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Re: [Phys-l] Relativity Question



On 05/14/2009 10:34 AM, Philip Keller wrote:
There is a really fun essay by David Mermin about something he calls
"The Amazing Relativity Engine". I read it in his collection:
"Boojums All the Way Through". It is about a simple way to
illustrate that time dilation and length contraction follow
automatically from the relativity of simultaneity.

In brief: he sets up two rocket trains, moving in opposite
directions, each numbered car with a clock on it. The scientists on
each train have been told that their clocks are synchronized though
we can see in a our spectator's frame that "really" they are not. We
collect photographs showing pairs of opposite train cars with their
clocks. By analyzing well-chosen pairs of such photos, each set of
scientists can prove that the other (moving) team's clocks are
running slow, are not synchronized and that the moving train is
shorter. And this is all because they "erroneously" believe that
their own clocks are synchronized.

I am not doing this justice, but I highly recommend the essay and the
approach, especially for less algebraically skilled students
(Mermin's originally intended audience).


Yes, Mermin is a highly entertaining raconteur and a top-notch
physicist.

He wrote an entire book on this subject:
_Space and Time in Special Relativity_

The book contains quite a few clever semi-classical models of
special relativity. I was particularly struck by the one that
uses shutter parallax in an SLR (single lens reflex) camera.

I recommend this book for the entertainment of anyone who has
already mastered special relativity. I do not recommend it
for those who are still struggling with SR, and I emphatically
do not recommend it for students, pre-algebra or otherwise.

Classical mechanical models of relativity can never really be
correct; typically they are incomplete in the sense that they
are consistent with only part of the real-world SR behavior,
and/or they involve some sort of swindle, such as lying to the
trainmen about their clocks.

Building elaborate mechanical models of SR is like trying to eat
vichyssoise with a fork. It's just silly, especially given that
spoons are readily available. If you want to be silly, that's OK.,
but please do it on your own time, and don't inflict it on students.

I recommend the direct approach. Draw the spacetime diagrams
already. No algebra required. Explain to students that a boost
mixes x and t in almost the same way that a spacelike rotation
mixes x and y.

Sometimes doing things right is easier and in every way better.