Martin Rivas of the University of the Basque Country published a book in 2002 called, "Kinematical Theory of Spinning Particles," in which, among many other things, he shows how the average electric field of a classical point charge moving in a circle at the speed of light is at sufficient distance identical to the field of a stationary charge. Also, the average magnetic field of the circulating charge is like that of an ideal magnetic dipole, at sufficient distance.
These fields arise out of what are called the "acceleration" fields of a charge; that is, they are present only when the charge is accelerating. The acceleration fields include the radiation fields, which fall off inversely with distance, unlike the field of a static charge, which falls of inverse-squarely.
I was struck at the time I first saw this, probably about 5 years ago, because I was not expecting to see the acceleration-derived field having this inverse-square law behavior. I had been thinking of the acceleration field as being the same as the radiation field, but this is not correct. It gives rise to radiation, but it can also give rise to non-radiative fields that fall off inverse-squarely as well as with higher powers of distance. (I should mention that the part of the field due to a static or uniformly-translating charge goes to zero as the charge velocity goes to the speed of light, except along the direction of motion, where it goes to infinity. You have to not worry about this for my proposal to make sense.)
It goes back to Dirac's relativistic electron theory, and to what Schrodinger called the "zitterbewegung," or zitter motion inherent in it, that the expected velocity magnitude of the Dirac electron is always the speed of light, even though the average velocity is sub-luminal. Various authors, maybe Huang was first, have noted that it's possible to interpret the Dirac electron as a point charge circulating at the speed of light, and if it has a radius of a Compton wavelength it will have similar angular momentum to that of the electron intrinsic spin. More recently (but still a while ago), David Hestenes developed what he called the Zitterbewegung Interpretation of Quantum Theory, and showed among other things that the phase of zitterbewegung could be equated to the phase of the wavefunction for the free Dirac electron.
Also, along not entirely unrelated lines of thought, there is what is known as the Quantum Theory of Motion, a.k.a. Bohmian Mechanics, a.k.a. the de Broglie-Bohm formulation of quantum mechanics. In Bohmian mechanics, an elementary particle motion is (or would be) well-determined, if an initial position and velocity is (or could be) known, along with the Schrodinger wavefunction. Bohm showed that one could derive a kind of a guiding force, eventually called the quantum force, from the Schrodinger equation, in 1952. Having been casually interested for a long time in the philosophical underpinnings of quantum theory I found this interesting, but I also found it off-putting that the quantum force has to be able to essentially exactly cancel the Coulomb force in atomic "s" states, such as in the ground state of hydrogen. In s states in Bohmian mechanics, the electron just sits still, more or less, which is why it doesn't radiate. I could not see how this could be correct so I mostly didn't think much further about Bohmian mechanics for a long time.
So then last year, because of a misunderstanding I had that doesn't need to be dwelt on here (this story already being long enough and too long for many I'm sure), I was playing around with Martin Rivas's equations for the acceleration fields from the circulating charge, and happened to substitute in to the Lorentz force law that the charge being acted on by the field is another luminally-circulating charge, and what I got is that the magnetic force in this case, although it has various other messy terms, has a term in it that at large enough distance, and when the spins are aligned, can on average exactly cancel the Coulomb force (or strictly, the average electric force due to the electric acceleration fields). Also, unlike the electric force, this inverse-square law magnetic force is modulated by the relative phase of the circulatory motions, so it can either cancel or double the Coulomb-like electric force between the charges. By this time I had mostly forgotten about the Bohmian quantum force, but I immediately thought this is a new way (for me at least) to classically-influence atomic level motions. The phase difference part made me think of quantized states of motion, because the phase difference that modulates the force depends on the phase difference including the delay due to the finiteness of the speed of light. When you take into account the fact that the circulatory motion radius has to be a Compton wavelength, and the speed is luminal, the sign reversals due to distance-dependent phase delay seem to be plausibly consistent with atomic scales.
I thought this was pretty interesting so I wrote it up quickly and with a minimum of speculation (by my usual standards at least) and posted it on arxiv.org, and then I sent it to a physics letters journal, but they declined to publish it. But, they encouraged me to send it to a journal "with a more pedagogical bias". I was going to sit on it for a while until I had a chance to investigate it further, until something jogged my memory about the Bohmain quantum force, which I thought made it worthwhile to resubmit it to another journal sooner rather than later. So I revised it a little bit and sent it to Foundations of Physics. That was Nov 1 last year. Then in mid January FOOP asked me to revise it "to make it more suitable for a journal on the foundations of physics," prior to peer review (although calling it peer review is not totally applicable here, as the reviewers are sure to be far beyond me in level of physics skills), and they gave me a two month deadline. So I (quite happily) revised it quite a bit and sent it back in mid-March. Then (they post status of your paper on their website) after a few weeks it showed as "under review," until yesterday morning, when it changed to "reviews complete". So hopefully it won't be too long before they make a decision, possibly any day now.
