Humanities Core Course Spring 2011 Instructor: Bencivenga

LECTURE NOTES

Lecture 4.

Aristotle’s universe was divided into two sharply distinct parts, which obeyed different laws. Things on earth behaved differently from those in the heavens (or, more precisely, from the moon up). Galileo’s gesture in the fall of 1609 of pointing his telescope toward the sky (though not being, in fact, the first of its kind, since the English Thomas Harriot had done the same a few months before him) was taken as symbolic of the breakdown of this distinction: from now on, the earth was to be just another celestial body, obeying the same laws as any other. These were, primarily, laws of motion, mechanical laws: necessary regularities connecting the positions and velocities of all bodies, hence making it possible to calculate the position and velocity of one of them from the positions and velocities of others. A new mathematics was needed to give a rigorous presentation of a new universal mechanics, and in 1687 Isaac Newton provided both. The new mathematics was the calculus; the new universal mechanics—known as “classical” or indeed “Newtonian”—was based on the law of gravitation, and applicable to both the movements of billiard balls and planetary revolutions. What some of the characters of Galileo’s Dialogue still presented as a project seemed to be fully realized: every physical event could in principle be given a full causal account, hence shown to be completely determined by its causes. If one knew the causes, one could know the effects. In 1814, Pierre-Simon Laplace gave a suggestive summary of this view in his Philosophical Essay on Probability, writing as follows:

We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.

This passage brings out what I take to be the essence of today’s most common view of science, the one that controls our everyday conversation. Science knows truths. Because science is practiced by humans, and humans are finite beings, (human) science does not know all truths; but what truths it does know it knows with absolute certainty, and it knows more of them the more factual information it acquires. Once it has all relevant information about a given area, science can proceed to give instructions as to how to be most successful in that area. Once we know all there is to know about the solar system, we can proceed to put rockets up there, and to land on the moon or on Mars. Once we know all there is to know about the structure and behavior of cells, we can proceed to find a cure for cancer. Once we know all there is to know about what makes people angry, we can proceed to eradicate violence. But this conception of science, first clearly articulated by Galileo, vindicated by Newton, and boldly asserted by Laplace, is not faithful to current scientific practice. As I suggested in my first lecture, though scientific practice has traveled into the 21^st century, the common ideology of science is still stuck, at best, in the 19^th century where Laplace belongs. Our second text will help us understand some basic ways in which practice and ideology differ here; before we open it, however, it will be useful to say something about how its topic—quantum mechanics, that is—originated within the field of physics.

A problem that plagued 19^th century physics was that of explaining the nature of light. Newton thought that light consisted of particles, and wanted to explain their behavior, too, by mechanical laws. However, a famous and simple experiment carried out in 1801 by Thomas Young seemed to prove otherwise. If you flash a beam of light onto a surface with two holes in it, and then look at what gets projected onto a screen positioned some distance behind the surface, then you would expect that, if light is made of particles, some of its particles will go through the first, and some through the second, hole, hence that the screen will show two cones of light, and that where the cones overlap (that is, supposedly, where particles from both holes are received) the light should be brightest. But this is not what happens: what you see in the area where the cones overlap is a variety of strips, some brighter than others. The only plausible explanation for this phenomenon was that light is constituted not of particles but of waves, which continue to oscillate after going through the holes and thus, by interfering with one another, produce the variable patterns.

Subsequent experiments of polarization appeared to establish another result: if indeed light is made of waves, those waves cannot be longitudinal like sound waves but must be transverse like those of the ocean.

