PSSC – Physical Science Study
Committee (1960)
Cap. 2 - Time and
measurement
2—1. The
Starting Point — the Senses
The most universal physical instruments are
built into our bodies. Through our eyes we get most of our information about
the world. Nearly as important are our ears, which bring us sounds. Then
there are the various impressions of touch. These include the very delicate
touch of our fingertips on which we rely for texture, the muscular senses of
pushing and pulling, by which we form the impressions of weight and solidity,
the feel of hot and cold, and our inner sense of balance. Smell
and taste — more important to chemistry than to physics — are also important
sources of what we know about the outside world. These tools, which
continually bring information to us, are, as you know, called the senses. Moreover,
we not only passively sense the world, but with our hands and lack and legs we
handle and move some parts of it.
It is true that no one has to manufacture
or buy his eyes or his ears, but their use is not entirely given to us at
birth. We all had to train ourselves to use them. We all had to learn to
interpret the images we see and the sounds we hear, to learn that the little
patch down the street is the school building, big as life when we get near it.
As babies we spent much of our time learning these things. We cannot remember
how hard it was, just as we cannot remember learning to talk.
The senses can be deceived. Optical
illusions are familiar. Perhaps the most common one forms the basis of the
“movies.” If you examine a strip of movie film, you will see that it bears a
sequence of slightly differing still pictures. Run them by fast enough, and the
eye will blend them into a smooth succession, which we recognize as motion.
Your sense of temperature can also be fooled: if you hold one hand in a pan of
hot water and the other in cold water and then put both hands simultaneously
into a pan of lukewarm water, the “cold” hand will feel hot, and the “hot” hand
will feel cold. (If you haven’t tried this, try it.)
Like the senses, all the other instruments
of the physicist can be deceived — even the most accurate and sensitive, such
as delicate balances, electronic meters, and timing devices. They all have
their limitations. Testing the readings of his instruments, like questioning
the first impression of the senses, is part of the cross-checking which has to
go into every conclusion made by the physicist. But this careful cross-checking
gives him confidence in his instruments, just as our sense of touch can be a
valuable cross-check to confirm what we see with our eyes.
2—2. The Key Concepts of Physics; the Need
to Extend the Senses
Let us consider a few of the most basic
notions of physics, time and space, and their combination in what
we call motion and matter. No doubt we gain our first impressions
of these through our senses. But it is pretty clear that in order to learn all
that we want to know about time, space, and matter we must extend and sharpen
our sense impressions by the use of other tools.
Consider first what we call time. Lying
in bed, running down the hail, riding in a plane, we are always aware (if we
are aware of anything) of the passage of time. We all have a measure of time
built into us: the heartbeat. About once a second — sometimes slower, sometimes
faster — it beats for our whole lifetime. We have other measures of time, too,
which we all know. The sun marks day and n1ght. The four seasons pass, and we
all hope to see a few hundred of them come and go. Much longer than that, or much
shorter than a heartbeat, or the blink of an eye, we cannot directly grasp. But
certainly time extends far beyond these bounds — back to before we were born,
ahead to after we die — and for moments too fleeting for us to capture. Our
parents recall what we cannot; the historians tell us more than that; big trees
go back centuries; and we do not doubt that the hills and the rocks themselves
are far older. All these things are beyond the direct grasp of our personal
time sense.
A second important notion in physics is distance,
or space. We can pace off a mile, with a little effort. We can span
a short distance with our fingers, or with our extended arms. We can even hold
our fingertips close together to show a hairsbreadth of space between them, but
it is hard to measure off less. How can we measure distances greater than we
can pace off or smaller than we can feel? As we shall see,
the measurement of extremely short and extremely long distances is important
for understanding the way the world works. To gain this understanding,
physicists have developed methods of measuring the distance to the planets and
the stars, and the means of measuring the size of atoms.
