Editing Longitudinal wave (section)

== Electromagnetics ==

[[Maxwell's equations]] lead to the prediction of [[electromagnetic wave]]s in a vacuum, which are strictly [[transverse wave]]s; due to the fact that they would need particles to vibrate upon, the electric and magnetic fields of which the wave consists are perpendicular to the direction of the wave's propagation.<ref name="griffiths">[[David J. Griffiths]], Introduction to Electrodynamics, {{ISBN|0-13-805326-X}}</ref> However [[plasma wave]]s are longitudinal since these are not electromagnetic waves but density waves of charged particles, but which can couple to the electromagnetic field.<ref name="griffiths" /><ref>John D. Jackson, Classical Electrodynamics, {{ISBN|0-471-30932-X}}.</ref><ref>Gerald E. Marsh (1996), Force-free Magnetic Fields, World Scientific, {{ISBN|981-02-2497-4}}</ref>

After [[Heaviside]]'s attempts to generalize Maxwell's equations, Heaviside concluded that electromagnetic waves were not to be found as longitudinal waves in "''[[free space]]''" or homogeneous media.<ref>Heaviside, Oliver, "''Electromagnetic theory''". ''Appendices: D. On compressional electric or magnetic waves''. Chelsea Pub Co; 3rd edition (1971) 082840237X</ref> Maxwell's equations, as we now understand them, retain that conclusion: in free-space or other uniform isotropic dielectrics, electro-magnetic waves are strictly transverse. However electromagnetic waves can display a longitudinal component in the electric and/or magnetic fields when traversing [[birefringent]] materials, or inhomogeneous materials especially at interfaces (surface waves for instance) such as [[Zenneck wave]]s.<ref>Corum, K. L., and J. F. Corum, "''The Zenneck surface wave''", ''Nikola Tesla, Lightning Observations, and stationary waves, Appendix II''. 1994.</ref>

In the development of modern physics, [[Alexandru Proca]] (1897–1955) was known for developing relativistic quantum field equations bearing his name (Proca's equations) which apply to the massive vector spin-1 mesons. In recent decades some other theorists, such as [[Jean-Pierre Vigier]] and Bo Lehnert of the Swedish Royal Society, have used the Proca equation in an attempt to demonstrate photon mass<ref>{{Cite journal |doi = 10.1103/PhysRevLett.80.1826|bibcode = 1998PhRvL..80.1826L|title = Experimental Limits on the Photon Mass and Cosmic Magnetic Vector Potential|year = 1998|last1 = Lakes|first1 = Roderic|journal = Physical Review Letters|volume = 80|issue = 9|pages = 1826–1829}}</ref> as a longitudinal electromagnetic component of Maxwell's equations, suggesting that longitudinal electromagnetic waves could exist in a Dirac polarized vacuum. However [[Photon#Experimental checks on photon mass|photon rest mass]] is strongly doubted by almost all physicists and is incompatible with the [[Standard Model]] of physics.{{cn|date=May 2021}}