Time dilation pre-Einstein

Electromagnetic theory says that a moving charge creates a magnetic
field that acts on any other moving charge with a force qv x B.

So let us consider two charged ping-pong balls at rest in the
laboratory frame of reference. If this laboratory happens to be in
outer space, we can release them and watch them move apart because of
electrostatic repulsion.

Another laboratory in another spaceship flies by. Relative to the
second laboratory, we have moving charges. One creates a magnetic
field with lines of force as circles around its path. Assume the
direction of motion is such that the two balls are on a line
perpendicular to the motion, so the second ball is moving right
alongside the first ball and can feel its magnetic field at maximum
strength.

We see that v x B is in the direction such that the force is
attractive, making the two balls repel each other with less force than
the electrostatic force. If you work it all out quantitatively, the
magnetic force is always weaker than the electrostatic force, but with
faster motion, it increases, approaching the strength of the
electrostatic force as the speed approaches the speed of light as a
limit. See the Feynman Lectures on Physics for the full details.

So if we release the balls and let them fly apart, we see that the
acceleration w.r.t. the second laboratory is slower. In the limit as
the speed approaches c, the acceleration stops, because the two forces
are equal and opposite.

This is exactly what happens if time is dilated. The motion slows down
because time slows down w.r.t. the second spaceship laboratory. Time
doesn't slow down w.r.t. the first spaceship laboratory, and the balls
fly apart quickly. Time is relative!

Isn't that amusing!

It shouldn't be surprising however if you understand that magnetism is
just the relativistic manifestation of electrostatics w.r.t. a
different frame of reference. But nobody realized that before
Einstein.

Uncle Ben

PS: Spaceman, what clock is malfunctioning? Your correction is based
on acceleration, and there isn't any.acceleration of the spaceships.
.

Relevant Pages

  • Re: Time dilation pre-Einstein
    ... |> So let us consider two charged ping-pong balls at rest in the ... |> laboratory frame of reference. ... |> It shouldn't be surprising however if you understand that magnetism is ... | electrostatics w.r.t. a different frame of reference". ...
    (sci.physics.relativity)
  • Re: Question about magnetic forces beyond saturation
    ... We did not cover magnetism in depth in my Year 12 Physics syllabus, ... particularly what happens beyond saturation. ... Based on my understanding of gravity and electrostatics, ... while diamagnetic materials will have negative B-fields? ...
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