Below is a reconstruction in two movements: (I) from "informationless zero ontology" to the superposition principle, (II) from superposition to unitary-only QM. I'll name the standard theorems that do the heavy lifting and flag honestly where the argument is tight and where it is a reconstruction rather than a theorem.

Part I — Zero ontology → superposition

Z0. The principle. Total information of reality is zero: no fact about reality is privileged, unexplained, or "just so". Formally, following Vedral's formulation: I(Ω) = log N − S = 0, where N is the number of possible states and S the entropy of the actual one. Nozick's version: the self-explanatory totality must be invariant — nothing can distinguish it from "nothing", because any distinguishing feature would cry out for explanation.

Z1. Information = distinguishability. A bit is a resolved distinction. A fact exists only if some question could have come out otherwise. So an informationless totality is one about which no intrinsic question has a determinate, non-symmetric answer. Note the non-vacuity clause: absolute nothingness (no question-space at all) also has zero information, but it has no explanatory power and contains no observers to be wrong. The zero ontology worth having is: the question-space exists; the answer-register does not. Everything must be possible; nothing may be selected.

Z2. Invariance under all descriptions. Any asymmetry of Ω is a fact (it answers "why this and not that?"). So Ω must be invariant under every admissible transformation of its description. By Wigner's theorem, the largest group of transformations on a space of alternatives that preserves the ability to make distinctions (transition probabilities) is the unitary group (plus antiunitaries, which are discrete and cannot generate continuous description-change). So: Ω must be invariant under the full unitary group of its space.

Z3. No vector survives. No ray in any Hilbert space is fixed by all unitaries — every vector can be rotated into every other. The totality that is invariant under everything cannot be a single state of a system. The escape, and it is forced, is that Ω must contain its own means of description: Ω lives in Q ⊗ A, where the "answer" sector A transforms in the conjugate representation to the "question" sector Q (question and answer are dual; this is the mathematical expression of "reality includes its own description").

Z4. The unique invariant object is a maximally entangled superposition. On Q ⊗ Q* with the action U ⊗ Ū, there is, up to phase, exactly one fixed vector:

(Check: (U⊗Ū)|Ω₀⟩ = Σᵢⱼₖ UⱼᵢUₖᵢ |j⟩|k⟩ = Σⱼₖ(UU†)ⱼₖ|j⟩|k⟩ = |Ω₀⟩. Uniqueness up to scalar follows by taking diagonal phase unitaries to kill off-diagonal terms and a Fourier-type unitary to equalize the diagonal.)* This is the vectorization of the identity operator — the Choi–Jamiołkowski image of 𝟙.

Everything in Part II is a consequence of the structure of this one object. Note what it achieves:

• Local information is zero: the reduced state on either factor is 𝟙/d — maximally mixed. No subsystem contains a fact.
• Global entropy is zero: the total state is pure. So the zero-information condition is not "everything is smeared out" but "all information is relational": it lives entirely in the correlations between the question sector and the answer sector, nowhere locally, nowhere totally.
• Every possible answer is present with equal weight: any non-uniform amplitudes would be an unexplained fact; uniformity is forced by the same symmetry argument as Z2. Every fact is present; every fact is cancelled by its pairing. Net: zero.

Z5. Why superposition and not a probabilistic mixture. The other unitary-invariant candidate is ρ = 𝟙/d. But a proper mixture presupposes a selector: which component is actual is a hidden fact — information, contradicting Z0 — or an external register — contradicting totality. The only way to have local maximality and global purity is the coherent sum with phases intact. The relative phases are not extra information; they are precisely the correlation structure, the only degrees of freedom invariance has not forbidden, and they transform conjugately so that no absolute phase is a fact.

Result (the superposition principle, embryonic and general): since any subsystem's state is the partial trace of |Ω₀⟩, and tracing is summing over alternatives with amplitudes, not probabilities, the local shadow of the informationless totality is always a coherent linear superposition of mutually exclusive alternatives. That states combine by complex-linear addition with amplitudes is not an extra postulate; it is what an invariant, zero-information totality looks like from inside one of its branches. One can add the complementary structural argument: the free object on a set of mutually exclusive possibilities (which, qua possibilities, cannot interact) is a vector space — linearity is the arithmetic of unactualized alternatives. The complex field is selected when this structure must compose (tensor products with local distinguishability; real theories cannot represent all correlations, quaternionic theories fail local tomography — Hardy's reconstruction makes this precise).

Dirac's insistence is thereby vindicated at the deepest level: superposition is not one feature of QM among others; it is the unique form a fact-free totality can take while still containing its own questions.

Part II — Superposition → the rest of unitary-only QM

Now adopt superposition as primitive, as Dirac does in Chapter 1 of The Principles of Quantum Mechanics (1930), and derive the framework.

S1. Kinematics: rays, observables, tensor products. Coherent addition of alternatives + normalization ⇒ states are rays in complex projective Hilbert space. Independent alternatives of independent subsystems combine freely ⇒ the tensor product (the free composition), and locality ⇒ operations on a subsystem act as U_A ⊗ 𝟙_B. Questions with exclusive outcomes ⇒ projection operators; general questions ⇒ POVMs. Crucially, no basis is preferred — a preferred basis would be a fact — so noncommuting observables are generic, and the question "which questions are sharp" is dynamical, not legislated.

