Electromagnetism: quantum mechanics or vortices?

[Farsight]

Science is progressive. We build on the empirical record of past experiment and observation, but we abandon utterly those unevidenced flights of fantasy that spring from the minds of man because they don't better the precise description of empirical phenomena.

Such as the notion that an electromagnetic wave doesn't need a medium because the electric wave creates the magnetic wave and vice versa, and it propagates in some dozy-doh style.

Maxwell's 1860's opinions on vortices were plagued with unknowns of the hypothetical luminiferous ether because the mechanical analogy depended on facts not in evidence.

Only Einstein reintroduced aether when he was doing GR, see Wikipedia and note the quote by Robert B Laughlin: "It is ironic that Einstein's most creative work, the general theory of relativity, should boil down to conceptualizing space as a medium when his original premise [in special relativity] was that no such medium existed". What's your explanation for the motion of electrons and positrons? Do you maintain that they're throwing light at one another?

Well said. Also, the direction and magnitude of the force associated with a particular E depends on the charge of the test particle being considered

It depends on the charges of two test particles. Two electrons move apart, two positrons move apart, an electron and a positron move together.

so the force isn't even intrinsically associated with E -- it's associated with the product with the charge of the test particle.

And each particle has an electromagnetic field, not an electric field. Linear "electric" force results when two electromagnetic fields interact when they have no passing motion.

Moreover the particular value of E varies in direction and magnitude depending on location and time, so it is a vector field by every conventional definition.

But a charged particle has an electromagnetic field, not an electric field. And as Einstein said, a field is a state of space. There aren't two states of space where an electron is.

If you read Maxwell's 1861-1862 "On Physical Lines of Force", much of it concerns the x-, y-, and z- components of the E (and B) vector fields. http://en.wikipedia.org/wiki/Vector_field

It also concerns the unification of electromagnetism. Which some here seem to know nothing about.

Your use of both vortex and spinor are as meaningless as a diploma-mill degree upon the wall. It's not enough to spell words correctly, you must use those words as they are conventionally understood or your writing just becomes a shambles of unconnected baseless assertions. You model no vortices and you calculate with no spinors, so you have only empty-headed drivel

You've got nothing, apart from a sneering ignorant arrogance that dismisses Maxwell and Minkowski and Einstein, and abuse.

regardless of the illustriousness of your abused sources. At the end of the next post, I will point out how your interpretation of the Einstein-de Haas effect as motion is not as well supported as the conventional interpretation of it as angular momentum.

Above, I faulted Maxwell for not having a deep understanding of geometry in his attribution of circulation to intrinsic rotational motion of magnetism in the Faraday effect and promised a devastating rebuttal of the vortex model. Now it is time to make good on my promise.

Your model of oppositely-spinning attractive vortices is 2-dimensional but we have three spatial dimensions. That means your model of vortices as charge fails because charges don't change sign when you flip them upside down. We don't get anti-matter explosions every time we turn over an egg-timer

Oh specious straw-man garbage. This is a spindle-sphere torus, and it is not two-dimensional:



So that's quite enough from you

 

[PhysBang]

Only Einstein reintroduced aether when he was doing GR, see Wikipedia and note the quote by Robert B Laughlin: "It is ironic that Einstein's most creative work, the general theory of relativity, should boil down to conceptualizing space as a medium when his original premise [in special relativity] was that no such medium existed".

Yet, as Einstein pointed out in the Leyden address that you love to selectively quote so much, the aether of GR has none of the properties of the aether imagined by the people trying to explain electromagnetism, all it has are the relationships of spacetime geometry to energy density. If you want to show otherwise, then show us your equations, show us how to test your theory.

What's your explanation for the motion of electrons and positrons? Do you maintain that they're throwing light at one another?

What is your explanation? So far you have yet to show us any physics, any way to perform an application with your ideas.

You keep ignoring my questions about applications because you know that you are lying to people about your ideas.

You've got nothing, apart from a sneering ignorant arrogance that dismisses Maxwell and Minkowski and Einstein, and abuse.

Nobody here is doing this more than you, Farsight. You ignore everything these people ever wrote about testing physical ideas and you ignore all of their mathematics, the way they sought to present their physics accurately and with detail. Then you insult everyone who asks you to present your details.

Oh specious straw-man garbage. This is a spindle-sphere torus, and it is not two-dimensional:

But that drawing you stole from someone else is not how you represent EM, you do that through 2D drawings. Now you are attempting to lie and pretend that you were doing 3D all along. If you would show us some equations, then we would know exactly what you were saying and we could consider you to be right or wrong. As of now, you are not even right, since what you present cannot possibly be physics.

 

[Fednis48]

Oh specious straw-man garbage. This is a spindle-sphere torus, and it is not two-dimensional:

View attachment 314

So that's quite enough from you

I was really looking forward to your response to rpenner's criticism, and am disappointed with how flippant you were. Your animation is very pretty, but tells me nothing; I assume something is being plotted as a function of the three spatial axes, but I don't know what it is or how the color choices correspond to its value.

So maybe you can answer for me a really, really simple problem. In your picture, an electron is comprised entirely of the electromagnetic field, yes? If so, please tell me the value of the electromagnetic field (as a function of x, y, z, and if necessary t) corresponding to the following scenario:

A single electron is at rest in a vacuum.

This is a really basic situation, but even so, it should give the rest of us some concrete details to work with for a change. In particular, this is your chance to prove that you can get isotropic fields from a 3-D vortex, which rpenner said was impossible. Please note that I don't want a picture, nor an analogy, nor a discussion of what Maxwell/Einstein/Bono thought of the issue. I want you to give me a formula. Can you do it?

 

[rpenner]

Sorry to be ungraciously tardy, rpenner.

