is the speed of light. So, while for <i>v</i> << <i>c</i> the quantity I obtained is very close to the de Broglie wavelength, it diverges from it significantly as <i>v</i> approaches <i>c</i>. Specifically, while for <i>v </i>approaching <i>c</i> the de Broglie wavelength approaches zero, the quantity I identified with the de Broglie wavelength approaches a finite limit of <i>h</i>/2<i>mc</i>, where h is the Planck constant and <i>m</i> is the particle mass.<br><br>I will put a new version on arxiv, to be more precise about the relationship of the Zitterbewegung-derived magnetic force to the de Broglie wavelength. I will try to keep the changes to a minimum. The current arxiv version is now at 10, so when it becomes 11 it will be the update. It may take a few weeks yet to get it posted.<br><br>I want to mention as well that I'm working on determining if perhaps the zitterbewegung can be connected with the de Broglie wavelength in a stronger fashion than I've found so far. In fact when I initially related the two I found a slightly different relationship that had an additional term, as evident in Eq. (50) of <a href="http://arxiv.org/abs/1409.8271v8" target="_blank">arxiv version 8</a>. The term with the square brackets of Eq. (50), for pure radial relative motion, leads to a modulation of the magnetic force that is exactly equal to twice the de Broglie wavelength, for all values of relative velocity. In spite of being off by a factor of two, that seems a better relationship than one that's correct only in the limit of small velocity. <br><br>The expression for (twice) the de Broglie wavelength as follows from Eq, (50) of arxiv v8 is obtainable only in the time-symmetric electrodynamics picture. When I originally evaluated the time-symmetric magnetic interaction, I was working in the rest frame of the particle (consisting of a relativistically-circulating point charge) being acted on by the magnetic force caused by the magnetic field of another similar particle (the field-source particle), for which the center of the charge circular motion is uniformly translating relative to the center of charge motion of the particle being acted on (i.e., the test particle). In the case of the radially-moving source particle, the time-retarded distance differs from the time-advanced distance, and this difference in interparticle separation leads to the modulation with twice the de Broglie wavelength. There is a problem with this approach however in that it violates the assumption I made in deriving the magnetic field that the field-source particle center of charge motion is stationary. I could have corrected this by Lorentz-transforming the electromagnetic field to the test particle rest frame, but I didn't want to do this, apart from that I was trying to meet the FOOP (Foundations of Physics) deadline, because it seemed a needless and confusing departure from the original approach of the analysis, which followed Rivas, all being done in the rest frame of the field-source particle. So prior to my final re-submission to FOOP, I revised the calculation to be, like the rest of the paper, for the rest frame of the source particle. Performing this calculation caused me a lot of consternation.<br><br><br><a href="http://quantumskeptic.blogspot.com/2016/03/more-on-relationship-between-de-broglie.html#more">Read more »</a>Quantum Skeptichttp://www.blogger.com/profile/17540964211124616979noreply@blogger.com0tag:blogger.com,1999:blog-646107687639208410.post-18059737037535737982016-02-20T20:25:00.000-08:002016-06-04T09:38:19.048-07:00A Short Description of How the Zitterbewegung is Related to the De Broglie WavelengthSchroedinger described the rapid oscillation of the electron electric dipole moment and velocity in the Dirac theory as "zitterwebegung," or jitter motion. In his 1930 paper he gave the zitterbewegung frequency as 2 <i>m c</i>^2 / <i>h</i>. Here, <i>m</i> is the electron mass, <i>c</i> is the speed of light and <i>h</i> is the Planck constant.<br /><br />The zitterbewegung frequency <i>f</i>_<i>z</i> = 2 <i>m c</i>^2 / <i>h</i> can be related to the de Broglie wavelength as follows. <br /><br />If the electron is moving with speed expressed as a fraction of the speed of light as <i>b</i> = <i>v/c,</i> then time dilation reduces the observed zitterbewegung frequency by the Lorentz factor of <i>L</i>=1/(1-<i>b</i>^2)^(1/2). Supposing <i>b</i> << 1, then <i>L</i> ~ 1 + <i>b</i>^2/2. The difference between the zitter frequency in the electron rest frame and as observed is <i>f_d</i> ~ (<i>b</i>^2/2)<i>f</i>_<i>z</i> = <i>v</i>^2 <i>m</i> / <i>h</i> = <i>v p / h</i>, where <i>p = m v.</i> The distance traveled by the electron in one period of an oscillation at the difference frequency is then <i>d = v / f_d = h / p</i>, that is, the de Broglie wavelength of the electron.<br /><br />I argue that all that needs to be assumed to find a physical interpretation for this distance is that the electron is a classical point charge and that classical electrodynamics and the Dirac theory are both true. Then a point charge moving as required to account for the observed intrinsic angular momentum of the electron and such that the electric dipole moment oscillates at the zitterbewegung frequency must magnetically interact with another similarly-moving point charge, and the magnetic force between them is sinusoidally modulated with frequency <i>f_d</i>. Further, the magnitude of the oscillating magnetic force between the two charges is equal to that of the Coulomb force between two stationary or relatively slowly-moving charges.<br /><br />The longer version of this is in my paper now published by Foundations of Physics here: <a href="http://link.springer.com/article/10.1007/s10701-016-9990-1" target="_blank">http://link.springer.com/article/10.1007/s10701-016-9990-1</a> The arxiv version is here: <a href="http://arxiv.org/abs/1409.8271" target="_blank">http://arxiv.org/abs/1409.8271</a> <script> (function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){ (i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o), m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m) })(window,document,'script','https://www.google-analytics.com/analytics.js','ga'); ga('create', 'UA-52589872-1', 'auto'); ga('send', 'pageview'); </script>Quantum Skeptichttp://www.blogger.com/profile/17540964211124616979noreply@blogger.com0tag:blogger.com,1999:blog-646107687639208410.post-48282677219308224332016-01-18T00:13:00.003-08:002016-01-18T00:13:43.705-08:00My Response to Reviewer #2's Most Recent CommentsOn December 7 I submitted the third revision of my paper on the possibility that the Bohmian quantum force may be of electromagnetic origin to Foundations of Physics. On January 6 I received a letter of final acceptance. There were no further comments from Reviewers #s 1 and 3, but the following comment from Reviewer #2 was attached:<br><br><br><br><a href="http://quantumskeptic.blogspot.com/2016/01/my-response-to-reviewer-2s-most-recent.html#more">Read more »</a>Quantum Skeptichttp://www.blogger.com/profile/17540964211124616979noreply@blogger.com0tag:blogger.com,1999:blog-646107687639208410.post-48615279929867580492015-10-11T11:47:00.000-07:002015-10-11T11:47:05.559-07:00A Decision on My PaperThe decision by the journal was, "Minor Revisions". So, my paper is provisionally accepted by Foundations of Physics. I have until December 7 to submit the revised version, all of which I may need as I'm planning to add some material in addition to even the current arxiv version. The current arxiv <a href="http://arxiv.org/abs/1409.8271v8" target="_blank">version 8</a> is already significantly beyond what I sent them in early July as the second revision, which was similar to <a href="http://arxiv.org/abs/1409.8271v6" target="_blank">version 6</a>.