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I LOVE this textbook example.with
It is VERY accessible to (bright) high school students,
(Einstein wrote a sort book using algebra in hopes that high school level
students would/could appreciate the 'theory'.)
Explaining 'paradoxes' such as yours is an excellent example of 'learning'
about SR.
You mustn't limit your analysis to just ONE weird result of the assumption
(c = constant), but must realize that ALL the important results are likely
to contribute to any interesting scenario.
In your particular problem - the impossibility of simultaneity in two
reference frames will easily save the day.
If the platform rigs the barriers to close simultaneously, then the train
will see the front barrier activate BEFORE the second one activates.
The wreckage of the train will be contained between the two barriers.
Other similar exercises have a pole vaulter running thru a (short) barn
front & back doors. One door is always closed and they switchsimultaneously
in the barn frame.laser
My personal favorite is the 3 meter Lamborghini passing thru the tollbooth
laser gates which are only 2 meters apart in the tollbooth frame.
The front laser goes off when the quarter hits the bucket and the rear
turns on at the same instant. A fast enough driver can easily pass throughby
unscathed even though the driver sees the gate to be less than 2 meters
long.
So far, no paradox with SR remains unresolved.
But, as Einstein himself said - only ONE result that conflicts with the
theory is required to refute it.
On 10/25/04 2:20 AM, "Pentcho Valev" <valevp@BAS.BG> wrote:
We can PROVE it is false since it produces absurd couples of propositions
of the type (p, not-p). As you know, length contraction is a corollary of
the axiom so let us consider the following textbook example:
"Two bombs lie on a train platform, a distance L apart. As a train passes
frame)at constant speed,the bombs explode simultaneously (in the platform
theand leave marks on the train. Due to the length contraction of the train,
the marks on the train will be a distance gamma*L apart when viewed in
thetrain's frame (since this distance is what is length-contracted down to
itgiven distance L in the platform frame)."
Millions of professors have taught this example and yet nobody has found
stretchedsuitable to introduce the following modifications. The bombs are replaced
with two barriers which are simultaneously (in the platform frame)
L<L'<gamma*L.across the railway. The barriers are strong enough to be able to stop the
train. Also, the length of the train is L', a value limited by
Is the barrier mechanism capable of "catching" the train? The observer in
the platform frame will first say "yes" since, in this frame, the moving
train is shorter than L. Then the same observer will say "no" since the
train cannot remain length-contracted after joining the platform frame.
Finally, millions of relativists will say "never mind" since for them
relativity is a cult, not a theory that should be verified.
Of course, if for some reason you don't like this textbook example, we
could analyse others.