Re: Is charge conserved between frames?

From: sal (pragmatist_at_nospam.org)
Date: 11/01/04 

Date: Sun, 31 Oct 2004 22:57:20 -0500

On Sun, 31 Oct 2004 14:29:55 +0000, Tom Roberts wrote:

> sal wrote:
>> All we've managed to do is split
>> the Faraday 2-form into an electric 4-vector and a magnetic 2-form which
>> are, if anything, harder to apply and more confusing than the original
>> object.
>
> No, you have done nothing of the sort. The {E_a} you've been discussing
> are NOT "the electric field", they are, as I said before, "the components
> of the electric field measured by the observer with 4-velocity U,
> expressed as the components of a 4-vector".

I understood that perfectly well before you interjected this comment. The
E_a definition has already been beaten to death and you're apparently just
trying to pick at the same old nits again, starting from the top.

There's a flaw in the statement I made, above, but you seem to
have overlooked it. Care to try to find it? I'll be happy to point it
out, if you're curious (do not take this as any attempted slur on your
abilities -- I know perfectly well you're capable of seeing it yourself
but I think you may really just have overlooked it).

> Note the 4-vector corresponding to the {E_a} is NOT a field -- it is NOT a
> function on the manifold (as is F(.,.) -- F(.,.) is the only field in this
> discussion[#]), but rather the {E_a} are a function of both location along
> U's worldline and of U. The {E_a} are not even defined off of U's
> worldline, so how could they possibly be interpreted as any sort of
> "electric field"????
>
> [#] OK, the {F_ab} is a set of scalar fields when expressed relative to a
> specific basis, within the region of the manifold in which that basis is
> valid.

Yes, E_a can be viewed as a field, as I already pointed out at rather
annoying length in another post. I'm sure you don't want to, though :-)
and neither does anyone else, really. 

-- 
I can be contacted through http://www.physicsinsights.org

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