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REVIEW 4 major objections 6 minor 24 references

Algorithmic Idealism III: "Algorithmic State" Formulation of Quantum Mechanics

T0 review · 4 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

Pith's one-line read The paper claims that quantum mechanics is what a utility-maximizing agent's optimal prediction of its own future self-states looks like, with measurement, entanglement, and quantum probability explained as informational updates rather…

desk verdict A ten-postulate wrapper for standard QM whose central bridge equation is asserted, not derived; worth a referee but not publication. read the letter →

arxiv 2502.08653 v1 pith:QFNXTUTV submitted 2025-01-20 physics.hist-ph quant-ph

classification physics.hist-phquant-ph
keywords algorithmicidealismquantumfoundationsprobabilityBornruleBayesianupdatingentanglementKolmogorovcomplexityutilitymaximization
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Quantum mechanics, the paper argues, is the optimal algorithm an agent uses to encode and evolve its own informational state, rather than a fundamental description of an external physical world. Reality is modeled as an agent-environment feedback loop: the agent's self-state carries its beliefs, memories, and policy, and transitions between self-states are chosen by balancing algorithmic simplicity against expected utility. The paper's ten postulates recast measurement as Bayesian updating, entanglement as joint utility optimization, and quantum probabilities as utility-weighted predictions, so that the Born rule and Schrodinger evolution are claimed to emerge from computational constraints. If this program is right, the long-standing puzzles about wavefunction collapse, nonlocality, and the origin of quantum probability would be resolved by showing that they are consequences of optimal prediction rather than features of the world.

What carries the argument

The load-bearing object is the self-state $S_t$, the agent's total informational configuration, together with the algorithmic transition probability $P(S_{t+1}|S_t,A_t)\propto 2^{-K(S_{t+1}|S_t,A_t)}$, where $K$ is conditional Kolmogorov complexity. Solomonoff induction (the algorithmic-probability rule that weights hypotheses by $2^{-K(h)}$) is the named mechanism: simpler hypotheses about the environment are assigned exponentially larger prior weight, and the agent's policy chooses actions that maximize expected discounted reward. The argument's hinge is Eq. (37), which asserts that Born-rule probabilities are exactly the utility-weighted algorithmic sum over successors; all ten postulates are organized around making that identification, with an idealized reinforcement-learning agent that combines algorithmic probability with utility maximization as the model of what a self-state is.

What would settle it

Take a single qubit and try to find any bounded utility function $U$ for which Eq. (37) reproduces $|\langle O|\psi\rangle|^2$ at every measurement angle while remaining normalized; a single angle where the two disagree, or a proof that no such $U$ can yield sinusoidal probabilities, would refute the central identification.

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Extended reading notes

Core claim

On the paper's own terms, the discovery is that the full phenomenology of quantum mechanics—states, unitary evolution, measurement, entanglement, and probability—can be restated as the behavior of an idealized utility-maximizing agent whose prior over futures is algorithmic probability. The central identification is the Born rule: the probability of observing $O_t$ from self-state $S_t$ is asserted to be $P(O_t|S_t)=\sum_{S_{t+1}}2^{-K(S_{t+1}|S_t)}U(S_{t+1}|S_t)$, a utility-weighted sum over algorithmically simple successor states, and the author takes this to explain why quantum probabilities have the amplitudes-squared form. Measurement is presented as Bayesian updating without collapse; entanglement is presented as shared utility information optimized jointly by subsystems; physical laws are presented as stable regularities in reward dynamics. The paper then shows that the usual CHSH calculation gives $2\sqrt{2}$ for the Bell state and that Schrodinger's cat has von Neumann entropy $S(\rho_{\rm cat})=1$ bit, presenting these as illustrations that the reinterpretation reproduces standard quantum results.

Load-bearing premise

The load-bearing premise is that there exists a way of assigning 'usefulness' to possible future states such that an agent's simplicity-weighted predictions come out exactly equal to the standard quantum probabilities; the paper asserts this equality rather than constructing the usefulness function or proving the sum behaves like a probability.

