How do we determine one clock is better?

[pellman]

A pendulum is a better clock than the solar day. The duration of the solar day varies from day to day. But how do we know this except by comparing it to another clock such as the pendulum? How do I know it is not the pendulum which varies from day to day and the solar day is constant?

Is it a theoretical assignment? Our theory tells us that the pendulum is periodic while the solar day is imperfectly periodic, so we choose the pendulum as the standard between the two? Or is there a purely empirical means of distinguishing them?

 

[Frame Dragger]

A pendulum is a better clock than the solar day. The duration of the solar day varies from day to day. But how do we know this except by comparing it to another clock such as the pendulum? How do I know it is not the pendulum which varies from day to day and the solar day is constant?

Is it a theoretical assignment? Our theory tells us that the pendulum is periodic while the solar day is imperfectly periodic, so we choose the pendulum as the standard between the two? Or is there a purely empirical means of distinguishing them?

Time is not absolute, so the best clock is the one which is most accurate (i.e. Atomic clock tracking Cesium decay). The reason is that it is the precision in the regularity between "intervals" that makes a clock "accurate". No clock can tell universal time, but an accurate local measurement is the tool you need to make the comparisons and calculations you describe.

One caveat, all observers agree on the outcome of events (the laws of physics), and therefore containing your "clock" to a mutually agreeable frame, and then you simply say "This is the standard". Like weighing yourself, the issue is more to do with relative accuracy, than the actual number because it's change (up or down) which concerns you. Then, the accuracy of the SCALE is defined as the accuracy of the weight-measuing element, and NOT the interpretive device such as the display.

Another way of looking at it: The best clock is one which packs the most regularity and accuracy regardless of the means by which that is interpreted. It is in short, more important that the eponymous Kilogram in France remain constant in mass so that we AGREE on what it is, and not the actual definition of the Kilo.

 

[LouMazero]

The Solar day can be shown to vary by monitoring a distant quasar's pulses from two or more points on the earth’s surface. We can then know we have completed one revolution when two designated locations have received the pulse simultaneously, this will happen once daily. This result is then compared to the Cesium clock to determine how much time has passed since the pulse was last simultaneously received. The solar day varies daily by milliseconds primarily due to the cumulative effects of the winds on the Earths surface.

The better clock will reproduce the same intervals with the most regularity, the Cesium is 9 billion time/sec.

 

[russ_watters]

Even if I buy that a pendulum clock is more precise/accurate over a day, it almost certainly isn't over a year. But that isn't the crux of the issue. The crux of the issue is that periodic processes can be measured by multiple, independent sources and according to different theories of operation (with clear/known sources of error) to find the best.

 

[yuiop]

One parameter for determining the accuracy of clocks is by comparing similar clocks against each other.

Let us say that we had 10 pendulum clocks and they differed from each other by 10 seconds per year and 10 mechanical watches of identical design differed from each other by 1 second per year and 10 identical atomic clocks differed from each other by 1 picosecond per year, then that would indicate that the atomic clocks are better time keepers than the mechanical watches which in turn are better than the pendulum clocks. Of course if we have a group of identical design clocks that remain perfectly synchronised with each other over a period of years, we can not rule out the clocks are speeding up or slowing down in a consistent way and I am not sure how we would exclude that possibility if these clocks are considered to be the most accurate time keeping devices we have.

Another factor is that clocks with with a higher intrinsic frequency at the heart of the clock tend to be more accurate and have a higher resolution. For this reason quartz watches that have a crystal that oscillates thousands of time per second tend to keep better time than a mechanical watch with a spring that oscillates once per second and quasars that rotate thousands of times per second tend to keep better time than the Earth that rotates once per day.

Ideal clocks of identical design should remain consistent with each other even when individual clocks are kept in different environments such as at different temperatures and if that is not the case then insulation from the environment or compensating mechanisms should be an intrinsic part of the design.

In Relativity there is no such thing as a “super-ideal” clock because all clocks are affected by relativistic velocities. It might be part of an interesting thought experiment to consider the implications of an ideal clock that has built in compensation for acceleration using the equations of relativity. Of course such a clock that is compensated for the acceleration in flat space according to the rules of SR would be hopeless when when subjected to different gravitational potentials.