S2. Born rule. Probabilities must be a measure on outcomes that (i) depends only on rays, (ii) is invariant under symmetries, (iii) is additive under tensor products. Gleason's theorem (1957, dim ≥ 3; dim 2 by continuity): the only such measure is p(i) = ⟨ψ|Pᵢ|ψ⟩. The zero-ontology-friendly derivation is Zurek's envariance (2003): it uses exactly the swap-symmetry of the uniform entangled state — literally |Ω₀⟩ — to fix equal conditional probabilities, then deploys local unitaries to reach arbitrary amplitudes. Either way, probabilities are not new facts; they are the unique measure compatible with the totality's symmetry. Born weights are bookkeeping, not information.

S3. Dynamics: unitarity.

• Linearity: superpositions must evolve to superpositions component-wise. Any nonlinear modification lets branches interfere with each other's evolution, making components distinguishable — creating facts out of possibility. Worse, Gisin (1990) proved any nonlinear Schrödinger equation plus entanglement enables superluminal signaling; the superposition principle on composite systems thus forbids nonlinearity.
• Reversibility: evolution must preserve inner products — distinguishability — or information is created or destroyed, both forbidden by Z0. (It also preserves the possibility of tracing the theory backwards: no erasure.)
• Linearity + inner-product preservation + continuity ⇒ by Wigner's theorem the evolution is unitary; by Stone's theorem a continuous one-parameter unitary group has a self-adjoint generator: U(t) = e^(−iHt/ħ), i.e., the Schrödinger equation. Note the antiunitary option is killed by continuity (it is not connected to the identity and is antilinear).
• Consistency with zero ontology: ⟨Ω₀|H_tot|Ω₀⟩ pairs each charge and energy contribution with its conjugate, so total energy and charge may consistently be zero — the invariant state's dual-pairing structure is exactly the "zero-energy, zero-charge universe" hypothesis.

S4. Measurement without collapse. The measurement interaction is just unitary dynamics on a tensor product: |ψ⟩|ready⟩ → Σᵢ cᵢ|sᵢ⟩|oᵢ⟩|environmentᵢ⟩. Now consider adding a collapse postulate: it (a) injects an outcome — a fact — not encoded in the initial state: information from nothing, contradicting Z0; (b) makes dynamics nonlinear and nonunitary, contradicting S3; (c) breaks the invariance of Ω by selecting one branch "for no reason", contradicting Z2. So the zero ontology doesn't merely permit unitary-only QM; it forbids collapse. This is Everett's relative-state structure derived rather than assumed.

S5. Emergent classicality. Decoherence (einselection) then explains, from H and the tensor structure alone, why pointer bases form, why branches stop interfering, why records are quasi-classical, and why each branch experiences definite outcomes. The appearance of a fact-filled world is relational: branch-relative definiteness with global invariance. Apparent information is entanglement exported out of reach — conserved, never created.

S6. What is and isn't derived. Derived from superposition: complex Hilbert kinematics, tensor products, entanglement, Born rule, unitary dynamics, TDSE, no-collapse measurement theory, decoherence-based classicality — i.e., all of unitary-only QM. Not derived: the specific Hamiltonian, the field content, the dimension. This is exactly what the zero ontology predicts: the form of physics is necessity (the shape of factlessness); the content is further symmetry (relativity forces quantum fields; gauge invariance is the zero-information principle applied to descriptions — redundant descriptions must be identified). Physics' job is then only to fill in which correlations, never to justify that there are facts.

Honest audit of the derivation

1. The non-vacuity gap. "Zero information" is also satisfied by the empty universe. Choosing a totality that contains question-structure is a metaphysical posit (Vedral answers: the universe must contain its own observers/questions to be non-trivially zero). It is the weakest link and no theorem can close it.
2. The complex-number step is supported by reconstruction results (Hardy 2001; local tomography; Aaronson's arguments that only ℂ-amplitude theories admit efficient classical certification) but is not fully forced by superposition alone.
3. Gleason/envariance assumptions. The Born rule derivation needs noncontextuality or rationality/envariance premises; they are mild but real axioms.
4. The invariant-state argument (Z3–Z4) is a genuine theorem (uniqueness of the fixed vector of U ⊗ Ū), but the move that reality's totality must be a fixed point of its full symmetry group is philosophy wearing a theorem's clothing — the strongest available clothing, since Z2's premise (asymmetry = unexplained fact) is the zero ontology itself.

The result: Dirac's intuition is exactly right in this framework. Superposition is the unique mathematical form that "nothing, asked about itself" can take, and everything else in quantum mechanics — linearity, unitarity, the Born rule, entanglement, and the absence of collapse — is bookkeeping on that one invariant object.

