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arXiv:2412.02826 · Foundations of Physics

Algorithmic Idealism: What Should You Believe to Experience Next?

Markus P. Müller

Published Feb 1, 2026• 3 citations
arXivHTMLPDF

Abstract

Abstract I argue for an approach to the Foundations of Physics that puts the question in the title center stage, rather than asking “what is the case in the world?”. This approach, algorithmic idealism, attempts to give a mathematically rigorous in-principle -answer to this question both in the usual empirical regime of physics and in some more exotic regimes within cosmology, philosophy, and science fiction (but soon perhaps real) technology. I begin by arguing that quantum theory, in its actual practice and in some interpretations, should be understood as telling an agent what they should expect to observe next (rather than what is the case), and that the difficulty of answering this former question from the usual “external” perspective is at the heart of persistent enigmas such as the Boltzmann brain problem, extended Wigner’s friend scenarios, Parfit’s teletransportation paradox, or our understanding of the simulation hypothesis. Algorithmic idealism is a conceptual framework, based on two postulates that admit several possible mathematical formalizations, cast in the language of algorithmic information theory. Here I give a non-technical description of this view and show how it dissolves the aforementioned enigmas: for example, it claims that you should never bet on being a Boltzmann brain regardless of how many there are, that shutting down computer simulations does not generally terminate its inhabitants, and it predicts the apparent embedding into an objective external world as an approximate description.