As I have long insisted that, outside of the moderators need to ascertain the intentions or positions of some potentially troublesome posters, no one on this forum has a right to demand a reply, and indeed intended no such obligation upon you, the elapsed time before your response is nothing that can be chalked up to a charge of ungraciousness towards you. Think nothing of it.

Quaint? That's not the sort of word I would expect. Visionary maybe. Or perhaps brilliant. Ahead of his time. Moving on:
Faraday rotation is perfectly real:

My use of "quaint" and "real" were, as in the case of most adjectives, used to modify specific nouns or are in turn modified by adverbial clauses which you in your haste to take umbrage seem to have mislaid. Pray thou good sir, make another attempt to parse the Queen's tongue, and let that generosity of human spirit, that milk of human kindness lift the cataracts of pride and posturing from thine eyes. Lo, those words, now lacking in all offense do appear again, as if summoned by some blithe goblin:

As a historical curiosity, Maxwell's 1861-1862 "On Physical Lines of Force" attempts to cover the intersection of analytic geometry, summaries of empirical observations and the Faraday concept of action-at-a-distance mediated by a spatially-extended field. It's quaint in how unnecessary hypotheses, that would later be stripped away, multiply.

Just as a relevant example, from part IV: "Professor Thomson has pointed out that the cause of the magnetic action on light must be a real rotation going on in the magnetic field."
But more viable is the QED model of electrons and photons with intrinsic angular momentum and exterior magnetic fields causing population shifts in the electron spin distribution which differentially affects the refraction index for left- and right-polarized light through a transparent medium. Because if Maxwell (and Thomson) were right, then the Faraday Effect would not be excluded from vacuum and wouldn't happen in opposite directions for diamagnetic (positive Verdet constant) and paramagnetic materials (negative Verdet constant), why it is temperature-sensitive for paramagnetic materials, and why it has the frequency-dependence it does.
http://en.wikipedia.org/wiki/Faraday_effect
http://www.physics.rutgers.edu/ugrad/389/Verdet constant-the properties of optical glasses.pdf

There you have it, only an aspect of the paper, its reliance on fanciful hypotheses, is labeled as "quaint" while it is not the phenomena of the Faraday effect which has its reality called into question but the alleged rotation in the magnetic field. The latter point is supported with evidence and argument that the Faraday effect not a magneto-optical effect, but a wavelength- and temperature-dependent magneto-optical-material effect which is successfully modeled in better detail without assuming the reality of even conceptual usefulness of a "rotation going on in the magnetic field" which in turn is evidence supporting the charge that Maxwell's paper has at least one quaint hypothesis advanced.

All well and good. But IMHO the important point is that Faraday discovered the Faraday effect in 1845,

That might be important to our discussion after you supported your baseless outburst over my use of "quaint" to describe Maxwell's 1862 endorsement of Thomson's use of "real" to describe a hypothetical mechanism which ignored aspects of the phenomenon known even back then and has never been a contender in useful descriptions of nature.

and here we are 170 years later with Fermilab telling us the electron is a point particle that spits out photons.

Also, some guy named Einstein.
http://www.nobelprize.org/nobel_prizes/physics/laureates/1921/press.html

If the charged particles did have initial relative motion they also rotate around one another, just like vortices.

That description is incompatible with the behavior of charged particles. The classical general motion of an isolated system of two charged particles results in approximate conic trajectories which depart from Newtonian 1/r² predictions of ellipses and hyperbolae due to loss of energy, angular momentum and momentum via radiation. The quantum mechanical solutions for oppositely charged pairs include states without orbital angular momentum. The QED solutions include mutual annihilation for matter-antimatter pairs. All of these models fit the behavior of phenomena in reality better than vortices...

No [the description of charged particles moving about each other like vortices] isn't [incompatible with the behavior of charged particles].

Well, I have given three empirically vetted theories which describe in detail the ways that the motion is quantitatively dissimilar from the general behavior of vortices on the surface of water as well as better known three-dimensional vortices like torodial smoke rings. So I assume you will back up your viewpoint with quantitative similarities, right?

Go and look up positronium. But beware of the picture on the right, it's misleading. The electron's field is what it is, it isn't some little ball.

You give me a source which says nothing I haven't already said and then you proceed to contradict it which leaves your side with, as I weigh the evidence, less than nothing.

[Quasi-Newtonian approximate conic sections as trajectories for charged particles is] a straw man.

It's Maxwell's pre-quantum theory that you started off vigorously defending beyond the bounds of evidentiary or textual support and are now arguing against. It's not a straw man, it's a viable model and empirically vetted as an accurate approximation of pairs of charges far from the ground state. In general, the correspondence principle makes it no surprise than Kepler and Maxwell and QED agree on the behavior of electrons in very excited hydrogen atoms.
http://en.wikipedia.org/wiki/Rydberg_atom#Classical_simulation
http://journals.aps.org/pra/abstract/10.1103/PhysRevA.35.2806

In atomic orbitals electrons "do not orbit the nucleus in the sense of a planet orbiting the sun, but instead exist as standing waves".

By definition, electrons in the ground state of an atom are fermions as closely packed as circumstances permit, so you see maximum divergence from the Kepler/Newton/Maxwell classical prediction. In addition, the ground state is stationary and the electron isn't well-localized as it can be in a n~300 Rydberg state.

 

[rpenner]

Did you look at Maxwell's page title and take note of his reference to a screw mechanism?

