arXiv subjects

Oliver Davis Johns

Publications and source records attributed to Oliver Davis Johns.

7 recordsLinked to original sources

arXiv2023

Helmholtz Theorem and Uniqueness

Vector calculus in three dimensions with a Euclidian metric is the lingua franca of classical physics, including classical electrodynamics. This article corrects some long-standing imprecision in a fundamental result. Some textbooks assert that a vector function defined in the whole of a three dimensional space is uniquely determined by its divergence, its curl, and the condition that the function goes to zero as the radius (distance from an origin) goes to infinity. This article suggests that this condition is not sufficient for uniqueness. A proof is given that a sufficient condition for uniqueness is for the vector function to approach zero more rapidly than radius to the minus 3/2 power as the radius goes to infinity. The issue is important because the same uniqueness condition also determines the uniqueness of the decomposition of a vector field into a transverse field plus a solenoidal field, as is done in the Coulomb gauge of electrodynamics.

physics.class-ph↗

arXiv2023

A Spherical Version of Feynman's Static Field Momentum Example

The Feynman demonstration that electromagnetic field momentum is real-even for static fields-can be made more pedagogically useful by simplifying its geometry. Instead of Feynman's disk with charged balls on its surface, this article uses the geometry of a hollow non-conducting sphere with uniform surface charge density. With only methods available in a typical upper-division electrodynamics course, the initial field angular momentum and the final mechanical angular momentum can then be calculated in closed form and shown to be equal. This simplified geometry also provides a counterexample for the idea that electromagnetic field momentum is due to the flow of an electromagnetic inertial mass, defined as the energy density divided by the square of the speed of light. The curved flow lines of an inertial field momentum would require a centripetal force to bend them, but no such force can be identified.

physics.hist-ph↗

arXiv2023

Is Electromagnetic Field Momentum Due to the Flow of Field Energy?

Conservation laws that are based on the divergence of a second-rank four-tensor are fundamentally different from conservation laws based on the divergence of a four-vector. This article investigates the consequences of this difference for understanding the relation between electromagnetic field momentum and the flow of electromagnetic field energy. Momentum and energy conservation require electromagnetic field momentum and energy to be treated as physically real, even in static fields. This motivates the conjecture that field momentum might be due to the flow of a relativistic mass density (energy density divided by the square of the speed of light). This article investigates the velocity of such flow and finds a conflict between two different definitions of it. This investigation is careful to respect the transformation rules of special relativity. The paper demonstrates that the consensus definition of the flow velocity of electromagnetic energy is inconsistent with the transformation rules of special relativity, and hence is incorrect. A correct flow velocity is then derived which is completely consistent with those transformation rules. The conclusion is that these conflicting definitions of flow velocity cannot be resolved in a way that is consistent with special relativity and that also allows electromagnetic field momentum to be the result of energy flow. Though real, field momentum cannot be explained as the flow of field energy. As a byproduct of the study, it is also shown that there is a comoving system in which the electromagnetic energy-momentum tensor is reduced to a simple diagonal form, with two of its diagonal elements equal to the energy density and the other two diagonal elements equal to plus and minus a single parameter derived from the electromagnetic field values, a result that places constraints on possible fluid models of electromagnetism.

physics.hist-ph↗

arXiv2023

Validity of the Einstein Hole Argument

Arguing from his "hole" thought experiment, Einstein became convinced that, in cases in which the energy-momentum-tensor source vanishes in a spacetime hole, a solution to his general relativistic field equation cannot be uniquely determined by that source. After reviewing the definition of active diffeomorphisms, this paper uses them to outline a mathematical proof of Einstein's result. The relativistic field equation is shown to have multiple solutions, just as Einstein thought. But these multiple solutions can be distinguished by the different physical meaning that each metric solution attaches to the local coordinates used to write it. Thus the hole argument, while formally correct, does not prohibit the subsequent rejection of spurious solutions and the selection of a physically unique metric. This conclusion is illustrated using the Schwarzschild metric. It is suggested that the Einstein hole argument therefore cannot be used to argue against substantivalism.

physics.hist-ph↗

arXiv2023

Magnetic Charge and Dyality Invariance

This paper is a critical study of non-standard Maxwellian electrodynamics. It explores two important topics: the inclusion of both magnetic and electric charge to produce what it calls Extended Electrodynamics, and the existence of a symmetry called Dyality Invariance that exchanges electric and magnetic quantities. First, the paper summarizes Extended Electrodynamics, including potentials, gauge transformations, and a new proof of the extended electrodynamic Poynting theorem. A formal Lagrangian derivation of the extended Maxwell equations is also given, but its value in fundamental studies is questioned. The paper then defines Dyality Invariance (form invariance under the so-called Dyality Transformation that exchanges electric and magnetic quantities) and shows it to be a valid symmetry if and only if electrodynamics is given the extended form. The paper suggests that the complete Maxwellian electrodynamics is extended electrodynamics with its dyality invariance. But dyality can be interpreted either actively or passively. Since magnetic charge has not been observed experimentally, the active interpretation is ruled out. But a passive interpretation can be used to avoid writing magnetic source and potential terms explicitly. The paper also refutes the idea that dyality invariance would permit a magnetic charge to be transformed away even if one existed. If nonzero magnetic charge exists, then experimental evidence for its existence cannot be hidden by a dyality transformation.

physics.class-ph↗

arXiv2021

Relativistically Correct Electromagnetic Energy Flow

Detailed study of the energy and momentum carried by the electromagnetic field can be a source of clues to possible new physics underlying the Maxwell Equations. But such study has been impeded by expressions for the parameters of the electromagnetic energy flow that are inconsistent with the transformation rules of special relativity. This paper begins by correcting a basic parameter, the local velocity of electromagnetic energy flow. This correction is derived by the direct application of the transformation rules of special relativity. After this correction, the electromagnetic energy-momentum tensor can then be expressed in a reference system comoving with the energy flow. This tensor can be made diagonal in the comoving system, and brought into a canonical form depending only on the energy density and one other parameter. The corrected energy flow and its energy-momentum tensor are illustrated by a simple example using static electric and magnetic fields The proposal that electromagnetic momentum results from the motion of a relativistic mass contained in the fields is examined in the context of the corrected flow velocity. It is found that electromagnetic field momentum, though real, cannot be explained as due only to the motion of relativistic mass. The paper concludes that introducing the requirement of consistency with special relativity opens the study of electromagnetic energy and momentum to new possibilities.

physics.gen-ph↗

arXiv2019

Leibniz Equivalence, Newton Equivalence, and Substantivalism

Active diffeomorphisms map a differentiable manifold to itself. They transform manifold points and objects without changing the system of local coordinates used to represent those objects. What has been called Leibniz Equivalence is the assertion that, although active diffeomorphisms do change manifold objects, they do not change what is called the "physical situation" being modeled by those objects. This paper introduces the contrasting idea of Newton Equivalence, which asserts that the different values of manifold objects produced by active diffeomorphisms do model different physical situations. But due to the assumption of general covariance, these different physical situations are all equally possible. They represent physically different situations all of which could happen. This paper compares these two interpretations of active diffeomorphisms, and comments on their importance in the substantivalism debate.

physics.hist-ph↗