Re: Does Newton's third law hold in Special Relativity?

On Tue, 8 Apr 2008, ram.rachum@xxxxxxxxx wrote:

On Apr 8, 10:49 pm, "Timo A. Nieminen" <t...@xxxxxxxxxxxxxxxxx> wrote:
a particle, if that force is carried by a finite-speed field?

Calculate the electric (+magnetic) field via the Maxwell equations (or, if
you have a couple of charged particles, perhaps the Heaviside-Feynman
equations or the Lienard-Wiechert potentials).

Timo - Assume I have two charged bodies. How do I know the force
between them? I mean, I can calculate the field that one body creates
at the location of the second body, but I need to remember that when
that field was created, the first body might have been somewhere else
entirely! So how do I calculate what it should be?

As I wrote, Heaviside-Feynman or Lienard-Wiechert. IIRC, Jackson gives
both. You need to keep track of the past trajectory of the particles.
Either set of equations will give you the current field at a point due to
the part motion of the particles.

This is not trivial, but can be done. You'd probably need to do it
numerically.

There's a good reason why people will resort to approximate methods (e.g.,
assuming that the instantaneous fields can be approximated by the Coulomb
field and the Biot-Savart field) when such will give good-enough answers.

--
Timo
.

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