<br /><br />The addition I'm working on beyond what's in version 8 is to derive the de Broglie wavelength in the rest frame of the field source particle. Currently it is only done is the rest frame of the test particle. This will provide more confidence in the correctness of the original (version 8) result. I don't see how anybody can object to that. Even if the journal doesn't want to print it, I want to have it and I will post it on arxiv.<br /><br />I sent an email to the journal immediately after uploading version 8 to arxiv, to let them know I'd resolved the problem of obtaining only half the de Broglie wavelength, and wanted to submit another revision that would be similar to the arxiv version 8. Also, versions 6 and 7 didn't take proper account of the interparticle separation, R, dependence on time in Equation (33), but this is corrected in version 8. I didn't receive an explicit direction one way or the other but the email is in the saved correspondence, so I take the decision of "minor revisions" as tacit permission to provide the improvements. Quantum Skeptichttp://www.blogger.com/profile/17540964211124616979noreply@blogger.com0tag:blogger.com,1999:blog-646107687639208410.post-69715281121102047732015-09-27T15:19:00.000-07:002015-09-27T15:19:59.570-07:00A Better Analysis of the De Broglie Wavelength Relationship to the ZitterbewegungThis is the <a href="http://arxiv.org/abs/1409.8271" target="_blank">latest version</a> of my paper on the magnetic force between Dirac particles due to the zitterbewegung, which as of this writing is version 8 and was posted late last week. This version is more successful in getting the de Broglie wavelength exactly as a modulation of the magnetic force for both non-radial and radial relative motion between Dirac particles. <br /><br />The new version solves the problem of getting a modulation that had a wavelength of half the de Broglie wavelength for radial relative motion. It also corrects a mistake of the previous two versions, and in what was sent to Foundations of Physics as a requested revision (which was similar to arxiv version 6). I overlooked the time dependence of the interparticle separation in deriving the preferred velocity and its relationship to the Bohr velocity. The new version recovers the idea that there is a preferred radial velocity where the advanced magnetic force will cancel the retarded magnetic force, but it is not completely satisfying in that it requires spiral motion. <br /><br />After I posted the new version to arxiv, I sent the journal an email to let them know in particular about the error in what I sent them. I'd only realized I'd made the mistake about five days previously. I haven't heard anything back yet about how they want to handle it, or if they're still interested, but it has only been a couple of days. Meanwhile, the status is still "under review". Quantum Skeptichttp://www.blogger.com/profile/17540964211124616979noreply@blogger.com0tag:blogger.com,1999:blog-646107687639208410.post-85372041587253049852015-09-12T11:59:00.004-07:002015-09-12T16:58:42.013-07:00Another Connection to the de Broglie Wavelength<br /><br />I found another connection to the de Broglie wavelength, when I took account of time dilation due to relative motion between Dirac particles. Assuming (after various authors) that a Dirac particle (such as the electron) consists of a point charge moving in a circulatory motion at the speed of light so that it has angular momentum of h-bar over two, then supposing one Dirac particle is stationary while another is moving, there will be a difference in frequency of the circulatory motion of one particle relative to the other. It's easy to calculate both the frequency of the circulatory motion and the amount of time dilation, and so also to get a difference in frequency due to the time dilation. The frequency difference depends on the speed of the relative motion. It turns out that the de Broglie wavelength can be equated to the time traveled by the moving particle during one period of the difference frequency due to time dilation.<br /><br />I put a new version of my <a href="http://arxiv.org/abs/1409.8271v7" target="_blank">paper</a> on arxiv to capture just this observation, about three weeks ago. Then I had to get about preparing a revised version of the same paper for re-submittal to Foundations of Physics. I had a lot of consternation in getting the revision done, because I'm still sorting things out about this on several fronts. The extension of the paper to include the connection to the de Broglie wavelength is unsatisfying in several ways, that I will perhaps describe in more detail later. The worst way is that I'm so far only able to make some sense of things when the spins are aligned; if they are opposite then the model seems to break down. But also, up to my re-submittal deadline, I was unable to directly explain how the observation about the de Broglie wavelength being related to time dilation could be related and reconciled to my other observation about the de Broglie wavelength as described in my previous post. So, I didn't include it in the resubmittal. (The journal would probably have given me an extension to the deadline, but I was eager to get a review of what I had so far, and had no idea when I'd be able to figure things out better. I'd already spent considerable effort trying to understand it, with scant success.) Now I want to report that I've made better sense of at least this bit, and was able to combine the new result with my previous derivation of the de Broglie wavelength, which I think is well motivated but gave a result too small by a factor of a half, and get the right result.