Forces on fields

Abstract

In electromagnetism, as in Newton's mechanics, action is always equal to reaction. The force from the electromagnetic field on matter is balanced by an equal and opposite force from matter on the field. We generally speak only of forces exerted by the field, not forces exerted upon the field. But, we should not be hesitant to speak of forces acting on the field. The electromagnetic field closely resembles a relativistic fluid and responds to forces in the same way. Analyzing this analogy sheds light on the inertial role played by the field's mass, the status of Maxwell's stress tensor, and the nature of the electromagnetic field.

Eliminating Electron Self-repulsion

“…This classical field 5 Given that the electron will be modeled classically in the next section as a lump of energy and charge in the classical Dirac field, one might wonder whether it makes sense to think of the above density of force as acting on a field (the Dirac field). For defense of the idea that forces act on both the electromagnetic and Dirac fields, see [28,29]. 6 Although I will not do so here, there are reasons (coming from quantum field theory) to treat the components of the Dirac field ψ at a given location as anticommuting Grassmann numbers instead of complex numbers (see [15] and references therein).…”

The Disappearance and Reappearance of Potential Energy in Classical and Quantum Electrodynamics

“…(If you do not agree that potential energy is extrinsic energy, you may read this paper as an exploration of intrinsic and extrinsic energy-asking whether there is a separate intrinsic energy density for the electromagnetic field and another for charged matter. 5 )…”

“…. The electromagnetic field has an energy density and, applying the above version of mass energy equivalence, it also has a relativistic mass density equal to its energy density divided by c 2 [2, box 8.3]; [5,25]. Similarly, the Dirac field has a relativistic mass density equal to its energy density divided by c 2 [67, p. 238]; [68, p. 35]; [63,64].…”

“…Third, given that the electromagnetic field is a real thing possessing energy and momentum, one might wonder how far the similarities between matter and field go. Like matter, the electromagnetic field possesses mass, has a velocity at each point in space, and experiences forces (equal and opposite the Lorentz forces exerted on matter [5]). Here I present a disanalogy in the context of a classical or quantum theory of electromagnetic and Dirac fields: the Dirac field has potential energy but the electromagnetic field does not.…”