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Sneaking a Look at God's Cards, Revised Edition
Unraveling the Mysteries of Quantum Mechanics
By Giancarlo Ghirardi Princeton University Press
Copyright © 2005 Princeton University Press
All right reserved.
Chapter One
The Collapse of the "Classical" World View
I remember discussions with Bohr which went through many hours till very late at night and ended almost in despair; and when at the end of the discussion I went alone for a walk in the neighboring park I repeated to myself again and again the question: Can nature possibly be as absurd as it seemed to us in these atomic experiments? -Werner Heisenberg
We are going to follow the fascinating trail that led to the scientific revolution of quantum mechanics in the first quarter of the twentieth century. Together with the theory of relativity, the conceptual structure of quantum mechanics is now the basis of the modern view of the physical world. Rarely in history has a new theory been so hotly contested, or called forth such great energies from such great minds. And even though its power to predict phenomena is unprecedented in the history of science, quantum mechanics has stirred up controversy-no less unprecedented-over its meaning. This will not seem surprising, once we penetrate the "secrets" of the new microcosm revealed by the theory. These secrets-the incredible feats we will discover microscopic systems can perform-are quite revolutionarywhen set beside the "classical" conceptions formerly elaborated to explain our macroscopic experience. It is only to be expected that the new theory would require so much effort and suffering to be worked out, or that such furious debate would still be raging today about its philosophical implications.
What the physicist Isidor Isaac Rabi said (quoted at the beginning of the preface) lamenting public ignorance of modern advances in physics, applies with particular force to quantum mechanics. In the words of the great Robert Oppenheimer, "As history, its re-creation would call for an art as high as the story of Oedipus or the story of Cromwell, yet in a realm of action so remote from our common experience that it is unlikely to be known to any poet or historian."
The prologue of such a drama would consist in the fundamental incapacity of "classical" conceptual schemes to explain certain fundamental physical phenomena. A complete list would be too lengthy, and an exhaustive analysis would require a discussion of sophisticated effects that would be inappropriate for the nontechnical spirit of the present work. Instead, I will limit myself to listing a few elementary processes that could not be explained within the conceptual system of the "classical" view of the physical world.
But before I begin, I should explain that such expressions as "the classical conception of the world" (or the equivalent) will be used in this work to designate the body of knowledge elaborated over the long course of development of scientific thought, from Galileo's revolution in the early 1600s to about 1800. This knowledge was synthesized into the two pillars of nineteenth-century physics, namely, mechanics and electromagnetism.
Classical mechanics, born in the early seventeenth century from the profound intuitions of Galileo, found its concrete realization in the inspired labors of Isaac Newton. Increasingly refined and generalized formulations were attained in the eighteenth century in the works of Joseph Louis de Lagrange, and in the nineteenth by William Rowan Hamilton. This superb theory, as is well known, treats the movement of material bodies as determined by forces acting upon them; such forces as the mutual attraction (or repulsion) between individual particles govern the motion of bodies down to the tiniest detail. Classical mechanics managed the unification of what appeared to be the most diverse phenomena: for example, the doctrine showed that the movement of the planets in the heavens was governed by exactly the same laws that regulate the movement of any physical object as it falls to the ground. And the theory would reach still farther, for, whereas scientists had formerly thought that the physical process involved in temperature exchange could not be explained in terms of mechanics, by the nineteenth century it was possible to show that even thermal processes had their origin in the disordered movements of material constituents. Classical mechanics saw one of its greatest triumphs in the nineteenth century, when Willard Gibbs, Ludwig Boltzmann, and James Clerk Maxwell realized a more profound unification of physical phenomena through the mechanical explanation of thermodynamic processes.
A parallel story can be told of the other great "classical" theory, electromagnetism. For a long time the phenomena of light seemed to have nothing to do with electrical or magnetic phenomena. The researches of Faraday, Maxwell, and others led to the recognition that these so disparate processes were nothing other than diverse manifestations of a single entity, known as the electromagnetic field: equations were worked out that governed precisely all the phenomena in question. In this way, the concept of field-that is, as we shall soon see, of a physical entity continuously distributed in space and time-made its dramatic entry into science, requiring the recognition of an existence just as fundamental as one of the material particles. The electromagnetic field is capable of transporting energy through empty space in the form of light waves, radio waves, x rays, and so forth. This "wavelike" nature then became the fundamental characteristic of all processes governed by the laws of electromagnetism, as formulated by Maxwell.
