On Tuesday, October 9, 2012 7:22:33 PM UTC-4, bismotwitter conjectured:
> @Don: Even a normal clock is wrong twice a day, I guess!
My conjecture:
A so-called "normal" clock, along with a stopped clock, is wrong an INFINITE number of times per day, like there are an infinite number of points on the x-axis between 0 and 24. But, while the stopped clock is correct twice a day, this "normal" clock can classically slither over and slide back across the correct time an infinite number of times during a day, technically, but that will still be infinitely less times than it will be wrong. It can never be correct for a given segment of time longer than the 1 point instant as it crosses back and forth between being slow and being fast. It must cross the correct line only at a point each time. However...there is a limit to how small a unit of time can be due to quantum dynamics - the so-called Planck unit of time would appear to preclude an infinite number of possible times in one day.
So, if we were to get pedantic, this quantum-time Planck unit would remove the continuity needed for a classical physics proof of my conjecture - that is, that the ratio of right times over wrong times will always be virtually zero. Nonetheless, today I would still wager big bucks that we would see results of any objective and unbiased experiments conducted on clock accuracy in our future to behave closely to the continuous, non-existent "normal" clock, and thus to my conjecture, in the sense that the ratio observed would be indistinguishable from zero given the minimized noise levels of the best state-of-the-art experimental equipment that could be deployed.
But then, not again, there may be, happily after all, no such thing as a "normal" clock.
- nate