Chemistry, Quantum Mechanics and Reductionism

“Knowledge of any kind is a thing to be honored and prized”, says Aristotle (384–322 B.C.) in the opening sentence of his On the Soul. According to the Auger report “the number of scientific journals and periodicals, which was about 100 at the beginning of the nineteenth century, reached 1’000 in 1850, more than 10’000 in 1900, approaches 100’000 in 1960 and — if this rate of growth remains constant — should be in the neighbourhood of a million at the end of the century” (Auger, 1961, p. 15). Linus Pauling (1958) guessed “that about 100’000 new chemical facts are being discovered each year, at present”. Stanislaw Ulam (1976, p. 288) estimated that contemporary mathematicians produce one or two hundred thousand theorems a year. Due to this explosive development of research, science has split into many different sciences. Chemistry has split into many disciplines only tenuously connected. No researcher can keep abreast with the work in his own narrow subfield. Nobody can digest even the most outstanding results of science, to say nothing of integrating them into our culture. “The man of knowledge in our time is bowed under a burden he never imagined he would ever have: the overproduction of truth that cannot be consumed. For centuries men lived in the belief that truth was slim and elusive and that once he found it the troubles of mankind would be over. And here we are in the closing of the 20th century, choking on truth” (Ernest Becker, 1973). This is something to worry about. The widely accepted tale “knowledge is good for mankind” has become suspicious.

Scientific method is one of many possible approaches to understanding the world. Science does not deal with every aspect of reality but only with a carefully selected part of reality. Science does not provide any premises for aesthetical, moral or political conclusions. There are complementary approaches such as the fine arts, poetry or religious experiences which are no less important than science.

Quantum mechanics was created in a unique effort of a small group of ingenious physicists during the period of 1922 to 1927. The leading pioneers were Niels Bohr, Louis de Broglie, Max Born, Werner Heisenberg, Pascual Jordan, Wolfgang Pauli, Erwin Schrödinger and Paul Adrien Maurice Dirac. By 1928 the new mechanics was sufficiently developed to be applied to the properties of atoms, molecules, solids and radiation. The first really authoritative text was Dirac’s “The Principles of Quantum Mechanics” of 1930. Von Neumann’s brilliant “Mathematische Grundlagen der Quantenmechanik” of 1932 contributed much to the mathematical refinement of the new theory, while Pauli’s article “Die allgemeinen Prinzipien der Wellenmechanik” in the “Handbuch der Physik” of 1933 gives an encyclopedic coverage from a more physical point of view. In spite of their slightly different positions, we regard the expositions in these classical works by Dirac (1930), von Neumann (1932) and Pauli (1933) as aspects of one single theory which we call pioneer quantum mechanics. More recent accounts of pioneer quantum mechanics are the monograph by Bohm (1951) and by Ludwig (1954).

The new era of quantum theory began around 1932, and witnessed a maturation, many extensive developments, and a striking turn to an abstract structural approach. Important results of modern quantum theory, although easily accessible, are as yet not very well known. In spite of its urgency, the conceptual recasting of pioneer quantum mechanics has been slow. Even slower is the transference of successful reformulations into our textbooks which are still full of archaisms and inconsistencies; they hardly reflect the important progress made in the last two decades. In this chapter we shall attempt to give a brief outline of the main trends in the development of quantum theory since 1932. In this period, the new results have been so voluminous that it is necessary to limit our discussion and to select a few topics which are of special importance for the theory of molecular matter. Naturally the selection is in part guided by my prejudices, so my apologies are due to all those whose work has been ignored or insufficiently discussed.

For decades, the presuppositions of pioneer quantum mechanics have served as paradigms for theoretical chemistry. Numerical quantum chemistry has become the natural way of looking at problems for most theoretical chemists. As stressed by Ludwik Fleck (1935) and Thomas S. Kuhn (1962), a paradigm on the one hand acts as a method by means of which facts are observed, interpreted and organized. On the other hand every paradigm acts also like a blinder. The snag is that the rules imposed by a paradigm are implicit and not recognized as tentative working hypotheses. In contemporary chemistry, the rules of pioneer quantum mechanics operate automatically, and a good theoretical chemist has become a person who feels that he is doing the obvious thing when using pioneer quantum mechanics to solve a chemical problem.

In spite of the obvious plurality of scientific explanations on various levels of description, there still exists a bias toward theoretical monism. Neglecting the possibility to view nature from different perspectives and ignoring the fact that the decomposition of nature into parts is not God-given, traditional reductionism treats the various theories and models as, to be sure, incompletely articulated but ultimately reducible to an all-embracing fundamental theory. In the context of biology, reductionism is the view that all phenomena of life can be ultimately reduced to the laws of physics and chemistry. There are many variants of reductionism differing in the explanation of what “reduced to” should mean; for example, it may be defined as “accounted for”, “described by”, or “deduced from”. In its extreme form, reductionism denies that a concept is scientifically meaningful unless it is unambiguously defined in terms of fundamental physics.