Empirical Equivalence of Interpretations of Quantum Mechanics

To what extent are these different interpretations empirically equivalent? All the non-collapse interpretations that we have been considering share the standard math­ematical formalism, with a wavefunction governed by the same evolution equation.

The very fact that the description of the physical world is different in these inter­pretations already shows that they cannot be empirically equivalent in the strongest possible sense, with regard to all logically possible observations. Indeed, one might imagine scenarios in which human beings develop new senses by means of which they are able to immediately “see” what physical reality is like, on all levels of com­plexity and on all scales. Such new sensory powers would open up the possibility of directly deciding between different hypotheses about physical reality, even if these hypotheses agree with respect to what is the case on the usual macroscopic scale. For example, if we developed an awareness of the values of (sub)microscopic momenta, we could immediately observe whether the Bohm theory is true or not: we could sim­ply check whether particles always possess the precise values for their momenta the Bohm theory prescribes, and we could see whether they indeed follow trajectories of the predicted sort.

But this argument for the drastic defeasibility of all empirical equivalence, on the basis of logical possibility, is obviously irrelevant to scientific practice.^[123] Empirical equivalence by definition refers to equal status with respect to observations by us, human beings who as a physical fact have a restricted repertoire of ways of interacting with the surrounding world. These possible interactions are physical, and therefore amenable to physical description and explanation; our best physical theories should be able to deal with them. For example, we communicate via electromagnetic radi­ation (light) and sound, and our theories describe the impact these signals have on our sensory organs, conceived as measuring devices. The best theory in principle to deal with these things is quantum mechanics, of which, as we have seen, there are diverse versions. But these different versions agree with each other on the macro­scopic level, which is the level on which we live and function. So if the different ver­sions of quantum mechanics satisfy the adequacy requirement that they all be able to recover our classical world, they all must say the same with regard to the sensitiv­ity of our sense organs. Moreover, because the relevant facts of sensory physiology are largely independent of quantum mechanics and were mostly established in the context of classical research already quite some time ago, they can be expected to be robust and remain the same even if quantum theory is going to be superseded by a better theory. It follows that in order to create new observational possibilities that go beyond the macroscopic surface of physical reality, new principles of physical interaction or a change in the formalism of quantum mechanics is needed, or both. But such changes would mean that all current versions of quantum mechanics, with their shared macroscopic predictions, are wrong.

We may conclude that the different interpretations of quantum mechanics that we have been considering are empirically equivalent in the sense that no future mea­surements that make use of the well-established interactions on which experimental practice is based will be able to destroy it. Of course, it is logically possible that macroscopic regularities of the past will discontinue at some future point in time; and that novel laws will come to replace them. But such contingencies will spell trouble for all interpretations.

This gives us an empirical equivalence that is pretty strong. However, we have to proceed with some caution. As mentioned above, it is an adequacy requirement for interpretations that they provide us with the usual classical characterization of the macroscopic world. But this will only be achievable to some degree of approxima­tion, of which it is usually assumed that it is irrelevant for observation. For example, although the Bohm theory tells us that all objects always possess definite position and velocities, other non-collapse interpretations will characterize objects with quantum properties that obey the uncertainty relations, so that there will be a finite spread (“latitude”, Bohr called it) in the values of the quantities characterizing them. In the latter case the classical world, with definite positions, momenta, etc., will not be com­pletely recovered. However, the spreads in question will be enormously small once we are dealing with macroscopic bodies with appreciable masses, and this usually is taken as sufficient justification for discarding them (“in the classical limit”). But in principle these quantum spreads never vanish completely and one could imagine that however tiny they are, they could play a role in some situation. Thinking back of our characterization of the human sensory organs as physical detection instruments, this would require that it could make a difference for our awareness of what we observe whether molecules in our brains, neurons, etc., have exactly definite positions a la Bohm or positions with a tremendously tiny “vagueness” or spread as predicted by other interpretations.

To sum up, the different interpretations of quantum mechanics that we have sketched can be taken to be empirically equivalent in a strong sense: no future macro­scopic observations can be expected to be able to distinguish between them. This is so in spite of logically possible scenarios according to which we might develop direct veridical insights into the (sub)microscopic world and in spite of the fact that quan­tum theory will only be able to recover the classical macroscopic world of experience to a high degree of approximation. In the former case the possibilities are merely log­ical and not physical, in the latter we have to expect that the differences are much too small to be significant for observations.

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