If you are referring to Maxwell's 1861-1862 "On Physical Lines of Force", I read more than just the section titles. He called out the Faraday effect including the contributions of Verdet with respect to paramagnetism and described left- and right-handed screws in direct parentage to the modern physical interpretation of the propagation of circularly polarized light. However, he didn't anticipate the superposition principle which allows decomposition of the description of linearly polarized light into equal-intensity beams of circularly polarized light. His other use of the term "screw" was an equally misguided attempt to tie magnetism to rotary phenomena where the modern interpretation ties the same observations to peculiarities of geometry in 3 spatial dimensions, where both the vector cross product exists.

He was perfectly clear on the screw.

"Perfectly clear" meaning what?
Well in part IV, he says that the Faraday effect of matter in a magnetic field differs from the optical rotation caused by materials outside a magnetic field, like quartz. So in that sense he is pretty clearly saying this particular magnetic effect is not like a screw.

In both cases the absolute direction of the rotation is the same, whether the light passes from north to south or from south to north,— a fact which distinguishes this phenomenon from the rotation produced by quartz, turpentine, &c., in which the absolute direction of rotation is reversed when that of the light is reversed. The rotation in the latter case, whether related to an axis, as in quarts, or not so related, as in fluids, indicates a relation between the direction of the ray and the direction of rotation, which is similar in its formal expression to that between the longitudinal and rotatory motions of a right-handed or a left-handed screw; and it indicates some property of the substance the mathematical form of which exhibits right-handed or left-handed relations, such as are known to appear in the external forms of crystals having these properties. In the magnetic rotation no such relation appears, but the direction of rotation is directly connected with that of the magnetic lines, in a way which seems to indicate that magnetism is really a phenomenon of rotation.

(emphasis added)​

And this empirical dissimilarity with a screw (or helix, if you prefer) follows the only other paragraph where he uses the term screw:

Now it seems natural to suppose that all the direct effects of any cause which is itself of a longitudinal character, must be themselves longitudinal, and that the direct effects of a rotatory cause must be themselves rotatory. A motion of translation along an axis cannot produce a rotation about that axis unless it meets with some special mechanism, like that of a screw, which connects a motion in a given direction along the axis with a rotation in a given direction round it; and a motion of rotation, though it may produce tension along the axis, cannot of itself produce a current in one direction along the axis rather than the other.

So it is clear he was thinking about screws and helices, but did not embrace the idea as one rooted in physical phenomenon. (There are two mentions of helix but always in the context of solenoid windings of a physical apparatus.)

Rotational force is converted into linear force and vice versa.

Human thought is not best summarized as slogans from an advertising campaign or China's cultural revolution. Real human thought is expressed in reasoned argument. Here some math would serve you.

Minkowski was clear too. And yet we have James R insisting that you create a magnetic field for the electron when you move past it.

In 2010 I wrote:

Inability to comprehend relativity is the inability to put oneself intellectually into the shoes of another and working out the consequences. It seems to me that this belongs on the non-clinical side of a spectrum of sociopathic disorders. http://www.squidoo.com/the-sociopath-next-door

I contend that you are dismissing what Maxwell actually said ...

I contend that you are distorting what Maxwell actually meant and are doing so in the pursuit of trying to take physics back to some mythical past knowledge without having a shred of evidence about your claims that what you are doing is physics.

 

[Farsight]

I was really looking forward to your response to rpenner's criticism, and am disappointed with how flippant you were.

Sorry, but he started off by dismissing what Maxwell said with words like quaint, and later on accused me of misrepresenting Maxwell and resorted to insults instead of sticking to the physics. I have the patience of Job, but it is not limitless.

Your animation is very pretty, but tells me nothing; I assume something is being plotted as a function of the three spatial axes, but I don't know what it is or how the color choices correspond to its value.

You need some background covering pair production and Dirac's belt and the Dirac spinor and the Williamson / van der Mark toroidal-photon electron. The colour isn't particularly relevant, what we're depicting is the central portion of a 3D optical vortex wherein a field variation looks like a standing field. And do note it isn't my animation, it's Adrian Rossiter's. See his Antiprism torus animations. Apologies, I should have put in an image credit.

So maybe you can answer for me a really, really simple problem. In your picture, an electron is comprised entirely of the electromagnetic field, yes?

Yes. There isn't anything else. We made it from a field variation which we "wrapped up". There is no billiard-ball in the middle, and no point-particle. The spindle-sphere torus looks like a ball, but it isn't a solid ball, it's represents the central portion of an optical vortex. I think "the eye of the storm" is a pretty good analogy.

If so, please tell me the value of the electromagnetic field (as a function of x, y, z, and if necessary t) corresponding to the following scenario:

A single electron is at rest in a vacuum.

This is a really basic situation, but even so, it should give the rest of us some concrete details to work with for a change. In particular, this is your chance to prove that you can get isotropic fields from a 3-D vortex, which rpenner said was impossible. Please note that I don't want a picture, nor an analogy, nor a discussion of what Maxwell/Einstein/Bono thought of the issue. I want you to give me a formula. Can you do it?

No, sorry. I don't know how to describe this 3D optical-vortex standing-wave standing-field-structure mathematically. But I know of a few people who are submitting some papers to the SPIE conference in San Diego in August. You'll forgive me if I respect their privacy.

 

[Farsight]

...Inability to comprehend relativity is the inability to put oneself intellectually into the shoes of another and working out the consequences. It seems to me that this belongs on the non-clinical side of a spectrum of sociopathic disorders. http://www.squidoo.com/the-sociopath-next-door...

You know rpenner, it's my policy to remain civil in my internet discussions. But for you, I'm getting very close to making an honourable exception. However, instead, I will merely advise you that your abuse does you no credit, and that it is no substitute for physics. Your two posts above say nothing of value, it's all thin gruel dismissal, and a contradictory hostility epitomized by this: let that generosity of human spirit, that milk of human kindness lift the cataracts of pride and posturing from thine eyes. There is no posturing to quoting Maxwell or Minkowski:

"a motion of translation along an axis cannot produce a rotation about that axis unless it meets with some special mechanism, like that of a screw"

"In the description of the field caused by the electron itself, then it will appear that the division of the field into electric and magnetic forces is a relative one with respect to the time-axis assumed; the two forces considered together can most vividly be described by a certain analogy to the force-screw in mechanics; the analogy is, however, imperfect".

