Law without law: from observer states to physics via algorithmic information theory (1712.01826v5)

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.

• The paper proposes that physical laws emerge statistically from an observer’s local algorithmic state via universal induction.
• It applies a version of Solomonoff induction to assign observer-dependent probabilities, questioning the conventional objective reality.
• The framework reinterprets quantum phenomena and thought experiments like Boltzmann brains, offering new insights into emergent physics.

An Examination of "Law without Law: From Observer States to Physics via Algorithmic Information Theory"

The paper "Law without Law: From Observer States to Physics via Algorithmic Information Theory" by Markus P. Müller proposes a fundamentally different approach to understanding physical theories by shifting the perspective from a traditional third-person view of the universe to a first-person observer-centric framework. Grounded in Algorithmic Information Theory, this work posits that the observer's local state determines the probabilities of their experiences, rather than an overarching objective world or set of physical laws.

Core Thesis and Methodology

Müller's approach challenges the conventional wisdom in physics which assumes an objective world governed by universal laws. Instead, he introduces a solipsistic framework based on a single postulate: universal induction dictates the probabilities of an observer's future experiences. In this model, the observer's local state alone is paramount, and the external world's apparent objectivity emerges as an asymptotic statistical phenomenon.

This shift in perspective is operationalized through the application of algorithmic probability, specifically a version of Solomonoff induction. By doing so, Müller aims to derive the physical world and its governing laws from the information-theoretic state of the observer. This method conjectures that, given enough observational data, statistical laws that resemble our classical and quantum mechanical understanding of the universe can be perceived by the observer.

Key Findings and Implications

1. Emergent Reality: One of the prominent claims of the paper is that the observer-centric framework can reproduce the appearance of an external world governed by coherent, probabilistic laws. Müller argues that objective reality is not a given but emerges statistically, which addresses conceptual puzzles like the "Boltzmann brain problem" and provides new insights into quantum mechanical phenomena such as Bell inequality violations.
2. Observer-Centric Probabilities: The paper suggests that what we perceive as laws of nature are actually observer-dependent probabilities. This implies that objective reality, as traditionally understood, may not be a fundamental aspect of the universe. Instead, it is a result of a convergence in the observer's information processing, providing a unique view on the philosophy of mind and quantum theory.
3. Applications to Thought Experiments: Müller uses his theoretical framework to reinterpret thought experiments such as brain emulation and Boltzmann brains. By redefining observers as purely informational entities, the research challenges the notion of existence and identity in a universe where memory and state transitions are algorithmically defined rather than physically instantiated.
4. Quantum Theory Insights: The paper speculates on the alignment between this framework and quantum theory. It suggests that features of quantum mechanics, like non-locality, might naturally emerge from a first-person perspective on information processing. However, the paper acknowledges that this claim necessitates further exploration and refinement of its foundational postulates.

Future Directions and Considerations

The implications of Müller's proposal are profound, both theoretically and practically, especially in the realms of AI and quantum computing where questions of autonomy and consciousness become increasingly pertinent. Although the paper posits an intriguing framework, it calls for the development of a rigorous mathematical formulation that can reconcile memory erasure and more complex observer interactions. Such advancements could refine the emerging parallels between probabilistic observer models and quantum physical phenomena.

Moreover, as this approach challenges deeply ingrained views in physics and philosophy, it provides fertile ground for interdisciplinary exploration. Future work must strive to reconcile these postulates with established empirical findings and explore experimental validations that might either support or refute Müller's observer-centric universe.

In summary, Müller's "Law without Law" offers a provocative shift in our understanding of physical reality, positioning observer states and algorithmic probability at the heart of experiential prediction. Its potential to reshape fundamental concepts in physics and beyond warrants attention and further rigorous examination within the scientific community.