What Kind of World Supports Darwinian Evolution? Quantum Foundational Options

Abstract: Darwinian evolution requires (i) heritable records, (ii) repeatable copying with variation, and (iii) routine irreversibility. Categorical quantum mechanics (CQM) makes precise why copy'' anddelete'' are not generic quantum operations: they exist only for a realized \emph{classical data} sector (a preferred basis/observable; a commutative structure). Decoherence explains how a pointer basis can be selected dynamically, but it does not by itself select a unique outcome. This motivates a neutral presentation of the main ontological options (unique-history, decohered multiplicity, agent-relative facticity, and a stochastic foundation with variable diffusion). We also note the relevance of the agency constraint'' argued by Adlam-McQueen-Waegell: in a strictly coherent, basis-unselectedpurely quantum'' regime, minimal agency fails due to no-cloning and linearity, which sharpens the role of classical resources for record-based processes. Extended Wigner's Friend scenarios then serve as a stress test, since they treat ``friends'' simultaneously as coherent quantum systems and as agents possessing stable records. Finally, a stochastic-mechanics foundation (with variable diffusion) offers a continuous bridge between quantum and classical regimes, and suggests a principled way to implement measurement update as conditioning plus a time-symmetric minimal-change rule.

• The paper argues that Darwinian evolution requires stable records, copying with variation, and irreversibility, which a purely unitary, basis-unselected quantum world does not generically provide.
• Categorical quantum mechanics identifies a copyable classical data sector, while decoherence explains pointer-basis selection but not single outcomes or a unique evolutionary history.
• The paper compares collapse, Bohmian, decoherent-histories, relational, QBist, and stochastic-mechanical frameworks, highlighting variable diffusion as a possible bridge between quantum and classical regimes.

This paper, by Partha Ghose (2602.16286), addresses a foundational question that sits at the intersection of quantum foundations and the physical preconditions of biology: what structural features must the underlying physics possess for Darwinian evolution to be well-defined? The author's central claim is that evolution is not merely a biological process but imposes nontrivial demands on ontology—specifically, on the existence of a copyable record sector and an arrow of irreversibility. In a strictly quantum world with only unitary dynamics and no preferred basis, these demands cannot be met generically, and the paper surveys which ontological options in quantum foundations can supply them.

Minimal physical requirements for Darwinian evolution

The paper begins by isolating three structural requirements that any physically instantiated evolutionary cycle must satisfy:

• (E1) Stable records: persistent, distinguishable states functioning as an "alphabet" (genotypes, memory traces).
• (E2) Copying with variation: approximate replication of records with occasional local errors.
• (E3) Irreversibility: systematic loss of alternatives and disposal of records via entropy export, so selection is not merely reversible reshuffling.

These are framed as constraints on physics rather than on biology. A world lacking a stable, distinguishable record basis or an effective thermodynamic arrow cannot host heredity in the ordinary sense. This framing sets up the central tension: in standard quantum mechanics, copying and deleting unknown states are obstructed by no-cloning [WZ1982] and no-deleting [PBNoDelete2000], respectively.

Categorical quantum mechanics and the classical data sector

The paper's sharpest technical point draws on categorical quantum mechanics (CQM), following Coecke and Kissinger [CK2017]. In CQM, "copy" ($$\Delta: |i\rangle \mapsto |i\rangle \otimes |i\rangle$$) and "delete" ($\varepsilon: |i\rangle \mapsto 1$) operations exist only for a commutative special $\dagger$-Frobenius algebra—a "classical structure" corresponding to a chosen observable's eigenbasis. For superpositions, the copying map fails:

$$\Delta(\alpha|0\rangle + \beta|1\rangle) = \alpha|00\rangle + \beta|11\rangle \neq (\alpha|0\rangle + \beta|1\rangle)^{\otimes 2}$$

The consequence is formalized as a proposition: if no physically selected classical data sector exists at the relevant scales, then heredity and repeated symbol-copying are not well-defined operations, and Darwinian evolution as ordinarily formulated cannot get traction. This is a strong claim—it asserts not merely difficulty but ill-definedness of evolution in a basis-unselected regime. It also makes explicit that CQM supplies a structural answer to the record question but leaves open how such a sector comes to be realized dynamically.

Decoherence: basis selection without outcome selection

Decoherence theory [Zurek2003] partially addresses the record question by explaining how pointer states emerge under environment-induced einselection. Measurement-like interactions produce system–environment correlations whose reduced state is approximately diagonal in the pointer basis; crucially, Ghose notes that re-expressing this reduced state in another basis does not recover genuine interference, since phase information resides in system–environment correlations that can only be reversed by joint action on both subsystems.

However, decoherence delivers only basis-selection, not outcome-selection: the global state remains entangled, and no single history is actualized. The paper is explicit that decoherence is therefore not a substitute for collapse if one demands a single-history ontology—an honest concession that shapes the subsequent taxonomy.

The agency constraint

Ghose incorporates the argument of Adlam, McQueen, and Waegell [Adlam2025] that minimal agency—world-model construction, deliberation over alternatives, reliable action selection—cannot be sustained in a strictly coherent, basis-unselected "purely quantum" regime, with the obstruction traceable to no-cloning and linearity. The paper extends this observation to evolution itself: even though Darwinian evolution involves no deliberative agent, it is still a record-driven copy-and-filter process subject to the same structural obstruction. Where no preferred copyable record basis exists, not only agency but any stable information-processing architecture—and hence the physical preconditions of heredity—is threatened.