The third key notion is substance or
material, or matter as it is more commonly called. It is one of the main
successes of physics in our times that we have learned a great deal about the
inner nature of matter. We have learned that all the differing materials —
skin, bone, blood, rock, steel, nylon, air, even the sun — are composed of the
same tiny building blocks, the atoms. Their combinations “spell out” the nature
of the complex world in which we live, and even the nature of our bodies. Just
as a couple of dozen letters of the alphabet make up all the books that have
ever been written in the English language, so the combination of a few building
blocks makes up all matter with its great variety. We did not discover these
atoms by the direct use of our senses. They are far too small for us to see in
everyday experience. We learned of their existence by extending our senses,
using the ideas and techniques of physics and chemistry.
Here we have not sharply defined space,
time, and matter. These fundamental concepts are familiar enough to everyone,
and yet they are hard to define. The main point is that we take these three key
concepts from everyday experience. We establish them by the use of our own
built-in detecting devices — eyes, muscles, and so on. For example, we sense
big pieces of matter: mountains, perhaps a stretch of ocean; and small ones:
down, it may be, to the fine grains that make up white flour, or the motes of
dust that we see in a sunbeam.
It is our first job to find how we can go
beyond these ordinary experiences. We must find out how to talk in an orderly
fashion about things far away from the familiar experience of everyday life. Doing this will bring us into the heart of the subject.
2—3. Time and Its Sweep
Close your eyes for a short time. Then open
them while you count “one, two, three.” Close them
again. Now what did you see while your eyes were open? If you were in a normal
room, not much happened. Things appeared unchanging. But if you sat for a few
hours with your eyes open you would find people going in and out, shifting
chairs, opening windows. The whole activity of the
things in the room appears to depend on the time interval over which you watch.
Watch for a year, and the plant in its pot will grow up, flower, and wither.
Keep the experiment going,
at least in thought. Watch for a hundred years, and the building may have come
down about you. A thousand years? No American town has lasted for a thousand
years, except possibly for the Pueblo Indian villages of the Southwest. Ten
thousand years? In that time the
We can try now to go from long time
intervals to short ones. Imagine the same room, but now open your eyes for
briefer and briefer times — “quick as a wink,” as the saying goes. Of course,
this is exactly what a camera does. Now that blur over there where the electric
fan is whirring stands still, and sharpens into a set of four fan blades. A little faster, and the wings of a fly, which you cannot see
normally even as a blur, will also appear clearly. At this stage your
eye — or its camera- shutter stand-in — is opening for only a few thousandths
of a second.
2—4. Time Intervals, Long and Short;
Multiple-Flash
Of course, you cannot blink your eyes fast
enough to notice the effects mentioned in the last section. However, the
shutter of a motion-picture camera can be opened and closed very rapidly. For
ordinary movies the camera exposes either sixteen or twenty-four frames
(individual pictures) in. each second, and the pictures are shown on a screen
at the same rate. (Fig. 2—2.) These rates were chosen
because our eyes actually retain images for a time somewhat longer than a
twentieth of a second. This retention is called persistence of vision and
is responsible for the appearance of smooth, continuous motion we see in a
movie.
In many instances the entire motion that we
want to photograph takes place while an ordinary motion-picture camera shutter
is open for just one frame. To photograph such motions we often use a more
refined technique — the multiple-flash — which enables us to measure very short
time intervals. Here, instead of opening and closing a camera shutter, we turn
on brief, intense flashes of light at regular intervals in a darkened room. A
camera, with its shutter open, then takes pictures only when the light flashes.
Repeated flashes produce a sequence of pictures which is recorded on the camera
film. Since the time between successive flashes is known, examination of the
series of still pictures thus obtained enables us to determine the time
interval of the action photographed.
For example, Fig. 2—3 shows a series of
thirteen pictures of a bullet as it punctures a toy balloon. In this case the
time between successive flashes was sec; therefore, the total time elapsed
between the first and last pictures is 12/4000 = 3/1000 sec. Also, by examining
the third, fourth, and fifth pictures, you can see that it took the bullet less
than 1/2000 of a second to enter and leave the balloon. Thus, from these flash
pictures we get two physical measurements — the time interval for the bullet to
pass through the balloon and the time interval for the balloon to collapse.
