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

[David Rutherford <drutherford@SOFTCOM.NET>]

On Tue, 19 Jun 2001 12:00:56 -0400, Bob Sciamanda <trebor@VELOCITY.NET>
wrote:

> One more try :)
>
> You wrote:
> > If the two electrons are initially travelling at constant speeds in
> opposite
> > directions (which they are in the CM frame) and the net forces on them
> are
> > zero at all times, then the center of mass is inertial. Why do you
> disagree
> > with that?
>
> 1.) You agree that the lab frame is an inertial frame.

Yes.

> 2.) You agree that the CM of the electron system is accelerating, as
> viewed from this inertial (lab) frame

Yes.

> (and therefore from all other inertial frames).

That's the way it's supposed to be. But in this case, if the forces are
analyzed using the Lorentz force law, it doesn't work out that way. That's
why it's a paradox.

> 3.) Therefore, an observer travelling with this CM is viewing the world
> from a non-inertial frame.

No, he's viewing the world from an inertial frame. Maybe it would be easier
if you explain to me why you think his frame is non-inertial.

> He will see objects accelerate with no forces
> acting on them;

All sorts of weird things will happen because the Lorentz force equations
give conflicting results, in this situation. That's my point.

> he will of course see objects at rest relative to him NOT
> accelerate even though there is a net force on them

 From where?

> (as there must be on him).

The observers are assumed not to interact with the particles.

> He cannot apply Newton's laws to his observations without adding
> corrections which take into account his own acceleration.

As I said, he's inertial according to himself.

> 4.)  I think that by your phrase "then the center of mass is inertial"
> you are asserting something other than the (false)statement that an
> observer travelling with the CM is at rest in an inertial frame.  What is
> it that you really mean?

By definition, if two particles start out with equal and opposite (or zero)
velocities, as in this case, and the net forces on the particles sum to zero
(which they do in the CM frame), then the velocity of the center of mass of
the particles is constant (or zero). That means that the reference frame of
the center of mass (CM frame) is inertial from the point of view of an
observer at rest in the CM frame.

Imagine two identical pool balls travelling with equal and opposite
velocities (CM frame view). They collide elastically then move away from
each other with equal and opposite velocities. The center of mass of the two
balls is stationary throughout the interaction, therefore it's inertial. If
there was a very short observer standing at the center of mass, he would say
that he is inertial, too.

Now just insert pool balls=electrons and you've got the situation in the CM
frame.

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