How can a single moving charge generate a magnetic field relativistically

[juanrga]

Unless I missed it the APS article presented an alternative formulation but did not demonstrate that the usual formulation was "ill-founded" as you have claimed. The Feynman quote certainly doesn't state that the "unsatisfactory" problems he refers to are not related to classical point charges.

If that is all you have then I am not terribly concerned. If you have something more explicit then I would be very interested. As I said above, I am not aware of any problems with classical EM which are not related to the classical notion of point particles.

I already answered this.

 

[juanrga]

Even in a system of two or more particles, the formalism presented makes no direct use of the concept of a field. It is not that for one particle there is no field and for two particles there is, it just doesn't directly use fields at all. Instead, it calculates the forces on the particle and works backwards to show what the usual formalism would describe as the field.

This is all wrong. They introduce the concept of adjunct field {*}:

... the field adjunct to a given particle...

For a single particle there is not adjunct field; only when there are 2 or more particles the adjunct field is nonzero (page 426). Of course, both statements are easy to check using equations 2 and 4.

There is no reason to continue this discussion when you are completely unaware of the topic and even cannot read simple text.

Again, AFAIK those are only due to classical point particles.

As said, that is not true.

{*} Also known as direct particle fields in the specialized literature.

 

[Dale]

This is all wrong. They introduce the concept of adjunct field {*}:

For a single particle there is not adjunct field; only when there are 2 or more particles the adjunct field is nonzero (page 426). Of course, both statements are easy to check using equations 2 and 4.

Sure, but with the action principle in 1 there seems to be no direct need to calculate the adjunct field. Wheeler and Feynman themselves say "In this description of nature no direct use is made of the notion of field". I believe that I said essentially the same thing.

There is no reason to continue this discussion when you are completely unaware of the topic and even cannot read simple text.

It is certainly your perogative to stop responding. However, since the purpose of the site is educational in nature my admitted ignorance doesn't preclude me from posting. With your vast wisdom and deep insight you could be helpful rather than petulant.

As said, that is not true.

You have said it, but not yet supported it with any evidence. Can you show a reference where there is shown to be some fundamental self-inconsistency in classical EM that does not arise from the concept of a classical point particle? If so, I would like the reference (it is not in the references provided thus far and I am not aware of it), if not then you should stop claiming it.

 

[neoplay]

Evidently, as Feynman and Wheeler stated in the paper cited, a single charged particle cannot generate anything. It is only when a second charge is present that the fields are non-zero. This eliminates all the nonsense (including divergences and other deficiencies) traditionally attributed to Maxwell theory.

Now you are just dragging the discussion out of perspective. The intention of Wheeler/Feynman article is not to state if the electric or magnetic field can or cannot be generated by a single charge. Instead, they used two particles system to express the causality concerns that is inherited from Maxwell Equations. What they were saying was that since the Maxwell Equations are time symmetric, whenever an electromagnetic wave is generated at time T(0), there should be another wave before T(0) i.e. at T(-) called Retarded Solution that is symmetric to the one after T(0) i.e. at T(+) called Advanced Solution for all time. However, in our physical world, we can’t detect any wave before T(0) and this is the problem they were trying to address.

Of course, Maxwell Equations did not lead to Quantum Theories while Maxwell Equations lead Einstein to discover Relativity due to the “C” constant in Maxwell Equation that is a constant in all frames of reference. As today, Einstein’s two Relativity Theories are still held true.

The discrepancies between Maxwell Equations and Quantum Theories are not a proof of Maxwell Equations being wrong. It only stating that Maxwell Equations are not complete, and so as Quantum Theory. We are far from getting a complete theory to explain everything and it is possible that we could never find one as indicated by Gödel's incompleteness theorems.

BTW, Wheeler and Feynman later abandoned their initial attempt stated in the article you cited.

 

[juanrga]

Now you are just dragging the discussion out of perspective. The intention of Wheeler/Feynman article is not to state if the electric or magnetic field can or cannot be generated by a single charge. Instead, they used two particles system to express the causality concerns that is inherited from Maxwell Equations. What they were saying was that since the Maxwell Equations are time symmetric, whenever an electromagnetic wave is generated at time T(0), there should be another wave before T(0) i.e. at T(-) called Retarded Solution that is symmetric to the one after T(0) i.e. at T(+) called Advanced Solution for all time. However, in our physical world, we can’t detect any wave before T(0) and this is the problem they were trying to address.

Of course, Maxwell Equations did not lead to Quantum Theories while Maxwell Equations lead Einstein to discover Relativity due to the “C” constant in Maxwell Equation that is a constant in all frames of reference. As today, Einstein’s two Relativity Theories are still held true.

The discrepancies between Maxwell Equations and Quantum Theories are not a proof of Maxwell Equations being wrong. It only stating that Maxwell Equations are not complete, and so as Quantum Theory. We are far from getting a complete theory to explain everything and it is possible that we could never find one as indicated by Gödel's incompleteness theorems.

The goals of Wheeler and Feynman are well-stated in the article introduction. The conclusion section is still more clever. If you read this section, you will discover that it says nothing about advanced waves. Pay attention to the phrase «free of the ambiguities associated with the idea of particle acting upon itself». Those ambiguities are characteristic of Maxwell theory because Maxwell theory allows a single particle to generate a field, whereas the new theory associates a field only when there are more than one particle.

BTW, Wheeler and Feynman later abandoned their initial attempt stated in the article you cited.

They abandoned only partially their original project due to posterior technical difficulties. Although Feynman used his classical formulation as basis for his development of QED.

Their approach has been revived in recent years (and early difficulties eliminated) because now it is broadly accepted that the concept of field is only approximated, not fundamental as Maxwell or Einstein incorrectly believed.

Extensions of Wheeler and Feynman theory are studied with an eye to its application to superstring theory, for instance. And there is also authors who have extended the theory to gravitation providing an improvement over GR similar to the improvement done by Wheeler and Feynman over Maxwell theory.