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Re: [Phys-l] how to explain relativity

The reference
< http://arxiv.org/PS_cache/arxiv/pdf/0906/0906.1919v3.pdf >
from the Wikipedia article states that:

<<Bell considered two spaceships starting from rest in a Lorentz system
S,
and undergoing identical accelerations a(t) in that system.>>

where frame S is what I called frame O and you call the Earth frame. So
they have identical projected accelerations implying different *proper*
accelerations.

Note that, in order to make sense of the statement that the two
spaceships undergo identical accelerations in that system (S/O/earth), I
need to consider each spaceship to be of negligible length or to be
accordian-like in that different parts of an extended spaceship would
have different *proper* accelerations with the forward parts having
higher proper accelerations than the after parts.

By the way, the rope breaks. Consider a taut horizontal rope segment of
length L with the sun directly overhead. It is casting a shadow of
length L. A person rotates the rope about a horizontal axis that is
perpendicular to the rope while at the same time stretching the rope so
that its shadow remains at length L. The rope breaks.

In the given problem the rope is rotated in spacetime by boosting its
ends in such a manner that the projection of the length of the rope on
frame (S/O/earth) remains constant. To keep the projection constant one
must stretch the rope. The rope breaks.

-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu
[mailto:phys-l-bounces@carnot.physics.buffalo.edu] On Behalf
Of William Maddox
Sent: Thursday, June 17, 2010 9:26 AM
To: Forum for Physics Educators
Subject: Re: [Phys-l] how to explain relativity

From: WC Maddox

Here is another way of stating the issue: " Since they have the* same*
*proper* accelerations their speeds should be equal at all
times (relative to Earth frame) so they should stay a
constant distance apart (in Earth frame). But after a time
they will acquire a large velocity so the distance between
them (and rope?) should suffer Lorentz contraction (in Earth
frame). Which is it?"
This is from a reference in Wikipedia article.

End Message



On 6/17/2010 7:50 AM, Jeffrey Schnick wrote:
John,
You seem to be solving a different problem. There's is an inertial
reference frame O in which the two spaceships, one in front of the
other, are initially at rest. There is a rope stretched
from the tail
of the spaceship in front (point A) to the nose of the
other spaceship
(point B). At time zero in that frame both spaceships start
accelerating.*/The way I read the problem, the spacecraft are
stipulated to accelerate in such a manner that the projected (onto
frame O) separation of point A and point B never changes. You have
them/* accelerating such that an accelerometer on the tail
of the lead
spaceship always has the same reading as an accelerometer
on the nose
of the trailing spacecraft. That's a different problem.




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