<br /><br />I'll be working on a new revision to post on arxiv, hopefully within a week or two, that will make better sense than the one I link to above, which is v7. So, v8 will be a better version, and I'm also planning to rewrite the narrative somewhat beyond what I did for the re-submittal to FOOP. Also at that time I will contact the journal to tell them I made a little more progress, to see if they're interested. Quantum Skeptichttp://www.blogger.com/profile/17540964211124616979noreply@blogger.com0tag:blogger.com,1999:blog-646107687639208410.post-50047737236489726502015-07-15T07:36:00.000-07:002015-07-15T07:36:24.248-07:00Did I explain the de Broglie wavelength?I've been working for the last week or so to extend my paper (although not in the direction suggested by Reviewer 1) and I think I've made some real progress. I was thinking that I might be able to obtain the Bohr velocity as the speed where the phase difference between the retarded and advanced zitter motions is pi. This would tend to cancel the zbw magnetic force. It turned out it worked; I got (pi over 2 times) the Bohr velocity if the separation is the Bohr radius. It's a completely distinct relationship between range and velocity than the circular orbit Coulomb attraction one, so it's not a trivial thing.<br /><br />A couple of days later I got to thinking that probably the de Broglie wavelength relationship was implicit in what I had done, and when I looked at my equations, I could see it right away. So I cleaned it up a little and stuck it up on arxiv. It's got an extraneous factor of a half in it, however, that I hope to resolve soon. Also all I did was add a new section (V) and one sentence to the abstract. I'll be making a more extensive revision soon enough for resubmittal to FOOP and will replace it again in any case, and certainly I will relace it promptly if I can resolve the excess factor of a half.<br /><br />As of this writing the version is 6. Here is the link to the newest version: <a href="http://arxiv.org/abs/1409.8271" target="_blank">http://arxiv.org/abs/1409.8271</a>Quantum Skeptichttp://www.blogger.com/profile/17540964211124616979noreply@blogger.com0tag:blogger.com,1999:blog-646107687639208410.post-18439302778568756482015-07-05T15:08:00.000-07:002015-07-05T15:08:20.245-07:00Brief Response to Reviewer 3Yesterday I posted the <a href="http://quantumskeptic.blogspot.com/2015/07/new-reviews.html" target="_blank">three reviews</a> of my <a href="http://arxiv.org/abs/1409.8271v5" target="_blank">paper</a> sent me last week by Foundations of Physics. I'm responding to Reviewer 3 first because I have no substantial disagreement with this review, and it raises an interesting question, which I will enjoy expanding on in my resubmission. Here is the Reviewer 3 comment: <br><br><br><span style="background-color: white;"><span style="color: blue;"><span style="background-color: white;"><span style="background-color: blue;"><span style="background-color: white;">The paper presents the computation of a magnetic force between two Dirac particles where the spin is interpreted as coming from Zitterbewegung. The idea follows from the earlier work by Rivas.<br>Here are my remarks.</span></span></span></span></span><span style="background-color: white;"><span style="color: blue;"><span style="background-color: white;"><br><span style="background-color: blue;"><span style="background-color: white;"><br></span><br><span style="background-color: white;">1) Many of the interesting questions are left out and only mentioned as "beyond the scope of the paper" - this makes the results rather restricted. I'd suggest that the author explains why this is not touched.<br>2) I have some doubts how this results affects interpretation of quantum mechanics. <br>The result is nice and (as a matter of fact) rather easy to obtain. <br>It might be interesting to see whether such computations would make any predictions that would enable to falsify it (say in atom spectroscopy).<br>3) I fail to see the relevance of the part of Section 6 (evaluation of the quantum force). <br>Would the author, please, relate it to the other results ? <br>Mixing the nonrelativistic quantum mechanics with relativistic computation of classical force is slightly dangerous. <br>4) I would suggest the author to correct the language - there are many prepositions missing, some of the sentences are also a bit awkward. Example " p3 lines 6-7 "has also" should read: "has also been...". P11 line 38 "An evaluation" etc etc.</span></span><br><br><br><span style="color: black;">In response to remark 1, I will look into not simply stating something is beyond the scope of the paper. I think in at least most cases there is a good reason why whatever is being referred to isn't relevant to the paper or otherwise shouldn't be included, and that reason can (perhaps should have been) stated. I thank Reviewer 3 for the helpful remark.</span><br><span style="color: black;"><br></span><br><span style="color: black;">I think remark 2 is most interesting. Rather than trying to define an experiment that might falsify the hypothesis that Bohm's quantum force is a consequence of the magnetic force, though, it will be more to the immediate point to better determine what the correspondence is. I already point out the quantum force cannot be directly equated to (even just one part of) the magnetic force between two Dirac particles. What's needed here is to derive the quantum force from the classical Hamilton-Jacobi equation by incorporation of the magnetic interaction. Bohm's original paper shows how the Schroedinger equation can be put in a form that can be regarded as the classical Hamilton-Jacobi equation with an additional term he named the quantum mechanical potential. The quantum force is then derived in the usual fashion, as a gradient of the quantum potential. So, it should be possible, if the hypothesis is correct, to derive the quantum potential from the magnetic interaction between two Dirac particles.</span><br><span style="color: black;"><br></span><br><span style="color: black;">A derivation of the quantum potential from classical principles would be a very powerful result that would greatly improve my paper, but I doubt I can do it within the two months proposed by FOOP for the creation of a revised submission. Not that I'm unwilling to try, but one reason the journal might want to publish is so that other people who might be more qualified than I am to carry this out can attempt it if they're interested.