Re: 4/3 problem resolution/Action-reaction paradox in pdf format

[David Rutherford <drutherford@SOFTCOM.NET>]

On Mon, 18 Jun 2001 23:41:40 -0400, Bob Sciamanda <trebor@VELOCITY.NET>
wrote:

> 1.)  I think you nave agreed that the accelerations of the two electrons
are
> not equal and opposite in the (inertial) lab frame.

Agreed.

> 2.)  At least for non-relativistic velocities, simply subtracting the CM
> acceleration (as measured in the lab frame) from these electron lab
> accelerations gives their accelerations in the CM frame.  They will clearly
> not be equal and opposite in the CM frame either.

It gives the acceleration of the CM frame from the point of view of the lab
frame, and it _should_ give the acceleration of the CM frame from the point
of view of an observer at rest in the CM frame, but the CM observer would
disagree. He says he's not accelerating.

> 3.)  Your statement:
>
> > "Thus, the center of mass of the electrons is stationary, from the
> viewpoint of an observer
> > at rest in the CM frame, so the CM frame is inertial."
>
> isn't even wrong! (borrowing from Pauli) - it is inscrutable; please
rethink
> it carefully.  This does not make a frame inertial!

Bob, I'm surprised at you :-). This is high school stuff. In the absence of
external forces, since the net change in the momenta of the particles is
zero in the CM frame, the motion of the center of mass of the particles is
constant (or zero), i.e., inertial.

> 4.)  Your words seem to imply that the CM frame is non-inertial as viewed
> from the lab, but is inertial as viewed from the CM frame itself.  A frame
> is either inertial or non-inertial, period.

That's my point. Using the Lorentz force law to find the change in momentum
in the two frames, gives conflicting results.

> This property (inertial vs
> non-inertial) is invariant.  Your argument seems to endow every frame with
> the "inertial frame property" to an observer at rest in that frame - not
so!
> Here lies self-contradictory madness!
>
> 5.)  Your symmetry arguments about the fields and forces omit the fact that
> the accelerations of the two electrons are not equal and opposite.

They aren't equal and opposite according to the Lorentz force law, but can
you show me evidence that they aren't equal and opposite in reality?

> Thus their fields (and forces) do not have the symmetry you suppose in your
> argument.  The electrons' fields are a function of position, velocity AND
> acceleration.  Feynman warned about this in developing the equations you
are
> using.

I think you're trying to throw up a smoke screen to avoid dealing with the
fact that the Lorentz force equations lead to a paradox, in this case :-).
As you know very well, it's sometimes necessary to simplify the situation in
order to analyze it. This method is common in physics (as I'm sure you also
know). In this example, the two electrons are considered to be inertial
prior to the moment we analyze the forces. Thereafter, they are free to
accelerate.

--
Dave Rutherford
"New Transformation Equations and the Electric Field Four-vector"
http://www.softcom.net/users/der555