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Overview
Product Details
| ISBN-13: | 9780520294639 |
|---|---|
| Publisher: | University of California Press |
| Publication date: | 09/12/2017 |
| Edition description: | First Edition |
| Pages: | 200 |
| Product dimensions: | 5.90(w) x 8.90(h) x 0.50(d) |
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CHAPTER 1
Our Idea of the Physical World
The earth was formed about four billion years ago. During the most recent few hundred thousand years, that is, during the most recent ten-thousandth of the existence of the earth, humans have evolved nervous systems that allow us to sense a little bit, actually a very tiny fraction, of what is going on around us. Our physiological mechanisms of communication — speaking, drawing, writing — have also evolved. As a result of that ability to communicate over time and location, we have been able to accumulate knowledge and understanding of more of the world we live in and to develop means — microscopes, telescopes, radar, X-rays, MRIs — that allow us to sense much more than our physiologies provide.
By far the most immediately useful information about the physical world comes to us directly by means of our senses, especially hearing, vision, and touch. We believe we can sense almost everything that's going on around us, but our senses provide us with an astonishingly small fraction of the information that we are actually imbedded in, and we have generated our conception of the physical world on the basis of the extremely limited range of things in the physical world that can be detected by our physiology.
For instance, we talk as if there are things, objects, around us that are fixed and solid — that table, this book — things that are there. We say we see this book, but we are actually interacting not with the book but rather with the light reflected from the book. Further, the properties of the book are not at all what our senses tell us. It is made of gigantic quantities of tiny bits, "subatomic particles," that are constantly in motion, with big spaces between them and forces that pull the bits together and push them apart. We talk as though in between objects there is just space, maybe filled with air and sometimes light, but the spaces are actually packed with streams of waves of all kinds of energies, which we know about only because of the accumulation of scientific information gathered from devices that can detect things we can't. Therefore, from our experiences, each of us has put together a concept of the world that is based on a severely restricted portion of the information that is actually present in the physical world, and most of the physiological mechanisms that have evolved in us support that often misleading concept of the world.
Our visual systems have evolved a way of sensing light, which will be discussed at considerable length in the following chapters, and it is a good example of how severely limited our view of the physical world really is. The world is permeated with electromagnetic waves of all kinds. The waves emitted by a typical am radio transmitter have wavelengths from about 1 meter to about 10,000 meters; X-rays have wavelengths around one ten-thousandth of a millionth (not a typo) of a meter; and various sources, for instance the sun, emit wavelengths at ranges in between. Our eyes have evolved in such a way that we can detect only wavelengths from about 0.4 millionths of a meter to about 0.8 millionths of a meter.
The gap in the middle of figure 1.1 is the way that the range of visible wavelengths is frequently presented. (The row of numbers at the top, labeled "wavelength in meters," is in what is called scientific notation: 10 raised to various exponents. For example, 10-12 means 0.000000000001, ten with 11 zeros in front of it.)
The whole width of the drawing represents a range of wavelengths of familiar sources, from gamma rays to radio, and that narrow strip near the middle that is stretched out below represents the range of visible wavelengths. That diagram is correct but extremely misleading. Note that the numbers given for wavelength represent what is called a logarithmic scale. That is, each equal space, such as between 10 (0.01) meters and 1 meter, represents not an equal increase but a 100-fold increase. The distances or lengths in the world we experience are not on a logarithmic scale, and very few people can look at such a scale and understand what it really means.
If, instead, we consider actual lengths or distances, not their logarithms, and we represent the range between am radio and X-ray wavelengths as the distance from New York to Los Angeles, then the wavelengths we are able to see would be represented on that scale as a distance of less than an eighth of an inch. Science had to invent instruments to detect wavelengths represented by the rest of that distance.
Within that extremely restricted visible range of wavelengths, we have evolved physiological devices, called the rod and cone systems, that actually sense different sub-ranges. The rod system is sensitive to one sub-range and the cones to three different sub-ranges, providing us with vision at very low light levels (rods) and in color (cones). Those mechanisms will be discussed in detail in later chapters. We are also limited in the range of brightnesses over which we can see. To understand that limitation, a different aspect of electromagnetic waves will be considered.
