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...