The classical field theory of matter and electricity - An approach from first principles

The most desirable classical field theory of the fundamental continuous substratum of matter, from which we can imagine particles are formed, would generally be considered to be the electromagnetic equations but for the fact that these are not consistent with the permanent existence of electrons. Instead of attempting (as has been usual) to modify the equations by special assumptions for the purpose, the problem is attacked here by deriving from first principles field equations which represent conserved matter; for the failure of the standard equations can be traced to the fact that they do not admit conservation of energy and momentum in general, but only in simple cases. The new equations are found to be identical with those of standard electromagnetic theory except that they contain two extra variables, which indicate the existence of additional energy, momentum and stress in the field. The two variables, however, come into the equations in a way which allows them to be included in the charge and current terms, so that they become there concealed and leave the form of the equations virtually unchanged. Consequently they do not affect the ordinary practical use which is made of the electromagnetic equations; they only come into open play in fundamental theory and in the presence of charge and current in the field, and there they remove the difficulties which the electromagnetic field theory in its accepted form presents.