This was the framework achieved by the end of the nineteenth century: a real existence had to be attributed both to discrete material particles ("corpuscles," from Latin corpusculum, "little body"), and to continuous fields. These physical entities were understood to evolve in a precise way in space, under the influence of their mutual interactions, and as codified in the equations of mechanics and electromagnetism. The equations, in turn, would permit the understanding of all other processes of the physical world.
Imagine, then, the crisis that occurred when some simple physical processes were discovered to be absolutely incomprehensible-to resist all attempts to reduce them to a classical understanding!
1.1. The Dependence of the Color of Objects on Temperature
It is common knowledge that a physical object, such as an iron bar, changes its color as its temperature changes. At low temperatures, the iron appears "natural" in color to us, but when its temperature is raised, it begins to give off heat (remember that thermal radiation is a form of electromagnetic radiation). Then the iron looks at first red, then yellow, and finally, white hot. This process involves thermodynamic effects, which bring an increase in thermal agitation of the constituents of the matter. These constituents, of course, are electrically charged particles, and the laws of electromagnetism teach us that charges in nonuniform motion release electromagnetic radiation. If the conditions are suitable, this radiation will appear as light. No matter how complex the process, in accordance with the previous remarks, it should eventually reenter the typical framework of "classical physics" and become perfectly intelligible. Unfortunately, such hope proved groundless. Despite the persistent efforts of the scientific community, even a process so common as this one did not admit of explanation in terms of classical laws of mechanics and electromagnetism. And it remained a mystery until Max Planck advanced an hypothesis of an absolutely revolutionary nature that would upset all classical ideas about light-or, to be more precise, about electromagnetic radiation.
1.2. Atoms and Their Properties
At the end of the nineteenth century, then, and at the beginning of the twentieth, a series of researches was undertaken (the most important being those conducted by Sir Ernest Rutherford) which would lead to a model of the atom very similar to the one used today. An atom was conceived as a miniature planetary system, having a positively charged nucleus where almost the entire mass of the atom was concentrated. Around the nucleus, revolving like planets around a tiny sun, were electrons, negative in charge, and of such a number as to neutralize exactly the positive charge of the nucleus. The attraction between the opposing charges (according to Coulomb's law) functioned like solar-planetary gravitation, and thus every electron was attracted by its nucleus (the law of attraction between two opposite charges has the same mathematical form as the attraction between two masses, that is, it decreases by the square of the distance that separates the two charges). But, once again, we will be surprised to learn that this analogy (which seems so natural to us) between atomic structure and a planetary system is, for various reasons, absolutely untenable within the classical scheme. Let us analyze a few of these reasons.
1. The constancy of atomic characteristics. It is only natural to wonder how all the atoms of one element-oxygen, for example-exhibit absolutely the same physical properties, however these atoms may have been produced; or again, we may wonder how such properties can persist unchanged, while the systems in question are subjected to highly invasive procedures, such as fusion or evaporation, and then returned to their initial state. Something analogous would be impossible for a classical system, qua planetary system. In fact, the orbits of the planets, especially in a system with many bodies, depend in an absolutely critical way on the initial conditions. Different procedures of "preparation" of a planetary system would inevitably lead to systems that are appreciably different. Interactions even of the most minute entity with other systems determine important changes in evolution and change the structure of any such system. Consequently, given a fixed nucleus of an atom and a fixed number of electrons to orbit it, the effective physical and chemical properties of the resultant system should show an enormous variety. There would have to be many atoms with a nucleus equal to that of oxygen (a mass sixteen times that of a proton with a positive charge equal to the eight electrons orbiting around it), and the variety of atoms would correspond to the different ways in which the nucleus has, so to speak, "captured" its electrons at the moment of its formation. But the opposite is true: all the physical and chemical phenomenology shows that the properties of an atomic element are absolutely identical, independently of preparatory conditions and any subsequent transformations.
2. These precise, persistent properties that characterize an atom also determine its behavior in physical and chemical processes. Nevertheless, as is well known, even in the case of an atom with many electrons, the characteristic properties change radically as we go from one atom to another with only one electron more or less. For example, we can consider an atom of xenon, a noble gas, which has a nucleus that contains (along with its neutrons) 54 protons, around which revolve an equal number of electrons. This atom is chemically inert, that is to say, it will be extremely difficult for it to form chemical compounds with other atoms. We only need to take away one electron and one proton (the relevant constituents for holding the system together) and a few neutrons to change it into an atom of the nonmetal solid iodine, a system with a very precise and conspicuous electronic affinity, and thus with radically different behavior and properties. This would certainly not happen in a planetary system with 54 planets: the passage from one system to another with one fewer planet (and with its sun correspondingly a little lighter in weight) would not, it would seem, bring with it such radical changes in the behavior of the system.
