I. Introduction: concerning Classical Physics, and its realm
In the upcoming part of our course we shall study physics in the realm of atoms, nuclei, and elementary particles. In so doing we will encounter new aspects of nature; new in the sense that they have not been systematically discussed in your study of physics heretofore. These aspects of nature are commonly referred to as quantum phenomena, and we, therefore, call the subject matter of this section quantum physics. The currently accepted basic mathematical theory of quantum physics is known as quantum mechanics, although we will not proceed very far along the road toward a full understanding of quantum mechanics, but will try to lay a good basic, experimental and historical foundation for that full understanding, which you may eventually decide you want, or need, to develop. As an additional introductory comment, we should also be sure that you understand that "quantum physics" is indeed something which does concern the everyday, macroscopic world. Actually all of the physical description of the actual world is quantum physics; the laws of quantum physics, as we know them today, are our most general set of laws of nature. Therefore, we will also endeavor to explain how it is that the particular sizes of objects and devices in our everyday world make their quantum nature much less obvious.
The laws of nature which you have previously discussed in your introductory sequence of physics courses are the laws of classical physics. Generally we can say that classical physics is concerned with those aspects of nature for which the question of the ultimate constitution of matter is not of immediate concern. On the other hand, in our new study, we will specifically ask questions concerning the elementary constituents of matter. We now know that matter is made of a relatively small set of elementary particles; we must therefore also now try to discover the laws which govern the behavior of these particles. We will naturally focus our attention on physical situations in which these laws stand out as clearly as possible; this means that we will study situations involving the interactions of only a few particles at a time. Most of the physics studied in the rest of this course could, therefore, be called "microphysics"; the study of "small" systems consisting of a relatively small number of elementary particles.
However, if we know the basic laws governing the elementary particles we can also, in principle, predict the behavior of macroscopic physical systems, consisting of a very large number of elementary particles. This means that the laws of classical physics follow from the laws of microphysics, and in this sense quantum mechanics is just as relevant in the macroscopic world as in the microscopic world.
When we apply the laws of classical physics to macroscopic systems, we only try to describe certain gross features of the behavior of the system. We may consider, for instance, the motion of a "rigid body" as a whole, but we do not try to discuss the motions of each and every elementary constituent of the body. This approach is a general characteristic feature of classical theories of physics as applied to macroscopic systems; the finer details of the behavior of the system are ignored, and we make no attempt to consider all aspects of the situation. In this sense the laws of classical physics are approximate laws of nature. We should regard them as limiting forms of the more basic and comprehensive laws of physics, which are indeed the laws of quantum physics.
The classical theories are, in other words, phenomenological theories. A phenomenological theory attempts to describe and summarize experimental facts within some limited domain of phenomena. It is not intended to completely describe everything in physics, but if it is a good phenomenological theory it does describe everything within the limited domain very accurately. The philosophically-minded reader may want to remark that ultimately every physical theory is "phenomenological," and that the difference between a basic theory and a phenomenological theory is only a question of degree. As physicists we recognize, however, a clear difference between the two kinds of theories. Our basic laws of nature are distinguished by their great generality; we are not aware of any exceptions to what they state. We regard them as true and exact and universally valid, until there is clear experimental evidence that they are false. In contrast to this, the laws contained in a phenomenological theory are recognized not to be of universal validity; we know that they are valid, i.e., sufficiently accurate, only in some limited domain of physics, and outside this domain the phenomenological theory may even be completely meaningless.
We should, of course, have no contempt for phenomenological theories. They serve the very useful purpose of summarizing our practical knowledge of the various domains of physics. There ar many instances in physics in which we do believe that we have available a basic theory, but where the complexity of the phenomena prevents us from making accurate predictions based on "first principles." In such a case we try a simplified phenomenological theory which is partly based directly on the experimental facts, and partly based on some general features of the basic theory. We let, in other words, "the physical systems do some of our theoretical work." There are, furthermore, many instances in physics where the basic theory is missing. Any phenomenological theory which we can construct (based on some simple model) is then useful as a stepping stone in the search for a more comprehensive theory.
When we try to understand an unfamiliar physical phenomenon it is clearly rational to try the simplest thing first, i.e., to try a theory, or model, which has worked successfully in a seemingly analogous situation. If our model turns out to be successful we have learned something; but, if it turns out to be unsuccessful we have also learned something. It is an important aspect of the study of physics to learn to use phenomenological models successfully, and to learn to understand their limitations. The important thing to keep in mind is that models are only models, and that all of physics need ot be describe in terms of a single model.
People often talk about the "revolution" in physics brought about through the discovery of quantum mechanics. This suggests that something has been completely overturned. However, it should be noted, that the laws of classical physics, as applied to those situations which the classical theory was designed to describe, have not been overturned. The motion of a pendulum, for example, is described today in the same way as it was described in the nineteenth century.
