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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: Saturday, June 19, 2010 3:04 AM
To: Forum for Physics Educators
Subject: Re: [Phys-l] how to explain relativity

On 06/18/2010 07:06 PM, Jeffrey Schnick wrote:

I don't get this, it seems to be inconsistent with your
statement that
<<all the fundamental laws of physics commute with
translation>>. If
they both have the same a(tau) profile, I think that
whenever they are
both coasting, their clocks will agree with each other. Please
explain how their clocks become offset by a constant.

Also, which clock will be ahead of the other?


That's an important question. The answer that the principle
is still valid. It disallows some things but allows others.
In this case, each observer can say "If I accelerate to the
right, everybody to the left of me gets redshifted." Such a
statement upholds translation invariance.
Could you or someone else please give a more complete explanation. I
still don't get it. I think this is actually a doable experiment.
Tunnel into a mountain to a location, point B, at which the acceleration
reading on an accelerometer at rest relative to the mountain is the same
as it is at the top. Given two identical clocks sitting side by side on
a lab bench, simultaneously take one to the top of the mountain and one
to point B. Leave them there for a year. Bring them both back to the
lab bench and compare readings. I think they'll be the same. Which one
will be ahead of the other?

Here's a multiple choice question:

You and another spacecraft captain (Harry) will be traveling toward a
very distant star (which remains very distant throughout the process)
along one and the same straight line. You are both currently at rest in
one and the same inertial reference frame and your clocks are
syncronized with each other. You are one light-year apart from each
other and based on two specified clock readings you are to tell me which
one of you is closer to the distant star. You are to follow this a(tau)
acceleration profile. Upon completion of your acceleration phase, you
will find yourself beside a spacecraft at rest relative to you, but,
that spacecraft is part of a fleet of spacecraft all at rest, throughout
the process, in the inertial reference frame in which you are finally at
rest. All the spacecraft in that fleet carry clocks that are
syncronized with respect to each other in that rest frame. Look at the
clock on the craft right beside you. When that clock reads noon on this
date, record your own clock reading. Harry has been instructed to do
the same thing with the same acceleration profile a(tau) and he winds up
at rest relative to a ship right beside him in the same fleet. It is a
given that you and Harry do what you are supposed to do correctly. You
are provided with the clock reading recorded by Harry and find that his
clock reading is later than the one you recorded. Which of the
following statements is most correct.
a) The question is flawed in there is no way that Harry could wind up
at rest relative to a ship in the same fleet.
b) The question is flawed in that Harry's clock reading would have to
be the same as mine.
c) I am closer to the distant star.
d) Harry is closer to the distant star.



It also upholds rotation invariance, which is equally
mandatory. That is, acceleration dot separation is a
rotationally-invariant scalar.
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