Constituents of Matter / 5 / 5.3

5.3 THE ACCURACY OF QUANTUM MECHANICS

The scientific community put-up with the strange features of the theory it was creating at the turn of the last century because the theory was accompanied by signal success. It is often said that the theory which was constructed to overcome the theoretical crisis of 1900 is far more accurate than the classical one it replaced; in fact, some would claim that it is the most accurate theory man had ever produced:

The theory of quantum electrodynamics has now lasted for more than fifty years, and has been tested more and more accurately over a wider range of condition. At the present time I can proudly say that there is no significant difference between experiment and theory. The theory describes all the phenomena of the physical world except the gravitational effect and radioactive phenomena. When I say that, we do not really know that. Most phenomena we are familiar with involve such tremendous numbers of electrons that is hard for our poor minds to follow the complexity. In such situations, we can use the theory to figure roughly what ought to happen and that is what happens, roughly, in those circumstances. But if we arrange in the laboratory an experiment involving just a few electrons in simple circumstances, then we can calculate what might happen very accurately, and we can measure it very accurately, too. Whenever we do such experiments, the quantum electrodynamics works very well. We physicists are always checking to see if there is something the matter with the theory. That’s the game, because if there is something the matter, it’s interesting! But so far, we have found nothing wrong with the theory of quantum electrodynamics. It is, therefore, I would say, the jewel of physics—our proudest possession.

Richard Feynman, QED: The Strange Theory of Light and Matter, 1985

The palpable sense of pride which is present here bespeaks the conviction that the more accurately a theory describes an experiment the closer it fits the reality which it strives to understand; there is more truth, in other words, in a more accurate theory than there is in a less accurate one. While such is clearly the case for theories that explain ordinary experiments designed to observe objects of experience, it is not the case for theories that explain predicated experiments designed to observe objects of explanation. The reason for the difference is simply that an object of experience, which is given to us to observe, can be approached to various degrees of closeness, but an object of explanation, which is something we give to ourselves as a mente concipio, cannot be approached at all. For quantum theory, therefore, there can be no talk of truth; what measures the distance of the theory from the experiments it explains is the degree of consistency between the object of explanation we had manufactured for observation and the object which explains the outcome of that observation, not the degree of fitness we can attain to an objects which was never given to us in the first place. For instance, the great accuracy with which Planck’s theory explains the Rubens-Kurlbaum experimental outcome is a consequence of the self-consistency requirement he imposed upon that theory when he set the energy of a photon proportional to the frequency of the radiation field; it had nothing to do with whether radiant heat was in fact a wave.

As a matter of fact, Feynman recognizes the same difference as we do when he distinguishes between the ability of quantum mechanics to explain phenomena which involve objects of experience with a “tremendous number of electrons” and its ability to explain those laboratory experiments which involve objects of explanation with 'just a few electrons in simple circumstances'. In the former case, he says, we can use the theory to figure roughly what ought to happen; in the latter, we can calculate what might happen very accurately. However, while for us that difference between “tremendous number of electrons” and “just a few electrons” is the ontological difference between an object of experience and one of explanation, for him the difference simply reflects the fact that “our poor minds find it difficult to follow the complexity” of experience, implying that, when our calculational capacity increased sufficiently, the difference would all but disappear. Thus, Feynman does not seem to have entertained the notion that when the object under observation is given to us, the guiding principle of the explanatory construct is serviceability, while when we must manufacture the object under observation, the guiding principle is self-consistency.

Indeed, in the explanatory construct built on serviceability, the behavior of an object of experience is first ascertained by performing ordinary measurements on it; mechanisms mediated by various objects of explanation are then freely considered and tested through experiment as to whether the propositions derived from them stand verified by experience; and finally, that one from amongst them is selected whose introduction serves to best explain the behavior of the object of experience which is under observation. Subsequently, the same object is expected to explain any other measurements pertaining to the same realm of experience as the one which selected it in the first place, as well as any other measurements suggested by the theoretical development of the mechanism it mediates; otherwise it gets discarded until another one could be selected.

By contrast, in the explanatory construct built on self-consistency, we give ourselves an object of explanation by setting-up the experimental context which we once explained with the aid of that object; measurements predicated on that original giving are then performed to ascertain the behavior of the object thus manufactured; mechanisms mediated by various objects of explanation are next considered and tested through experiment; and only that one is finally selected from amongst others which explains the results of the predicated measurement. But precisely because the measurement was predicated on an original self-giving, the integrity of the experiment demands that the object under observation and the object explaining its behavior be consistent with each other. That consistency is realized in a giving from unity of the two objects. Subsequently, the object of explanation is self-consistently modified to encompass an ever-growing set of predicated measurements that explore its content.

The former construct is designed to fit a freely conceived explanatory mechanism to the quantified experience we gain in ordinary experiments. The latter construct is designed to clarify the conceptual content of the object of explanation which mediates that mechanism. If the former conceives of electrons in order to explain the conduction of electricity through rarefied gases, the latter explores what it is that we mean by an electron. For all that difference, however, both constructs deal with measurements involving experimental apparatuses consisting of various organized sets of objects of experience and therefore they identify stable relationships that obtain between those objects. These relationships enlarge our understanding of the structure of the world, structure which, as we said in Chapter 3, guides man’s employment of the things he encounters within it. Consequently, both explanatory constructs, though different from each other, offer information about the structure of the world, information which man can then use to develop technology.

There is little substance therefore to the claim often made that we should accept the uncomfortable strangeness of quantum mechanics because it led to the explosive development of modern technology. The fact of technology is independent of the specific features of science; it simply attends scientific explanation in general. What does depend upon those specifics is the form of the technology it suggests. The explanation of ordinary measurements provided by classical physics led to the industrial revolution, the explanation of predicated measurements provided by quantum physics led to the information revolution, but both revolutions were an unfolding of the scientific project.