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Australasian Journal of Philosophy

Undermined

Gordon Belot

Published Apr 6, 2016• 5 citations
Publisher

Abstract

A popular strategy for understanding the probabilities that arise in physics is to interpret them via reductionist accounts of chance—indeed, it is sometimes claimed that such accounts are uniquely well-suited to make sense of the probabilities in classical statistical mechanics. Here it is argued that reductionist accounts of chance carry a steep but unappreciated cost: when applied to physical theories of the relevant type, they inevitably distort the relations of probability that they take as input.

DOI
10.1080/00048402.2016.1139604

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A popular strategy for understanding the probabilities that arise in physics is to interpret them via reductionist accounts of chance—indeed, it is sometimes claimed that such accounts are uniquely well-suited to make sense of the probabilities in classical statistical mechanics. Here it is argued that reductionist accounts of chance carry a steep but unappreciated cost: when applied to physical theories of the relevant type, they inevitably distort the relations of probability that they take as input.
Everettian quantum mechanics tells us that the fundamental dynamics of the universe are deterministic. So what are the `probabilities' that the Born rule describes? One popular answer has been to treat these probabilities as rational credences. A recent alternative, Isaac Wilhelm's centered Everett Interpretation (CEI), takes the Born probabilities to be centered chances: the objective chances that some centered propositions are true. Thus, the CEI challenges the `orthodox assumption’ that fundamental physical laws concern only uncentered facts. I provide three arguments against the centered Everett Interpretation. First, I argue that the CEI is in apparent tension with a significant motivation for adopting Everettian quantum mechanics: rejecting the attribution of special significance to observers or agents in fundamental physics. I suggest the CEI can avoid this tension, but only at the cost of sacrificing its central claim that there are objective chances in an Everettian multiverse. My second argument concerns the CEI’s claim that the centered Born rule is a fundamental physical law. I provide two plausible notions of fundamentality for physical laws, and I argue that the centered Born rule satisfies neither. My final argument is that the CEI’s branch-relative laws cannot explain or constrain an agent’s rational credences in the way that the CEI claims.
Our article described an experiment that adjudicates between different causal accounts of Bell inequality violations by a comparison of their predictive power, finding that certain types of models that are structurally radical but parametrically conservative, of which a class of superdeterministic models are an example, overfit the data relative to models that are structurally conservative but parametrically radical in the sense of endorsing an intrinsically quantum generalization of the framework of causal modelling. In their comment (arXiv:2206.10619), Hance and Hossenfelder argue that we have misrepresented the purpose of superdeterministic models. We here dispute this claim by recalling the different classes of superdeterministic models we defined in our article and our conclusions regarding which of these are disfavoured by our experimental results. Their confusion on this point seems to have arisen in part from the fact that we characterized superdeterministic models within a causal modelling framework and from the fact that we referred to this framework as "classical" in order to contrast it with an intrinsically quantum alternative. In this reply, therefore, we take the opportunity to clarify these points. They also claim that if one is adjudicating between a pair of models, where one model can account for strictly more operational statistics than the other, the first model will tend to overfit the data relative to the second. Because this model inclusion relation can arise for pairs of models in a reductionist heirarchy, they conclude that overfitting should not be taken as evidence against the first model. We point out here that, contrary to this claim, one does not expect overfitting to arise generically in cases of model inclusion, so that it is indeed sometimes appropriate to consider overfitting as a criterion for adjudicating between such models.
This chapter deals with the question of how we should think of the probabilities introduced in statistical mechanics. It is usually said that these probabilities are introduced on the basis of our ignorance of the precise state of the system, or our incapacity to treat analytically the equations of motion in order to deliver a detailed account of the evolution of the system, or both. This suggests an epistemic reading. However, we make predictions on the basis of them, that are verified by experiment. This suggests that they be thought of as objective chances. It looks as if we have to employ both the epistemic and the objective concept, in an inconsistent way. Moreover, the standard equilibrium probabilities, applied to a system that has relaxed to equilibrium while isolated from its environment, cannot be either credences or chances. It is argued that the hybrid concept, epistemic chance, resolves these puzzles and is suited to play the role required of probability in statistical mechanics.