Measurement of Time

I was having a conversation with a professor after my Measurements and Engineering Data Analysis lab.  During the lab, we were talking about ways to reduce parallax error (an error that occurs when one misjudges the liquid level in a tube or beaker), one of which was converting analog readings into digital readouts using some kind of machine.

Basically, once any measurement has been converted into a voltage, the professor explained that it is fairly easy for a circuit to convert that into a digital output.  This got us talking about all sorts of things, one of which was the measurement of time.  He mentioned how our measurement of time is quite precise compared to other measurements, such as length.  Even a simple wristwatch keeps time precise to one second per day.  That is an error of +/- 1/86400.  Imagine getting that precision on something like length.

I asked him why our measurement of time is so precise.  He mentioned how the precise measurement of time has been a long sought historical goal.  This is because of the importance of keeping good time before the invention of GPS for navigation.  On the sea, it is fairly easy for a navigator to determine latitudinal position (north/south) by checking the angle of the sun from the horizon and comparing it to a table.  However, accurate time must be kept for determining longitudinal (east/west) position by timing when the sun rises and sets.  An error of one minute over a day could lead to a longitudinal position error of 16 miles.

Fair enough, but isn't precision just relative to us humans?  The larger something is, the more precisely we can measure its length.  If we measured something an inch long and had 5% error, we would have, on average, 0.5% error on a ten inch object using the same method.  For example, if we manufactured ten one inch rulers with +/- 0.05 in resolution, lining them side by side to measure 10 inches would give us the unlikely worst case scenario of having .5 in error, but more likely than not, the tolerances would balance each other out, giving us something closer to 0.05 in error, which is 0.5% of 10 in.

So this whole subject of relative measurements brings up a possible hypothesis for why we are able to measure time so precisely.  Maybe in 3 dimensions, we are too big to be able to measure things with high resolution, but in the 4th dimension, where our big bodies and big tools have no relevance on its measurement, it is easier for us to be precise.

Or maybe our internal clocks are just crappy.

Food for thought.

Highest resolution.