{"id":"5500fd52-321d-4ab5-b116-4ec09b67d9a2","arxiv_id":"2502.08653","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":0,"one_line_summary":"The paper restates quantum mechanics as utility-maximizing self-state transitions, but its central equations re-assert the Born rule rather than deriving it from algorithmic probability.","lead":"This paper claims that quantum mechanics is really a computational process: an agent predicting its own next state to maximize a reward. It argues that measurement, entanglement, and the laws of physics all emerge from algorithmic simplicity and utility optimization.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (37) does not define a probability measure, and the claimed derivation of the Born rule from algorithmic priors plus utility is never given; the central 'emergence' claim is therefore unsupported.","rationale":"I agree with the reader's identification of Eq. (37) as the load-bearing point. The mathematical gap is concrete: the expression is not normalized, U is an expected utility rather than a probability, and no construction is given that connects K and U to Hilbert-space amplitudes. Consequently the central claim that quantum mechanics emerges from algorithmic constraints is unsupported. This is not a matter of interpreting the equations differently; the text itself moves from Eq. (35) to Eq. (37) without proof. The Bell section is a standard calculation, not a test of Eq. (37). A minimal qubit model is the right way to settle the issue. Since the reader already reached REJECT and the concern supports that verdict, I recommend no change.","tokens_in":21658,"tokens_out":4905,"duration_ms":55309,"concrete_test":"Build the minimal nontrivial model: a qubit in state |ψ⟩=α|0⟩+β|1⟩, measurement basis {|0⟩,|1⟩}, and a finite set of computational states S'. Fix a concrete universal Turing machine for K. Search symbolically or numerically for functions U(S'|S) that are not allowed to depend on the measured outcome O_t except through S', such that Eq. (37) equals |α|² and |β|² for all α,β and sums to 1. If no such U exists, or if the only solutions are those that already encode the Born probabilities into U, the proposed derivation does not go through. This check is decisive because Eq. (37) is the only equation connecting algorithmic probability and utility to quantum probabilities.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central bridge is Eq. (37), P(Ot|St)=Σ_{St+1}2^{-K(St+1|St)}U(St+1|St). For this to reproduce quantum mechanics, the right-hand side must be nonnegative, sum to 1 over outcomes O_t, and equal |⟨O_t|ψ_t⟩|² for every state and measurement. None of these properties is shown. U is defined in Eq. (34) as an expected utility R+γE[U]; utility is not a probability and no bounds or normalization conditions are imposed, so the sum in Eq. (37) need not even be a probability distribution. Eq. (35) simply asserts the Born rule, and §5's Bell calculation uses the standard expression |⟨O_A,O_B|ψ⟩|² directly rather than deriving it from Eq. (37). The paper never constructs the mapping from Hilbert-space states to the computational states S_t, never defines K for a concrete model, and never shows that the algorithmic prior and utility assignments yield the Born rule. This is not a disagreement with consensus; it is a missing derivation at the single point where the framework is supposed to generate quantum probabilities.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":21912,"tokens_out":3369,"duration_ms":36235,"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":[{"comment":"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.","section":"§4.5, Eq. (37)"},{"comment":"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.","section":"§4.1, §4.4, §4.6, §4.7, §5"},{"comment":"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.","section":"§5, Eqs. (75)–(81)"},{"comment":"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.","section":"§3.3–§3.4, §4.4"}],"minor_comments":[{"comment":"The text of Postulate 4 is identical to that of Postulate 3; one of the two postulates should be removed or given distinct content.","section":"§3.4"},{"comment":"There is a typo in the final paragraph of Section 8.2.5: 'electrenergy' should be 'electron energy' or 'energy transfer'.","section":"§8.2.5"},{"comment":"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.","section":"References"},{"comment":"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.","section":"§8"},{"comment":"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.","section":"Abstract and §7"},{"comment":"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.","section":"Notation throughout"}],"recommendation":"reject","confidential_remarks":"This is a philosophy-of-physics paper that makes extremely strong claims about deriving quantum mechanics from algorithmic probability and utility. The key derivation is absent: Eq. (37) is asserted rather than proven, and the Bell section merely reproduces standard quantum mechanics. The paper would need to construct an explicit utility function U and demonstrate equality with the Born rule for all measurements, plus provide a concrete mapping from self-states to Hilbert-space states, before it could be considered a serious contribution to the reconstruction program. As it stands, the manuscript is a reinterpretation rather than a derivation, and the central claim is not supportable within the current scope. I recommend rejection, though the author may resubmit a completely reworked version with actual proofs."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nHere's the honest read. The paper is a philosophical proposal, not a derivation. It introduces ten postulates that recast QM in terms of self-states, algorithmic probability, and utility. What's actually new is the packaging: the postulates themselves and the explicit claim that Born probabilities are utility-weighted algorithmic predictions. The survey of existing work (Wheeler, Hardy, Masanes–Müller, CBH) is competent, and the writing is clear.\n\nWhat the paper does well: it lays out a coherent narrative for how one might want QM to emerge from agent-based computation, and it correctly reproduces textbook results in the Bell and Schrödinger-cat sections. Those sections are standard calculations, but they are not wrong.