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Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: Interpreting Quantum Mechanics in Infra-Bayesian Physicalism, published by Yegreg on February 12, 2024 on The AI Alignment Forum.

This work was inspired by a question by Vanessa Kosoy, who also contributed several of the core ideas, as well as feedback and mentorship.

Abstract

We outline a computationalist interpretation of quantum mechanics, using the framework of infra-Bayesian physicalism. Some epistemic and normative aspects of this interpretation are illuminated by a number of examples and theorems.

1. Introduction

Infra-Bayesian physicalism was introduced as a framework to investigate the relationship between a belief about a joint computational-physical universe and a corresponding belief about which computations are realized in the physical world, in the context of "infra-beliefs". Although the framework is still somewhat tentative and the definitions are not set in stone, it is interesting to explore applications in the case of quantum mechanics.

1.1. Discussion of the results

Quantum mechanics has been notoriously difficult to interpret in a fully satisfactory manner. Investigating the question through the lens of computationalism, and more specifically in the setting of infra-Bayesian physicalism provides a new perspective on some of the questions via its emphasis on formalizing aspects of metaphysics, as well as its focus on a decision-theoretic approach. Naturally, some questions remain, and some new interesting questions are raised by this framework itself.

The toy setup can be described on the high level as follows (with details given in Sections 2 to 4). We have an "agent": in this toy model simply consisting of a policy, and a memory tape to record observations. The agent interacts with a quantum mechanical "environment": performing actions and making observations. We assume the entire agent-environment system evolves unitarily.

We'll consider the agent having complete Knightian uncertainty over its own policy, and for each policy the agent's beliefs about the "universe" (the joint agent-environment system) is given by the Born rule for each observable, without any assumption on the correlation between observables (formally given by the free product).

We can then use the key construction in infra-Bayesian physicalism - the bridge transform - to answer questions about the agent's corresponding beliefs about what copies of the agent (having made different observations) are instantiated in the given universe.

In light of the falsity of Claims 4.15 and 4.17, we can think of the infra-Bayesian physicalist setup as a form of many-worlds interpretation. However, unlike the traditional many-worlds interpretation, we have a meaningful way of assigning probabilities to (sets of) Everett branches, and Theorem 4.19 shows statistical consistency with the Copenhagen interpretation.

In contrast with the Copenhagen interpretation, there is no "collapse", but we do assume a form of the Born rule as a basic ingredient in our setup. Finally, in contrast with the de Broglie-Bohm interpretation, the infra-Bayesian physicalist setup does not privilege particular observables, and is expected to extend naturally to relativistic settings. See also Section 8 for further discussion on properties that are specific to the toy setting and ones that are more inherent to the framework.

It is worth pointing out that the author is not an expert in quantum interpretations, so a lot of opportunities are left open for making connections with the existing literature on the topic.

1.2. Outline

In Section 2 we describe the formal setup of a quantum mechanical agent-environment system. In Section 3 we recall some of the central constructions in infra-Bayesian physicalism, then in Section 4 we apply this framework to the agent-environment system. In Sections 4.2 and 4.3 we write down various...