</span><br><span style="color: black;"><br></span><br><span style="color: black;">In remark 3, </span></span></span></span><br><a href="http://quantumskeptic.blogspot.com/2015/07/brief-response-to-reviewer-3.html#more">Read more »</a>Quantum Skeptichttp://www.blogger.com/profile/17540964211124616979noreply@blogger.com0tag:blogger.com,1999:blog-646107687639208410.post-43389040708903753012015-07-04T14:44:00.000-07:002015-07-04T15:01:40.255-07:00New Reviews I have received three reviews from Foundations of Physics on my paper about the similarity of the magnetic force between relativistically-circulating charges to the quantum force of Bohmian mechanics. I didn't get a final decision; they requested "major" revisions. I'm willing to make any reasonable revisions, but I don't think certain of the revisions requested by two of three reviewers are well justified or reasonable. So I don't consider the revisions I'll be making all that major. <br><br>Maybe I will discuss my disagreements and objections to the reviews briefly here soon but not in this post. For now I will just post the reviews. In any case I will be creating both a revised version of the paper and a specific response to the reviews, as requested by FOOP, and can post that response when it's available. Also, I might mention that I recently posted on arxiv a version of the paper that is identical to the submittal to FOOP that the reviews apply to, except for being in two-column APS-like format rather than the FOOP format. So, the page references in the reviews may not line up exactly. Here's the (re-)submittal that was reviewed: <a href="http://arxiv.org/abs/1409.8271v5" target="_blank">http://arxiv.org/abs/1409.8271v5</a><br><br>Now the reviews:<br><br><br><a href="http://quantumskeptic.blogspot.com/2015/07/new-reviews.html#more">Read more »</a>Quantum Skeptichttp://www.blogger.com/profile/17540964211124616979noreply@blogger.com0tag:blogger.com,1999:blog-646107687639208410.post-42542072849915559662015-03-20T13:42:00.000-07:002016-06-04T09:40:34.182-07:00Status Update and What Martin Rivas DidI haven't posted in a while because I've been preoccupied rewriting my paper at the request of Foundations of Physics. They still haven't sent it to referees but they did send it to a member of the editorial board, apparently, and gave it a revise-before-review status, in mid-January, with a due date of 20 March for a new version. I guess I won't reproduce here what the board member said, which was brief, but the general idea was that it was not written appropriately for a journal on the foundations of physics and would I please make it so. This I was entirely willing and happy to do, as it was originally written for a letters journal (Physics Letters A, as I have already posted about), and not tailored much for FOOP. I probably would have done more on this account, except when I got the rejection letter from PLA I was only two days away from departing on a month-long overseas assignment for my engineering job which I knew would be demanding, and didn't have time to revise it much, but at the same time wanted to have somebody else looking at it based on what I thought were encouraging words from the PLA editor in spite of not wanting to publish it. It was nice on that assignment to not have to worry about it or work on it and yet my project could still make progress by having it be considered by illustrious others. Another factor is that it's a difficult chore for me to build a narrative around an analysis, for an audience that I know is generally much more sophisticated than I am. I'm happier just pushing the equations around.<br /><br />In any case I have given it my best attempt, I feel, and used the available time as best I could, rewriting it to a large extent, and then going over it a lot of times and long past the point where I was getting tired of re-reading words that I am still not all that happy with. Hopefully in the end it will sink or swim based on the physics contained within.<br /><br />About the physics of my paper, what I wanted to mention is that since I noticed how the magnetic force between to classical spinning particles could apparently cancel the Coulomb force, and even before I realized that that is similar to the Bohmian quantum force, I knew that this result followed very readily from work done by Rivas at least ten years ago. So far as I have been able to determine he has not published explicitly that magnetic forces can cancel Coulomb forces, but some of his figures that show numerical modeling results, both in his book and published papers, are certainly very close to realizing this to be the case. It's surprising to me that these results seemingly have not attracted more attention. So, one of the things I attempted to do in the re-write is to be more clear about how much of what I wrote in the first version of the paper is actually prior work of Rivas in showing that the time-averaged acceleration field of a luminally-circulating charge can reconstitute, as it were, the usual electric and magnetic fields of a static charge and magnetic dipole. I found this result astonishing from the first time I really noticed it in his book, which was after I decided that I had to calculate these fields for myself. But, I was only planning on calculating the velocity fields and for the case of motion that was only asymptotically close to luminal, not exactly luminal. When I found that Rivas had already addressed this problem, I saw right away that he had both done a far better job than I probably could ever have done, and also that the result was quite surprising and not at all what I was anticipating.<br /><br />As I try to say more clearly in the new version, given that Rivas has already shown that the average electric acceleration fields of a luminally circulating charge are identical to the Coulomb field of a static charge, and given that with luminal motions for both the field source charge and the charge being acted on, it should not be surprising that the magnetic interaction can have an inverse square dependence on interparticle separation and be of similar magnitude to the Coulomb interaction. It is less obvious, to me at least, that it should end up being radial. That it should also depend on the phase differences in the luminal motions and that this difference has to account for retardation is at least obvious once pointed out. So, perhaps what I foind is not news after all and if so, I will be happy to see Martin Rivas get 100% of the credit he deserves. On the other hand, if I truly am the first to notice this, I will be very proud, but still want to say that I probably would never have figured this out on my own, and that Rivas deserves most of the credit for it. I hope I have made that clear enough in the version I sent to FOOP last Monday.