This paper explores the concept of infra-Bayesian physicalism and its application to interpreting quantum mechanics, particularly in the context of an agent-environment system. The author outlines their formal setup, including the definition of key terms such as 'agent', 'observation', and 'state'. They also delve into the differences between the traditional many-worlds interpretation and the infra-Bayesian physicalist setup. Finally, they provide an overview of the structure of the paper, dividing it into various sections.
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Anywhere, not only in quantum mechanics, where one deals with operators, the space on which these operators operate must be specified; otherwise, one would be dealing with undefined objects. In quantum mechanics, Hilbert space (a complete inner-product space) plays a central role in view of the interpretation associated with wave functions: absolute value of each wave function is interpreted as being a probability distribution function. Probability distributions are by definition non-negative and normalizable (to unity). It is thus that Hilbert space takes a central position in quantum mechanics. I should add that in scattering theory (within the framework of quantum mechanics) one deals with functions that are not normalizable. Here, one deals with fluxes (that is, fluxes of incident and scattered particles), which must be well defined.