Re: Help with apparent paradox please?


"sal" <pragmatist@xxxxxxxxxx> wrote in message news:pan.2006.04.14.01.25.09.50915@xxxxxxxxxxxxx
On Thu, 13 Apr 2006 17:17:01 -0400, Eli Botkin wrote:


<dunxuk@xxxxxxx> wrote in message
news:1144956723.578186.281080@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Can anyone help me with this; I'm getting increasingly confused by this
puzzle:

=====

Two carriages rush along together travelling nearly at c. The rear
carriage has a guardsman at the back that can apply brakes to the
rear wheels. The driver at the front of the front carriage can
apply brakes to the front wheels. All of the other wheels turn
freely and both sets of brakes have exactly the same decelleration
affect (they have been calibrated).

The ticket collector stands in the middle at the joint between the
carriages and sets off a pulse of light. As soon as the guardsman
and driver receive the pulse they slam on their
brakes. Unfortunately the carriages haven't been coupled but
luckily the pulse reaches both ends at precisely the same time and
both carriages screech to a halt together.


Unfortunately the whole incident was observed by a railway
inspector standing some distance away. As the train was nearly at c
he saw the light flash from the middle reaching the guardsman at
the rear very quickly but it took ages to reach the driver at the
front as the train was travelling almost as fast as the light. The
net result was the guardsman at the back received the light pulse
and applied the brake long before the pulse reached the driver and
the rear carriage started braking first. A gap immediately opened
between the carriages and the poor ticket collector fell to a
horrible death. The carriages eventually stopped some distance
apart.


Well, did the ticket collector die or not?


The application of brakes at one point of the carriage cannot have
an instantaneous effect on other parts of that carriage. The
fastest that such a signal can be transmitted is at the speed of
light. There are no rigid bodies; that's an idealization. So as
different parts of the carriage slow down, the railway inspector
sees sections of the carriage changing length at different rates.

Though the railway inspector would claim that the guardsman applied
his brakes first, he would also agree with the ticket collector that
the braking signals from front and rear reached the center at the
same time.

The ticket collector lives.

Not if they keep braking, he doesn't! :-)

It's Bell's paradox in reverse. If the front and rear brakes are
calibrated so that they result in equal acceleration (as measured by a
person standing at each brake lever) then, from the point of view of
someone standing on the train, the front and rear of the train have
started to accelerate, uniformly, at the same moment in the (initial)
rest frame of the train. If that acceleration continues, with each
end accelerating uniformly, the proper distance between the ends will
increase.

In Bell's paradox, the string breaks.

In this case, the cars, which aren't connected, must separate.

But, as you pointed out, the initial signal reaches the center from
both ends simultaneously, so it doesn't happen right away -- and in
fact if the conductor is paying attention he'll notice that the cars
are starting to separate and he'll have time to jump to safety.

One reason I did not attempt to answer this question is that the OP
greatly complicated matters by making acceleration part of the
question.

'Dunxuk', if you are reading this, the answer to your question
is rather complicated and involves issues other than the one
you were asking about, which I take to simultaneity.

It might be better to understand the pole and barn paradox
first. It is not that physicists cannot answer your question
just that the answer involves accelerations, which are
difficult to deal with.

You may also have noticed that there are many crackpots
on this group who know nothing about relativity. Just
ignore them.

Martin Hogbin.



.

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