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*From*: David Rutherford <drutherford@SOFTCOM.NET>*Date*: Mon, 18 Jun 2001 22:54:54 -0700

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 electronsare

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:rethink

"Thus, the center of mass of the electrons is stationary, from theviewpoint 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

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 vsso!

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

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 yourare

argument. The electrons' fields are a function of position, velocity AND

acceleration. Feynman warned about this in developing the equations you

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

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