- How to compute a universe
The Universe as a single, self-consistent initial seed:
{ Ψ[X,0], Gᵢⱼ[R(X,0)] }
This pair, the universal wavefunctional Ψ and its Fisher-information metric G, forms the sPNP seed. Once specified, it deterministically unfolds into everything that exists. No regress, the universe can be an algorithm.
- The deterministic law
The dynamics obey a reflexive Schrödinger-type equation:
iℏ ∂τΨ[X,τ] = Ĥᴳ[Ψ] Ψ[X,τ]
where Ĥᴳ[Ψ] is the Hamiltonian built from the Laplace–Beltrami operator on the configuration-space metric Gᵢⱼ[R]:
Δᴳ f = |G|⁻¹ᐟ² ∂ᵢ(|G|¹ᐟ² Gⁱʲ ∂ʲ f)
Because the metric Gᵢⱼ depends on the amplitude R = |Ψ|, the geometry and the wavefunctional evolve together. This coupling makes the law fully deterministic yet reflexive, the state defines the geometry that defines the state.
Equivariance is not assumed to persist trivially under a time-dependent Fisher metric. In sPNP it is enforced in one of two equivalent ways.
First, the inner product and density are defined with respect to the evolving measure ∣G[R(τ)]∣ dS, so the Schrödinger flow is understood covariantly: the generator Ĥᴳ[Ψ] is self-adjoint at each τ relative to the instantaneous Fisher measure, and the continuity equation carries the corresponding connection term.
Alternatively, since the metric is itself a reflexive functional of Ψ, the ∂τ∣G∣ contribution exactly balances the nonlinear terms in Ĥᴳ[Ψ], yielding a conserved current in the Bohm–Madelung picture. Thus, equivariance is built into the geometry by construction, not assumed by analogy with the linear case.
The initial wavefunctional
{ Ψ[X,0] } or equivalently { R(X,0), S(X,0) } specifies the full relational amplitude of the universe. The pair { Ψ[X,0], X(0) } is the first relational distinction: X(0) is the single configuration that establishes the reference from which all relational amplitudes are defined. The Fisher curvature G is fixed by the initial amplitude R(X,0), and this curvature becomes the geometry that constrains every future distinction. Knowing this single seed is, in principle, knowing the whole universe.
- Relational physics and the impossibility of signaling
The standard no-signalling theorems (Gisin, Polchinski) assume that reality splits into independent subsystems A ⊗ B, so one can act locally on A without changing B. But sPNP lives on a relational configuration space with no such split.
For N particles in ordinary 3-space:
Q = ℝ³ᴺ and S = Q / E(3)
where E(3) removes global translations and rotations. This leaves a shape-plus-scale manifold S of dimension 3N − 6. Coordinates on S describe only the internal relationships among all particles, no external frame, no absolute position, no global orientation.
Therefore:
• There is no tensor-product factorization H = H_A ⊗ H_B.
• There are no independent local operations on “A only.”
• Reduced states come from geometric marginalization on S, not Hilbert-space tracing.
A nonlinear evolution on this global manifold cannot be used for superluminal signaling, because no agent can act locally in the fundamental variables. All probability flow is governed by a single geometric continuity equation:
∂τρ + ∇ᵢ(ρ Jⁱ) = 0, ρ = |Φ|² |G|
where Φ is the reduced wavefunctional on S, and Jⁱ is its probability current. Equivariance, the conservation of total probability, holds automatically in this relational geometry.
Even keeping scale does not re-introduce absolutes. Scale is a relational measure of the whole configuration, not an external ruler. Thus, the assumptions behind Gisin/Polchinski’s argument never arise.
- Planting the initial seed
At τ = 0, the sPNP seed contains both geometry and phase structure:
Ψ[X,0] = R(X,0) e^{i S(X,0)/ℏ} Gᵢⱼ[R] = Fisher metric built from R
From this reflexive pair, all curvature, potential, and configuration follow by deterministic Jacobi dynamics. Mass-energy and spacetime structure emerge as curvature features within this evolving Fisher geometry. In sPNP, the Big Bang is not merely a singular event; rather, it represents the first emergence of curvature from the initial distinction encoded in the universal seed.
- Could it be simulated?
In principle, yes.
If sPNP is exact, the universe is a deterministic PDE on configuration space. Given unbounded computation and the exact seed { Ψ[X,0], Gᵢⱼ[R(X,0)] }, the evolution
iℏ ∂τΨ = Ĥᴳ[Ψ] Ψ
could be numerically integrated to reproduce the complete cosmic trajectory. It would be unimaginably costly, but logically possible. The universe is a self-executing deterministic computation, and any perfect simulation of its seed would evolve identically.
- The vision
Reality is the deterministic evolution of the wavefunctional Ψ. The Fisher metric G encodes the shape of its curvature and the geodesics are deterministic trajectories. Together they evolve as a closed, reflexive system whose unfolding we call the universe.
Particles, fields, and observers are not inputs, they are emergent relational features within the continuous flow of the Fisher geometry.
The sPNP seed can be a computation; Laplace's Destiny. The sPNP seed not as something inside the universe, but an algo that can map the evolution of the Universe.