It is furthermore the case that classical concepts often can be successfully employed to gain some understanding of phenomena in micro-physics: those concepts are of approximate validity. It is therefore important that we understand the limits of applicability of classical ideas. That the classical theories of physics are not of universal validity has been convincingly established through many experiments performed during the twentieth century. During the remainder of this course we shall present some of the relevant experimental evidence to convince the reader of this fact of life.
It is important to realize that whereas the laws of classical physics are good phenomenological laws, they do not tell us everything about macroscopic bodies. We can describe the behavior (motion) of a mechanism consisting of springs, levers, flywheels, etc., if we are given some "material constants," such as the density, the modulus of elasticity, the spring constant, etc. of the materials of which the mechanism is built. However, if we ask why the densities are what they are, why the elastic constants have the values they have, why a rod will break if the tension in the rod exceeds a certain limit, and so on, then classical physics is silent. Classical physics does not tell us why copper melts, why sodium vapor emits yellow light, why hydrogen has the chemical properties it has, why the sun shines, why the uranium nucleus disintegrates spontaneously, why silver conducts electricity, why sulfur is an insulator, nor why permanent magnets can be made of steel. We could go on and on listing everyday observational facts about which classical physics has nothing to tell us. This is an important fact to recognize: there never was any comprehensive classical theory of matter. The reader want to know, then, do we now have a comprehensive theory of matter? The answer is no; we do not have a detailed theory for everything taking place in our world. However, our knowledge about nature has expanded enormously during the last hundred years. We have discovered aspects of nature never dreamed of before, and we have succeeded in solving many old problems. It is, for instance, fair to say that we now understand the facts of chemistry and the properties of matter in bulk quite well: in those domains of physics we can now answer the questions which could not even be truly discussed within classical physics.
II. The Idea of Elementary Particles:
Let us now talk about the idea of elementary particles. Some ancient Greek philosophers are credited with being the first to introduce the concept of atoms into the theory of matter. It should of course be stated immediately that the "atoms" of the ancients are most certainly not the same things as our current conception of atoms. However, the central issue can be stated very simply: Either matter is infinitely divisible, or else, it is not infinitely divisible. If matter is not infinitely divisible, then we must discover, on a sufficiently small scale, elementary constituents of matter, or "atoms." We take a chunk of matter, and we divide it again and again into smaller and smaller pieces. Eventually this splitting comes to an end; we find something which cannot be split further, and that is the "atom." (The Greek word simply means "not divisible.")
The "atoms" of the Greek philosophers do not correspond to our use of the word atoms today, because our atoms are in fact not indivisible; they are instead made of protons, neutrons, and electrons. It is rather the protons, neutrons, electrons, and a whole host of other elementary particles which come closer to playing the role of the Greek "atoms." [On the other hand, for the last, perhaps thirty years, it may well be that the "quarks" and "gluons" of modern-day particle physics come even closer to being those "atoms." However, for now at least, we will ignore this possibility, and try to concentrate on these slightly more familiar elementary particles, namely the protons, neutrons, and electrons.] What do we actually mean by an "elementary particle"? The precise definition of this term is still controversial today; however, for our present purposes we may regard a particle as elementary if it cannot be (usefully) described as a composite system of still more elementary entities. This is more or less the same as saying that an elementary particle has no "parts"; i.e., it is not built of anything simpler. With this definition, we will consider the proton, the neutron and the electron as all being elementary, while the hydrogen atom or the uranium nucleus are not.
However, we should now ask the question as to how we can assert that the electron is really elementary? Could it not happen that what is regarded as elementary today is found to be composite tomorrow? After all, the atoms of today were the elementary particles of the nineteenth century; could it not happen that history will repeat itself? There is considerable experimental evidence that suggests the contrary of this, i.e., that the electron will never be found to be composite in the same sense that the hydrogen atom is now thought to be composite. Let us try to describe some of the nature of this evidence.
If we now consider the collision of two marbles, with a sufficiently high relative velocity, they will break apart into smaller fragments. In the same way two hydrogen molecules colliding with a high relative velocity will break into fragments. Unless the velocity is very high we will find among the fragments such things as hydrogen atoms, or protons, or electrons; in other words we will find the components of which hydrogen molecules are built. In both these cases it is fair to describe what happened as follows: The violence of the collision overcame the cohesive forces which keep the parts together, in a marble, or in a hydrogen molecule, and the objects therefore broke apart. A similar interpretation can be given to many nuclear reactions. Nuclei are made of protons and neutrons, and if an energetic proton collides with a nucleus it may happen that a few protons and neutrons are knocked out of the nucleus. However, if we study a violent collision of two elementary particles, such as two protons, we discover phenomena which are qualitatively different from the phenomena considered above. For instance, if a proton of very high energy collides with another proton it may happen that the two protons remain after the collision but that in addition we find one, or several, new elementary particles such as pi-mesons, among the reaction products. We say that the pi-mesons are created in the reaction. This is not the only thing that may happen in a proton-proton collision. It may also happen that the protons disappear and instead a number of entirely new particles appear, known as K-mesons and hyperons.
