Harry: 
 >
 >"Bilge" <dubious@radioactivex.lebesque-al.net> wrote in message
 >news:slrnbvmv8g.93j.dubious@radioactivex.lebesque-al.net...
 >> Harry:
 >
 >SNIP
 >
 >>  >Except for low velocities, Einstein's theorems are incompatible with
 >>  >Newton's equations.
 >>  >Similarly, Ampere's equations are partially incompatible with those of
 >>  >Maxwell.
 >>
 >>   That's non-sense. Newtonian physics is a limiting case of relativity.
 >> Ampere's law is a limiting case of maxwell's equations (i.e., quasi-
 >> static fields). A theory which is a limiting case of another theory
 >> indicates compatibility and specifies why one is the limit of the
 >> other. Two theories which are incompatible make different predictions
 >> about the same phenomena in a way that the difference cannot be
 >> resolved in terms of a domain of applicability.
 >
 >Now this is a point that has been a bit foggy to me for a long time, and
 >advice is welcome.
 >
 >Ampere's electrical force law uses the third law of Newton.
 >According to a number of people, the third law of Newton is violated with
 >Maxwell's and relativity theory. But despite reading about it, and despite
 >the apparent simplicity of the issue, I'm still not sure if they are right
 >or not; it seems you disagree. Perhaps the issue is more subtle than that?

  No, I don't think it's all that subtle. You're making a semantics
issue out of this similar to the one concerning "null result".
It just is not that intricate. Anywhere you can use newtonian
mechanics, you can use relativity. Relativity reduces to newtonian
mechanics. For example:


  t' =  lim  t/sqrt(1-(v/c)^2)  = t
       c -> oo

  Newton's third law fails only when an object is moving at a velocity
which is much larger than the propagation of a signal through the object
and large enough for the simultaneity of different points on the object to
matter. Then, newton's third law doesn't really fail so much as it needs
to be analyzed more carefully to account for the difference in
simultaneity.

  I'm not really sure what you mean by ampere's law needing newton's third
law. Anpere's law doesn't contain any forces. You need the lorentz force
law for that. Neither ampere's law nor any of the other maxwell equations
even describe charges, moving or stationary. Maxwell's equations describe
fields associated with charge densities and current densities. Maxwell's
equations are not even capable of describing the current in a wire as
moving charges. Ampere may have deduced the form of his equation
by measuring forces on current carrying wires, but I'm not really
sure what you are getting at.

  Getting back to your the point of all this, however, I'm not sure
why you find the term "compatible" to mean equivalent. In my opinion,
it's possible for two theories to be mathematically equivalent but
still be incompatible physically because the premises of one theory
(or interpretation) contradicts the physics of the other. Two examples
that come to mind are LET/special relativity and quantum mechanics/
bohmian mechanics. In both cases, the two theories assert the same
mathematics (more or less), but require a very different reality.
By contrast, newtonian mechanics is compatible with with all of
those theories because newtonian mechanics represents a well-defined
limiting case of esch of those theories.