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Thomas Heger wrote:

> The concept of time is actually based on counting events, about which we 
> assume, they would occur always with the same frequency.

> That was the year or the day in ancient times and later the hour and the 
> second.

> Much later men counted the waves in certain kinds of exitations of 
> certain atoms.

> But in all cases a process of counting was meant, where the underlying 
> frequency was assumed to be universally constant.

> But: that is problematic, because actually we don't know, whether these 
> frequencies are universally constant or not.

> This is so, because the second is defined and measured by the same 
> process, which frequency we like to measure.

This all comes down to the age-old question that has been repeatedly
debated on these forums: What is a clock?

Several years ago, Franz Heymann made a good start in defining the term. 
The following represents my feeble attempt to improve on his definition. 
I invite others to make corrections and enhancements to what I have written
here.

A "clock" is an artifact (possibly including natural components) comprising
a component (A) that undergoes cyclical changes of state, and a monitoring
component (B) that indicates each return of the cyclically varying
component to a particular state of its cycle. A "useful clock" will
optionally include a component (C) that scales the output of component (B)
so as to mark off units of time that have greater utility and/or which
will allow the clock output to be compared with that of other clocks.

Component (A) must be self-contained in that its period of repetitive
cycling must not be dependent on the application of external forces or
timing signals. (However, it is not necessary that the clock be self-
contained in its power requirements.)

If one has a large ensemble of "useful clocks" in a common location at
the same gravitational potential and in the same state of motion, the
"good clocks" among the ensemble may be distinguished by how closely
their timing outputs maintain a constant ratio with the timing average
of the ensemble. Successive winnowing of "good clocks" enables the
selection of "better clocks".

A "better clock" in which the period of its repetitive cycling component
is set by a fundamental physical process that may be independently and
locally reproduced by individuals well-versed in the art of clock
manufacture is a "candidate standard clock". "Candidate standard clocks"
are not broadly tunable. Variations in timing from one "candidate
standard clock" to another arise depend on the quality factor (Q factor)
of their repetitive cycling components and the quality of the
instrumentation that monitors their cycles.

Given different classes of "candidate standard clock" distinguished by the
physical processes that they monitor as their central timing components,
one or another class may be designated, for a time, as a "standard clock".

By the above definition,
1) A wall clock plugged into 50 or 60 Hz mains is not a "clock" because it
is dependent on the externally generated mains frequency for its timing.
2) A pendulum clock is not a "clock", because the repetitive cycling of the
pendulum is dependent on the local force of gravity.
3) Stonehenge is not a "clock". However, the Stonehenge-Earth-Sun system
comprises not just a "clock", but a "useful clock" that had utility in
timing religious ceremonies and crop plantings.
4) Hourglasses and water clocks are not "clocks".
5) A clock based on a quartz crystal, although potentially highly stable,
cannot be a "candidate standard clock" because the frequency of
crystal oscillation is not set by a fundamental physical process, but
rather depends on details of how the crystal is cut.
6) Although a clock based on, say, the period of a millisecond pulsar may
be an "extremely good clock", it cannot be a "candidate standard clock"
because its central timing component cannot be locally reproduced by
individuals in different areas of the universe. Individuals in different
states of motion and in differing gravitational potentials will observe
that the pulsar period, although highly stable, will not correlate
exactly with times they they measure on "local standard clocks".
Furthermore, the phase of the received signal depends on one's location
with respect to the distant timing component, which varies with the
Earth's rotation, its orbit around the Sun, the Sun's travel through
the galaxy, etc. 

Suggestions for improving on my attempt at defining different types of
clock are welcome!

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Re: ? ? ? Thomas Heger <ttt_heg@web.de> - 2024-02-23 08:09 +0100
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