The Concept Of Quantum Mechanics And Experience By David Z. Albert

In many of our daily observations in life, we tend to assume that things are predictable, well-defined and most importantly, somewhat intuitive. This assumption seems reasonable given that, for the most part, the physical systems we normally encounter do fit these properties. Naturally, it should be safe to believe that these assumptions are valid for all physical systems. However, as Albert notes in his opening paragraph, the empirical reality can be rather unsettling (p. 1). In fact, as the systems in question become smaller, some of the basic beliefs about those physical systems have to be rejected or, at the very least, reconsidered. As experiments have shown, quantum systems act rather counter-intuitively, and several concepts, such as superposition, have been introduced in an attempt to model or explain their behavior.

One of the most striking experiments that demonstrate the odd properties of quantum systems is the Stern-Gerlach Experiment. In chapter 1 of Albert’s “Quantum Mechanics and Experience”, the author abstracts away the technical details of the experiment and, instead, considers a simpler variant. Firstly, he defines two properties that electrons can take, namely color and hardness. Each of these properties can take on exactly one of two values. For the case of color, electrons can be either white or black. In terms of hardness, electrons can be either soft or hard. Next, he defines two types of boxes, each with one input and two outputs. He calls those boxes “color-” and “hardness-” boxes. Each box takes in a beam of electrons and separates it into two beams according to their properties. For example, a color box takes in a beam of electrons and outputs two beams: one beam containing only the white electrons and another containing only the black electrons. Similarly, a hardness box takes in a beam of electrons and outputs two beams: one beam containing only the hard electrons and another containing only the soft ones (p. 2).

As one would expect, if a beam of electrons emerges out of, say, the black output of a color box, then feeding that output into a second color box would result in all the electrons emerging from the black output of the second color box. This is also true for white electrons emerging out of color boxes and both hard and soft electrons coming out of hardness boxes. Albert then introduces a more interesting configuration. This time, the electrons first go through a hardness box, with half of them emerging as hard electrons and the other half as soft ones. Then, one of the halves, say, the hard half, is fed into a color box. Those too, will come out evenly split between white and black. At this point, we could reasonably expect the electrons at the black output of the color box to be both hard and black. To verify this, the electrons are then sent into another hardness box. However, the electrons do not all emerge as hard ones. Instead, what is observed is that only half of the electrons come out black, and the rest come out white (p. 4). Furthermore, if the setup were tweaked by merging the two beams that initially came out of the color box, those same electrons will all come out hard again (p. 9).

The aforementioned observation is a fundamental illustration of a real experiment, namely the Stern-Gerlach Experiment (Hughes p. 2). It provides experimental evidence that physical systems aren’t as intuitive as we would like them to be. Nevertheless, there ought to be some way to explain this result. While a complete explanation doesn’t seem clear at this point, there are a few points to keep in mind. First, it is quite clear that the act of observing an electron’s color will tamper with its hardness and vice versa (Hughes p. 6). Second, it is possible for electrons with different properties to interfere and “cancel out”, as exemplified by the result of merging the two color beams. At the very least, any explanation to the results of the experiment must be in agreement with these conditions.

Before attempting an explanation, a little more intuition is needed. For that reason, consider one last experiment Albert describes. A barrier with two slits in the center is placed between a screen and a source of electrons. Statistically speaking, most electrons, acting as particles, should be scattered somewhere directly behind the centers of either slit. This, however is not what is observed. Instead, the electrons form an interference pattern similar to the one created by waves of light1 (p. 14). This suggests that electrons have some wave-like behavior. However, unlike waves, when one slit is blocked, the observed pattern on the screen collapses back to the one we would expect from particles (Bach et al. ). This raises several questions. Is the electron a particle or a wave? If it is the former, then what path did one electron take when both slits where unblocked? If it is the latter, then how can one explain the pattern obtained after blocking one of the slits?

In an effort to explain these odd facts of nature, we must introduce a new concept: the superposition. Whatever it may be, this concept should allow us to justify the results of the experiments discussed. From the intuition we’ve built, a superposition is some way of describing a system that is unobserved. Given system with some set of properties, so long as the system remains unobserved, it is said to be in a superposition of configurations (states) that it could be in. This doesn’t mean that the system occupies all possible states at once. It means that the system is in some additional “quasi-state” that shares some properties of its constituent states. Since a system can only physically exist in one state, an observation of the system will always yield one and only one of the superimposed states. Moreover, as seen in the Stern-Gerlach Experiment, systems in a superposition can interfere with one another and intensify some constituent properties more than others. Any action onto the system will affect all the intensities of the superposition. These “intensities” determine the probability of observing the system in the corresponding state. Furthermore, some properties of a system, such as color and hardness or “wave-ness” and “particle-ness”, seem to be complementary. The more well-defined one property is, the greater the uncertainty in the other. To put it in another way, if one property is observed, then the system doesn’t have the other property (Scully et al. p. 1). This would explain why feeding hard electrons into a color box “shuffles” their hardness. It effectively erases the hardness property of the electrons and leaves them in a superposition of hard and soft, yielding either hardness value once observed.

In conclusion, quantum systems highlight the odd effect simple observation can have on an experiment. It is significant to remark, however, that macroscopic, classical systems are somehow more robust to our observation. Therefore, any theory that intends to generalize the above conclusions to classical systems must predict that quantum effects fade out as systems become bigger, slower or more massive.