Charges without fields, fields without charges

[lalbatros]

Hello,

As many people, I have been fascinated by the "Classical electrodynamics in terms of direct interparticle interaction" theory developped by Feynman and that he abandonned later. This is a representation of electrodynamics where fields play no direct role: they do no appear in the least action principle and pop up only as auxilliary quantities. There is no action of an electron on itself.

I would be curious to know if an opposite theory has been investigated: "fields without charges".
This would be a theory where only electromagnetics fields have the major role.
Charges would not appear in the Lagrangian, only fields.
Of course, singularities of the fields would be identified to charges, but they would not appear as primitive concepts, but as secondary a secondary concept: fields could have singularities, with some consequences.

Would some of you have seen something like that?

Thanks,

Michel

 

[dgOnPhys]

Hi Michel,

I do not know in detail Feynman theory for interaction-based-only electrodynamics (nor I understand how you could not have self-force) but for its basic equations.

I have wondered myself about your source-less interpretation of electromagnetic theory because as you said the fields and their singularities already tell the whole story.

I guess it is mainly a question of conventions and formalism, some problems will be harder to describe without mentioning isolated particles.

One point that I find particularly interesting is the connection between quantization of charge and theory of residues (encirclements of singularities)

 

[lalbatros]

You are right dgOnPhys.

If the game was only about making maths more intricate just to avoid the sight particles in the Lagrangian, it would really be useless. In addition we would need to detect singularities! We could better pretend that the classical formulation is simpler and complete, why bother then?

In contrast, the "charges without fields" theory developed by Wheeler and Feynman, comes with a bonus: no self action of a charge on itself. And there is also a cost for this: an advanced force appears in the equations of motion. This advanced force could be considered a defect on the ground of causality. It can also be shown to disappear under certain assumptions, as Wheeler and Feynman did in their paper "http://books.google.com/books?id=qn...bsorber as a mechanism of radiation’&f=false"". Dissipation on the edge of the universe, as I understood it, would in the end remove the advanced term and pay the bonus back: a consistent self-reaction of the charge that explains radiative damping.

I wonder if there would be any bonus in a field-only point of view.

Michel

 

[dgOnPhys]

Thanks for the article and your explanation about self-force as induced by charge at infinity, I will definitely have a look.

Your question about possible payback of an alternative point of view makes a lot of sense to me but I am not sure I can take much of a guess as of what that could be.

As I mentioned before I have always been surprised that quantization of charge (discrete singularities) does not induce any effect in classical electromagnetic theory as for example quantization of energy does in the black body radiation.

There are plenty of shady areas in classical electromagnetism that are currently being neglected as most focus their efforts on more fashionable areas of physics... too bad!

I guess I have some work cut out for my retirement years...

 

[sardar]

I find the idea of a theory where only fields have the major role to be intriguing. While there have been various attempts to formulate electromagnetism without charges, none have been fully successful. The main challenge is that charges are fundamental quantities in our understanding of electromagnetism, and it is difficult to completely eliminate them from the theory.

One approach that has been explored is to consider a theory where charges are not point-like particles, but rather extended objects, such as strings or membranes. In this way, the concept of a point charge is replaced by a distribution of charge along a one-dimensional or two-dimensional object. This approach has shown some success in certain contexts, but it still relies on the concept of charges and does not completely eliminate them from the theory.

Another approach is to consider a theory where the fundamental quantities are not charges, but rather field strengths. This idea has been explored in the context of Kaluza-Klein theories, where the electromagnetic field is unified with the gravitational field in higher dimensional spacetimes. In these theories, charges arise as a consequence of the topology of the higher dimensional spacetime, rather than being fundamental quantities. However, this approach also has its limitations and has not been fully successful in eliminating charges from the theory.

Overall, while it is an interesting idea to explore a theory where only fields have the major role, it is a challenging task to completely eliminate charges from our understanding of electromagnetism. Charges and fields are deeply intertwined in our current understanding of the theory, and it is difficult to separate them completely. However, this does not mean that the idea should not be explored further, as it may lead to new insights and understanding in the future.