Editorial extensions

If this is right

  • The measurement problem would dissolve: 'collapse' becomes an ordinary Bayesian update of an agent's model, so no physical wavefunction collapse mechanism is needed.
  • The Born rule would stop being a primitive axiom and become a corollary of the optimal-prediction principle, which would change how quantum theory is axiomatized.
  • Bell-inequality violation would be read as shared utility optimization across subsystems rather than as nonlocal physical influence, so no faster-than-light signaling is implied.
  • Conservation laws and symmetries would be understood as stable regularities of reward-invariant self-state transitions, placing algorithmic information theory beneath dynamical physics.
  • Simulated and base realities would be treated as equivalent informational structures, so the simulation hypothesis would cease to be a physically distinguishing claim.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A natural test of the framework is to reverse-engineer the utility function: measurable Born-rule statistics for a simple system would constrain $U(S_{t+1}|S_t)$, and no consistent function over a family of measurement settings would count as evidence against the identification.
  • The same machinery should reproduce the classical limit: if measurement is Bayesian updating under an algorithmic prior, decoherence and the emergence of classical probabilities should be derivable from the utility-weighted sum, which the paper leaves as a program rather than a derivation.
  • The entanglement-as-joint-utility reading suggests a quantitative check on where quantum correlations end: modeling two agents that share a common algorithmic prior and asking whether the resulting correlations reach the Tsirelson bound $2\sqrt{2}$ or only a weaker value would test whether the framework actually implies quantum nonlocality or merely accommodates it.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper proposes 'Algorithmic Idealism III', a framework intended to reinterpret quantum mechanics as arising from algorithmic probability, utility maximization, and agent-environment feedback loops. It states ten postulates that recast measurement, entanglement, and quantum probabilities in informational terms, and it claims that physical laws, including the Born rule and Bell correlations, emerge from these computational principles. The mathematical sections introduce self-states, algorithmic transition probabilities, utility-weighted predictions, and then apply these ideas to the Bell CHSH inequality and Schrödinger's cat. The central claim is that quantum mechanics is the optimal algorithm for encoding and evolving informational states, with probabilities and entanglement explained as utility-weighted predictions and shared utility information.

Significance. If the claimed derivation were correct, the framework would offer a genuinely novel unification of quantum mechanics with algorithmic information theory and decision theory, with potential implications for the philosophy of physics and for interpretations of quantum probability. The paper is clearly written in its exposition of the postulates and situates itself within the literature on informational reconstructions of quantum theory. However, the significance currently rests entirely on a missing derivation: the key equations connecting algorithmic priors and utility to Born-rule probabilities are asserted, not proven. The paper does not provide machine-checked proofs, reproducible code, or a concrete construction of the utility function that would realize quantum probabilities, so its central forward-looking claim is unsupported.

