On 25/03/11 14:17, Daryl McCullough wrote:
Alfonso says...

To distinguish the three meanings of 'time' I will re-express the set I
in the following not unnatural ways:
Set III
(a) The journey occurred in eternity.
(b) The instant of starting was 1 o'clock.
(c) The duration of the journey was 2 hours." Dingle

Note that only (c) has units of seconds. I think that part of the
problem is that we are all familiar with clocks# and think of them as
something which tells time in hours minutes and seconds. In scientific
terms we should perhaps not use the term clock but "duration meter" -
envisaging something with a digital reading which increments at some
interval 1/10^n seconds. The larger n then the better the resolution -
which is started by one detected event and stopped by another event.
Your statement:
"What time is, is what a clock locally at rest measures".
Becomes
What time is, is what a "duration meter" locally at rest measures.
In terms of my scenario the only interval which the duration meter can
measure is the interval between the ticks - the reciprocal of which is
the frequency of the ticks.

Right. Time in the sense of (b), which is a way of assigning
labels to events, requires two things: (1) a clock for measuring
durations, and (2) an initial setting.

Under what circumstance would you consider an "initial setting" essential?



The Lorentz transformations involve both.

The Doppler shift involve only duration, though.
There are two events, e_1 and e_2 occurring at the
sender. There are two corresponding events, e_3 and e_4
occurring at the receiver, where e_3 = the event in which
the receiver gets the light signal from e_1, and
e_4 = the event in which the receiver gets the light
signal from e_2. The Doppler shift is about the ratio

T_r/T_s

where T_r = the time between e_3 and e_4, as measured
by the receiver's clock, and T_s = the time between
e_1 and e_2, as measured by the sender's clock.

--
Daryl McCullough
Ithaca, NY