 

[rpenner]

abuse ... is no substitute for physics.

One difference between them appears to be that you respond to abuse.

 

[PhysBang]

Sorry, but he started off by dismissing what Maxwell said with words like quaint, and later on accused me of misrepresenting Maxwell and resorted to insults instead of sticking to the physics. I have the patience of Job, but it is not limitless.

This is a lie. rpenner has asked you many, many physics questions that you have dodged again and again.

While your inability to understand mathematics does not mark you as a bad person, your continued dishonesty does.

You need some background covering pair production and Dirac's belt and the Dirac spinor and the Williamson / van der Mark toroidal-photon electron. The colour isn't particularly relevant, what we're depicting is the central portion of a 3D optical vortex wherein a field variation looks like a standing field. And do note it isn't my animation, it's Adrian Rossiter's. See his Antiprism torus animations. Apologies, I should have put in an image credit.

At least my pointing out that you stole the image finally gets you to credit the source. The rest of the passage above is simply more dodging the question.

No, sorry. I don't know how to describe this 3D optical-vortex standing-wave standing-field-structure mathematically. But I know of a few people who are submitting some papers to the SPIE conference in San Diego in August. You'll forgive me if I respect their privacy.

Finally, you admit your ignorance.

Farsight, if your theory has no mathematics, then there is no reason to favor it rather than established physics. You have no theory.

 

[PhysBang]

Your two posts above say nothing of value,

You seem jealous that he did a better job at textual analysis than you did: your entire argument for the screw nature of electromagnetism relies on Maxwell, and rpenner demonstrated that Maxwell rejected this screw nature. Since you have no mathematics whatsoever, the textual evidence indicates that you should either abandon this theory or claim that it is a hypothesis until you can produce some mathematics and some tests.

There is no posturing to quoting Maxwell or Minkowski:

"a motion of translation along an axis cannot produce a rotation about that axis unless it meets with some special mechanism, like that of a screw"

There is posturing there, since you aren't looking at the part where Maxwell says that there isn't this kind of rotation.

"In the description of the field caused by the electron itself, then it will appear that the division of the field into electric and magnetic forces is a relative one with respect to the time-axis assumed; the two forces considered together can most vividly be described by a certain analogy to the force-screw in mechanics; the analogy is, however, imperfect".

So your entire theory now relies on an "analogy" that is "imperfect".

Do you feel like that's a good basis on which to build electronics?

 

[Farsight]

You seem jealous that he did a better job at textual analysis than you did: your entire argument for the screw nature of electromagnetism relies on Maxwell and rpenner demonstrated that Maxwell rejected this screw nature.

No he didn't, and LOL, you haven't even read the thread. You haven't followed anything, you've just jumped in with naysaying abuse like the dishonest troll you are. Now pay attention, and note that in post #87, I quoted Minkowski:

"In the description of the field caused by the electron itself, then it will appear that the division of the field into electric and magnetic forces is a relative one with respect to the time-axis assumed; the two forces considered together can most vividly be described by a certain analogy to the force-screw in mechanics; the analogy is, however, imperfect".

The electron has one field, the electromagnetic field. Electromagnetic field interactions between such particles result in linear electric force and rotational magnetic force.

 

[OnlyMe]

No he didn't, and LOL, you haven't even read the thread. You haven't followed anything, you've just jumped in with naysaying abuse like the dishonest troll you are. Now pay attention, and note that in post #87, I quoted Minkowski:

"In the description of the field caused by the electron itself, then it will appear that the division of the field into electric and magnetic forces is a relative one with respect to the time-axis assumed; the two forces considered together can most vividly be described by a certain analogy to the force-screw in mechanics; the analogy is, however, imperfect".

The electron has one field, the electromagnetic field. Electromagnetic field interactions between such particles result in linear electric force and rotational magnetic force.

That quote is of historical significance and pretty much out of date, as far as the progress that science has made since.

 

[PhysBang]

No he didn't, and LOL, you haven't even read the thread. You haven't followed anything, you've just jumped in with naysaying abuse like the dishonest troll you are.

As others have said, you seem to claim mind-reading abilities.

If anyone has not paid attention, it is you, since you have failed to answer any one of my physics questions. Others asked you two of them, to both of which you finally admitted that you cannot perform the answer.

I am satisfied that you have admitted and demonstrated your ignorance of physics and I will recommend to others that they read this thread and some of your particular responses in order to wholly discount your opinions.

Now pay attention, and note that in post #87, I quoted Minkowski:

You have been mis-quoting Minkowski for years. Your lies about him are no more interesting now than they were when you began.

If you could produce a mathematical description of your ideas, then they could be considered right or wrong. Now they can only be considered sad fantasies.

 

[Fednis48]

You need some background covering pair production and Dirac's belt and the Dirac spinor and the Williamson / van der Mark toroidal-photon electron.

