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Re: A mixture of time dilations and constrictions



--- Stephen Speicher <sjs@COMPBIO.CALTECH.EDU> wrote:
On Wed, 16 Jul 2003, pvalev wrote:

What is wrong with discussing this stuff?


There is absolutely nothing wrong, per se, with discussion of
these matters. In fact, personally, I take great pleasure in
discussions about Einstein, technical relativity and the history
thereof, with experts and novices alike. I have spent countless
hours explaining aspects of relativity to non-technical people,
so ignorance of the subject is certainly not a criterion for
ending discussion. However, there is such a thing as self-imposed
ignorance, where the issue is not simply the struggle for
knowledge, but rather the refusal to allow knowledge to take its
rightful place in pushing ignorance aside.

Should such problems be discussed on this list?


Absolutely. But note that there is a fundamental difference
between one who says I am ignorant of relativity and want to
learn, and one who, in all ignorance, claims relativity is wrong.


If this person gives problems similar to the problems given in
textbooks and then resolves them, rightly or wrongly, his activity is
useful for the process of education. Then his pompous claims simply
do not matter.
The new problem. Let the traditional beam be replaced with a
perfectly elastic ball bouncing up and down on the train, along the
y'-axis. On the train, its speed is w' and the time of a one-way
movement is t'. Special relativity assumes that distances
perpendicular to the axis of relative motion are equal in the two
frames so in the track frame the vertical, y-component of the path of
the ball is h=w't'. Now the Pythagorean theorem gives

(w't')^2 + (vt)^2 = (st)^2 /1/

where s is the speed of the ball in the track frame (along a path
oblique to the axis of relative motion).
Eq. /1/ can be transformed into

t'/t = [(s/w')^2 - (v/w')^2]^(1/2) /2/

This is a general result giving time dilation for any speed
perpendicular to the axis of relative motion in the primed frame.
When this speed is c (the ball is replaced with a beam again and
w'=s=c), /2/ gives the familiar

t'/t = 1/gamma /3/

Now the problem for discussion: In case w'<<c (for simplicity, assume
w'=v), is the time dilation predicted by /2/ reasonable?

Pentcho