"Bilge" <dubious@radioactivex.lebesque-al.net> wrote in message
news:slrnbvpddm.dan.dubious@radioactivex.lebesque-al.net...
> 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".

I'm not making one, but stumbled on one! Your help is appreciated.

Note that the M-M "null result" you refer to was a little different, as in
that particular case the FAQ's citation of the term twists its original
meaning, suggesting that it was determined that the result was compatible
with zero within the precision of the experiment - no such determination had
been done or was even intended.

> 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 must read the allegations again! It is not just about high velocity, but
force balance with the Lorentz force, for example when a charged object
moves slowly perpendicular to a wire with a DC current. Perhaps I missed out
on a textbook that carefully analyses this simple looking case.

>   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.

Sorry, perhaps Ampere had several laws?!
I meant the Ampere force law, which is very roughly:

F = -i_m * i_n *(dm . dn / r^2) * (2 cos phi - 3 cos a cos b)

See for example
http://ieeexplore.ieee.org/iel1/27/6502/00256790.pdf?isNumber=6502&arnumber=
256790&prod=JNL&arSt=701&ared=713&arAuthor=Graneau%2C+N.

> 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.

In fact I meant the Lorentz force, sorry.

> 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.

Yes.

> 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.

I have no clear opinion yet!

Harald