<br /><br />I posted a new version on arxiv that is not quite the final version that I sent to FOOP, but fairly close. The new arxiv version has all of the minor math corrections I found (none of which affected the original thesis) and the general overall rewrite. The FOOP version has still a newer title, however, and at least another week's worth of word-smithing which I think (or hope at least) further improved its read-ability. Here's the current arxiv version: <a href="http://arxiv.org/abs/1409.8271v4" target="_blank">Similarity of the Magnetic Force between Dirac Particles to the Quantum Force of Bohmian Mechanics</a><br /> <script> (function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){ (i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o), m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m) })(window,document,'script','https://www.google-analytics.com/analytics.js','ga'); ga('create', 'UA-52589872-1', 'auto'); ga('send', 'pageview'); </script> Quantum Skeptichttp://www.blogger.com/profile/17540964211124616979noreply@blogger.com0tag:blogger.com,1999:blog-646107687639208410.post-10305686248804648212014-10-31T13:09:00.000-07:002014-10-31T13:22:17.918-07:00Is the Quantum Hamilton-Jacobi Equation just the Classical Hamilton-Jacobi Equation Properly accounting for Magnetic Interactions?Wikipedia has a nice description of the <a href="http://en.wikipedia.org/wiki/Quantum_potential#Quantum_force" target="_blank">quantum potential</a> of <a href="http://en.wikipedia.org/wiki/De_Broglie%E2%80%93Bohm_theory" target="_blank">Bohmian Mechanics</a>, and the more I read it, the more I think it can fit in with the idea that quantum behavior is just the classical electrodynamical consequences of elementary particles being charges circulating at the speed of light. In the quantum potential article, it is already discussed that the quantum potential can be equated to the internal energy of the zitterbewegung. What better way for this to influence the motion than via magnetic interactions? <br /><br />However, de Broglie-Bohm theory is, like quantum mechanics generally, a non-local theory. Classical electrodynamics is of course Einstein-local, but it's also widely recognized that time-symmetric electrodynamics, while remaining Einstein local, has a substantial similarity to non-locality. <a href="http://en.wikipedia.org/wiki/Wheeler%E2%80%93Feynman_absorber_theory" target="_blank">Wheeler and Feynman</a> famously used time-symmetric interactions with the rest of the universe to explain radiation reaction. So, the classical time-symmetric Hamilton-Jacobi equation accounting for magnetic zitterbewegung interactions may lead to a theory that has the apparent non-locality of quantum mechanics.<br /><br />So far I've been focusing on just one small part of the total magnetic interaction; the part that's radially-directed and has a non-vanishing average and falls off inverse-squarely at long distance. There are many other terms that would also need to be taken into account, particularly at distances where the separation is not large compared to the Compton radii of the interacting particles. On the other hand, those that fall off less than inverse squarely will have a longer-range character, and when treated time-symmetrically, can plausibly interact significantly and seemingly non-locally with, say, slits in an obstructing plane.<br /><br /><br />A couple of days ago I got my <a href="http://arxiv.org/abs/1409.8271" target="_blank">paper</a> returned from Physics Letters A. Here is what the editor said:<br /><br /><span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.7272720336914px;">Ms. Ref. No.: PLA-D-14-02082</span><br style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.7272720336914px;" /><span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.7272720336914px;">Title: Radially Acting, Relative Spin Phase and Polarization Modulated, Inverse Square Law Magnetic Force Between Spinning Charged Particles</span><br style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.7272720336914px;" /><span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.7272720336914px;">Physics Letters A</span><br /><br /><span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.7272720336914px;">Dear Mr. Lush,</span><br /><br style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.7272720336914px;" /><span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.7272720336914px;">Thank you for submitting your work to our journal.</span><br /><span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.7272720336914px;">I have read your manuscript with interest.</span><br /><span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.7272720336914px;">I regret that it is not suitable for publication in Physics Letters A since it does not satisfy our criteria of urgency and timeliness.</span><br /><span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.7272720336914px;">Please consider submitting your work to a journal which has a more pedagogical bias.</span><br /><br style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.7272720336914px;" /><span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.7272720336914px;">Yours sincerely,</span><br /><br style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.7272720336914px;" /><span style="color: #222222; font-family: arial, sans-serif; font-size: x-small;"><span style="background-color: white;">{name removed)</span></span><br /><span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.7272720336914px;">Editor</span><br /><span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.7272720336914px;"><br /></span><span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.7272720336914px;"><br /></span><span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.7272720336914px;">I think I will take the kind editor's advice and submit it to a different journal, but first I'm going to add some speculation about the quantum force and the quantum Hamilton-Jacobi equation.</span><br /><span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.7272720336914px;"><br /></span><span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.7272720336914px;"><br /></span><span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.7272720336914px;"><br /></span><span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.7272720336914px;"><br /></span><span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.7272720336914px;"><br /></span><span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 12.7272720336914px;"><br /></span>Quantum Skeptichttp://www.blogger.com/profile/17540964211124616979noreply@blogger.com0tag:blogger.com,1999:blog-646107687639208410.post-73498144566625423182014-10-30T07:57:00.000-07:002014-10-31T12:33:09.250-07:00Is the Quantum Force of Bohmian Mechanics the Magnetic Force Between Spinning Dirac Particles? In Bohmian mechanics there is a quantum potential, and from its gradient<br />can be obtained a "<a href="http://en.wikipedia.org/wiki/Quantum_potential#Quantum_force">quantum force</a>." A few days ago I calculated the quantum force for the ground state of hydrogen and got that it's equal and opposite the Coulomb force between two charges. This is consistent with what I remembered about Bohmian mechanics, that in the s states the electron is stationary. This seemed far-fetched to me. However, it is not entirely unlike my recent finding regarding the magnetic force between two spinning charged particles where their spin is a consequence of circulatory motion of the charges at the speed of light.