The creation and destruction processes which we have mentioned are important aspects of nature. It should be obvious that these phenomena are in no way analogous to the shattering of marbles, and it is also obvious that we would find it difficult to understand what takes place on the basis of classical theories of physics.
We are not going to discuss the early history of the atomic theory of matter; but the reader is urged to meditate about the remarkable understanding of natural phenomena which was achieved during the nineteenth century on the basis of the hypothesis that matter is made of atoms. On this assumption we can understand the basic fact of chemistry, namely that a given chemical compound always consists of certain basic chemical elements in fixed, definite proportions, characteristic of that compound.
Experience shows that we do not overcome our prejudices easily; we resist giving up our erroneous mental images. I want to state that it is not only beginning physics students who have prejudices about physics; the distinguished senior physicists have them as well. Let us consider, through a particular example, how prejudices influence our thinking. Many people have asked, and it may be that some people still do ask: "Since the electron is a charged particle the different parts of the electron must repel each other. what are the forces that keep the electron together?" Nobody has been able to "explain what are the forces that hold the electron together." In view of this discouraging circumstance, many physicists have proposed that we should not think about the electron as being a small charged sphere; suppose, instead, that the electron is just a point, a mathematical point with no extent whatsoever. If we do that we get into a different sort of trouble; the Coulomb field around it now becomes infinite, so that the electrostatic energy is infinite.
III. Thoughts about some Experiments beginning Quantum Physics
Let us now think calmly about all of this. In asking our questions we have clearly made many assumptions which reflect our prejudices. We have assumed (tacitly) that the electron is a small charged sphere and we have assumed that Coulomb's law can be applied to the parts of this sphere. How do we know that Coulomb's law applies to this situation? And what about the idea that a force has to hold together the "parts" of the electron against the electrostatic forces of repulsion? We have said earlier that the electron has no parts; it is an elementary particle. If we ask what holds the electron together it means that we contemplate the possibility that it could break into parts, but that is indeed a very questionable idea. Most physicists have realized by now that to try to create some kind of classical model for the electron is an utterly meaningless activity. The electron does not behave like a charged sphere, and all discussions about what would keep it together, if it would be like a charged sphere, are irrelevant in physics.
Now let us think about the meaning of the word "particle." A particle is an object which behaves in accordance with the ordinary laws of classical mechanics. A particle may be of finite size like a small billiard ball, or we may consider just the abstraction of a point particle. With a moving particle there is associated a trajectory; this trajectory is the curve traced ut by, say, the center of mass of the particle, as it moves in space. Furthermore a particle is something which "stays together." It is some sense a single, localized, coherent object. In particular, if a stream of particles collide in some random fashion with a screen with two holes in it, then each one of the particles can do one of three things. Either the particle is reflected by the screen, or it goes through the first hole, or it goes through the second hole. These three events are mutually exclusive; the particle cannot go partly through the first hole and partly through the second hole.
Later in this course we shall discuss experiments which have been performed with electrons, and which show that if an electron is incident on a screen with two holes in it, then the electron is partly reflected by the screen, and it goes partly through the first hole and partly through the second hole. "Impossible" exclaims the reader immediately. "How could nature be so contradictory?" This reaction is in fact correct; without preliminary definition of what a particle is, no particle can go simultaneously through two holes. It is, however, not impossible at all that an electron can go through two holes simultaneously; it if happens experimentally we must accept this fact. The conclusion to be drawn is that an electron is not a particle, in the classical sense of this word. We can then proceed to determine whether or not other objects in the world are particles, or behave like the electron, or perhaps are fashioned in yet some third way. Experimentally, we find that a proton, and in fact, all the objects in nature which we earlier thought were particles are actually not, but, rather, thins which can through two slits simultaneously, like the electron. However, if everything is really one of these new things, then we can go ahead and call them particles, just remembering that the other kind of particles are just something that was made up in the theory of classical physics. In fact, the world contains only one kind of particle, and they can indeed go through two slits at once.
It is an important aspect of our study of microphysics to learn to recognize the physical situations in which true particles can be described as if they were classical particles. We will also find, among other things, that true particles also have wave properties; in certain circumstances a true particle can behave like a wave. It would be a big mistake, however, to think that this is all there is to quantum physics; that particles are actually waves, as described by classical wave theory. As we shall see, this is not so; the classical waves are also figments of imagination, just like classical particles. Our prejudices about what a "particle" is are probably stronger than what a "wave" is, however; therefore, it may perhaps be easier to change your ideas about a wave than about a particle.
The important point to remember is that all the true particles in the world behave just as they do behave, and in certain situations their behavior approximates that of a classical, and in other situations their behavior approximates that of a classical particles. In yet other situations, they act like neither!
adapted from The Berkeley Physics Course: Vol. 4, Quantum Physics, by E. H. Wichmann