A LITTLE BACKGROUND ABOUT LIGHT
To combine, and modify a little, things that Einstein, Bohr, and Feynman have said, "If you think you understand light, you haven't thought deeply enough." Light will be discussed a lot in this book without trying to explain it. But it will be helpful, and not entirely wrong or misleading, to think of light and all other forms of electromagnetic radiation, such as radio waves and X-rays, in the following way.
Water Waves
Try partly filling the bathtub and dropping a pea into the middle of the water. Waves will of course radiate out from where the pea was dropped because the molecules of water under the pea will be pushed down, which will push the molecules next to them away and up, making a rising hump, and since water has the same properties in every direction, it will form in all directions, making a ring. Then those risen molecules will be higher than the rest of the water, so they will push down on their neighbors, making a new ring of humps, and the ring will expand. Meanwhile, the molecules that were pushed down by the pea will be pushed back up by their neighbors, and, having momentum, will keep going up (but not as far as they went down, because of friction among them). Then they will fall back down, starting the cycle over again, each time moving up and down a little less, until the ripples die out.
Why do waves seem to get smaller as they move away from their source? To detect a wave, like the one in the bathtub, the wave has to be detected over some finite part of it. For example, a cork intersects the wave over the width of the cork and detects the wave by its up-and-down motion. Similarly, if you look at a wave to try to determine its height, you only make the height judgment by watching a short stretch of the wave. Each wave forms a circle that expands as it travels away from its source, so the farther a wave has traveled, the greater is its radius and the smaller is the proportion of the wave that will be detected.
Because the circumference of a circle increases in direct proportion to its radius (circumference = pi × radius × 2), the proportion of the energy in a water wave that is detected is inversely proportional to the distance it has traveled. (That's not quite true with a water wave in a bathtub because the molecules of water exert a little friction on each other, which uses up some of the energy that the pea transferred to the water. A wave in the ocean can gather energy from wind and differences in water temperature, and so usually doesn't get smaller as it travels.)
That is a very crude and not quite accurate description of why water waves radiate out from a dropped pea, making a little group of rings that decrease in height as they travel away from the center, but it's a start on an explanation of electromagnetic waves.
Now suppose you want to detect or sense the water wave. You might put a cork in the water and measure how it moves up and down as the wave passes. The distance the cork travels up and then down is a measure of the strength, really the amplitude, of the wave at that particular place, and the number of times the cork moves up and down each second is the frequency of the wave at that point. If you have two corks and move one farther away from the center of the wave than the other until the two corks are moving up and down together, as in figure 1.2, the distance between the corks is what's called the wavelength of the wave.
Here are some more words and concepts that are useful in understanding waves. A force is a push or pull against an object. Energy is basically defined as the amount of whatever it is that moves something against a force. For the water wave, since the water molecules are pushed and pulled by the force of gravity, the wave must carry energy, but figuring out how much is a little tricky. You can weigh the cork and measure its amplitude of movement, which gives you a measure of energy, but that is just sampling the energy in the short segment of the wave that intersects the cork. That is just the energy that hits the cork. To have a measure of the energy of the entire wave, all the vertical movements should be added around the entire circumference of the wave.
Light and Other Electromagnetic Waves
Suppose somebody hands you two objects, one to hold in each hand, and you find that you have to make an effort to hold them apart; they keep trying to get together. Or you have to exert effort to keep them from flying apart. The experience of that effort is what physicists call force. You have to exert a force to keep them from coming together or moving apart.
It is critically important to be clear about the subtle distinction between how we conceive of the world and what we actually observe. For example, the first few sentences in the preceding paragraph could have said "A force is strength or energy as an attribute of physical action or movements," or "A force is a push or pull upon an object resulting from the object's interaction with another object," both quotes from definitions of "force" on the internet. But that kind of sentence implies that there are forces, things, out there. No one has seen piles of forces lying around. Instead, scientists have observed the behaviors of objects, have had experiences, and have given the experiences names. Making this important distinction often requires somewhat awkward and wordy sentences, but it is worth it. In fiction brevity is elegant. In explanations, it can sometimes be confusing.
