Re: A mixture of time dilations and constrictions

[Pentcho Valev <pvalev@BAS.BG>]

Ken Caviness wrote:

> Stephen's answer below really is the best one to the questions in this
> thread.  I second his high recommendation of Taylor and Wheeler's
> "Spacetime Physics".  I read it and worked through the problems in the
> first edition when I was a senior in high school, the math is not at all
> onerous.  It's worth the expense and time spent to study this book, which I
> believe is now in the second edition.
>
> But since I've already said a few words about the "complex analysis" of
> Pentcho's latest question, let me add one more thing:
>
> It's not hard to apply the Lorentz transformations and find the speed of
> the tip of the clock arm in any inertial observer's reference frame.  But
> that doesn't say anything about the nature of time in the different
> reference frames, nor identify time dilations nor indicate "time
> constrictions" at all.  It was precisely to separate out the behavior of a
> moving object (the tip of the clock arm) from the actual passage of time
> that I introduced the minute and second hands (and in principle, as many
> more as we want).  But the same effect is achieved by achieved by using a
> simpler clock, such as the light-clock I mentioned.  In any case, the main
> misunderstanding is dealing with the tip of the clock arm without taking
> into consideration that it is an accelerated object even in the clock's
> rest frame, adding up the speeds without even using the Lorentz velocity
> transformations (!), and then expecting to get meaningful insights about
> time.  One doesn't.
>
> Over and out,
>
> Ken

The problem has remained - it is easy and I suggest giving it to your students
- some of them may be interested. Its general version is:

Consider two consecutive positions of a moving material point - e.g. the tip of
a clock's hand. The first position is Event 1  and coincides with the origin
(x=x'=t=t'=0). The second position is Event 2  and is characterized by x, x',
t>0, t'>0. By using Lorentz transform, compare t and t' for movements with
various speeds and directions.

Pentcho