Can a clock with Poisson counting statistics replace your watch?
- Published: Sunday, 17 March 2013 14:34
Thinking about Poisson statistics I was wondering how much use a clock would be that would count the seconds with counting statistics or Poisson statistics. That is: it has the irregularity of radio-active decay. Some people put their watch a few minutes ahead of the true time to make sure that they are never too late, but the problem is that they can start counting on that after a while. A true random clock might be unreliable enough that you would need to always stay carefully ahead….
Counting statistics make a variance that is equal to the value. Therefore, the standard uncertainty is the square root of the value.
Lets see what that means: our watch, after a minute, has an uncertainty of about 8 seconds. After an hour, a minute. After a day, five minutes. After a month, half an hour. And after a year, the uncertainty would be a little over one and a half hours.
To be 95% sure to be in time for an appointment a day after synchronizing your Poisson watch, you need to arrive 10 minutes ahead of your watch. And there is a 5% chance you will be 20 minutes early…..
No, I’ll stick with just being in time.
Still, I think it would be kind of cool to have a watch that goes “tick tick tick tick tick tick titick tick……”