So that is my story and maybe some here will be interested. Here's the current arxiv version, which is close to what I submitted, but not quite. I kept working on it until the 16th of March, and changed the title (again) for the FOOP submittal.
http://ift.tt/1eLYNYK
These fields arise out of what are called the "acceleration" fields of a charge; that is, they are present only when the charge is accelerating. The acceleration fields include the radiation fields, which fall off inversely with distance, unlike the field of a static charge, which falls of inverse-squarely.
I was struck at the time I first saw this, probably about 5 years ago, because I was not expecting to see the acceleration-derived field having this inverse-square law behavior. I had been thinking of the acceleration field as being the same as the radiation field, but this is not correct. It gives rise to radiation, but it can also give rise to non-radiative fields that fall off inverse-squarely as well as with higher powers of distance. (I should mention that the part of the field due to a static or uniformly-translating charge goes to zero as the charge velocity goes to the speed of light, except along the direction of motion, where it goes to infinity. You have to not worry about this for my proposal to make sense.)
It goes back to Dirac's relativistic electron theory, and to what Schrodinger called the "zitterbewegung," or zitter motion inherent in it, that the expected velocity magnitude of the Dirac electron is always the speed of light, even though the average velocity is sub-luminal. Various authors, maybe Huang was first, have noted that it's possible to interpret the Dirac electron as a point charge circulating at the speed of light, and if it has a radius of a Compton wavelength it will have similar angular momentum to that of the electron intrinsic spin. More recently (but still a while ago), David Hestenes developed what he called the Zitterbewegung Interpretation of Quantum Theory, and showed among other things that the phase of zitterbewegung could be equated to the phase of the wavefunction for the free Dirac electron.
Also, along not entirely unrelated lines of thought, there is what is known as the Quantum Theory of Motion, a.k.a. Bohmian Mechanics, a.k.a. the de Broglie-Bohm formulation of quantum mechanics. In Bohmian mechanics, an elementary particle motion is (or would be) well-determined, if an initial position and velocity is (or could be) known, along with the Schrodinger wavefunction. Bohm showed that one could derive a kind of a guiding force, eventually called the quantum force, from the Schrodinger equation, in 1952. Having been casually interested for a long time in the philosophical underpinnings of quantum theory I found this interesting, but I also found it off-putting that the quantum force has to be able to essentially exactly cancel the Coulomb force in atomic "s" states, such as in the ground state of hydrogen. In s states in Bohmian mechanics, the electron just sits still, more or less, which is why it doesn't radiate. I could not see how this could be correct so I mostly didn't think much further about Bohmian mechanics for a long time.
So then last year, because of a misunderstanding I had that doesn't need to be dwelt on here (this story already being long enough and too long for many I'm sure), I was playing around with Martin Rivas's equations for the acceleration fields from the circulating charge, and happened to substitute in to the Lorentz force law that the charge being acted on by the field is another luminally-circulating charge, and what I got is that the magnetic force in this case, although it has various other messy terms, has a term in it that at large enough distance, and when the spins are aligned, can on average exactly cancel the Coulomb force (or strictly, the average electric force due to the electric acceleration fields). Also, unlike the electric force, this inverse-square law magnetic force is modulated by the relative phase of the circulatory motions, so it can either cancel or double the Coulomb-like electric force between the charges. By this time I had mostly forgotten about the Bohmian quantum force, but I immediately thought this is a new way (for me at least) to classically-influence atomic level motions. The phase difference part made me think of quantized states of motion, because the phase difference that modulates the force depends on the phase difference including the delay due to the finiteness of the speed of light. When you take into account the fact that the circulatory motion radius has to be a Compton wavelength, and the speed is luminal, the sign reversals due to distance-dependent phase delay seem to be plausibly consistent with atomic scales.
I thought this was pretty interesting so I wrote it up quickly and with a minimum of speculation (by my usual standards at least) and posted it on arxiv.org, and then I sent it to a physics letters journal, but they declined to publish it. But, they encouraged me to send it to a journal "with a more pedagogical bias". I was going to sit on it for a while until I had a chance to investigate it further, until something jogged my memory about the Bohmain quantum force, which I thought made it worthwhile to resubmit it to another journal sooner rather than later. So I revised it a little bit and sent it to Foundations of Physics. That was Nov 1 last year. Then in mid January FOOP asked me to revise it "to make it more suitable for a journal on the foundations of physics," prior to peer review (although calling it peer review is not totally applicable here, as the reviewers are sure to be far beyond me in level of physics skills), and they gave me a two month deadline. So I (quite happily) revised it quite a bit and sent it back in mid-March. Then (they post status of your paper on their website) after a few weeks it showed as "under review," until yesterday morning, when it changed to "reviews complete". So hopefully it won't be too long before they make a decision, possibly any day now.
So that is my story and maybe some here will be interested. Here's the current arxiv version, which is close to what I submitted, but not quite. I kept working on it until the 16th of March, and changed the title (again) for the FOOP submittal.
http://ift.tt/1eLYNYK
via International Skeptics Forum http://ift.tt/1I6x3Ic
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