major comments (4)
  1. [§4.5, Eq. (37)] The claimed bridge to quantum probabilities is not derived and does not define a probability measure. The right-hand side of Eq. (37), P(Ot|St) = Σ_{St+1} 2^{-K(St+1|St)} U(St+1|St), is asserted to be the probability of observing Ot, but U(St+1|St) as defined in Eq. (34) is an expected utility, not a likelihood; it need not be nonnegative, bounded, or normalized over outcomes. No proof is given that this expression sums to 1 over distinct outcomes Ot, nor that it equals |⟨Ot|ψt⟩|². Eq. (35) simply asserts the Born rule without connecting it to Eq. (37). Without a construction of U and a proof of these properties, the central claim that quantum probabilities emerge from algorithmic priors and utility is unsupported.
  2. [§4.1, §4.4, §4.6, §4.7, §5] The manuscript imports the full Hilbert-space formalism and the Born rule as assumptions and then presents these same objects as outputs of the framework. Eqs. (3), (30), (35), (42), (52), and (76) all use |⟨O|ψ⟩|² directly; Eqs. (6) and (7) assume unitary evolution and the Schrödinger equation. No mapping is given from the computational self-states St to Hilbert-space vectors, and no definition of K(St+1|St) is provided for a concrete physical model. Consequently, the framework does not derive quantum mechanics; it assumes quantum mechanics and then re-labels its ingredients. This circularity undermines the abstract's claim that physical laws are 'shown to emerge' from algorithmic constraints.
  3. [§5, Eqs. (75)–(81)] The Bell inequality violation section reproduces the standard CHSH calculation without using the framework's proposed probability expression. Eq. (76) again invokes the Born rule, and Eq. (77) uses the standard quantum expectation value ⟨ψ|A⊗B|ψ⟩. The calculation of −cos(θA−θB) and the resulting 2√2 are textbook quantum mechanics. The statements that shared utility or algorithmic complexity 'leads to nonlocality' are post hoc verbal explanations, not derivations from Eq. (37) or from any framework-specific quantity. Thus this section does not demonstrate that Algorithmic Idealism explains Bell correlations.
  4. [§3.3–§3.4, §4.4] Postulate 4 (Section 3.4) is a verbatim duplicate of Postulate 3 (Section 3.3), which is a presentation error. More substantively, Eq. (31) in Section 4.4 embeds the Born rule inside the Bayesian update, so 'measurement as Bayesian updating' presupposes the very quantum probabilities it is meant to explain. The update rule therefore cannot serve as a derivation of measurement probabilities from algorithmic priors alone.
minor comments (6)
  1. [§3.4] The text of Postulate 4 is identical to that of Postulate 3; one of the two postulates should be removed or given distinct content.
  2. [§8.2.5] There is a typo in the final paragraph of Section 8.2.5: 'electrenergy' should be 'electron energy' or 'energy transfer'.
  3. [References] Reference [5] combines two separate Zurek papers into one entry, and several references lack page numbers or complete publication details; this should be cleaned up.
  4. [§8] The Outlook section on the evolution of photosynthetic reaction centers is unrelated to the paper's stated topic of quantum mechanics and appears to be a speculative autobiographical addendum; it should be removed or clearly separated as speculative future work.
  5. [Abstract and §7] The abstract and summary claim that physical laws 'emerge' and that quantum mechanics is 'the optimal algorithm', but no optimality theorem or derivation is presented; the claims should be tempered to match what is actually proven.
  6. [Notation throughout] The symbol St is used both for a self-state and as an element of a Hilbert space (e.g., St ∈ H in §4.1), conflating computational states with quantum states; a clear distinction between these two levels would improve readability.

Circularity Check

3 steps flagged · score 8.0 of 10

The claimed derivation reduces to restating the Born rule and standard Bell-state QM: Eqs. (3), (35), and (76) import the quantum probability rule, and Eq. (37) is never shown to reproduce it.

  1. renaming known result [Section 4.1, Eq. (3); reused in Section 4.4, Eq. (30)]
    "In quantum mechanics, P (Ot|St+1) is derived from the Born rule: P (Ot|St+1) = |⟨Ot|St+1⟩|2, (3) ... Upon observing Ot, the agent updates its belief ... P (Ot|St) = |⟨Ot|ψt⟩|2. (30)"

    The Born rule is written in as an input of the measurement update, not derived from algorithmic probability or utility. Later sections present it as the framework's account of quantum probabilities. The central claimed output is therefore identical to the input.

  2. renaming known result [Section 4.5, Eqs. (35) and (37)]
    "If |ψt⟩ represents the agent’s probabilistic model of its self-state, the probability of observing Ot is: P(Ot|St)=|⟨Ot|ψt⟩|2, (35) ... Combining algorithmic priors and utility predictions, the probability of observing Ot is derived as: P(Ot|St)=Σ_{St+1} 2^{−K(St+1|St)}U(St+1|St). (37)"

    Eq. (35) asserts the ordinary Born rule. Eq. (37) is labeled as the derivation from algorithmic priors and utility, but no proof is given that the algorithmic-weight sum equals |⟨O|ψ⟩|², nor that it is normalized. The utility function U is never constructed. The 'utility-weighted prediction' is a new name attached to the same expression, not an independent derivation.