If you have exerted force over some distance, you have expended energy. The definition of energy is the exertion of a force over a distance. An object is said to have potential energy if there is a force acting on it but it doesn't move, and kinetic energy if there is a force acting on it and it does move. When electromagnetic energy, for example light, travels through a vacuum — think of it as fast-traveling packets of energy — nothing pushes against it and it doesn't push against anything, but if it hits an object, it will transfer some or all of its energy to the object, making the object move (or move in a different way than it was already moving), and that requires energy. So we say that a beam of light traveling in a vacuum has potential energy, and if it hits something, some or all of that energy becomes kinetic energy.
We describe matter as made up of things we call atoms. Some of the things all atoms contain are called electrons, and others are called protons; atoms of different materials normally contain different numbers of electrons and protons. Protons exert forces against each other but attract electrons, and electrons exert forces against each other but attract protons.
Usually, the forces among electrons and protons in the atoms that make up any object are balanced. However, it's easy to spoil that balance. For instance, walk across a carpet on a dry day, shuffling your feet a little. That will rub off some of the electrons from the atoms in the carpet and attach them to your feet, giving you more electrons than are balanced by your protons, and those extra electrons, pushing against each other, will spread over your whole body. Then if you touch a doorknob or your dog, unless they happen to have the same imbalance between electrons and protons, your electrons will push the extra electrons to the knob or dog in the form of a spark of "static electricity."
When an object has more electrons than it would at balance, it is said to have a negative charge. Too few electrons create a positive charge. All these words have been leading up to describing what creates an electromagnetic wave. Whenever an object has a charge and it moves, a particular kind of wave, an electromagnetic wave, is emitted and travels off. If you walk across a carpet, picking up electrons, and then wave your hand back and forth, you generate an electromagnetic wave. The frequency of the wave equals the number of times you wave back and forth per second, and the amplitude of the wave is proportional to the distance your hand travels in each cycle.
The electromagnetic waves your charged hand makes travel away at the speed of light (very slightly slower in air than in a vacuum), so each movement back and then forth creates a wave that goes back and then forth over some distance, the wavelength. For instance, if your hand made one complete cycle back and forth in a hundredth of a second (so the frequency of the electromagnetic wave is a hundred cycles per second) and it travels 300,000,000 meters per second, its wavelength is 300,000,000/100 = 3,000,000 meters.
(We don't actually observe the wave traveling from the source to its detector. We observe that when a charge moves, some time later a detector responds, and there is a delay between the movement and the detection that depends on the distance between the two. Whatever it is that traveled from the source to the detector exhibits some properties of waves that we can observe, for instance water waves — and some properties of particles, as will be discussed below.)
Radio broadcasting stations have electronic devices that cause electrons to move back and forth and emit wavelengths in the neighborhood of one meter. Cell phones transmit and receive signals at about three-tenths of a meter. Wi-Fi is about one-tenth of a meter. Visible electromagnetic radiation, which we call light, has wavelengths between about 0.4 millionths of a meter and 0.8 millionths of a meter. X-rays have wavelengths in the neighborhood of one ten-thousandth of a millionth of a meter. All electromagnetic waves have the same basic properties; they are waves of energy of different frequencies and amplitudes, traveling extremely fast. Our space is crammed full of electromagnetic waves traveling in all directions, but, as shown in figure 1.1, our physiology is capable of sensing only a very narrow range of them.
In many ways, electromagnetic energy acts as water waves do. However, when electromagnetic waves are being detected, they act as though they consist of a stream of separate packets of energy, like bullets. Suppose the amplitude of the light wave, where it hits the detector, is extremely small. The kinds of devices used to detect light contain a material that converts the energy in light into what we can think of as shifts in the position of one or more electrons in the molecules of the material, and the physics of that material permits electrons to shift only among a limited number of positions. (These "positions" are usually called energy levels.) As a result, an extremely weak wave may not deliver enough energy to shift even one electron, and the presence of the wave may not be detected.
If, as it intersects the detector, the wave has a little more energy, it may trigger the shift of one or maybe two electrons, and as the energy contained in the portion of the wave intersecting the detector increases, the number of electron shifts or jumps will increase. If the energy in a wave is too small to shift an electron in a detector, there is no way to know whether or not the wave is actually present, so we say there was no wave, or if it has enough energy to shift some number of electrons but not enough to shift that number plus one, then we say that the amount of light, when it's being detected, increases in steps. It acts as though it consists of particles of energy.
(Continues…)
Excerpted from "Seeing"
by .
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