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Re: [Phys-l] how to explain relativity



-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu
[mailto:phys-l-bounces@carnot.physics.buffalo.edu] On Behalf
Of John Denker
Sent: Thursday, June 17, 2010 1:04 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] how to explain relativity

On 06/17/2010 09:42 AM, Jeffrey Schnick wrote:
1. Given that two particles separated by distance L'=L
initially at rest in inertial frame O' accelerate along the
line through both.
2. Given that the distance L' as measured in O' between the
two particles is always equal to L.
3. Assume the acceleration is such that a(tau) is the same
for both particles.
4. Item 3 implies that the two particles have zero velocity
in a comoving inertial reference frame O.

Sorry, there is no comoving inertial reference frame that
both rocket captains can agree on.

Thanks John. This is helpful. Let me limit my argument to the class of
cases for which, for some times, there is a comoving reference frame
that both crews can agree on. For the case of an acceleration profile
a(tau) in which the acceleration is non-zero for a period of time tau_c
and after that it is zero, at times for which all parties agree that the
acceleration of both spaceships is zero, the rest frame of either
spaceship is such a co-moving reference frame. Under these special
circumstances, the argument remains the same except that item 4 needs
the condition that we consider great enough times that the accelertation
of both spacecraft is zero in all three reference frames and item 10
becomes, <<The assumption in item 3 is not true for all acceleration
proviles a(tau).>>


5. Item 4 implies the separation between the two particles
in O is L.
6. Item 1 and the definition of acceleration implies that
at any time later than the time at which the acceleration
started, frame O' has an non-zero velocity along the line
through both particles relative to frame O.
7. Special Relativity implies that the on O' projected
separation of the particles L' is less than L.
8. Item 7 contradicts the given item 2.
9. The assumption in item 3 leads to a contradiction.
10. The assumption in item 3 is false.

No, it is the assumption in item 4 that is false.

Timekeeping in an accelerated reference frame is tricky, if
you try to keep track of anything other than your own proper time.

In particular, trying to keep track of the other guy's proper
time is of course possible, but it is tricky, laborious, and
unnecessary.
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