I looked into the terms you mentioned, and the paper I found that seemed closest to what you're talking about was this one by Williamson and van der Mark. (In particular, you've used figure 2 before to illustrate your arguments.) In it, the authors propose a model for the electron in which a photon is bound into a "twisted strip" path, causing it to undergo one full twist before doubling back on itself. The result is that while the photon's field rotates as it travels, the twisting of its internal space counteracts that rotation, such that the electric field is everywhere pointing outward and the magnetic field is always pointing up. It's an interesting article, although it does raise some immediate questions in my mind:

1. In the diagrams, it does look like the net electric field is everywhere outward, but is it really? The authors specifically say that they can't prove that the electric field actually diverges from their proposed electron, mostly because they don't have a specific model of the topology yet (the torus in the figures is just the simplest among many topologies that meet their requirements). More concerning to me is the related question: even if the electric field diverges, does it do so isotropically? Any model of the kind they discuss will necessarily have a preferred axis in the direction of the electron spin, and it's not at all obvious that the electric field should be the same along that axis and orthogonal to it.

2. What makes the electric field so special? The authors discuss two ways in which the photon can be tied to itself: with the electric field pointing inward, to make an electron, or with it pointing outward, to make a positron. But as Farsight is so keen on pointing out, there really is just one electromagnetic field, and breaking it into electric/magnetic components is just a convenient decomposition. One could just as easily arrange things with the magnetic fields pointing radially, leading to a magnetic monopole with an electric "spin". More generally, an arbitrary rotation could point any quadrature of the oscillating field outward, leading to a whole spectrum of electromagnetic monopoles. But we don't see such particles - why not?

3. How do electrons interact in their model? It's all well and good to show that a properly twisted photon can produce a field of the desired type, but I can't see anything in the model that would cause twisted photons to react to fields in the way that electrons do. The only type of direct photon-photon interaction I know of is pair production, and that operates on much higher energy scales and shorter distances than the electric field.

Thinking about this last point had me confused for a while, because Farsight's talk about vortex interactions made at least qualitative sense from the moment I read it. Then it hit me: this is not Farsight's model! In this model, the photon's circulation is used to counteract its rotating polarization while producing a spin. Farsight, on the other hand, is talking about a sort of "dragging" effect, where the circulating photon causes the electromagnetic field itself to move vortically. Farsight's model may avoid some of the pitfalls of the Williamson/van der Mark proposal, but it runs into a big one of its own:

4. As rpenner insightfully noted, a 3-D vortex cannot be isotropic, according to the hairy ball theorem. I am skeptical that the field described in the link is isotropically radial, but as far as I know there is no reason in principle why it couldn't be so. On the other hand, the field definitely can't be isotropically vortical, because it's geometrically impossible to make a 3-D vector field do that, regardless of the underlying physical mechanism.

For that reason alone, Farsight's model seems wrong a priori. Finally, I have one objection that applies equally well to both models:

5. There are two types of bound states: global and local. In globally bound states, the energy of the bound state is less than that of its unbound counterpart, and it takes some external energy source to break the bond. By the Schrodinger equation, the amplitude of such a state decays exponentially beyond its classical boundary. The field from an electron only drops off as 1/r^2, even far outside the classical electron radius, so the photon comprising it cannot be globally bound. In locally bound states, the energy of the bound state is greater than or equal to the unbound energy, but a surrounding barrier of intermediate states have higher energy still, so the bound state is a local minimum. Such states can have significant amplitudes outside their classical boundaries, but if they do, then they also have a high chance of tunneling out of their local minima and becoming permanently unbound. We never see an electron spontaneously decay into a single photon, so the photon comprising it cannot be locally bound. Since an electron cannot be comprised of a globally or locally bound photon, it cannot be comprised of a bound photon at all.

 

[rpenner]

[Minkowski and Maxwell] both talked about the screw nature of electromagnetism.

a sneering ignorant arrogance that dismisses Maxwell and Minkowski and Einstein

I lack your arrogance to claim to be the sole inheritor of their vision and secret decoder ring and I bring evidence and argument to show where your interpretation of their words is strained, awkward, wrong and irrelevant. For the most part, this means I disagree with you as to facts and values, so I must leave it to the reader to judge which of us has argued better. (Or even which of us has read the same documents better.) Here is a pastiche of some posts that I don't feel you have argued against even though they contradict your position, as best as I can determine. I believe they stand firmly for the position that you have badly misinterpreted Minkowski's paragraph by stripping it of its context and connection to a larger sphere of mathematical physics than you have mastered.

Here you conflate Scottish author Maxwell's use of the terms "vortex" and "screw" (meaning the simple machine and the helix that makes it work) with the German author Minkowski's use of the phrase Kraftschraube der Mechanik which refers to a field of rigid-body dynamics. To explain the latter, if you are in free-fall and you poke a nearby body with a stick, usually you will impart both translational momentum and some sort of angular momentum to the body. How much depends on where you poke the body and the direction and magnitude of the poke. That's a field of dynamics all by itself because the math of 3-D rigid body motions is complex enough to be worthy of study, leading to such non-intuitive behavior as spinning tops that don't fall down. What Minkowski was saying in his 1908 address, "Raum und Zeit," was that the geometric transformation laws of the electromagnetic field was not trivial given a change in the standard of rest, and that similar results have been seen in the field of rigid-body dynamics because 3-D space is mathematically tricky. Both the theory of electromagnetism and the theory of spinning tops make use of vectors and cross-production for that underlying reason and Minkowski saw some analogous math between the topics.

Both $$\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})$$ and $$\vec{B} = \nabla \times \vec{A}$$ are commonly taught which compactly describes the way 3-D geometry enters into electromagnetism.

All analogies are imperfect. To understand the analogy you have to understand both endpoints and then you can see the similarities highlighted by the analogy and the dissimilarities where the analogy is not reliable.

Minkowski was a mathematically sophisticated person talking to an audience of people well-versed in physics and mathematics. Moreover, in context, Minkowski cited the Liénard–Wiechert description of electromagnetism of a moving charged particle in the immediately prior paragraph to make it clear what he was describing by analogy.

