Every possibility.
An amplitude.
Enter configuration space. Follow the phase, recombine alternatives and discover what changes when another system retains a record.
Finite unitary model. Outputs show the end of the experiment; the slider explores intermediate states. Connections represent couplings and succession, not observed trajectories.
The points are possibilities.
The state is the set of amplitudes.
A binary coordinate gives two basis configurations, not just two possible quantum states. a|0⟩ + b|1⟩ is also a state. Three binary coordinates give eight basis configurations and eight complex amplitudes.
An empty node has zero amplitude. An active node carries a weight and a phase: two contributions can reinforce or cancel each other.
One slice.
Or the whole history.
In the time view, each layer contains configurations at the same t. Selecting a layer still gives a superposition. Adding an axis to a drawing does not automatically create a physical degree of freedom.
This is one discrete encoding of a history in a register C. In relational models such as Page–Wootters, a physical clock and a dynamical constraint describe evolution through correlations. The view above shows ψ(t); it does not simulate that constraint.
Relativity joins space and time in spacetime. It does not imply that t is an observable identical to x in the Hilbert space of ordinary quantum mechanics.
Same outcome.
Different phases.
Amplitudes leading to the same outcome add before calculating probability. Two basis configurations can be orthogonal and still contribute to the same output after recombination. Distance between drawn points does not measure their ability to interfere.
Dynamics determines which configurations couple: Hamiltonian terms Hᵢⱼ transfer amplitude, while energy differences accumulate relative phase. These are not particles hopping independently between nodes.
A record changes
what can interfere.
If both alternatives correlate with the same state of S′, the state stays separable. If they leave different states in S′, the joint state becomes entangled. Correlation is what matters, not whether S′ occupies one or several configurations.
When observing only S, the interference term is multiplied by ⟨e₀|e₁⟩. Identical records preserve interference. Orthogonal records remove interference from unconditional local statistics. Coherence of the joint state can remain.
One state.
Many components.
Decoherence helps explain why some alternatives effectively stop interfering. Reading them as “parallel worlds” is one interpretation, not an additional result of this experiment.
Model and sources
S: 1–3 binary coordinates. Spectators start in |+⟩. φ₁ starts in |0⟩; rotation R(π/4) splits amplitude. Path 1 accumulates phase and can rotate S′ from |0′⟩ to cos θ|0′⟩ + sin θ(|1′⟩+|2′⟩)/√2. R(−π/4) recombines paths. θ ranges from 0 to π/2. Time and energies use conventional units; no collapse is simulated.
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