Law without law: from observer states to physics via algorithmic information theory

Abstract

According to our current conception of physics, any valid physical theory is supposed to describe the objective evolution of a unique external world. However, this condition is challenged by quantum theory, which suggests that physical systems should not always be understood as having objective properties which are simply revealed by measurement. Furthermore, as argued below, several other conceptual puzzles in the foundations of physics and related fields point to limitations of our current perspective and motivate the exploration of an alternative: to start with the first-person (the observer) rather than the third-person perspective (the world). In this work, I propose a rigorous approach of this kind on the basis of algorithmic information theory. It is based on a single postulate: that universal induction determines the chances of what any observer sees next. That is, instead of a world or physical laws, it is the local state of the observer alone that determines those probabilities. Surprisingly, despite its solipsistic foundation, I show that the resulting theory recovers many features of our established physical worldview: it predicts that it appears to observers as if there was an external world that evolves according to simple, computable, probabilistic laws. In contrast to the standard view, objective reality is not assumed on this approach but rather provably emerges as an asymptotic statistical phenomenon. The resulting theory dissolves puzzles like cosmology's Boltzmann brain problem, makes concrete predictions for thought experiments like the computer simulation of agents, and suggests novel phenomena such as "probabilistic zombies" governed by observer-dependent probabilistic chances. It also suggests that some basic phenomena of quantum theory (Bell inequality violation and no-signalling) might be understood as consequences of this framework.

38+2 pages, 6 figures. V3: extensive revision and shortening. V5: further substantial clarifications and simplifications; accepted by Quantum

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Cited by in corpus (16)

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• A no-go theorem for the persistent reality of Wigner's friend's perception
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• Thermodynamic costs of Turing Machines
• First Principles Numerical Demonstration of Emergent Decoherent Histories
• The Montevideo Interpretation: How the inclusion of a Quantum Gravitational Notion of Time Solves the Measurement Problem
• Probabilistic Theories and Reconstructions of Quantum Theory (Les Houches 2019 lecture notes)
• Quantum Reconstructions as Stepping Stones toward Psi-Doxastic Interpretations?
• Multiclass classification utilising an estimated algorithmic probability prior
• Witnessing Bell violations through probabilistic negativity
• Algorithmic idealism: what should you believe to experience next?
• Undecidability and unpredictability: not limitations, but triumphs of science
• Do qubits dream of entangled sheep? Quantum measurement without classical output
• The Standard Model Symmetry and Qubit Entanglement
• On the significance of Wigner's Friend in contexts beyond quantum foundations
• Towards violations of Local Friendliness with quantum computers