On the Limits of "Undecidability": Quantum Physics, Deconstruction, and Anti-realism

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Philosophers of science have responded in various ways to the conceptual and interpretative problems thrown up by quantum mechanics. These problems emerged a century ago from Planck’s researches into black-body radiation and have scarcely been resolved—rather, if anything, deepened and complicated—by the intensive debate that has surrounded them since that time.¹ For some theorists, the resultant dilemmas (of observer “interference,” wave/particle dualism, quantum superposition, nonlocal causality, superluminal [faster-than-light] propagation, etc.) are such as to entail drastic revisions to our very idea of the physical world as existing and exerting its causal powers quite apart from our current best theories or investigative methods.² For others again, quantum mechanics just is the best theory currently available, whatever the problems that it happens to create for our normal habits of logical thought or consistent reasoning on the evidence. Thus logic itself may have to be revised—right down to putative “laws of thought” such as noncontradiction and excluded middle—if these turn out to conflict with the results of quantum-mechanical theory or experiment.³

This is the view taken by Hilary Putnam in his writings on quantum logic and also by others, von Neumann among them, for whom the working rule in any such trade-off is to keep the physics as simple as possible even if the result is to complicate logic by introducing values other than those of determinate (bivalent) truth or falsehood.⁴ Very often it consorts with the argument that if quantum mechanics is right—at any rate on the standard Copenhagen interpretation—then we had best give up any hope of retaining a “classical” Einsteinian ontology, that is to say, a Lorentz-invariant account of space-time coordinates where the speed of light is the limiting value for assignments of position, velocity, and causal propagation.⁵ Hence Einstein’s famous series of debates with Niels Bohr when he devised a whole range of increasingly elaborate thought-experiments designed to prove that the quantum-mechnical description of reality had to be in some way “incomplete,” or not to have reckoned with some crucial factor that would bring it into line with logical reasoning and a causal-realist ontology. For on Einstein’s view there was simply no room in science for a theory—such as Bohr’s—that involved either the suspension of classical truth/falsehood values or the idea of some “spooky action-at-a-distance” which contravened both commonsense realism and the requirements of Special Relativity.⁶

However it is Bohr who is generally thought to have carried the day in these debates. In which case—so it is argued—we are left with a choice between three possible “solutions.” These are (1) the hypothesis that quantum mechanics is “incomplete” or open to an alternative (“hidden-variables”) interpretation;⁷ (2) the adoption of an alternative (many-valued or non-bivalent) quantum logic that effectively conjures such problems away;⁸ or (3) the conclusion that realism may have to be abandoned in favour of some radically different ontology or worldview which counts this a price worth paying in order to conserve the predictive power of the standard quantum formalisms.⁹ On option (3) there is a further choice of interpretative views according to the theorist’s preferred choice between the various models (or possible-world scenarios) currently on offer. Thus the model may be one that embraces nonlocal simultaneous particle interaction, or which gives up space-time covariance (relative to the speed of light) as required by Einstein’s Special Theory. Or again it may be one that somehow envisions—strangest of all—the splitting-off of multiple coexistent but non-interacting “worlds” whenever the wave-packet collapses or whenever an act of measurement is performed upon any such quantum-system whose properties must be thought of as strictly indeterminate until that moment.¹⁰ For, according to its partisans, this theory is the most economical—i.e., involves least conflict with the standard quantum formalisms—despite its baroque proliferation of alternative worlds and its well-nigh unthinkable implications when applied...