Quantum Mechanics, Instrumentalism and Empirical Equivalence

It may strike strange to search for cases of empirical equivalence in quantum theory, of all scientific theories. Indeed, there is a well-entrenched account in the philosophy of science literature according to which quantum theory is the paradigm example of explicit instrumentalist thinking.^[111] If this were accurate, there would be no point in being worried about empirical equivalence and underdetermination in this area of scientific research.

However, the thesis that instrumentalism may be considered the “official philos­ophy” of quantum physics does not sit well with scientific practice. Of course, it is true that this practice focuses on predictions and the exploitation of new phenomena, especially in applied research. But this focus on empirical results should not be mis­taken for a philosophical position implying that it does not make sense to inquire into mechanisms behind the phenomena or that it is inappropriate to wonder about the properties of the underlying physical reality. Quite the contrary, physicists have been fiercely debating such interpretational issues, especially in connection with effects that resist explanation by processes known from classical physics; and they have done so since the beginning days of quantum theory.

This attention for the nature of physical reality is not a new development: already the founding fathers of quantum mechanics were wrestling with the question of how quantum reality should be described and understood. It is true that Heisenberg in his ground-breaking papers on the new quantum theory announced that he would only allow quantities that were open to observation—but this should not be interpreted as a basic resolution in favor of instrumentalism. Rather, at the time the breakthrough to quantum mechanics took place, it had become clear that the classical world pic­ture was deeply inadequate for the explanation of atomic phenomena and that one could not rely on the actual existence of things like “the orbit of an electron in an atom”. Heisenberg therefore took the methodological decision to start anew, almost from scratch, by allowing only concepts whose applicability could nearly directly be verified by observation. It is a serious misunderstanding to think that by this he confessed to philosophical instrumentalism: Heisenberg spoke freely about submi- croscopic entities like electrons and atoms, although taking into account that their properties were still obscure and should certainly not be thought of as classical. In fact, Heisenberg devised thought experiments involving such quantum objects (like his famous X-ray microscope).

Bohr attempted in a more focused and systematic way than Heisenberg to charac­terize salient features of the new quantum domain. For this purpose he developed his notorious doctrine of complementarity, whose central idea is that quantum objects cannot possess properties like position and momentum at the same time; according to Bohr such properties are only well-defined if the quantum system interacts with quite specific environments. In particular, in a context in which a particle interacts with a measuring device that is sensitive to position, “position” becomes well-defined; and mutatis mutandis for momentum. Bohr has frequently been criticized for being obscure in his explanations of complementarity and in how he proposed that prop­erties should be attributed to quantum particles like electrons—sometimes they can be thought of as point masses and then again as if they were waves (e.g., Cushing (1994), Beller (1999)). But this very criticism testifies to the fact that Bohr did not propose a simple instrumentalist reading of quantum mechanics. Indeed, what could be simpler than explaining the instrumentalist position that the formalism of quan­tum mechanics should not be taken as possessing physical meaning and that only empirical predictions possess “cash value”?^[113]

The present-day situation is that there exist two versions of the quantum for­malism, which differ slightly in their dynamics and the mathematical representa­tion thereof. Traditionally, a special dynamical principle has been assumed for mea­surement interactions: the core idea is that in a measurement the wavefunction sud­denly “collapses” in order to represent the single outcome that materializes. Indeed, before the measurement there generally are many outcomes possible, each with its own probability (the wavefunction predicts only possible values and probabilities for measurement results, this is the notorious indeterminism of quantum theory).

A more modern alternate approach is to treat all interactions, whether measure­ments or not, in the same way. This means that in all cases an evolution equation like the Schrodinger equation is applied. This has the consequence that the evo­lution of the wavefunction is always continuous, so that no collapses can happen. Conceptually speaking, all possibilities that were present before the measurement are still represented in the post-measurement wavefunction, but now including the result indicated by the pointer of the measuring device. If before the measurement there was a probability p for a certain outcome, the non-collapse approach says that after the measurement there is the same probability p for the device being in the state indicating the relevant outcome.

These two theoretical schemes (collapse and non-collapse) make the same pre­dictions in all ordinary circumstances, but could in principle give rise to empirical differences in very peculiar, not yet practically realizable, situations.^[114] We are thus dealing with two theoretical schemes that are not empirically equivalent in the strong sense, and an empirical decision between them should be possible in delicate exper­iments (although not yet in present-day practice).

These two versions of the theory, collapse and non-collapse quantum mechanics, have their own classes of interpretations. We shall here concentrate on non-collapse interpretations.^[115]

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