\n\nThe soft spot is load-bearing. Eq. (37), the supposed derivation of quantum probabilities, is not a valid probability measure unless U is nonnegative and normalized, and no such U is constructed. The Born rule appears in Eq. (35) as an assertion, not as a consequence of Eqs. (33)–(34). The Bell section simply writes down the standard |⟨O_A,O_B|ψ⟩|² joint probability and calls it a consequence of shared utility; no derivation from algorithmic priors is given. So the central claim—that QM emerges from algorithmic probability plus utility—remains unproven. The paper does not offer new predictions or a concrete model that would falsify the framework.\n\nThe citation pattern is fine; the author builds on Müller's work and says so. The outlook section is a personal anecdote and has no bearing on the argument.\n\nIf I were editing, I would send this to a referee because it is part of an active research program and the gaps should be documented, but I would expect the referee to reject it as a derivation. It could be resubmitted as a purely philosophical interpretation of QM, with the mathematical claims toned down. As it stands, it is not a sound contribution to physics.\n\nWould I cite it? No. Would I bring it to reading group? Maybe, as an example of how algorithmic-idealism claims fail to connect to the Born rule.","headline":"A ten-postulate wrapper for standard QM whose central bridge equation is asserted, not derived; worth a referee but not publication.","tokens_in":22433,"tokens_out":2195,"would_cite":false,"duration_ms":22560,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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…","keywords":["algorithmic idealism","quantum foundations","algorithmic probability","Born rule","Bayesian updating","entanglement","Kolmogorov complexity","utility maximization"],"falsifier":"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.","tokens_in":21429,"feed_emoji":"⚛️","tokens_out":8913,"duration_ms":84616,"temperature":0.7,"pith_summary":"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.","feed_headline":"Quantum mechanics emerges from agents maximizing utility","feed_subtitle":"Measurement, entanglement, and Born probabilities become Bayesian updates and utility-weighted predictions.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Defines the Algorithmic Idealism framework that this paper extends into a quantum-state formulation.","marker":"[10]"},{"why":"Supplies the earlier derivation of physics from observer states via algorithmic information theory, which the postulates take as the starting point.","marker":"[11]"},{"why":"Introduces the self-state and identity-as-decision-consistency ideas, including the treatment of simulation equivalence, used in Postulates 8 and 9.","marker":"[12]"},{"why":"Reassesses competing theories of reality and motivates the algorithmic-state picture the paper proposes.","marker":"[13]"},{"why":"Provides an antecedent axiomatic derivation of quantum theory from operational physical requirements, cited as support for the general reconstructive program.","marker":"[14]"},{"why":"Gives a five-axiom reconstruction of quantum theory that the paper positions alongside its own postulate-based derivation.","marker":"[23]"},{"why":"Defines the CHSH inequality whose violation the paper reproduces to argue that the framework retains quantum nonlocality.","marker":"[7]"},{"why":"Provides the Bell-theorem review that frames the inequality's violation as a test of local realism.","marker":"[9]"}],"fun_headline_variants":["Quantum mechanics from utility-maximizing agents","Born rule as utility-weighted algorithmic probability","Measurement as Bayesian updating without collapse","Entanglement as shared utility optimization","QM unified with computation via algorithmic utility"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Quantum mechanics from utility-maximizing agents","Born rule as utility-weighted algorithmic probability","Measurement as Bayesian updating without collapse","Entanglement as shared utility optimization","QM unified with computation via algorithmic utility"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000253,"raw_usage":{"total_tokens":1545,"prompt_tokens":903,"completion_tokens":642,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":519,"completion_tokens_details":{"reasoning_tokens":582}},"tokens_in":519,"tokens_out":642,"duration_ms":7064,"temperature":1.0,"reasoning_tokens":582,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T18:25:36.964905+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Algorithmic Idealism: What Should You Believe to Experienc e Next? arXiv preprint arXiv:2412.02826 (2024)","cited_arxiv_id":null,"evidence_quote":"Defines the Algorithmic Idealism framework that this paper extends into a quantum-state formulation."},{"cited_title":"Law without Law: From Observer States to Physics via Algorit hmic Information Theory","cited_arxiv_id":null,"evidence_quote":"Supplies the earlier derivation of physics from observer states via algorithmic information theory, which the postulates take as the starting point."},{"cited_title":"Algorithmic Idealism I: Reconceptualizing Reality Through Information and Experience","cited_arxiv_id":"2412.20485","evidence_quote":"Introduces the self-state and identity-as-decision-consistency ideas, including the treatment of simulation equivalence, used in Postulates 8 and 9."},{"cited_title":"Algorithmic Idealism II: Reassessment of Competing Theories","cited_arxiv_id":"2501.00022","evidence_quote":"Reassesses competing theories of reality and motivates the algorithmic-state picture the paper proposes."},{"cited_title":"A Derivation of Q uantum Theory from Physical Requirements","cited_arxiv_id":null,"evidence_quote":"Provides an antecedent axiomatic derivation of quantum theory from operational physical requirements, cited as support for the general reconstructive program."},{"cited_title":"Probability Theories in General and Qu antum Theory in Particular","cited_arxiv_id":null,"evidence_quote":"Gives a five-axiom reconstruction of quantum theory that the paper positions alongside its own postulate-based derivation."}],"review_version":1}