Time

Our subjective experience of time passing convinces us that time "exists", but what is it really? Einstein's relativity theory is careful to say that time is what shows on the face of a good clock, but what is a good clock? And how do we know that it is good? If two clocks disagree, do we have any way to know which one, if either, is right? You could say that nowadays we appeal to a standard time -- but that raises exactly the same question again. Standard time is simply the time kept by a set of clocks (atomic clocks) that are agreed to be good for theoretical reasons, and which don't quite agree among themselves. For want of anything better, the standard is obtained by averaging the readings on atomic clocks.

In the end, all we can do is compare clocks with each other. If clocks of different construction keep "the same time", pretty nearly, this justifies the notion of time as something objective and real, and also validates these clocks as good clocks.

For life on Earth, the original clock is the turning earth, and its "hands" are read by noting the position of the stars. There is every reason to think the earth would be extremely regular in its turning -- after all, it is enormous: what could speed it up or slow it down? Nonetheless, its slight disagreements with atomic clocks are interpreted as meaning that the atomic clocks are more nearly correct, and that the earth actually does turn slightly irregularly. Since our lives are regulated by the day, standard time -- the reading on the face of atomic clocks -- is occasionally altered by a "leap second" to stay synchronized with the turning earth, now regarded as a bad clock, but the one we care most about, in some sense.

1. Pulse and pendulum

According to his first biographer Viviani, Galileo experimented with synchronizing two clocks -- the human pulse, and a pendulum -- in his student days at Pisa. The resulting invention, the "pulsilogium", represented the pulse rate as the length of the pendulum. Try making a pulsilogium: adjust the length of a pendulum so that its rate of swinging agrees with your own pulse. Mark the length. Then adjust the same pendulum for your lab partner's pulse -- is there a detectable difference in pulse rate?

2. Pendulum length and frequency

It would be good to know what pendulum length means as a frequency (or pulse rate). You can easily find out the relationship between pendulum length and frequency by running one pendulum against another. (In the process, check that two pendulums really do keep the same time, but just in different units: is there a fixed proportionality between the number of swings of one and the number of swings of the other?) To be systematic, compare pendulums of length 1, 2, 3, and 4 (in some convenient unit). The shortest one, of length L=1, will have the highest frequency. Now in the time that this one makes N=100 swings (say), how many swings does the pendulum of length L=2 make? If it only makes N=60 swings, then its frequency is f=60/100, in units of the first pendulum (in particular, its frequency is less). You could organize observations into a table like the one below:

Length L

1

2

3

4

N (swings)

100

Frequency f

1

Period T=1/f

1

    

Graph T vs. L, and also T2 vs. L.

3. Water Clocks

Water clocks have been used since antiquity. They depend on the assumption that in some situations water should flow at a constant rate. Check whether a simple water clock really keeps the same time as a pendulum by running one against the other. Collect water over some fixed interval, as measured by a pendulum clock, and weigh it. Repeat a few times, and average, to get better accuracy. You can even let the water do the addition for you by collecting it again and again in the same beaker, weighing the total, and dividing by the number of samples. Then double the interval, triple the interval, and quadruple the interval, measuring the time in quantity of water for each interval. You could make a table with columns representing length of interval and quantity of water. Then graph -- see if the two columns are proportional. If they are, you could replace a pendulum clock by a water clock, more convenient for some purposes, since with a water clock you don't have to count swings.

4. Tide Clock

Galileo was very fond of his theory of the tides, which asserted that the tidal motion was driven by the movement of the earth, and that the timing of the tides was determined by the natural frequency with which water sloshed back and forth in the basins of the oceans and the seas. See if sloshing in a basin makes a good clock. Run the "tide clock" against a pendulum clock and check proportionality.