<br /><br />In any case, if we have two particles that are going around in little circles at the speed of light (what I called zitter particles in my new paper, but Rivas refers to in the electron case as a Dirac electron, if I understand him correctly) then it's easy to have that the magnetic force between them exactly cancels the Coulomb force expected if the were static charges, if the circular motion centers stay fixed. The phase relationship between the two particles' positions in their circulatory motions however must be evaluated accounting for the propagation delay. This means that the phase relationship including retardation changes with separation, modulating the inverse square law magnetic force radially-acting part. The modulation wavelength is the Compton wavelength.<br /><br />It's not obvious to me how this might correspond precisely to the quantum force of Bohmian mechanics but it's at least reminiscent of it. Of course, a classical force corresponding to the quantum force cannot cancel the Coulomb force precisely everywhere. Quantum Skeptichttp://www.blogger.com/profile/17540964211124616979noreply@blogger.com0tag:blogger.com,1999:blog-646107687639208410.post-22900461278808209742014-09-27T17:43:00.000-07:002014-10-31T10:39:35.284-07:00My new paper on relative spin phase modulated magnetic force<br /><br />When I was thinking it was necessary to take a difference between retarded and advanced fields to have a time-symmetric electrodynamics that's Lorentz covariant, I investigated whether a magnetic interaction between point charges moving in little circles at or near the speed of light could play the role of the Coulomb force in binding atoms. Really it can't, but it's remarkable how close it comes. <br /><br />I needed a force that was radial and of the same strength and range dependence as the Coulomb force. Rivas shows in his book, Kinematical Theory of Spinning Particles, how the electric acceleration field of a point charge moving in a circle of an electron Compton wavelength radius has an average that is inverse square like the Coulomb force and of the same strength. (That is pretty surprising given that the acceleration field falls off explicitly only directly inversely with distance, hence it's characterization as the radiation field.) But, since the magnetic field in Gaussian units is just the electric field crossed by a unit vector, the magnetic acceleration field for a charge doing the relativistic circular motion has the same strength as the electric field. <br /><br />If we have a magnetic field that's just as strong as a Coulomb field, and the charge moving in it is moving at the speed of light, then v/c for the charge is one and the resulting magnetic force via the Lorentz force law is just as strong as the Coulomb force. So, if we suppose the test charge is going in the same type of little circle as the field-generating charge, if the two motions are exactly aligned and in phase, then it turns out there's a purely radial component of the force that's constant in time and just as strong as the Coulomb force. If the circular motions of the two particles are out of phase, then the strength varies sinusoidally with the phase difference, and so it could either double or cancel the electric force. But the phase difference has to include the time delay of propagation from one circulating particle to the other. (It's important to realize that the charges aren't orbiting around each other, but each doing their little circular motions separately, with the circle centers many (Compton wavelength) diameters apart.) So there can be a very substantial influence on the motion of the center of the test charge's circular motion due to the magnetic force, if it is already also moving because of the electric field, due to the relative orientation of the charges plane of motion (which translates to the spin polarization) and the difference in phase of the internal motions of their spins. The phase of the zitterbewegung motion of the Dirac electron has already been shown by David Hestenes to correspond to the phase of the wave function of a free electron. So for bound particles, it doesn't seem unreasonable to suppose that the wavefunction involves the relative zitterbewegung phase of the interacting particles.<br /><br />In the process of putting the story together about this magnetic force as an alternative to the Coulomb force in the time-symmetric picture, I realized (see the previous post) that I missed a sign change in going from retardation to advancement of the magnetic field, so that it does not change sign, and so the magnetic force does not need to replace the Coulomb force but only augment it, in order to plausibly explain quantum behavior.<br /><br />I'm looking forward to understanding how this picture plays out, but that will take a while, so for now I am putting out what I have. It will appear on arxiv tomorrow, but I have already posted it to Researchgate <a href="https://www.researchgate.net/publication/266142106_Radially_Acting_Relative_Spin_Phase_and_Polarization_Modulated_Inverse_Square_Law_Magnetic_Force_Between_Spinning_Charged_Particles" target="_blank">here</a>.<br /> Quantum Skeptichttp://www.blogger.com/profile/17540964211124616979noreply@blogger.com0tag:blogger.com,1999:blog-646107687639208410.post-11647043256207754012014-09-24T09:54:00.000-07:002014-09-24T09:54:08.013-07:00CorrectionA few days ago I realized I'd overlooked a different way out of the problem that time-advanced magnetic fields want to reverse sign compared to retarded ones, and so causing magnetic effects to cancel out in the time-symmetric picture. The cancellation doesn't happen because the sign on the unit vector from the source to field point, that is crossed onto the electric field to obtain the magnetic field, also changes sign in going from retardation to advancement. That is, in the retarded case we have <span style="font-family: Arial, Helvetica, sans-serif;"><i><b>B</b></i> <b>=</b> <i><b>n</b></i> x <i><b>E</b></i></span>, but in the advanced case this becomes <i style="font-family: Arial, Helvetica, sans-serif;"><b>B</b></i><span style="font-family: Arial, Helvetica, sans-serif;"> <b>=</b> <b>-</b></span><i style="font-family: Arial, Helvetica, sans-serif;"><b>n</b></i><span style="font-family: Arial, Helvetica, sans-serif;"> x </span><i style="font-family: Arial, Helvetica, sans-serif;"><b>E</b></i>. The unit vector <i style="font-family: Arial, Helvetica, sans-serif;"><b>n</b></i> here changes sign because it originates as the gradient of the retarded or advanced time, so the sign change that changes retardation to advancement applies directly to it.