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-----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'=Linitially at rest in inertial frame O' accelerate along the
line through both.
2. Given that the distance L' as measured in O' between thetwo particles is always equal to L.
3. Assume the acceleration is such that a(tau) is the samefor both particles.
4. Item 3 implies that the two particles have zero velocityin a comoving inertial reference frame O.
Sorry, there is no comoving inertial reference frame that
both rocket captains can agree on.
5. Item 4 implies the separation between the two particlesin O is L.
6. Item 1 and the definition of acceleration implies thatat 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' projectedseparation 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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