Transverse waves require a medium for transmission (they are, in essence, ways in which the medium vibrates), and they travel faster the more solid the medium is. As a good approximation to the speed of light had been available since the 17^th century, and that made light extremely fast, the medium for the transmission of light waves had to be more solid than any metal. But light travels through the whole universe, hence the whole universe must be pervaded by a substance—the luminiferous ether—which is more solid than any metal while it is also more rarefied than any gas, as no one can see it. How celestial bodies could move with this stuff impeding them was anybody’s guess, and a number of fanciful proposals were made to address this issue; besides, despite a number of experiments devised explicitly for this purpose (the most famous one by Michelson and Morley, in 1881 and then again in 1887), no evidence could be found that the ether existed. By the end of the 19^th century, the physical explanation of light was thus in great trouble, and help was to come through a theory that challenged the entire conception of science prevalent in the previous three centuries. That theory was quantum mechanics, initiated by Max Planck in 1900 and given prominence in 1905 by Einstein, who used it to explain a phenomenon until then mysterious—the photoelectric effect. (Heisenberg mentions this development on p. 6, and explains the photoelectric effect as “the emission of electrons [that is, electricity] from metals under the influence of light.”)

“Quantum mechanics” owes its name to Planck’s initial intuition: he realized that, when an atom radiated energy, it could only do so in the form of discrete packets—or quanta (also called photons). This was, Heisenberg says, “a result that was so different from anything known in classical physics that he certainly must have refused to believe it in the beginning” (p. 5). The universe of classical physics is continuous: in it, a quantity grows in a time t from size A to size B, or a body travels in that time from a point A to another point B, by going through the infinitely many intermediate steps between A and B in the infinitely many instants of which t is constituted (and, in fact, Galileo refers to this feature of the universe on pp. 22-24 of the Dialogue). Now, suddenly, the universe appeared to be no longer continuous but indeed discrete, evolving not smoothly but by jumps—much the way you turn up the volume on your TV set by a digital device. That was, as it turned out, only one of the many ways in which the new theory was to contradict old views. In Heisenberg’s words, “the change in the concept of reality manifesting itself in quantum theory is not simply a continuation of the past; it seems to be a real break in the structure of modern science” (p. 3).

Some of the contradictions were as follows: Rutherford and Bohr had developed a model of the atom, where electrons rotated around a nucleus, but often experiments made it look as if electrons were not moving at all. “Does this mean that there is no orbital motion?”, Heisenberg asks, and continues: “But if the idea of orbital motion should be incorrect, what happens to the electrons inside the atom?” (p. 9). Or consider the following: radiation still manifested the same interference patterns Young had first pointed out, but other phenomena, like the photoelectric effect, were strongly suggestive instead of small bodies being thrown around. So, “[h]ow could it be that the same radiation that produces interference patterns, and therefore must consist of waves, also produces the photoelectric effect, and therefore must consist of moving particles” (p. 9).

Heisenberg describes a situation in which, “during the early twenties, the physicists became accustomed to these difficulties, they acquired a certain vague knowledge about where trouble would occur, and they learned to avoid contradictions” (p. 10). They had, in other words, a fairly successful laboratory practice but no theory that accounted for that very success, and were indeed aware that the existing theory (that is, classical mechanics) was inadequate for that purpose. Eventually, young Heisenberg came to the rescue. With characteristic modesty, he says on p. 13: “The idea suggested itself that one should write down the mechanical laws not as equations for the positions and velocities of the electrons but as equations for the frequencies and amplitudes of their Fourier expansion.” This idea “suggested itself” to Heisenberg, it was his own; and it was a revolutionary one. As Lindley explains in his introduction, a “Fourier series is the standard mathematical device by which any vibration of a violin string, for example, can be represented as a suitable combination of the string’s elementary tones. In such a representation, the instantaneous position and velocity of any point along the string is expressed in terms of some weighted sum of the string’s fundamental and harmonic notes” (p. ix). That is, a point in the string is not given a single value for its position or velocity but rather something like the following: “40%A + 30%C + 30%E” (where A, C, and E are notes). By extending the same device to electrons, and to bodies in general, Heisenberg was to deny that they have any definite position or velocity—to put it simply, and somewhat drastically, that an electron, or a body in general, is at any one time in any specific place. And this revolutionary idea was to be the basis of the so-called “Copenhagen interpretation” of quantum mechanics, which resulted from the interaction between Heisenberg and Bohr (not an easy one, as we are told that their discussions “went through many hours till very late at night and ended almost in despair,” p. 16) and was available, Heisenberg says, by the spring of 1927 (p. 17).