<br /><br />This means the problem I've been working to overcome for the last eight or ten months does not even exist. In particular, the cancellation of the strong magnetic force that I was getting in the time symmetric picture does not occur. So, it can account for preon binding (for charged preons, at least) just fine. What I have been saying recently, that Lorentz covariance requires magnetic forces be preserved in the time-symmetric picture, if there is one, is perfectly true, but it is also completely consistent with electrodynamics and time-symmetric electrodynamics under the usual assumption that the retarded and advanced solutions are summed rather than differenced. Writing it up for publication forced me to realize this, because when I went through, as a simple demonstration of the problem, calculating the magnetic moment from a static current loop from the retarded potentials (see, e.g., Landau and Lifshitz Eq. 66.2) I discovered that it absolutely does not change sign when going over to the advanced case.<br /><br />Now, everything is better except the idea that the electron g factor of (about) 2 can be explained as the difference between retarded only and time symmetric electrodynamics. I still think this is a very attractive idea, but the story isn't as compelling because it isn't true as I said that in the conventional time-symmetric picture the g factor would be zero, i.e., that the electron magnetic moment would vanish. In the usual picture (attributable to Dirac 1938) the time symmetric field is the mean of the retarded and advanced fields, which leads to a g-factor of one.<br /><br />Maybe I should give up my obsession with the electron g factor, now that I am routinely thinking of the electron as a composite particle. If it has a positive charge part with opposite but smaller spin, doesn't that give a g factor larger than unity? Maybe g factor two is easy to get in the preon model. I am still used to thinking of an electron as a structureless object so this kind of thinking is not natural. Maybe g-factor two is simply a confirmation that it's a composite particle.<br /><br />Later I think I will look more at the g factor of a composite electron, but for right now I'm trying to complete something entirely new to put on arxiv and hopefully soon after submit to a journal. Hopefully I will upload it to arxiv within a day or two. Before that happens, I am also planning on revising my kinematics arxiv paper to remove the new section I just added a few weeks ago. Probably I will do that later today. I can't let it stay up there long knowing it is dead wrong.<br /><br /> <br /><br /><br />Quantum Skeptichttp://www.blogger.com/profile/17540964211124616979noreply@blogger.com0tag:blogger.com,1999:blog-646107687639208410.post-65108099998723655682014-08-10T19:50:00.001-07:002014-08-10T19:50:54.225-07:00Why the electron g-factor is 2<br />Today I realized (I think) that if electrodynamics is time-symmetric, and if the magnetic force does not flip its sign for the advanced magnetic forces compared to retarded magnetic forces, then this will naturally double the strength of the magnetic forces at scales where the retarded and advanced interactions are experienced close to in phase. So the electron magnetic field, if produced by moving charge, will be twice what it would be for retarded only forces. So perhaps the electron g-factor being (about) 2 can be taken as confirmation that electrodynamics is time-symmetric.<br /><br />After mulling it over for a while today, I decided to do a quick update to my arxiv paper to include this observation. I added a new section V that consists of 3 paragraphs with no equations. It will post tomorrow (as v8) if I don't change it further and reset the clock. (I also corrected Eq. (8), which did not affect any subsequent results. It may become relevant in the next update (v9) however. I have a lot of material towards a new version beyond v7/v8, but it was inconclusive until the new ideas of the last few weeks, which tentatively seem to be panning out nicely. I have only been working on it again for the last few days, though. Prior to that I was unusually tied up for several weeks with my engineering job on a hot project.)<br /><br />Another thing I want to mention, that I was being coy about in my last post, is how it might be possible to have electrical velocity fields invert sign between retardation and advancement, and still have apparent electrostatic forces between (apparently) stationary charges. The way it might possible is if what we take as electrostatic electric fields and forces are actually time averages of electric acceleration fields. Martin Rivas (citation will be in the new posted version, and is in some of the earlier versions already) has already shown how if the electron is modeled as a circulating point charge moving at the speed of light (and it will still be true for asymptotically close to the speed of light), then the time-averaged acceleration field is Coulomb-like by several Compton radii away (when the radius of the circular motion is the Compton wavelength). Also, for the ultra-relativistic charge, the velocity field collapses to a point and so doesn't contribute to the average Coulomb-like field.<br /><br />I spent today trying to modify Rivas' calculation to see if I can get a similar result in spite of switching the sign of the advanced forces. It seems intuitively that it couldn't but I am encouraged, as far as I got today. It doesn't make it vanish identically, as my intuition predicts it should have. This is a very preliminary observation, so maybe it will fall apart, but it shouldn't take long to get an answer one way or the other. I have another reason to be optimistic, though, because I also tried yesterday adding sign-reversed (compared to the usual) advanced fields into my attempted derivation of anti-Euler forces from the velocity magnetic field terms, and now it does seem to be emerging. I have spent six long months trying to get this with no prior success, so it seems very encouraging. This is also only a preliminary observation that could evaporate. I still have a lot of work to do before I can have something to submit to a journal, but I feel like I'm making serious progress again finally, after months of getting nowhere fast. <br /><br /> Quantum Skeptichttp://www.blogger.com/profile/17540964211124616979noreply@blogger.com0tag:blogger.com,1999:blog-646107687639208410.post-9608251826444265642014-07-28T00:08:00.000-07:002014-07-28T00:08:15.825-07:00About the sign of advanced magnetic forcesIn time-symmetric electrodynamics, it is always assumed that the sign of the electric force is the same for the advanced force as for the retarded force. This must be so (one would think) because in the inertial reference frame where an infinitely heavy charge is at rest, a test charge held initially at rest and then released would experience no net Coulomb force if it were otherwise.<br /><br />It follows from this seemingly necessary choice that the sign of the magnetic force in a different inertial reference frame, where the heavy charge is in motion, will invert for advanced compared to retarded magnetic forces. So, in time symmetric electrodynamics, magnetic forces tend to cancel out. This appears at least at first glance to keep the magnetic force that seems to correspond to my predicted anti-centrifugal force from being able to overcome Coulomb repulsion.