1 more flagged steps
  1. renaming known result [Section 5, Eqs. (76)-(81)]
    "Using the entangled state framework from Postulates 6 and 7, the article expresses joint probabilities as: P(OA,OB|SAB)=|⟨OA,OB|ψAB⟩|2, (76) ... For the Bell state ... E(A,B)=⟨ψAB|A⊗B|ψAB⟩. (77) ... Using the quantum prediction ... = 2√2. (81)"

    The Bell-CHSH violation is computed with the standard quantum Born rule and Bell-state expectation values. No term involving algorithmic complexity K, utility U, or self-state transitions enters the numerical calculation. The 'prediction' that quantum mechanics violates Bell inequalities is the standard input, not a consequence of the proposed framework.

full rationale

The paper's central claim is that quantum mechanics emerges from algorithmic simplicity and utility maximization. In the mathematical development, however, the quantum formalism is presupposed: self-states are placed in a Hilbert space, unitary evolution is identified with the Schrödinger equation, and measurement probabilities are set equal to the Born rule (Eqs. (3), (30), (35)). The promised bridge Eq. (37) is asserted without a proof of equivalence or normalization, and no concrete U reproducing |⟨O|ψ⟩|² is supplied. The Bell and Schrödinger-cat sections likewise reuse standard quantum computations unchanged. I do not count the authors' self-citations as the main problem; the circularity is that the framework's central explanatory outputs are the same equations it takes as postulates. There is no external benchmark or independent derivation against which the claimed unification could be tested. Score 8 reflects a central claim that reduces by restatement while still leaving open the possibility that a future construction of U could add content.

Assumptions & free parameters 0 free parameters · 5 assumptions · 1 invented entities

The central claim relies on unproved assumptions: computational ontology, the Hilbert-space/Born-rule structure of QM, and the existence of an unspecified utility function that makes algorithmic priors coincide with quantum probabilities. No fitted numbers appear because the paper makes no novel quantitative predictions.

assumptions (5)
  • domain assumption Reality is a computational process and self-state transitions are governed by conditional Kolmogorov complexity.
    Postulate 3 and Eq. (1) assert transition probabilities proportional to 2^{-K}; this presupposes that physical dynamics are computable and that K is the right prior.
  • domain assumption The Hilbert space formalism of quantum mechanics, including the Born rule, is assumed as the correct description of observations.
    Eqs. (3), (7), and (30) import standard QM without deriving it from the algorithmic postulates.
  • ad hoc to paper A utility/reward function U exists such that utility-weighted algorithmic priors equal quantum probabilities.
    Eq. (37) identifies P(Ot|St) with a utility-weighted sum over 2^{-K}, but no explicit U is given and its consistency with probability axioms is not shown.
  • ad hoc to paper Entanglement is equivalent to shared utility information between subsystems.
    Postulates 6 and 7 assume that entangled-state correlations are explained by joint utility optimization; this identification is asserted, not derived.
  • domain assumption Agents maximize expected discounted utility in the AIXI style.
    Eqs. (16) and (59) adopt the AIXI framework as a given, used as the decision-theoretic backbone.
invented entities (1)
  • Self-state S_t
    purpose: Fundamental informational state of an agent, encoding beliefs, memories, observations, and policy; replaces the physical wavefunction in this formulation.
    No independent falsifiable handle is provided; self-state is defined by the framework itself.

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Cite this review

Pith. "Pith review of Algorithmic Idealism III: "Algorithmic State" Formulation of Quantum Mechanics." pith.science (2026). https://pith.science/paper/QFNXTUTV

@misc{pith2026250208653,
  author       = {Pith},
  title        = {Pith review of: Algorithmic Idealism III: "Algorithmic State" Formulation of Quantum Mechanics},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QFNXTUTV}},
  note         = {Machine review of arXiv:2502.08653}
}
read the original abstract

This work introduces Algorithmic Idealism a framework that reinterprets quantum mechanics as a computational process governed by algorithmic probability informational simplicity and utility optimization Reality is modeled as an agentenvironment feedback loop where agents maximize utility by predicting selfstate transitions Core quantum phenomena such as measurement entanglement and probabilities are explained through informational constructs The paper presents a set of quantum mechanics postulates inspired by this framework and explains their mathematical meaning in detail These postulates include measurement as Bayesian updating entanglement as joint utility optimization and quantum probabilities as utilityweighted predictions Physical laws are shown to emerge as informational regularities from algorithmic constraints By defining identity through decisionmaking consistency and treating simulated and base realities as indistinguishable the framework also resolves philosophical questions about identity and reality This approach unifies quantum mechanics with computational theory offering a novel perspective on foundational physics and its connection to information and computation

Discussion (0). Continue with ORCID to comment.

Reference graph

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