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

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

You confound fastness and precission.
Let's see deeply your example:
Although the hand of that analog stopwatch (ASW)
sweeps once around every second, that doesn't mean
that ASW had a clock's frequency higher than that
of a conventional watch (CW). The clock's frequency
is number of ticks per second. Actually, a ASW and
a CW might have the same clock's frequency. The
internal gears of both clock are what make the clock's
frequency be as a gear ratio. Suppose both the ASW
and the CW have the same clock's frequency f (same
precission = same ticks per second). Then, in ASW
the number of ticks per second (f) are uniformly
distributed along 360 degrees, but in CW the number
of ticks per second are uniformly distributed along
each 360/60 = 6 degrees. Therefore, although you see
the ASW running faster, that doesn't mean it had a higher
precission, because the motion of the hand is governed
by the ticks, so it is not a uniform motion, it is in
some sense discontinuous. Actually, the hand remains
stopped in a mark waiting for the next tick to occur
and then to advance to the next mark. The hand can
physically move from one mark to the next in smooth
motion, at definite mean speed v, but it must wait for
the next tick in each mark. You are free for featuring
the clock as you like concerning the hand's wait time (t)
for the next tick and the mean speed v to move to the
next mark, but both parameters must be related as

r/v + t = constant = 1/f

where, r is the distance between to adjacent
marks, and f is clock's frequency.


In a ASW the distance r between adjacent marks is larger
than that for a CW, so in the case where the wait time is
t=0 for both ASW and CW, you get v = r*f. Thus, if the
precission is the same (f), you have featured the ASW
with a higher speed v, because of the distance r between
adjacent marks is larger.

Let's see now what an infinitely precise clock would nean.
This would mean a clock's frequency of f = oo, so we'd get

r/v + t = 1/f = 0,

and this means there is no room for any wait time t, and the
speed v of the hand must be infinite if r is finite, or r zero
if v is finite. That v were infinite is physically unreal, and
that r=0 would mean the hand never advances in extension to a
next mark for a next tick.

.

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