DOI
10.1007/s10701-026-00913-1

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Cambridge University Press eBooks•Jul 28, 2011•0 citations
Abstract I argue for an approach to the Foundations of Physics that puts the question in the title center stage, rather than asking “what is the case in the world?”. This approach, algorithmic idealism, attempts to give a mathematically rigorous in-principle -answer to this question both in the usual empirical regime of physics and in some more exotic regimes within cosmology, philosophy, and science fiction (but soon perhaps real) technology. I begin by arguing that quantum theory, in its actual practice and in some interpretations, should be understood as telling an agent what they should expect to observe next (rather than what is the case), and that the difficulty of answering this former question from the usual “external” perspective is at the heart of persistent enigmas such as the Boltzmann brain problem, extended Wigner’s friend scenarios, Parfit’s teletransportation paradox, or our understanding of the simulation hypothesis. Algorithmic idealism is a conceptual framework, based on two postulates that admit several possible mathematical formalizations, cast in the language of algorithmic information theory. Here I give a non-technical description of this view and show how it dissolves the aforementioned enigmas: for example, it claims that you should never bet on being a Boltzmann brain regardless of how many there are, that shutting down computer simulations does not generally terminate its inhabitants, and it predicts the apparent embedding into an objective external world as an approximate description.
Algorithmic idealism represents a transformative approach to understanding reality, emphasizing the informational structure of self-states and their algorithmic transitions over traditional notions of an external, objective universe. Rooted in algorithmic information theory, it redefines reality as a sequence of self-state transitions governed by principles such as Solomonoff induction. This framework offers a unified solution to longstanding challenges in quantum mechanics, cosmology, and metaphysics, addressing issues like the measurement problem, the Boltzmann brain paradox, and the simulation hypothesis. Algorithmic idealism shifts the focus from describing an independent external world to understanding first-person experiences, providing epistemic interpretations of physical theories and dissolving metaphysical divides between "real" and simulated realities. Beyond resolving these conceptual challenges, it raises profound ethical questions regarding the continuity, duplication, and termination of informational entities, reshaping discussions on identity, consciousness, and existence in the digital and quantum age. By offering a mathematically rigorous yet philosophically innovative framework, algorithmic idealism invites a rethinking of reality as an emergent property of informational dynamics rather than a static external construct.
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.
In physics, there is the prevailing intuition that we are part of a unique external world, and that the goal of physics is to understand and describe this world. This assumption of the fundamentality of objective reality is often seen as a major prerequisite of any kind of scientific reasoning. However, here I argue that we should consider relaxing this assumption in a specific way in some contexts. Namely, there is a collection of open questions in and around physics that can arguably be addressed in a substantially more consistent and rigorous way if we consider the possibility that the first-person perspective is ultimately more fundamental than our usual notion of external world. These are questions like: which probabilities should an observer assign to future experiences if she is told that she will be simulated on a computer? How should we think of cosmology's Boltzmann brain problem, and what can we learn from the fact that measurements in quantum theory seem to do more than just reveal preexisting properties? Why are there simple computable laws of physics in the first place? This note summarizes a longer companion paper which constructs a mathematically rigorous theory along those lines, suggesting a simple and unified framework (rooted in algorithmic information theory) to address questions like those above. It is not meant as a "theory of everything" (in fact, it predicts its own limitations), but it shows how a notion of objective external world, looking very much like our own, can provably emerge from a starting point in which the first-person perspective is primary, without apriori assumptions on the existence of "laws" or a "physical world". While the ideas here are perfectly compatible with physics as we know it, they imply some quite surprising predictions and suggest that we may want to substantially revise the way we think about some foundational questions.
The assumption of an objective world underlying all our experiences is deeply embedded in our everyday thinking and in our language, and has been an unquestioned presupposition of the scientific enterprise for at least four centuries. Yet it is well known that quantum physics raises some highly problematic questions in this respect, questions that are still open, almost a century from the inception of the theory. I would like to propose that these questions stem from deep philosophical assumptions and can be answered in a much more coherent way if we understand the notion of an objective world not as a primary reality, but as an emergent aspect of a primary process that can be described as “experiencing”. A coherent description of the appearance of an objective world in the process of experiencing relies on a certain understanding of what is technically known as the “quantum measurement problem”, i.e. the description of the process of observation in quantum physics, which is the key problematic aspect of the theory. I will propose that the basic features that characterize a quantum observation have a much wider scope, and describe in fact all acquisition of information by an “embodied observer”, in short all experiencing happening in the world. By applying to this larger context work I have done in the more technical frame of the quantum measurement problem it can be shown that the nature of the process of experiencing is such as to inevitably generate the appearance of an objective world. Thus the objectivity of the world, although not primary and ultimately real, is an intrinsic consequence of our “experiential embodiment”, i.e. of the fact that we are in the world and all our experiences correspond to physical happenings in the world. When examined in this perspective, the “paradoxes” of quantum physics are an invitation to abandon the metaphysical assumption of the primacy of the objective dimension of reality. A philosophical position much more in tune with quantum physics views the process of experiencing as the primary source of both subject and object, consciousness and world.
Physicists usually admit a rather naive concept of physical reality: it is the object they are investigating using experiments understood as actions in the real world.in theoretical physics, the object of investigation is not the real world itself but its mathematical description which is considered as describing physical reality as exactly as possible.i present arguments from philosophy of science and from recent work in the theory of gravitational physics which indicate a possibility to defend also antirealistic views, and clarify in which sense both standpoints can be viable.
The odd concepts of quantum physics are nearly a century old. They may seem difficult and forbidding at first sight, but the barrier to understanding is not their difficulty but their differentness . Unlike classical models, quantum theory does not attempt to simulate Nature. It gives us information about observations of Nature. But it does contain a “theoretical entity” that claims to contain all information, observation notwithstanding, namely the quantum state vector in Hilbert space. Scientists routinely use the language of Hilbert space, and nonscientists do not use it at all, which is understandable but unfortunate. A sort of baby-talk has become the lingua franca for much of the popular journalism of quantum physics, an awkward patois that combines some of the early groping language of Bohr, de Broglie, Schrödinger, and Heisenberg with more modern words about symmetries and states. Earnest amateurs still ask me about the mystery of Bohr orbits. There is no mystery because there are no orbits, except as historical curiosities. Same for “wave–particle duality.” Same for “quantum jumps.” A friend once asked me to address a philosophy seminar about the “paradoxes of quantum mechanics.” He said he had approached C. N. Yang first, who replied “What paradoxes?” There are some mathematical and logical rough spots in our current best theory of matter, and perhaps some of them can be framed as paradoxes. But the theory is actually rather straightforward, and it has a perfectly clear interpretation linked to experiments that, in their simplest form, anyone can perform (and students do routinely in college laboratories). No empirical observations are known that are inconsistent with the quantum framework.