Dirac, Bernstein, Weinberg and the limits of reductionism

Jeremy Bernstein is a physicist and science writer who has worked with some of the leading physicists of the twentieth century and has penned highly engaging volumes about science, scientists and society which I have enjoyed reading. I was thus disappointed to read his review of a new book on quantum theory by Jim Baggott in the Wall Street Journal which opens thus:

In 1929, theoretical physicist Paul Dirac announced: "The general theory of quantum mechanics is now complete. . . . The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known." The discipline at the point was four years old. Dirac himself was just 27. But eight decades later, we see that his optimistic evaluation was too modest. In addition to a "large part of physics and the whole of chemistry," the theory now is extended to a significant part of biology, essentially all of electronics and nuclear physics, and a large part of astrophysics and cosmology.

Really? A significant part of biology and the whole of chemistry? Both chemists and ecologists may be interested to know this. Let's take stock of this viewpoint since it highlights a quote by Dirac which has been marshaled all too often in support of reductionism. It's time to put the quote in context. Paul Dirac was one of the greatest scientists of the twentieth century and perhaps of all time, but he was no chemist or biologist. He made that statement about quantum mechanics in 1929 when quantum mechanics was at the height of its powers. The complete theory had just been developed by Heisenberg, Born, Schrodinger, Dirac and others and it had turned into physics's crowning achievement. At the same time scientists like Pauling and Slater were applying the theory to chemistry. Suddenly the world seemed to be at physicists' feet and there seemed to be no limit to what physics could achieve.

But this was not the case. The optimism about reductionism endured for the next couple of decades when physicists made monumental contributions to chemistry and molecular biology. And yet the waning years of the millennium indicated that the reach of reductionism was distinctly limited. We were just getting warmed up. As we made forays into expansive fields of chemistry and biology like self-assembly, chemical biology, population genetics, ecology, systems biology and neuroscience, it became clear that the essence of complex systems was emergence. Emergent properties seemed to demand understanding at their own levels and could not be reduced to interactions between particles and fields. At the level of every science there emerged foundational laws, not reducible to deeper principles, that served as the bedrock for that particular science. Today, as we encounter new horizons in the study of signaling networks, brain plasticity and chaotic ecological systems, it's clear that we will have to find and formulate fundamental laws specific to every system and science. No, if anything, Dirac's statement was not too modest but too ambitious; as spectacular as its predictions have been, "a significant part of biology" and chemistry cannot be explained on the basis of quantum theory.

In fact, although I am not an expert in cosmology, the extension of quantum predictions even to cosmology seems surprising to me. Isn't gravity the other dominant force that needs to be taken into account when formulating cosmological explanations? And isn't the welding of quantum theory and gravity the great unsolved problem of physics? To me the inclusion of large parts of cosmology and astrophysics under the quantum fold seems premature.

Interestingly, this abiding interest in reductionist statements reminds me a of minor debate about reductionism between Freeman Dyson and Steven Weinberg that took place in the 90s. Dyson who has been critical of reductionism for a while penned an expressive piece arguing against reductionist philosophy in the New York Review of Books. In reply, Weinberg who has been an arch reductionist replied with his own spirited rebuttal. This rebuttal has been discussed in Weinberg's engaging collection of essays "Facing Up: Science and its Cultural Adversaries".

Weinberg defined what he thought were two distinct critiques of reductionism. One was the critique of reductionism as a working principle. The other was a more fundamental, philosophical critique of reductionism as being unable to account for higher-order phenomena even in principle. Weinberg thus was making a distinction between reductionism in practice and reductionism in principle. According to him, scientists like Dyson who criticized reductionism really had a problem with the former manifestation of reductionism, as a working principle that did not really allow them to solve problems in chemistry, biology, economics or psychology. In contrast, reductionism in principle was alive and well and was being the unwitting victim of the anti-reductionists' axe. In essence Weinberg was saying that, sure, even if quarks cannot directly help you to solve the mysteries of chromosomes, they still surely account for chromosomal properties in principle.

But to me such a distinction is meaningless beyond a point. The working scientist in his or her everyday scientific life really only cares about reductionism as a working principle, not as final causation. The fact that quarks can account for chromosomes in principle is not very consequential; a biologist could care less if there were elves manipulating the fundamental constituents of biological systems. In addition, a lot of biology and chemistry progresses through the construction of models which are not even required to reflect the presence of the very fundamental laws. At the very least, the extolling of reductionism as being able to ultimately account for all kinds of phenomena is a trivial statement; it's like saying that everything is made out of atoms. So what? That hardly helps us cure cancer.

Ultimately, I suspect the argument may be more about semantics, about the meanings of the words "explain" and "account for". But the last word actually belongs to Paul Dirac. In his quote, Bernstein left out something crucial that Dirac said. Yes, Dirac did seem to claim that quantum mechanics could explain "the whole of chemistry", but he also said later that

"...The difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation."

It's those words "approximation", "complex" and "computation" that encompass the essence of chemistry, biology and all the other sciences which Dirac did not mention.

He may have been right after all.