3. Finally, another fundamental fact generates an incurable conflict between the stability of atoms and the "planetary" model within the conceptual structure of classical physics. According to the equations of classical dynamics, a system of electric charges can remain in equilibrium only if the charges are in motion. The fact that the atom has a limited extension requires that the charges present in it should move in circular or elliptical orbits (similar to the planets), and thus have acceleration. Now, according to securely established laws of electromagnetism (Maxwell's equations), an accelerated charge inevitably emits electromagnetic waves, or radiation. By radiating, the electron would lose energy and its orbit would decrease, causing it to fall into the nucleus within a very short period of time. Exact calculation brings the conclusion that every atom ought to have a very ephemeral life, showing "constant" properties for extremely brief periods (fractions of a second). Of course, this would contradict all the familiar phenomena.
Many other facts too-in particular the specific modes of interaction between atoms and electromagnetic radiation-bring us into an irreconcilable conflict with classical conceptions. This is how a crisis began to prepare the way-as has often happened in the history of science-for a true scientific revolution. Thanks to the combined strength of a remarkable group of geniuses, that revolution arrived in the form of quantum theory, the theme of this book.
1.3. Wave Phenomena
Once having derived the laws of electromagnetism, Maxwell came to the conclusion that an accelerated charge radiates electromagnetic energy. This energy propagates itself in space in waves characterized by a double field, electrical and magnetic. This was verified by Hertz in 1888, and in 1901 Marconi succeeded in transmitting electromagnetic waves across the Atlantic Ocean. This phenomenon-the transmission of radio waves-is probably the most well-known example of the propagation of electromagnetic waves. In this case, the variable current (that is, the accelerated movement of the electrical charges contained in it) which runs through a radio antenna produces the emission of waves (Figure 1.1), which are propagated in space. Afterward, the information that these waves transport can be, as it were, decoded by the receiving apparatus.
We now need to examine this phenomenon more profoundly, in order to grasp the essential points we need to know, for understanding what follows. In fact, this part of the book, including the rest of this chapter and the first sections of the next, is dedicated to the discussion of the phenomenon of light polarization, and will appear rather technical, even though the exposition of the important points will stay at an elementary level. I need to ask the reader for a little extra effort to master the few, simple concepts I am going to explain, since their correct understanding will pave the way for the rest.
Suppose we have an electric charge, moving with a periodic motion along a certain segment, represented by the dark vertical line in Figure 1.1. The charge will radiate electromagnetic waves of the same frequency in the surrounding space. One electromagnetic wave consists of two field vectors, mutually perpendicular, and perpendicular to the direction of the propagation of the wave. These two vectors represent the electric field E and the magnetic field H, respectively (see Figure 1.2). The velocity of propagation of the wave in a vacuum is the same as the velocity of light, which means that it is traveling at about 300,000 kilometers per second.
Let us study the electric field first. We can observe it from two perspectives: we can study how its magnitude and direction vary at a given point in space with the passage of time, or, alternatively, we can study what values it assumes at various points of space at one given instant of time. In the first case we have a sinusoid or "foldlike" shape like that in Figure 1.3, which tells us, for example, that at the considered point, and at time [t.sub.1] the field points upward, and has the value [E.sub.1]. The time T that it takes the field to return to exactly the same value at the same point in space, is the period of oscillation, and coincides with the oscillation of the charge that generates it. In the second case (Figure 1.4) we have an analogous representation, but giving us an image of the field at different points of space, along the direction of wave propagation, at one given instant. This also is sinusoidal in shape. We can define the wavelength [lambda] of the electromagnetic field as the spatial distance between the two successive troughs, or crests, of the wave itself.
In place of the period T, it is also convenient to introduce its inverse, i.e., the frequency v of the wave:
(1.1) v 1/T
which represents the number of oscillations the field (or the charge which generates the field) performs in one second.
It is true in general of wave phenomena (whether electromagnetic, liquid, or sound waves) that the distance a wave is propagated in one second (its velocity) is equal to the distance [lambda] covered by a single oscillation, times the number of oscillations per second (the frequency v). If the velocity of propagation is equal to c, then
(1.2) [lambda] v=c,
a formula that represents the relation between wavelength, frequency, and velocity of light.
In principle, electromagnetic waves can have any frequency between zero and infinity. The classification of radiations according to their frequency is known as the electromagnetic spectrum, as shown in Figure 1.5 below.
(Continues...)
Excerpted from Sneaking a Look at God's Cards, Revised Edition by Giancarlo Ghirardi Copyright © 2005 by Princeton University Press. Excerpted by permission.
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