Symmetric but non-local pure-field expression of EM interactions

ABSTRACT

A fields-only formulation of EM interactions that does not invoke charge explicitly is presented. The EM interaction ceases to be the result of an asymmetric action of a field on a point charge locally, but instead is the result of applying Hamilton’s principle of virtual work to the symmetric but non-local interaction of space-filling EM fields themselves. The fields themselves are therefore the only fundamental entities. A fields-only understanding of EM interactions is important in situations where the EM fields are knotted, for example in plasma confinement and nuclear magnetic resonance devices where EM knots have been realised, as well as in models of elementary particles as knotted solutions of EM fields.

KEYWORDS:

• Field interactions
• non-local interaction
• electromagnetic knot
• Lorentz force

Acknowledgements

The initial investigation of a pure field form of the electromagnetic force was inspired by a discussion between P.H.B. and Martin van der Mark on topological fields and the (inter)action between fields. It is a pleasure to acknowledge the implicit contribution to that conversation by John Williamson.

Notes

No potential conflict of interest was reported by the authors.

1 The required calculations are straightforward albeit tedious. The reader is referred to [1,26] for more detailed calculations.

Additional information

Funding

This work was supported by Xi’an Jiaotong-Liverpool University [grant number RDF-14-03-13] and Natural Science Foundation of China [grant number 11505143].