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