<br /><br />On account of the considerations above, I have recently been going carefully over how to get the time-advanced and time-retarded fields and forces by Lorentz transforming from the reference frame where the field-source charge is stationary. (The retarded case is already analyzed quite a bit in the appendices of my arxiv paper.) There haven't been any surprises there, but a few days ago I began to realize that the derivation of the magnetic force as the anti-Coriolis force of the Thomas precession doesn't care whether the field or force is retarded or advanced. It can't change sign from retardation to advancement because neither has entered into the derivation in any way. Thus, if the anti-Coriolis force is a real force, then either time-advanced electromagnetic forces cannot exist, or the sign of the Coulomb force must flip between retardation and advancement. Consistency of the force law with relativistic kinematics demands this, if I am correct. Quantum Skeptichttp://www.blogger.com/profile/17540964211124616979noreply@blogger.com0tag:blogger.com,1999:blog-646107687639208410.post-34383222537973700022014-04-05T21:54:00.000-07:002016-06-04T09:44:08.230-07:00Superstrong electromagnetic interactions<br />Since I've given up trying to put out a separate paper quickly on the superstrong magnetic force between highly accelerating ultrarelativistic charges, as I said in the previous post, and have gone back to trying to finish my more general paper on the relationship between electrodynamics and relativistic kinematics, I should report out a little on what I found and didn't find.<br /><br />The strong attractiveness of the magnetic force in the retarded magnetic acceleration field is already shown in the version posted on arxiv. What I was trying to determine was whether there's an obvious way there can be net attraction in the time symmetric case, as considered by Schild, where the magnetic force due to the advanced field tends to cancel the force due to the retarded field. My idea was that in the ultrarelativistic case the delay and advance angles approach 90 degrees, so maybe it might be possible to change the phase relationship so that the net force is strongly attractive on average. <br /><br />It turned out that although I was able show tentatively that the retarded and advanced forces don't have to exactly cancel and can easily exceed in magnitude Coulomb repulsion, I wasn't able to generate a net attractive force. I may try further later but for now I have gone back to trying to finish the more general argument. <br /><br />What I did was to assume two charges were circularly orbiting each other in an approximately circular orbit with an orbit diameter smaller than one one-hundredth the size of a proton, and at a velocity very close to the speed of light. I wrote a matlab program to calculate the full retarded and advanced, and non-radiative and radiative, electric and magnetic fields at the position of one particle due to the other, and accounting for delay and advancement, where the motion was assumed to be circular and periodic, but allowing the accelerations to depart from the strict centripetal acceleration of a pure circular orbit. That is, I let the non-centripetal acceleration affect the fields but not the orbit. Then I looked at the induced acceleration of one particle due to the other, and attempted to construct a configuration where the motions of each particle induced by the other would be consistent. I totally ignored radiation damping, as did Schild, although it's enormous in this configuration.<br /><br />It turned out to be pretty simple to build a configuration where the motions seem approximately consistent in the time-symmetric electrodynamic sense. A lot more work would be needed to determine if this is a real or meaningful result, and I don't mean to assert that it is. If I had more confidence I could build something convincingly meaningful in a reasonable amount of time, I'd continue to work on it, but for now I think my time is better spent elsewhere.<br /><br />To illustrate what I'm trying to describe, I captured a plot from my matlab program, see below. Clicking on the figure should expand it. The top two strip plots are what is used to calculate the full em field at the position of the second (test) particle, and then the bottom two plots are the acceleration induced on the test particle. The scales are not very meaningful because the magnitudes depend on how close the velocity is to the speed of light, and the orbital radius, and the invariant particle masses, and in a complicated way.<br /><br /><br />The top two strip plots show the motion of the charge the generates the field that the test particle moves in. That's the field source particle. The field that the test particle generates isn't allowed to affect the source particle here. The top plot shows that I arbitrarily imposed a strong radial oscillating (at the orbital period) acceleration on top of the constant radial centripetal acceleration in it's circular circular orbit. The second plot is showing that there's no comparatively significant motion in the tangential or axial directions. That's just the noise level when some large positive and negative numbers got added together, at matlab default precision. <br /><br />Then the time retarded and advanced fields at the test particle position, moving oppositely in a nominally circular orbit, are calculated and the corresponding acceleration of the test particle due to their sum is plotted on the two lower strips. What's interesting to me is that the oscillating radial acceleration of the source particle has induced a similar radial acceleration in the test particle, out of phase such that if it were allowed to act back on the source particle has a hope of leading to a consistent periodic motion, perhaps. There is also a tangential acceleration induced, but it's much smaller in magnitude. The smaller magnitude is in part at least due to the difference in relativistic mass along track versus cross-track. <br /><br />This would be a rabbit hole to pursue seriously, that one might never emerge from. But it would be fun.<br /><br /><br /><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-p3quW5OMGEE/UxP1C9Y_l6I/AAAAAAAAAEQ/_CU0JiWf0AM/s1600/meson.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://3.bp.blogspot.com/-p3quW5OMGEE/UxP1C9Y_l6I/AAAAAAAAAEQ/_CU0JiWf0AM/s1600/meson.jpg"></a></div><br /><br /><br /> <script> (function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){ (i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o), m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m) })(window,document,'script','https://www.google-analytics.com/analytics.js','ga'); ga('create', 'UA-52589872-1', 'auto'); ga('send', 'pageview'); </script> Quantum Skeptichttp://www.blogger.com/profile/17540964211124616979noreply@blogger.com0