Roll the Bones said:Dr Chaos said:Prominent Bethelite said:In news message <3f1b4e79$1@cicada> Stephen Andrewartha
<[email hidden]> wrote:-
>I've openly confessed my atheist leanings to some JWs,
Gen 1:3 (Authorized PB Version)
div(B)=0
div(D)=Pf
curl(E)=-dB/dt
curl(H)=jf+dD/dt
And then Einstein asked, 'excuse me Herr yhvh, didn't you
mean to say
e^iklm dF_lm/dx^k = 0
dF^ik/dx^k = -4pi/c j^i ?'
'oh yeah.'
Could you please say where those equations come from? And the relation
to Maxwell's equations?
They are Maxwell's equations (in vacuum) in four-vector form, which
exposes their relativistic invariance and transformations.
The first equation is equivalent to the two Maxwell equations
curl E = -1/c dH/dt and div H = 0.
The second gives the Maxwell equations with sources.
F_{ik} is the 4x4 electromagnetic field tensor, and 'j' the
four-vector of charge and current density.
Maxwell did not write his equations in either of these forms
as vector notation had not been invented (though the concepts
had been), and obviously relativity hadn't either.
Quoted message said:I'm not a mathematician or physicist, but they
don't look like the equations from either Special or General
Relativity.
They are.
When you go to moving reference frames, not only do lengths
and times transform, so do electromagnetic fields, with magnetic
and electric fields mixing together---i.e. what was once a magnetic
field at rest could be an electric field and vice versa.
This, in fact, was the subject of Einstein's famous 1905 paper.
The equations of electromagnetism shown above look nearly the same in
general relativity, replacing some ordinary of the derivatives with
the appropriate covariant derivatives, and this gives the equations of
electromagnetism in a gravitational field.
