The Measure Stack
System
A qubit in superposition. Density matrix, off-diagonals explicit.
decoherence — physical, no observer required
Environment
Spin bath causing decoherence. Diagonal density matrix plus redundancy curve.
Modelling assumption: Zurek's pure-dephasing spin bath. Exact and closed-form, but it models dephasing only, not dissipation.
t = 0.00
Quantum Darwinism: redundancy
Between layer 2 and layer 3: a gap this simulator does not model
Layer 2 leaves the system in a diagonal density matrix: decoherence has picked out a pointer basis, but every outcome the diagonal assigns a probability to is still there. Layer 3 shows an observer with one settled percept. The step from the first to the second — how a diagonal mixture of possibilities becomes a single experienced outcome — is absent from this codebase by design, not by oversight. No panel here computes it, samples it, or assumes an answer to it, because physics itself does not currently supply one. What follows are four live, competing positions on that question, each still defended by working physicists, presented in no particular order and with no ranking implied. This simulator takes no side:
- Many-worlds
- Proponents hold that nothing is selected — every branch persists, and an "outcome" is only ever relative to a branch.
- Dynamical collapse (GRW, CSL)
- Proponents add a physical collapse term to the dynamics itself, which spontaneously localizes the state onto one branch. GRW is one model in this family, not the family itself.
- Bohmian mechanics
- Proponents hold that a hidden variable — the particle's actual position — was determined all along, alongside the wavefunction, which guides the particle rather than sitting inertly beside it. The theory is explicitly non-local.
- QBism
- Proponents hold that the state was always an agent's degree of belief, not a property of the world, so there is nothing further to collapse.
These four are not exhaustive. Relational quantum mechanics, consistent histories, and other readings are also live. The list is a sample of the disagreement, not a complete map of it.
None of these is assumed by any panel above or below this one. The Bayesian update in layer 3 models an observer's belief-updating; it is silent on which, if any, of these four is correct.
Bayesian update — requires an agent
Observer
Bayesian agent with a prior. Posterior over the outcome.
Layer 3a — NNGP kernel
Demonstrated, not asserted: sampled ReLU MLPs' output variance converges to the analytic NNGP kernel as width grows. The quantum machinery above describes the world; this describes the observer's model of it.
sampling… 0%
analytic K^1(x,x) = 1.0400
Layer 3b — the predictive observer
Bayesian update — requires an agent. Evidence reliability is read live from the current decoherence: as |r_F| for a sampled fragment falls, the Helstrom error P_error falls, and readings become trustworthy.
σ₀² (from the NNGP kernel) = 1.0400
settled percept: 0.300