Die durch das Weltpostulat geschaffenen Vorteile werden vielleicht durch nichts so schlagend belegt wie durch Angabe der von einer beliebig bewegten punktförmigen Ladung nach der Maxwell-Lorentzschen Theorie ausgehenden Wirkungen. Denken wir uns die Weltlinie eines solchen punktförmigen Elektrons mit der Ladung e und führen auf ihr die Eigenzeit τ ein von irgendeinem Anfangspunkte aus. Um das vom Elektron in einem beliebigen Weltpunkte P₁ veranlaßte Feld zu haben, konstruieren wir den zu P₁ gehörigen Vorkegel (Fig. 4). Dieser trifft die unbegrenzte Weltlinie des Elektrons, weil deren Richtungen überall die von zeitartigen Vektoren sind, offenbar in einem einzigen Punkte P Wir legen in P an die Weltlinie die Tangente und konstruieren durch P₁ die Normale P₁Q auf diese Tangente. Der Betrag von P₁Q sei r. Als der Betrag von PQ ist dann gemäß der Definition eines Vorkegels r/c zu rechnen. Nun stellt der Vektor in Richtung PQ vom Betrage e/r in seinen Komponenten nach den x-, y-, z- Achsen das mit c multiplizierte Vektorpotential, in der Komponente nach der t-Achse das skalare Potential des von e erregten Feldes für den Weltpunkt P₁ vor. Hierin liegen die von A. Liénard und von E. Wiechert aufgestellten Elementargesetze.⁷

Bei der Beschreibung des vom Elektron hervorgerufenen Feldes selbst tritt sodann hervor, daß die Scheidung des Feldes in elektrische und magnetische Kraft eine relative ist mit Rücksicht auf die zugrunde gelegte Zeitachse; am übersichtlichsten sind beide Kräfte zusammen zu beschreiben in einer gewissen, wenn auch nicht völligen Analogie zu einer Kraftschraube der Mechanik.

⁷ A. Liénard, "Champ électrique et magnétique produit par une charge électrique concentrée en un point et animée d'un mouvement quelconque", L’Éclairage électrique Vol. 16, issue 27 (July 2, 1898), p. 5, 53, 106;
E. Wiechert, “Elektrodynamische Elementargesetze,” Archives Néerlandaises, Vol. 5, 1900, pp. 549-573.

It is the second of these paragraphs that uses the phrase I mentioned before, Kraftschraube der Mechanik. Lets see how this can be translated.

In the description of the field induced by the electron itself it then emerges that the divorce of the field into electric and magnetic force is a relative one with respect to the underlying time axis; most clearly both forces are to be described together in a certain, though not complete, analogy to a force-screw in mechanics.

If the field caused by the electron be described in the above-mentioned way, then it will appear that the division of the field into electric and magnetic forces is a relative one, and depends upon the time-axis assumed; the two forces considered together bears some analogy to the force-screw in mechanics; the analogy is, however, imperfect.

In the description of the field caused by the electron itself, then it will appear that the division of the field into electric and magnetic forces is a relative one with respect to the time-axis assumed; the two forces considered together can most vividly be described by a certain analogy to the force-screw in mechanics; the analogy is, however, imperfect.

The whole point of saying A is analogous to B is to say A shares some-but-not-all features of B. To learn what Minkowski is saying about electromagnetism, one must understand the physics and math of Kraftschraube der Mechanik.

Farsight misunderstands a reference to "force screw" (also called "wrench" ) in Newtonian mechanics of rigid bodies referring to a six-dimensional description of linear force + torque. No "twistyness" of the electromagnetic field† is implied by Liénard and Wiechert and therefore not by Minkowski, either. Thus Minkowski was just saying there was a six-dimensional mathematical object that describes the electromagnetic field at a point in every inertial frame. Today we call that geometric object the electromagnetic tensor.

http://de.wikipedia.org/wiki/Dyname (Notice mention of Kraftschraube)
http://en.wikipedia.org/wiki/Screw_theory
http://www.euclideanspace.com/maths/geometry/affine/screwTheory/index.htm
http://en.wikipedia.org/w/index.php?title=Liénard–Wiechert_potential&oldid=557636754

† The spin of the photon was not necessarily anticipated at this time. That would wait for generalizations of Dirac's equation in the 1920s, sensitive experimentation in the 1930s and for a 1939 paper by Wigner which is foundational for QFT.

Almost every time I read one of your posts these days I am reminded of one of rpenner's posts in another thread,

The sterility of an argument from authority is probably not obvious to those that have never supported empiricism. You have to have an open mind and an ability to fairly weigh the evidence and arguments for both sides of a proposition before judging it as acceptable, possibly acceptable at some later date, or unacceptable.

A purported quote or other reliance on an authority figure is not the same thing as a well supported argument based on all the evidence. For one, the authority is necessarily rooted in the past and may have not had access to the modern totality of evidence. Secondly, even the best authorities get things wrong in ways small (typos) and large (misguided rejection of well-supported arguments). Thirdly, some authorities speak on a wide range of topics, including those where they have no basis. Fourthly, some authorities write on their subject matter for average audiences in quite a different manner than to their fellow experts, because they know only a dilettante would refuse to look past some popular press explanation or analogy. And finally, distortions intentional and accidental happen when an authority's statement in the past is transcribed, translated, edited, quoted, paraphrased, cited and interpreted.

I was indeed thinking of your behavior when I wrote that post, Farsight. Good catch, OnlyMe!

 

[rpenner]

And,

Farsight asserts that there is a screw nature to electromagnetism and attempts to leverage an out-of-context reference by Minkowski in support of this.