Neither of these measurements could possibly have been made without a method of
extending our senses.
With multiple-flash photography, we can
make pictures of many rapidly moving objects — familiar things from raindrops
to machine parts, baseballs, and bullets. We can also take pictures of things
that we may want to measure as part of our investigation in physics. In this
book you will find many examples of the use of the flash technique to study
motion. This technique, and a similar technique that you will develop in
laboratory, will be among our most important tools. It is not necessary to take
each successive flash picture on a separate frame. We can make a multiple
exposure at equal time intervals on one piece of film. See Fig. 6—19 for an
example.
Taking photographs at regular time
intervals not only allows us to analyze motions that would otherwise be mere
blurs to our eyes; it also allows us to see these motions slowed down. For
example, frames taken at a rate of 4000 per second may be shown at a rate of 24
per second. We use this technique in reverse to study motions which take place
slowly. The growth of a flower, the motion of the tides, and the movement of a
glacier are all motions that span long time intervals. These intervals are so
long that normally we get no feeling of motion by direct observation.
2—5. The Stroboscope
The blades of an electric fan and the
clapper of an electric bell both exhibit a motion that repeats over and over in
exactly the same way. You can measure the short time intervals involved in
these motions by a simpler method than multiple-flash photography. For this
purpose we use a stroboscope. One form of this instrument is shown in the
Laboratory Guide. It consists of a large disc with slits spaced at equal
intervals around the circumference.
To see how this device allows us to measure
short time intervals, consider first a disc stroboscope with only one slit. We
can use this one- slit stroboscope to measure the time it takes the turntable
of a record player to go through one rotation. First we mark the turntable with
an arrow and let the record player settle down to its steady motion. Then we
set the stroboscope spinning and look through the slit as shown in Fig. 2—7.
Each time the slit passes we get .a glimpse of the turntable.
Now suppose that we spin the stroboscope so
that the slit goes all the way around in exactly the time of rotation of the
turntable. Then, each time that we can see through the slit the arrow on the
turntable will be in the same position. It will appear to stand still even
though it is really rotating. In this instance, then, the time for one rotation
of the stroboscope measures the time for one rotation of the turntable. On the
other hand, if the stroboscope spins faster than the turntable, the arrow on
the turntable will not get all the way around between glimpses, so it will not
seem to stand still. Also, if the stroboscope goes too slowly, the arrow will
move around by more than one rotation between glimpses; so again it will appear
to move. Consequently, by adjusting the speed of the stroboscope to make the
arrow stand still, we automatically set the times of rotation equal; and we can
use the stroboscope speed — at our control — to measure an unknown time of
rotation.
The stroboscope can be used to measure the
time for one rotation of an object that is turning too fast for this time to be
measured directly. if the disc has twelve equally
spaced viewing slits then the viewer gets twelve glimpses for each rotation of
the disc. This means that a stroboscope with many slits can measure a time
interval much shorter than the disc’s rotation time — as many times shorter as
there are equally spaced slits in the disc.
As an example, suppose we use the
stroboscope to watch a small ball being whirled around on the end of a short
string. We find that the ball appears to stop when the disc makes one rotation
every two seconds. If our instrument has ten slits, then in 2 seconds we get
ten glimpses — the time between glimpses is sec. Since the ball appears stopped
at each glimpse, the time for one rotation of the ball is 1/5 sec.
A stroboscope, like any other instrument,
has its limitations. If the disc is spinning too fast or the slits are too
numerous and small, so little light may pass through the slit that you cannot
see. There is a kind of confusion possible, too. Consider our example of the
one-slit stroboscope “stopping” the motion of a record-player turntable. Since
the turntable appeared at the same place each time we could see it, we assumed
that its time for one rotation was equal to that of the disc. There are,
however, other possibilities. The turntable could have gone around two, three,
four … times during one rotation of the stroboscope; and we still would have
observed the same effect. How can we be sure that we eal1y see the turntable on
successive rotations? This problem occurs quite frequently when using a
stroboscope, but there is a simple way to get around it. When you have the
motion stopped, simply increase the speed of the stroboscope. The motion may or
may not appear to be stopped again at some higher speed. If it does not, then
you know that the original speed of rotation of the stroboscope was the correct
one. If it does, then continue increasing the speed of the stroboscope until
you can no longer stop the motion. The highest speed of the stroboscope which
stops the motion will give the time of rotation of the turntable.
