
Originally Posted by
Quantum immortal
I interpret it in precisely the way I was explaining it before - the presence of a magnetic field allows you to deduce the presence of an electric charge at some state of relative motion, and all other observers will agree ( charge is invariant ). However, the reverse is
not true - the absence of a magnetic field in some frame does not mean there is no electric charge present, or alternatively, the presence of an electric field does not allow you to deduce the presence of magnetic fields, because both
E and
B fields are observer-dependent. The upshot is that you need relations for
both fields to uniquely specify the laws of electromagnetism - as I have stated earlier. Magnetism alone isn't enough, but then neither is the electric field.
If I can't visualise the concept I have difficulty taking the maths as physically real.
Consider electromagnetism as formulated in the language of differential forms, and the associated plain text meanings :
"No magnetic tubes ever end" = "Magnetic field lines form closed loops" = "There are no magnetic charges"
"The number of electric tubes that end in an elementary volume is equal to the amount of charge enclosed in that volume"
Maybe I have some special insight that others don't have ( which I sincerely doubt ! ), but to me the meaning of these expressions is so visual and intuitive that I really don't think one could formulate them any more clearly, or elegantly. Or am I missing something ?