[Above], I challenge this as a farcical misunderstanding of "Kraftschraube der Mechanik" as used by Minkowski. It is a pretty narrow comment directly addressing what Farsight wrote and the reason Farsight gave for what he wrote and why it seems like a poor reason to believe Farsight is correctly interpreting his sources.
Farsight does not defend his original assertion by explaining the analogy between the six-dimensional electrodynamic field of a charged particle according to Liénard, Wiechert, and Maxwell and the six-dimensional "force-screw of mechanics" so his repetition of an English translation of an out-of-context sentence from Minkowski is not illuminating.
...
Farsight continues to evade his responsibility to his readers to either support his claim about Minkowski or drop it in favor of my alternate explanation [above].
He challenges all interpretations but his own, but doesn't give any logical reason to believe.

He misstates the nature of electromagntism (possibly because he has confused magnetic field lines with the direction of magnetic force). He also contradicts himself on the nature of the electromagnetic field, because all tensors are geometric objects. He misstates my refutation of his interpretation of Minkowski as ignoring Minkowski.

So Farsight owes it to his readers and himself to either support his claim about Minkowski's use of analogy or explicitly drop it in favor of my alternate explanation [above].

 

[Farsight]

Damn, I've just lost my post because of some "accelerator key". That is so irritating, and I suspect it's the result of an automatic update. Sorry Fednis, this is going to be briefer than it was.

I looked into the terms you mentioned, and the paper I found that seemed closest to what you're talking about was this one by Williamson and van der Mark. (In particular, you've used figure 2 before to illustrate your arguments.) In it, the authors propose a model for the electron in which a photon is bound into a "twisted strip" path, causing it to undergo one full twist before doubling back on itself. The result is that while the photon's field rotates as it travels, the twisting of its internal space counteracts that rotation, such that the electric field is everywhere pointing outward and the magnetic field is always pointing up. It's an interesting article, although it does raise some immediate questions in my mind:

1. In the diagrams, it does look like the net electric field is everywhere outward, but is it really?

No. The field is the electromagnetic field. But cut them some slack, they wrote the paper in 1991. And a lot of teaching talks about electric fields and magnetic fields separately.

The authors specifically say that they can't prove that the electric field actually diverges from their proposed electron, mostly because they don't have a specific model of the topology yet (the torus in the figures is just the simplest among many topologies that meet their requirements). More concerning to me is the related question: even if the electric field diverges, does it do so isotropically?

The field is the electromagnetic field. Depict it like you'd depict the gravitomagnetic field, with Fibonacci spirals, but "curled" in three dimensions. As for isotropically I imagne you're talking about hairy-ball theorem wherein "A hairy doughnut (2-torus), on the other hand, is quite easily combable." Remember we inflate the torus to a spindle-sphere torus with a toroidal topology and a spherical geometry, see Adrian Rossiter's torus animations. .

Any model of the kind they discuss will necessarily have a preferred axis in the direction of the electron spin, and it's not at all obvious that the electric field should be the same along that axis and orthogonal to it.

It's got an electromagnetic field, and the spin is biaxial.

2. What makes the electric field so special? The authors discuss two ways in which the photon can be tied to itself: with the electric field pointing inward, to make an electron, or with it pointing outward, to make a positron. But as Farsight is so keen on pointing out, there really is just one electromagnetic field, and breaking it into electric/magnetic components is just a convenient decomposition. One could just as easily arrange things with the magnetic fields pointing radially, leading to a magnetic monopole with an electric "spin". More generally, an arbitrary rotation could point any quadrature of the oscillating field outward, leading to a whole spectrum of electromagnetic monopoles. But we don't see such particles - why not?

Because we're wrapping an electromagnetic field variation into a standing electromagnetic field.

3. How do electrons interact in their model? It's all well and good to show that a properly twisted photon can produce a field of the desired type, but I can't see anything in the model that would cause twisted photons to react to fields in the way that electrons do.

They don't cover it, but it's easy to conceive of interaction akin to cyclones and anticyclones. Dynamical spinors in frame-dragged space and all that.

The only type of direct photon-photon interaction I know of is pair production, and that operates on much higher energy scales and shorter distances than the electric field.

Yes, and that photon-photon interaction is the photon self-interaction that keeps it in a closed path.

Thinking about this last point had me confused for a while, because Farsight's talk about vortex interactions made at least qualitative sense from the moment I read it. Then it hit me: this is not Farsight's model! In this model, the photon's circulation is used to counteract its rotating polarization while producing a spin. Farsight, on the other hand, is talking about a sort of "dragging" effect, where the circulating photon causes the electromagnetic field itself to move vortically. Farsight's model may avoid some of the pitfalls of the Williamson/van der Mark proposal, but it runs into a big one of its own:

4. As rpenner insightfully noted, a 3-D vortex cannot be isotropic, according to the hairy ball theorem. I am skeptical that the field described in the link is isotropically radial, but as far as I know there is no reason in principle why it couldn't be so. On the other hand, the field definitely can't be isotropically vortical, because it's geometrically impossible to make a 3-D vector field do that, regardless of the underlying physical mechanism.

Ha! See above.

Damn I have to go out. To be continued.

 

[PhysBang]

Damn, I've just lost my post because of some "accelerator key". That is so irritating, and I suspect it's the result of an automatic update. Sorry Fednis, this is going to be briefer than it was.

Even if this claim is true, briefer is better because it will contain less words that dodge and say little.

No. The field is the electromagnetic field. But cut them some slack, they wrote the paper in 1991. And a lot of teaching talks about electric fields and magnetic fields separately.

This is a dodge of the question. The authors made a claim about the different components of the electromagnetic field. Either you have an answer to the question or they do or the physics doesn't work.