2—6.
Comparing Times; Counting Units
One of the physicist’s big tasks is to find
a way to talk clearly about all these time intervals. He must be able to
compare them, to use them, to predict them, however large or small they may be.
He needs a measure.
The measurement of time is familiar to
everyone. We all know about the second, the day, week, month, year, century. All of these are built on a single simple
principle: counting. The part of mathematics most important in physics is
counting. To measure time intervals, physicists simply count off seconds.* Every
time interval can be expressed as so many seconds. It is sometimes convenient
to use days, just as it is sometimes convenient to count by dozens instead of
by ones. A day is shorthand for 86,400 seconds. For time intervals shorter than
one second we have to count by fractions of a second. The physicist uses
decimal fractions, like tenths, hundredths, thousandths, and so on.
* A “minute”
is a tiny part of an hour; 1/60 of a minute is a kind of minute of a minute. In
old time it was called a second minute. We have
shortened our speech, and call it just
a “second.”
All of our time counts are in terms of
seconds. What is a second and why was it chosen? There is no particular reason
for the choice. It is completely arbitrary. We might as well have chosen a time
unit twice as long, or half as long. It would have worked just as well. There
is no natural division of time known to us that would apply throughout ‘the
universe. Perhaps the second is convenient because it is not very far from the
interval between heartbeats. This is not fundamental, however. What is
important is that a unit be clearly defined and easily reproduced so that it is
available to everybody.
A second is approximately defined as the
time between “ticks” on a clock which makes 86,400 ticks while the sue, moves from its noon position on one day to its noon
position the next day. From measurements of the sun’s motion, astronomers can
calculate with great accuracy just when it crosses the highest point in its
journey, and from that they fix the time. Because the sun moves at somewhat
different speeds across the sky during the year, an average is taken over all
days, and this average defines the second.
The earth is ever changing. Earthquakes,
floods, eruptions, freezing, and melting take place. Even the earth’s rotation,
which causes the apparent motion of the sun in the sky, is not really
unchanging. We know it changes a little, because some very good clocks agree
among themselves better than any of them agree with the observations of the
sun. Therefore the physicist usually defines the second by the careful
maintenance and cross-checking of the best observatory clocks. Any laboratory
time measurement must in the end be referred to them if high accuracy is
needed.
Just what makes a clock keep accurate time
is a very hard and deep question. This is not simply a matter of the
complicated works you see in an ordinary watch or clock. It is rather what you
mean by time itself. Let us be satisfied with the idea that very carefully
protected beating pendulums, or the newer electronic clocks which depend on the
vibrations of a thin slab of quartz crystal, all count off accurate time. If
they are compared over years and years, they agree with one another with high
precision all over the world. Still I newer ones, using as vibrators certain
atomic vibrations themselves, are now being built. No one knows if there may
not be some slight differences among all these means of marking time. We know
that so far there have been none big enough to notice. One of the tasks of
future physics is to press this question further.
Time measurement gives rise to what appear
to be two different questions: “How long did it take?” and “When was it?” The
first question we answer by giving a time interval: “The race took four
minutes.” The second question is answered by a statement such as “The race
started at five o’clock yesterday afternoon.” For the first measurement, a stop
watch is good enough; it ticks off, starting at zero, and measures the length
of a time interval. In
the second case, the reading on a correct clock is needed. But this is really
much the same thing, for a clock simply measures the interval from some arbitrary
starting time, say midnight. The exact date is just another interval of time,
measured from an agreed fixed point of time, say New Year’s, while we count the
years themselves from A.D.
[…]