Re: Time dilation pre-Einstein

On Jul 24, 9:10 am, Uncle Ben <b...@xxxxxxxxxxx> wrote:
On Jul 24, 8:11 am, "harry" <harald.vanlintelButNotT...@xxxxxxx>
wrote:



"Uncle Ben" <b...@xxxxxxxxxxx> wrote in message

news:c0a17537-e183-468a-99ad-0269bddcb67a@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

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!

The nice thing of physics is that it all fits together - or at least, it
should be like that! :-)

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.

I'm afraid that that is a (popular) misconception. For example: you would
impress me if you could correctly describe the magnetic field of a magnetic
coil (fed by a battery) as "just the relativistic manifestation of
electrostatics w.r.t. a different frame of reference".

Harald- Hide quoted text -

- Show quoted text -

Sure. I would think that the ping-pong ball example would do it for
you, since the field is made up of contributions from the electrons.
But I can go farther; it just consists of treating the collection of
electrons as a group instead of individuals.

Start with a short straight wire carrying a current of electrons. I
can show that it produces a magnetic field related to length
contraction of the system of electrons. (This is at the heart of your
answer. Give me a while to collect my references so I don't goof it
up.)

For a coil, its complication is sheer geometry: analyze in terms of
segments of wires considered separately; then sum their contributions
in the center of the coil. I'll post later on the straight wire.

Please include the speed of the electrons and the
energy required to accelerate them.

Sue...


Ben

.

Relevant Pages

  • Re: Time dilation pre-Einstein
    ... laboratory frame of reference. ... making the two balls repel each other with less force than ... since the field is made up of contributions from the electrons. ...
    (sci.physics.relativity)
  • Re: Time dilation pre-Einstein
    ... laboratory frame of reference. ... alongside the first ball and can feel its magnetic field at maximum ... since the field is made up of contributions from the electrons. ...
    (sci.physics.relativity)
  • Re: Time dilation pre-Einstein
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    (sci.physics.relativity)
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    ... laboratory frame of reference. ... since the field is made up of contributions from the electrons. ... But I am satisfied by Feynman's argument that magnetism is basically a ...
    (sci.physics.relativity)
  • Re: Time dilation pre-Einstein
    ... laboratory frame of reference. ... since the field is made up of contributions from the electrons. ... But I am satisfied by Feynman's argument that magnetism is basically a ...
    (sci.physics.relativity)