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 Niagara River will have cut away the rock, and the falls will have receded far upstream. In a million years much of the American landscape will be unfamiliar. (Fig. 2—1.)

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. 1. In both kinds of question, a time interval must be stated in the answer. In the answer to “when,” however, one end of the interval must be agreed upon. In physics, we most often need to answer the question “How long does it take?” because the things we talk about happen over and over. But if you want to catch a train on a particular day, you also need to know when the time count begins. The problems of standard and daylight time, of time zones, and so on, are really problems of agreeing on such a starting time. Once you agree on a starting time, the questions are really the same. We must measure an interval.