Three questions and four ontological options

A key methodological contribution is the separation of three logically distinct questions:

• (Q1) the record question: what guarantees a robust, copyable record sector?
• (Q2) the outcome question: do measurement-like interactions yield one actual outcome per run?
• (Q3) the agency/evolution question: what resources make copying, discarding, and selection well-defined?

Against this backdrop, the paper presents four ontological packages in deliberately neutral fashion:

Option	Answer to (Q1) records	Answer to (Q2) outcomes	Representative frameworks
A: Unique-history realism	Grounded by added ontology (beables/trajectories)	Single realized history	Objective collapse (GRW, CSL, Diósi, Penrose); Bohmian mechanics
B: Unitary-only + decohered multiplicity	Dynamic pointer-basis emergence within sectors	No fundamental outcome selection; many decohered histories	Consistent histories, decoherent histories
C: Agent-relative facticity	Tied to inter-agent communicability	Outcomes relative to agents/relations	Relational QM, QBism
D: Stochastic foundation	Individual trajectories are ontological events	Single trajectory per run; probabilistic ensemble predictions	Nelson stochastic mechanics with variable diffusion

Stochastic mechanics as a continuous bridge

Option D receives the most detailed treatment. On a Nelson-type view [Nelson1985], the fundamental ontology consists of classical diffusion trajectories $x(t,\omega)$, with the Schrödinger equation emerging as an ensemble-level representation at a specific diffusion strength $\nu \sim \hbar/(2m)$. The paper proposes allowing $\nu$ to vary by regime: $\nu \to 0$ recovers classical Hamilton–Jacobi behavior, intermediate values yield mesoscopic interpolation (claimed to be, in principle, testable), and the quantum value yields standard quantum behavior. Classicality is thereby demoted from a primitive ontological kind to a regime of small effective diffusion.

On measurement, Ghose adopts Pavon's result [Pavon1999] that collapse need not be postulated independently: it can be derived as Bayesian conditioning on the obtained outcome, followed by selection of the post-measurement diffusion that is minimally invasive relative to pre-measurement dynamics in a time-symmetric variational sense. This yields post-measurement wavefunctions consistent with standard reduction rules. A notable claim here is that on this view the measurement problem—and much of the proliferation of interpretations—is largely obviated, because individual outcome events are ontological at the trajectory level while Hilbert-space structure functions as an emergent description. This is one of the paper's bolder assertions, and it should be read against the acknowledged status of stochastic mechanics as a minority foundational program whose equivalence to standard quantum mechanics holds only under specific assumptions about the diffusion process.

Extended Wigner's Friend scenarios as stress test

Extended Wigner's Friend setups [FR2018, Brukner2018, Proietti2019] are deployed as diagnostic tools: they force a simultaneous assignment of (i) a fully coherent quantum description of a laboratory containing an observer and (ii) the friend's status as a record-bearing agent with communicable facts. The agency constraint sharpens the resulting tension—treating the friend as an agent already presupposes substantial classical resources (stable records, a copyable basis)—and experimental tests of observer-independent facts have been performed [Proietti2019], albeit at scales far removed from genuine agential systems. Any option in the taxonomy must specify explicitly where its record basis comes from, whether and how outcomes are selected, and what resources underwrite agents' use of facts. The paper uses these scenarios evaluatively rather than claiming to resolve the underlying no-go results.

Limitations and open questions

The paper is candid about several dependencies. First, it is a conceptual synthesis rather than a derivation: the proposition linking classical sectors to evolvability is a structural argument within CQM's framework, not a theorem constraining all possible physics, and it presupposes that "Darwinian evolution in the ordinary sense" is the correct target characterization. Second, the variable-diffusion proposal remains programmatic—the existence of mesoscopic regimes with intermediate $\nu$ is asserted as testable in principle, but no specific experimental protocol or bound on $\nu$-variation is given. Third, Pavon's collapse-as-conditioning result inherits whatever limitations attach to Nelson's stochastic mechanics, including the unresolved question of whether the required osmotic velocity construction extends to relativistic and field-theoretic settings. Finally, the neutral presentation deliberately refrains from adjudicating among Options A–D; the Wigner's Friend analysis identifies what each option must supply but does not establish which option succeeds. Open questions include: whether intermediate-diffusion mesoscopic regimes can be isolated empirically, and whether the agency constraint can be sharpened into quantitative bounds on record stability in near-coherent regimes.

Conclusion

The paper's contribution is a disciplined decomposition of the question "what kind of world supports Darwinian evolution?" into three separable requirements—records, outcomes, and agency resources—mapped against the principal ontological options in quantum foundations. Its core structural result is that copyability and deletability exist only relative to a realized classical data sector, so that any account of evolution in a quantum world must either posit additional ontology, invoke dynamical basis-selection plus an outcome-selection mechanism, relativize facts to agents, or adopt a trajectory ontology in which classicality is a regime of vanishing diffusion. The synthesis does not settle the choice among options, but it makes explicit which physical resources each option owes, and it identifies extended Wigner's Friend scenarios as the setting in which those debts become most visible.