Re: Electromagnetic stress-energy tensor :)

Ken S. Tucker:
>Hi
>
>Lacustral wrote:
>> So I've been reading about the stress-energy tensor.
>I don't understand the
>> stress-energy tensor for the electromagnetic field.
>>
>> The book
>
>whose book?

Ken, don't waste someone's time with your bull***.

>
>> says the space-space components of the stress tensor describe a
>> tension (E^2 + B^2)/8pi along the field lines.
>> And a pressure (E^2 + B^2)/8pi perpendicular to the field lines.
>>
>> What the space-space components of it look like, is:
>>
>> T^jk = 1/4pi ( -(E^j*E^k + B^j*B^k)) + 1/8pi (E^2 + B^2)*I
>>
>> where I is the identity matrix.
>>
>> I can see how there is a pressure (E^2 + B^2)/8pi in the E x B direction -
>> since E x B would be in the null space of the E^j*E^k + B^j*B^k matrix.
>>
>> But I don't see where there's a tension (E^2 + B^2)/8pi along
>> the field lines.
>
>Try hovering one repelling magnetic over another,
>there are little toys that do that. Well it's easy
>to imagine. Push the magnets together, and note
>how you are adding energy that appears kinetically
>when the magnets are released. An "energy density"
>term like B^2 above needs to account for that in
>the hypothetical field.
>
>Calling S_uv the EM-stress and M_uv the material
>energy, see how, that's an example of how the
>S_uv and M_uv of the T_uv = S_uv + M_uv interact,
>i.e. EM-stress == kinetic energy density.
>
>> The E^j*E^k + B^j*B^k matrix does map the (E,B) plane into itself. But
>> neither E or B are necessarily eigenvectors of this matrix. It would have
>> real eigenvalues because it's symmetric, but the eigenvalues don't seem to
>> be E^2 + B^2, either.
>>
>> So I don't get it. Can some kind person explain this?
>> Laura
>
>IMO the continuum field concept is a bit primitive,
>a hang-over from Newtonian Theory. The example I
>provided above uses a relation between magnets,
>that some theoreticians favor.
> Consider the energy stored in either a capacitor
>or an inductor. It's *traditional* to refer to that
>energy storage as in a field, but in fact it's
>really stored by a relation of charged particles.
>
>Regards
>Ken S. Tucker
>
.