Comparison with the Arguments of Laudan and Leplin

Empirical equivalence thus does occur in the practice of modern science and is not a mere harebrained philosophical scheme. How does this observation compare to the arguments we rehearsed in Sect.

The first criticism Laudan and Leplin brought against the significance of empiri­cal equivalence was that it necessarily is defeasible: because new experimental tech­niques are constantly being developed, not yet verified empirical differences between theories will come to light sooner or later. We have already dealt with this objection in the previous section: in the quantum case, the discovery of such empirical dis­tinctions is not plausible and is not expected to occur. Therefore, a strong form of empirical equivalence obtains here.

This may raise the question of whether we are dealing with different theories at all; isn’t the designation “interpretations of quantum mechanics” by itself already a sign that we are facing one single theory (quantum mechanics), although in multiple formulations? This reaction, however, fails to appreciate that the different interpre­tations draw very different pictures of the submicroscopic world. The problem of empirical underdetermination of theory choice is therefore certainly present here, in the form of the empirical underdetermination of the choice of one picture of the world over another—which is the problematic kind of underdetermination in the context of the realism debate.

In cases of persistent empirical equivalence, as we are facing, Laudan and Leplin suggest that the contending schemes will likely be artificial variations on a standard form of the theory; and that these artificial rivals will not satisfy certain standards of “theoreticity” so that they can be discarded. These theoreticity criteria are of two sorts: artificial pseudo-theories will not pass the test of testability because they con­tain empirically unverifiable parts that do not contribute to the derivation of empiri­cal results; and/or they will contain hypotheses that are highly implausible given our empirical background knowledge of what the physical world is like.

In our case of different quantum interpretations it not clear whether it can be said that new physical hypotheses are added to “standard quantum mechanics” in order to create the various interpretative schemes. The mathematical formalism that is vital for the derivation of empirical results is the same in all interpretations, and it is first of all the physical meaning of this formalism that is different. It is true, though, that depending on the nature of the interpretation additional symbols and equations will be necessary to make the theoretical scheme complete. For example, in the Bohm theory symbols are introduced for the definite particle positions and momenta that are central in this theory, x_i and p_i, and these symbols are obviously not needed in interpretations that do without Bohmian particle properties—although other sym­bols will be necessary to denote the “elements of reality” of these rival interpreta­tions. Staying with the Bohm theory, we need a dynamics for the particles in order to make the total system, including the Schrodinger equation and the wavefunction, complete and self-consistent; one way of implementing this dynamics is by specify­ing the “guidance equation” we mentioned before, p = VS.

The particle properties in the Bohm theory, and the equation defining their evolu­tion, may be said to embody physical hypotheses but these are not gratuitous exten­sions or embellishments added to the physics of other interpretations or to “quantum mechanics proper”. They play an integral part in the physics of the Bohm scheme. Moreover, they do not at all appear artificial or implausible given our background knowledge. Indeed, the notion of a particle with a well-defined trajectory is part and parcel of the usual conceptual toolkit of physicists and plays a major role in expli­cating the meaning of causality in classical physics. Accordingly, adherents of the Bohm theory often argue that their scheme succeeds in providing a clear causal pic­ture of how experimental results come about, whereas other interpretations propose more unusual and rather nonintuitive pictures of reality in which the causal connec­tions remain unclear.

This is not to say that Bohmian quantum mechanics is clearly superior to other interpretations. In fact, the history of quantum theory has taught us that the clas­sical world picture of localized particles and local fields is problematic—think of the well-verified phenomenon of particles that “interfere with themselves”, as in the double-slit experiment. In Bohm’s theory these unexpected non-classical phenom­ena are handled by the introduction of a couple of unorthodox features of the particle dynamics; in particular, the dynamics is non-local, so that changes in the position of one particle will be immediately felt by all other particles (cf. what was said in note 3), and there is the nonclassical guidance by the ¥ field. Other interpretations obvi­ously also have to accommodate interference, wave-particle duality, non-locality and similar symptoms of non-classicality, and claim to do so in a more natural and sim­pler way by renouncing the concept of a classical particle from the outset, and setting themselves the task of explaining the appearance of an “almost classical” world as the macroscopic limiting case of a description that overall is typically quantum. In all these interpretations the postulated ontology plays a direct role in the explanation of empirical results, so the Laudan and Leplin criterion of no superfluity does not disqualify any of them.

It should be recognized that all interpretations have their own unusual features, which make them all distinctly non-classical in their own way. As we have seen, there is the strange non-locality of interactions in the Bohm theory,^[124] whereas there is the seemingly metaphysically extravagant multiplicity of worlds in the many worlds interpretation.

The methodological desideratum that superfluity, artificiality and testability are to be avoided is thus too ambiguous and weak to come to an objective decision about which interpretation is to be preferred. But there is also the second prong of Laudan’s and Leplin’s analysis, according to which different empirically equivalent theories may well be differentially supported by empirical evidence because they relate dif­ferently to other theories or background knowledge. If one theory T₂, of a pair of empirically equivalent theories T1 and T₂, can be subsumed under a more encom­passing theory T, it may happen that evidence E comes in that supports T, although it does not directly support T₂ (in the sense that E is not a prediction of T₂ and may even pertain to a domain of reality T₂ does not speak about).

In order to apply this line of reasoning to quantum mechanics, we should find a more general theory T into which the quantum formalism can be imbedded, in such a way that the imbedding goes well for one (or some) interpretations and does not succeed, or does not go too well, for other interpretations. Empirical evidence for T will then count against interpretations that cannot easily be imbedded. Now, quantum mechanics can be seen as a special case of a more general quantum theory, namely quantum field theory. In quantum field theory more complicated physical interactions can be handled than in quantum mechanics, in particular processes in which quantum systems are created and annihilated.

However, the use of quantum field theory as the theory T in the just-explained scheme of empirical support does not lead to unambiguous results. The reason is that quantum field theory has different interpretations itself, analogous to our ear­lier interpretations of quantum mechanics. That is, also here there is a core math­ematical quantum field formalism that is shared by different interpretations and to which different “rules of correspondence”, which stipulate the physical meaning of the mathematical symbols, are applied. Where needed, new symbols may be added to denote quantities that are specific to an interpretation (like x and p for definite particle position and momentum). In this way, for example, a Bohmian version of quantum field can be developed (see, e.g., Durr et al. (2004)); other non-collapse interpretations can similarly be extended. The condition that some of the empiri­cally equivalent theories fit better with more general theories than others is therefore not fulfilled—rather, the original question about which theory to prefer is repeated on the more general level, without an unambiguous objective resolution.

The story does not end here, for one may also consider the compatibility of the different interpretations of quantum mechanics with general space-time features, as specified by relativity theory. Here there is at least a prima facie problem for the Bohmindex theory, because this theory requires a notion of simultaneity (to make sense of instantaneous interactions) that is at odds with the standard interpretation of special relativity. However, the manoeuvre of constructing different empirically equivalent interpretations at a more general theoretical level can be repeated: it is possible to introduce a minimum of additional structure in relativity and to accom­modate the Bohmian scheme in the resulting enriched relativistic spacetime. Impor­tantly, this can be done without changing the empirical content of relativity theory (actually, various ways of doing this have been proposed, see e.g.

Summing up, it seems safe to say that no argument has been presented that singles out one of the various interpretations of quantum mechanics as objectively better than the others. There is no direct experimental evidence in the offing that might be able to enforce a decision between the alternatives; and the various more theoretical arguments—Laudan and Leplin style—about superfluity, testability and support do not convincingly identify one option as superior either.

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