The field is the electromagnetic field. Depict it like you'd depict the gravitomagnetic field, with Fibonacci spirals, but "curled" in three dimensions. As for isotropically I imagne you're talking about hairy-ball theorem wherein "A hairy doughnut (2-torus), on the other hand, is quite easily combable." Remember we inflate the torus to a spindle-sphere torus with a toroidal topology and a spherical geometry, see Adrian Rossiter's torus animations. .

Here it seems that you really do not understand the question. That's good. What isn't good is that you attempt to lie about this fact by throwing random jargon and references at the problem.

Either you or the authors have a mathematical proof of the isotropy of the different components of the electromagnetic field or not. If not, then the physics doesn't work.

It's got an electromagnetic field, and the spin is biaxial.

Let's see the mathematics that establishes this. We cannot simply take your word that this magically works.

Because we're wrapping an electromagnetic field variation into a standing electromagnetic field.

This is, not surprisingly, a non-answer. Explain, in mathematical detail, the difference and why it prevents the monopole states. Either you or the authors have an answer or not; if not, then you do not have physics.

They don't cover it, but it's easy to conceive of interaction akin to cyclones and anticyclones. Dynamical spinors in frame-dragged space and all that.

At least here we have an admission that this is your idea and not someone elses. Still, if it is easy to conceive of things this way, let's see the mathematics. Let's see how your conception actually works.

Yes, and that photon-photon interaction is the photon self-interaction that keeps it in a closed path.

That is simply begging the question. Your circular reasoning is that the photon self-interacts because the photon self-interacts. Let's see the details, let's see the numbers.

Ha! See above.

Nowhere above have you addressed the problem of isotropy. I doubt that you really know what the problem is. Yet another thing you will lie about to cover your incompetence.

Damn I have to go out. To be continued.

Ah, more dodging.

 

[Farsight]

Thinking about this last point had me confused for a while, because Farsight's talk about vortex interactions made at least qualitative sense from the moment I read it. Then it hit me: this is not Farsight's model!

If you were to talk to Williamson and van der Mark today, their model wouldn't be the same as in the paper they wrote in 1991.

In this model, the photon's circulation is used to counteract its rotating polarization while producing a spin. Farsight, on the other hand, is talking about a sort of "dragging" effect, where the circulating photon causes the electromagnetic field itself to move vortically.

No, the electromagnetic field is the frame-dragged space.

Farsight's model may avoid some of the pitfalls of the Williamson/van der Mark proposal, but it runs into a big one of its own:

4. As rpenner insightfully noted, a 3-D vortex cannot be isotropic, according to the hairy ball theorem.

It was a straw-man argument. Rpenner knows full we that we're talking about a torus wherein A hairy doughnut (2-torus), on the other hand, is quite easily combable.

I am skeptical that the field described in the link is isotropically radial

There is no radial field. The radial E-field isn't a field, those lines aren't field lines, they're lines of force. Co-rotating vortices repel, counter-rotating vortices attract.

but as far as I know there is no reason in principle why it couldn't be so. On the other hand, the field definitely can't be isotropically vortical, because it's geometrically impossible to make a 3-D vector field do that, regardless of the underlying physical mechanism.

The g-factor is 2.002319 rather than 2. The magnetic moment tells you there's something going round, and the anomalous magnetic moment tells you that there's an asymmetry.

For that reason alone, Farsight's model seems wrong a priori.

There's hard scientific evidence in things like the Einstein-de Haas effect which "demonstrates that spin angular momentum is indeed of the same nature as the angular momentum of rotating bodies as conceived in classical mechanics". We make the electron (and the positron) out of light, it's got a magnetic moment, there's something going round and round, what can it be? Cheese?

Finally, I have one objection that applies equally well to both models:

5. There are two types of bound states: global and local. In globally bound states, the energy of the bound state is less than that of its unbound counterpart, and it takes some external energy source to break the bond.

OK. After pair production the electron is a self-bound photon, as is the positron, and if they aren't moving fast there's not enough energy to separate them, and they're bound together, and will annihilate. So...

By the Schrodinger equation, the amplitude of such a state decays exponentially beyond its classical boundary. The field from an electron only drops off as 1/r^2, even far outside the classical electron radius, so the photon comprising it cannot be globally bound. In locally bound states, the energy of the bound state is greater than or equal to the unbound energy, but a surrounding barrier of intermediate states have higher energy still, so the bound state is a local minimum. Such states can have significant amplitudes outside their classical boundaries, but if they do, then they also have a high chance of tunneling out of their local minima and becoming permanently unbound. We never see an electron spontaneously decay into a single photon, so the photon comprising it cannot be locally bound. Since an electron cannot be comprised of a globally or locally bound photon, it cannot be comprised of a bound photon at all.

Oh phooey! We do our pair production, we get our electron and our positron, each has its magnetic moment etc, and when we annihilate them we get the photons back. You're clutching at straw men, Fednis. Look at what you're saying. It can't be bound because we don't see it spontaneously unbind itself!

 

[PhysBang]

If you were to talk to Williamson and van der Mark today, their model wouldn't be the same as in the paper they wrote in 1991.

Perhaps because they abandoned the idea as not feasible?

It was a straw-man argument. Rpenner knows full we that we're talking about a torus wherein A hairy doughnut (2-torus), on the other hand, is quite easily combable.

Since you have never provided the equations for your "vortex", you can easily dodge the question of its nature. Please give us the equations for your now torus vortex.

Oh phooey! We do our pair production, we get our electron and our positron, each has its magnetic moment etc, and when we annihilate them we get the photons back. You're clutching at straw men, Fednis. Look at what you're saying. It can't be bound because we don't see it spontaneously unbind itself!

Your only answer to the relevant physics is, "Oh phooey!" If you have a problem with the empirically determined nature of bound states, then show the flaw in the reasoning, don't just say it is wrong because you don't like the result.