Re: An infinitely precise clock would run at a rate of zero seconds per second

On Jul 5, 1:37 pm, "Sue..." <suzysewns...@xxxxxxxxxxxx> wrote:
On Jul 5, 6:53 am, Albertito <albertito1...@xxxxxxxxx> wrote:

On Jul 5, 1:02 am, PD <TheDraperFam...@xxxxxxxxx> wrote:

On Jul 2, 9:21 am, Albertito <albertito1...@xxxxxxxxx> wrote:

An infinitely precise clock would run at a rate of
zero seconds per second. Furthermore, it would not
be affected by any relativistic time dilation. The higher
the precission, the slower a clock runs. A clock
moving at speed v>0 wrt a frame has higher precission
that a clone clock at rest. A clock close to a massive
body has higher precission than other located further.
The precission of a clock is relative, you must always
ask with respect to which frame of reference is that
precission considered.

Maybe it's just me, but it would seem that a clock that runs very fast
would be the one that is most precise. Consider an analog stopwatch,
which has a hand that sweeps once around every second, which is much
fast than the hand on a conventional watch.

PD

Albertito <albertito1...@xxxxxxxxx> wrote:

<< You confound fastness and precission. >>

The experimental clock, which measures the oscillations
of a mercury ion (an electrically charged atom) held
in an ultra-cold electromagnetic trap, produces “ticks”
at optical frequencies. Optical frequencies are much
higher than the microwave frequencies measured in
cesium atoms in NIST-F1, the national standard and
one of the world’s most accurate clocks. Higher
frequencies allow time to be divided into smaller
units, which increases precision. >>http://www.nist.gov/public_affairs/releases/mercury_atomic_clock.htm

Sue...

[...]

So what? Yes, higher frequencies allow time to be
divided into smaller units, which increases precision,
but only is they are stable frequencies. Yet, an eventual
infinite frequency would be unphisical.

What Paul Draper was talking about is speed of the hand
of an analog stopwatch, but that has nothing to do with
clock's precission. As I've pointed out above, that speed
v is related to the frequency as

r/v + t = 1/f

where t is the wait time of the hand for the
next tick, and r is the distance that hand will
travel to the next mark.

Let v=c be the highest physical speed for that clock's hand.
Then,

r/c + t = 1/f,
f = 1/(r/c + t),

would be the highest physical clock's frequency for an
analog clock. You can't increase the frequency toward the
limit f --> oo, keeping t constant, because there must be
a limit for r, as r = c (1/f - t) being non-zero.

.

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