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(Nooøn is here defined øø# as 12:00 o'clock, but that instant when the sun is at its
highest point.) We would fnd, this tỉme, that the number of “hours” each day is
the same.
WS now have some confidence that both the “hour” and the “day” have a
regular periodicity, 1.e., mark of successive equal intervals of time, although we
have not proued that either one is “really” periodic. Someone might question
whether there might not be some omnipotent being who would slow down the
fow of sand every night and speed it up during the day. Our experiment does
not, OŸ course, give us an answer to this sort of question. All we can say is that
we fñnd that a regularity of one kind fits together with a regularity of another
kind. We can just say that we base our đefinztzon of tỉme on the repetition of
some apparently periodic event.
5-3 Short tỉmes
We should now notice that in the process of checking on the reproducibility
of the day, we have received an important by-produect. We have found a way of
measuring, more accurately, ƒracfions of a day. We have found a way of counting
time in smaller pieces. Can we carry the process further, and learn to measure
even smaller intervals of tỉme?
Galileo decided that a given pendulum always swings back and forth in equal
intervals of time so long as the size of the swing is kept small. Á test comparing
the number of swings of a pendulum in one “hour7” shows that such is indeed
the case. We can in this way mark fractions of an hour. lÝ we use a mechanical
device to count the swings—and to keep them going——we have the pendulum
clock of our grandfathers.
Let us agree that iŸ our pendulum oscillates 3600 times in one hour (and if
there are 24 such hours in a day), we shall call each period of the pendulum
--- Trang 103 ---
one “second.” We have then divided our original unit of time into approximately
10 parts. We can apply the same prineiples to đivide the second into smaller
and smaller intervals. lt is, you will realize, not practical to make mechanical
pendulums which go arbitrarily fast, but we can now make electricøal pendulums,
called oscillators, which can provide a periodie occurrence with a very short
period of swing. In these electronie oscillators it is an electrical current which
swings to and fro, in a manner analogous to the swinging of the bob of the
pendulum.
W© can make a series of such electronie oscillators, each with a period 10 times
shorter than the previous one. We may “calibrate” each oscillator against the next
slower one by counting the number oŸ swings it makes for one swing oŸ the slower
oscillator. When the period of oscillation of our clock is shorter than a fraction
of a second, we cannot count the oscillations without the help of some device
which extends our powers of observation. One such device is the electron-beam
oscilloscope, which acts as a sort of microscope for short times. 'This device plots
on a fuorescent screen a graph of electrical current (or voltage) versus time. By
connecting the oscilloscope to two of our oscillators in sequence, so that it plots a
graph first of the current in one of our oscillators and then of the current in the
other, we get two graphs like those shown in Eig. 5-2. We can readily determine
the number of periods of the faster oscillator in one period of the slower oscillator.
With modern electronic techniques, oscillators have been built with periods
as short as about 1012 second, and they have been calibrated (by comparison
methods such as we have described) in terms of our standard unit oŸ tỉìme, the
second. With the invention and perfection of the “laser,” or light amplifier, in the
past few years, it has become possible to make oscillators with even shorter periods
than 10~!2 second, but it has not yet been possible to calibrate them by the
mmethods which have been described, although ï© will no doubt soon be possible.
Times shorter than 107!2 second have been measured, but by a diferent
technique. In efect, a diferent definmition of “time” has been used. One way has
been to observe the đistønce between two happenings on a moving object. lỸ, for
example, the headlights of a moving automobile are turned on and then of, we
can fgure out ho+ long the lights were on if we know œere they were turned on
and off and how fast the car was moving. The time is the distance over which
the lights were on divided by the speed.
Within the past few years, just such a technique was used to measure the
lifetime of the x?-meson. By observing in a microscope the minute tracks left in
a photographic emulsion in which 0-mesons had been created one saw that a
--- Trang 104 ---
Ị hị I NNẽ.
II IIITIIIIIIIIIIIH
IH[IIIIIIIIIITIIHIIHIIIIHIIHIII
IIIIIIIIIIIIIIIITITITIIIII
HÍIƒHHÍTH.HIHTHHIHHHHHHI
II IHHI lÌ IIfIIIIIIIIIIIII
IlliilfllllHÚI
WlÌ Ũ Ili
Fig. 5-2. Two views of an oscilloscope screen. In (a) the oscilloscope
is connected to one oscillator, in (b) it is connected to an oscillator with
a period one-tenth as long.
U-meson (known to be travelling at a certain speed nearly that of light) went
a distance of about 10” meter, on the average, before disintegrating. It lived
for only about 10718 sec. It should be emphasized that we have here used a
somewhat diferent defnition of “time” than before. 5o long as there are no
Inconsistencies in our understanding, however, we feel fairly confdent that our
defñnitions are sufficiently equivalent.
--- Trang 105 ---
By extending our techniques—and if necessary our defnitions—still further
we can infer the time duration of still faster physical events. We can speak of
the period of a nuclear vibration. We can speak of the lifetime of the newly
discovered strange resonances (particles) mentioned in Chapter 2. 'Their complete
life occupies a time span of only 10?“ second, approximately the time it would
take light (which moves at the fastest known speed) to cross the nucleus of
hydrogen (the smallest known object).
'What about still smaller times? Does “time” exist on a still smaller scale?
Does it make any sense to speak of smaller times iŸ we cannot measure——Or
perhaps even think sensibly about—something which happens in a shorter time?
Perhaps not. These are some of the open questions which you will be asking and
perhaps answering in the next twenty or thirty years.
5-4 Long tỉmes
Let us now consider times longer than one day. Measurement of longer times
1s easy; we just count the days—so long as there is someone around to do the
counting. Eirst we fnd that there is another natural periodicity: the year, about
365 days. We have also discovered that nature has sometimes provided a counter