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Re: A mixture of time dilations and constrictions



On Mon, 30 Jun 2003, Pentcho Valev wrote:

Stephen Speicher wrote:


The phrase "Processes characterized only by time dilation are
traditionally called 'stationary'" is much too vague and
imprecise to convey meaning. In a given inertial frame, a clock
which is present at two contiguous events having the same spatial
coordinates may loosely be thought of as being "stationary."

I am afraid it is the concept of stationary process that is
much too vague, as you adimit above.


I "adimit"[sic] no such thing. It is your own notion --
"Processes characterized only by time dilation are traditionally
called 'stationary'" -- which is too vague and imprecise to
convey any meaning. The meaning in my characterization of
stationarity in special relativity is quite clear; the "loosely"
refers to its marginal utility.

Please give a straightforward definition of stationary
processes and then describe some particular one.


What part of what I said is not clear to you?

"In a given inertial frame, a clock which is present at
two contiguous events having the same spatial
coordinates may loosely be thought of as being
'stationary.'"

A particular instance would be the clock present at the (x,y,z,t)
spacetime coordinates of the pair of events, (1,1,1,1) and
(1,1,1,2).

Consider, for instance, a clock's hand rotating in the
x'-y'-plane, and two consecutive positions (events) of the tip
of the hand. When and in what sense can the two events be
thought of being "stationary"? Or does "stationary" apply only
to clocks with immobile parts, as has been suggested in
sci.physics.relativity?


I do not know what you have been told on other lists, but special
relativity is a geometric theory with the notion of a point-like
event as a fundamental concept. Clocks are idealized to be
present at any given event, not as an extended object but as a
point-like particle. One can deal with a clock as an extended
object in relativity, but such techniques are _vastly_ more
complex than standard analysis. One needs to first master the
basics of the theory before becoming involved in such
complexities as this. As before, I suggest you first become
familiar with the basic concepts of special relativity as
presented in the excellent non-technical book "Spacetime
Physics," Edwin F. Taylor and John Archibald Wheeler, _W.H.
Freeman and Company_, 1992.

(For the more advanced student: To determine the proper time of
today's accurate clocks -- say, for instance, a standard cesium
beam atomic clock -- since the atoms are in motion relative to
the device which notes their frequency, the second order Doppler
effect must be taken into account. This frequency shift induced
by the Doppler effect is on the order of 10^-13. This cesium
frequency standard represents a complex of processes, and the
location of the proper time in this clock is given at a very
specific connector. As the accuracy of these clocks increase
with added technology, general relativity is required to fix the
proper time at some specific connector within the mechanism
itself.)

--
Stephen
speicher@caltech.edu

Ignorance is just a placeholder for knowledge.

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