LEE SMOLIN

Founding and Senior Faculty member at Perimeter Institute for Theoretical Physics in Waterloo, Canada; Adjunct Professor of Physics at the University of Waterloo; Author, The Trouble With Physics Perhaps the most embarrassing example from 20th Century physics of a false but widely held belief was the claim that von Neumann had proved in his 1930 text book on the mathematical foundations of quantum mechanics that hidden variables theories are impossible. These would be theories that give a complete description of individual systems rather than the statistical view of ensembles described by quantum mechanics. In fact de Broglie had written down a hidden variables theory in 1926 but abandoned work on it because of von Neumann's theorem. For the next two decades no one worked on hidden variables theories. In the early 1950's David Bohm reinvented de Broglie's theory. When his paper was rejected because von Neumann proved what he claimed impossible, he read and easily found a fallacy in the von Neumann's reasoning. Indeed, there had been at least one paper pointing out the fallacy in the 1930s that was ignored. The result was that progress on hidden variables theories in general, and de Broglie and Bohm's theory in particular, was delayed by several decades. An example in economics is the notion that an economic markets can usefully be described as having a single unique and stable equilibrium, to which it is driven by market forces. As described by neoclassical models of markets such as the Arrow-Debreu model of general equilibrium, equilibrium is defined as a set of prices for which demand for all goods equals supply, as a result of each consumer maximizing their utility and each producer maximizing their profit. A basic result is that such equilibria are Pareto efficient, which means no one's utility can be increased without decreasing some body else's utility. Furthermore, if the economy is in equilibrium there are no path dependent effects, moreover it can be argued that market prices in equilibrium are perfectly rational and reflect all relevant information. If equiilibrium were unique, then one could argue that the most ethical thing to do is to leave markets free and unregulated so that they can find their points of equilibrium where efficiency and utility are maximized. This kind of thinking to some extent motivated choices about leaving financial markets under-regulated resulting in the recent economic crisis and current difficulties. However, it was learned in the 1970s that even if efficiency and equilibrium are useful notions, the idea that equilibria are unique is not true in generic general equilibrium models. The Sonnenschein-Mantel-Debreu Theorem of 1972 implies that equilibria are in general highly non-unique, and it is not difficult to invent models in which the number of equilibria scales with the number of producers. But if there are multiple equilibria, most will not be stable. Moreover supply and demand are balanced in each of the many equilibria, so market forces do not suffice to explain which equilibria the market is in or to pick which would be preferred. The consequence theoretically is that path dependent effects which determine which of many the equilibria the market is in must be important, the political consequence is that there is not an ethical argument for leaving markets unregulated. Since then some of the more interesting work in economics studies issues of path dependence and multiple equilibria. I cannot comment on why economists made the mistake of thinking about market equilibrium as if it were unique. I do think I have some insight into why a false belief about the possibility of alternatives to quantum mechanics could persist for more than two decades. During this period there was rapid progress in the application of quantum mechanics to a wide set of phenomena from astrophysics to nuclear and solid state physics. Meanwhile the most popular interpretation of quantum mechanics was Bohr's, which is now hardly taken seriously by anyone. Those who concentrated on the foundations of the subject were left behind, especially as it was convenient for the progress that was being made, to believe that the foundations were surer than in fact they were. Perhaps there are periods in science where it makes sense for most scientists to sweep foundational worries under the carpet and make progress on applications, postponing the inevitable reckoning with the inconsistencies to a time when there are better hints from experiment.