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arXiv:1508.02048 · Studies in History and Philosophy of Science Part B Studies in History and Philosophy of Modern Physics

The logic of experimental tests, particularly of Everettian quantum theory

David Deutsch

Published Jul 10, 2016• 29 citations

Abstract

Claims that the standard procedure for testing scientific theories is inapplicable to Everettian quantum theory, and hence that the theory is untestable, are due to misconceptions about probability and about the logic of experimental testing. Refuting those claims by correcting those misconceptions leads to an improved theory of scientific methodology (based on Popper׳s) and testing, which allows various simplifications, notably the elimination of everything probabilistic from the methodology (‘Bayesian’ credences) and from fundamental physics (stochastic processes). • Everettian quantum theory is testable. • Stochastic theories suffer from a flaw in the logic of their testability. • Popper׳s methodology is needed to understand the testability of quantum theory.

DOI: 10.1016/j.shpsb.2016.06.001

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Claims that the standard procedure for testing scientific theories is inapplicable to Everettian quantum theory, and hence that the theory is untestable, are due to misconceptions about probability and about the logic of experimental testing. Refuting those claims by correcting those misconceptions leads to an improved theory of scientific methodology (based on Popper׳s) and testing, which allows various simplifications, notably the elimination of everything probabilistic from the methodology (‘Bayesian’ credences) and from fundamental physics (stochastic processes). • Everettian quantum theory is testable. • Stochastic theories suffer from a flaw in the logic of their testability. • Popper׳s methodology is needed to understand the testability of quantum theory.

Statistical physical theories are frequently formulated in terms of probabilistic structures founded on a ’’logic of experimentally verifiable propositions.’’ It is argued that to each experimentally verifiable proposition there corresponds an experimental procedure which, in general, alters the state of the system, and is completely characterized by a ’’measurement transformation’’ or ’’operation.’’ An analysis of the relations among these experimental procedures leads us to a ’’logic of operations’’ which is quite different from the ’’lattice theoretic logics’’ that are often considered (albeit inadequate empirical justification), as models for the calculus of experimentally verifiable propositions of quantum theory. It is seen that the quantum probability theory based on the logic of operations provides the proper mathematical framework for discussing the statistics of successive observations in quantum theory. We also indicate how a theory of quantum stochastic processes can be formulated in a way similar to the Kolmogorov formulation of the classical theory.

This chapter extends chapter 5's formal proof into a general discussion of how we should assess evidence — and, in particular, how we should test scientific theories — given the possibility that Everettian quantum mechanics is correct. The chapter proves — initially with informal arguments, but in due course with full mathematical rigor — that rational scientists should treat the branch weights assigned by quantum theory to quantum-mechanical branches exactly as if they were probabilities; as such, the chapter argues, probability is actually on firmer conceptual footing in quantum theory than in classical physics. After a brief digression to consider probability in approaches to quantum theory other than the Everett interpretation, the chapter concludes by placing the work in the broader context of recent work on Everett probability.

Popper's original thought experiment probed some fundamental and subtle rules of quantum mechanics. He claimed that quantum mechanics was incomplete and devised an experiment to prove it. Two experiments have directly and indirectly tested Popper's hypothesis, and they provide some evidence that Popper's prediction may have been correct. The equations governing these two experiments and Popper's thought experiment will be derived from basic quantum principles. The experimental constants will be inputted and it will show that the two experiments reinforce each other and agree completely with quantum theory.

This chapter demonstrates a similar impasse has again been encountered recently in areas of physics like high-energy physics and cosmology. Carroll is weary of a section of the physics community that deems such theories non-scientific, basing their argument on Popper and falsifiability. Popper is clear about the fact that the demarcation between science and metaphysics that he is seeking is only being done to arrive at a theory of knowledge. Like scientific realism, the constructive empiricism of van Fraasen also accepts a literally account of scientific theories, but only for the observable entities in the theory. Anti-realists refuse to equate the validity of a scientific theory with the existence of the entities it postulates. String theory and, in general, any approach to quantum gravity, can be tested only at energy scales which are so high that they are completely out of the realm of experimental testability.