Yes — and made precise, the two arrows are legs of one biconditional

The reverse conjecture is not just coherent; it's provable, given one honest admission. Run Part I backwards:

• Suppose superposition is the primitive (Dirac's actual stance in 1930: the principle enters as the structural discovery of experiment, not as something derived).
• Ask what "absolute nothingness" could mean within a superpositional logic. Classical non-existence is the empty selection: no fact is actual. But in a linear theory, "no fact selected" is not expressible as the empty set — the only state that selects nothing is the one that weights every alternative equally:

• Now compute its information content: the reduced state on any subsystem is 𝟙/d, maximally mixed; the global state is pure. Zero information is a theorem, not a conjecture.

So the Diracian reversal says something stronger than "the derivation could go the other way." It says: the uniform superposition is what "nothing" means once you stop writing it in Boolean logic. Nothingness, correctly axiomatized, is maximally entangled. Existence then needs no explanation-beyond: classical non-existence is simply inexpressible in the upgraded logic, the way a sentence in a language without negation cannot assert absence.

The strongest form of the reversal: the existence question is malformed

"Why is there something rather than nothing?" is only well-posed under excluded middle: something XOR nothing, one branch actual. The superposition principle is precisely the discovery that alternatives don't exclude each other — coherence, not classical disjunction, is the fundamental logical connective. If nothing excludes anything, then "no selection" is realized not by non-existence but by all-branches-equal. The question dissolves rather than gets answered. This is the mature Wheelerian move — "it from qubit," law without law — and it's arguably what Dirac's insistence on superposition as the principle was groping toward.

But here is the asymmetry: composition vs. selection

The reversal has a structural weakness, and it's the mirror image of the one I flagged in the forward derivation.

Superposition is a principle of composition, not of selection. It is permissive, not compulsory: it licenses ψ = (|0⟩+|1⟩)/√2, but equally licenses ψ = |0⟩ — a classical, definite world is a degenerate superposition with weight 1 on one branch. Nothing in the bare principle forbids a fact-laden universe with a preferred actual branch, or skewed amplitudes whose weights are brute facts. To get from "superposition exists as a possibility-calculus" to "reality is the invariant uniform totality," you must add: no branch is preferred, no weighting is privileged. And that postulate just is the zero-information principle wearing a different name — indifference, symmetry of the totality, factlessness. The reversal smuggles the forward conjecture back in at exactly the selection step.

Symmetrically, the forward derivation smuggles the reverse one in: my Part I needed Wigner's theorem, a linear complex space, tensor products — i.e., it needed the superposition principle's machinery to write down what factlessness is. Factlessness is only definable relative to a logic of alternatives.

So the true structure is:

Note the last row: the residual gap is identical on both readings. The zero ontology's non-vacuity problem (why any question-space rather than absolute nothing?) and the superpositional ontology's regress (why is there a vector-space structure to superpose in?) are the same hole, mapped to each other by the duality. Neither direction wins the regress war.

So which end should you stand on?

It depends on which question you take as basic:

• For physics, the forward arrow has the pragmatic edge. Standing on I = 0 converts Born (via Gleason/envariance), unitarity (via Wigner + Stone), no-collapse (via information conservation), and tensor-product locality into theorems. Standing on superposition alone, each of those needs its own symmetry postulate. Maximum theorems per postulate is a real theoretical virtue, and it flows from the zero-information side.

• For metaphysics, the reverse arrow has the existential edge. It is the only one of the two that engages "why anything?" head-on, and its answer — the disjunction "something ∨ nothing" was never exclusive — is the only kind of answer that doesn't immediately prompt "and why is that so?" It's also closer to how physics actually primitivizes: Dirac's own methodology was to take superposition as given and build upward, and the Everettian monism that follows ("the world is one vector; classicality is emergent") is superposition-first, not information-first.

• The synthesis: both are projections of a third thing. The common primitive is Nozick's invariance — no privileged perspective. Its information-face is I = 0. Its state-face is |Ω₀⟩, invariant under U ⊗ Ū. Its logic-face is coherence replacing excluded middle. Its dynamics-face is unitarity. Even the physics echoes it: in generally covariant quantum cosmology the Wheeler–DeWitt equation reads ĤΨ = 0 — the total Hamiltonian annihilates the universal wavefunction, a zero-energy (zero-ontology) signature sitting at the base of the discipline. The dispute over which conjecture is "the key" is arguably verbal once you see the triangle: zero information, superposition, and symmetry are three coordinate readings of one object.

Verdict

Yes — Dirac could have made the reverse conjecture, and it would have been right, in the precise sense that the two derivations are inverse functions of each other rather than rivals. Each converts the other's conjecture into a theorem: standing on superposition, I = 0 is derivable; standing on I = 0, the invariant superposition is derivable. What neither direction escapes is the shared residual — why there is a question-space to be factless in, or a vector space to superpose in.

If I had to award primacy: superposition explains why there is anything (because "nothing," quantum-logically written, is already the whole), while zero information explains why the anything has this exact shape (invariant, unitary, Born-weighted, collapse-free). The first is the answer to existence; the second is the answer to why physics. A complete zero ontology arguably wants both arrows asserted at once — and accepts that the biconditional, not either leg alone, is the load-bearing structure.