[time-nuts] question about multi-way measurement

[Tom Van Baak]

> I see the different forms of deviation measurements and they are all 
> one-to-one comparisons.

Not all. But, yes, often. UTC itself is a wonderful example of making mutual measurements of several hundred atomic clocks and establishing a superior "paper" clock out of them collectively.

But most people have only one counter (one internal or external timebase reference) and one clock to be measured. So the measurements are one-to-one. If you have more references or more clocks, you're welcome to combine 2, or 3, or as many as you want. It gets complicated but in some cases this complexity is justified.


> For example, if I had a device of relatively good resolution that would let me
> timestamp the events from 100 different clocks, then questions about the
> change of the mean of the cloud of events, distance from the mean of 
> individual events, etc. could be obtained.

Right, in some cases this works. If you had 100 cesium clocks and combined them all, then the result would be a paper clock that's about sqrt(100) or 10x better than any one of them.

But in other cases, the improvement is not so good. For example, if you combined 100 quartz wristwatches you may find that the improvement is only a tiny bit better. The reason: it's likely that most of your watches all gain or lose time in proportion to temperature, a common mode effect. So your cloud result is more likely to be a 10x better paper thermometer than a 10x better paper clock.


> It seems like, if there were a significant number of clocks involved, 
> the mean of the cloud of events would help cancel out positive and negatives and 
> particularly remove the short term randomness ?

It's important to look at the statistics to make sure that negatives and positives do in fact cancel. Depending on the type of clock noise and over a finite time span, this assumption is not at all guaranteed.

Also note, especially for short-term, that your success depends on how precisely can you compare the clocks and how long it takes to make an accurate comparison. If you measure too quickly or not accurately enough then the measurement noise will ruin your paper clock.

If you have some specific use case in mind, let us know. It might be easier to talk real numbers and real clocks than to discuss this topic in generalities.

/tvb