Delayed choice and quantum erasure: SMM/DTT and standard Hilbert-space quantum mechanics

01The question behind this comparison

Delayed-choice experiments compare different ways of completing an interference experiment. A later choice of measurement can determine which joint correlations are accessible, but it does not license changing an already stored, unconditional earlier detection record. Quantum erasure is clearest when the path becomes correlated with a marker: interference disappears from the unconditioned signal and reappears in suitably sorted coincidence subsets.

DTT’s emphasis on completed records can clarify the difference between a partially available correlation and a final joint archive. The relevant completion is the availability of the required data and measurement context, not a physical revision of the past. A stronger temporal model would calculate why the same local marginal survives all permitted later choices and why the conditional subsets exhibit complementary fringes. ^{[2] [3]}

02The SMM/DTT starting point

The Single Monad Model begins with one nonspatial generative source. The Duality of Time Theory distinguishes the source’s inner production from the outer order in which completed records become accessible. Its six inner levels are nested functional roles of one process: a higher role organizes lower-level work. The seventh is the completion or observation interface. They are neither six independent clocks nor six additional time coordinates.

This distinction supplies a useful research question: which features of an observed world can follow from the way a source produces, retains and releases information? A concrete answer needs a state space, an autonomous update, retained memory and a rule connecting completion to an accessible measurement. In the constructions discussed here, those mathematical ingredients are stated explicitly. A successful finite example establishes what its specified mechanism can do; further arguments connect it to physical particles, spacetime or universal laws. ^[1]

03How the comparator works

Operational quantum mechanics represents a preparation by a positive density operator of unit trace. A measurement outcome corresponds to an effect, and an instrument specifies both its probability and the conditional state left behind. Closed evolution is unitary; an open system can evolve by a completely positive, trace-preserving map. These ingredients are sufficient to calculate laboratory statistics without deciding whether the wavefunction describes an ontic object, a relation or an agent’s expectations.

The instrument language is especially close to DTT’s distinction between production and accessible records. An unobserved interaction and a registered outcome are mathematically different objects. Yet an ordinary instrument does not itself contain a hidden generative time, nor does a sequence of instruments derive the space in which laboratories operate. It provides a precise interface against which a proposed inner process can be tested: if the process reproduces exactly the same instruments, the difference is explanatory or structural unless another accessible measurement distinguishes it. ^[2]

04The decisive comparison

Operational quantum mechanics distinguishes the signal’s local instrument from the later joint conditioning on the marker result. DTT’s completion language can make that distinction intuitive: one detector may release a local record before the full coincidence archive is assembled. Yet the later archive contains correlations between earlier records; it does not replace the earlier local sample with a different one.

The calculation gives a strong constraint on any proposed hidden production story. If the plus and minus marker results are ignored, their fringes cancel exactly. A source model that lets a later choice change the unsorted signal frequencies would make a new retrocausal signalling prediction, rather than explain the ordinary eraser experiment. The useful source contribution would be a mechanism that guarantees this cancellation for every allowed marker basis while maintaining the conditional phase relations. That is an interface consistency result that can be proved for a specified instrument. A genuine DTT deviation would then have to appear elsewhere, such as a separately derived relation between marker memory and completion timing, without being confused with postselection. ^{[2] [3]}

05Worked benchmark

Let signal paths and marker states be in (|0⟩|m₀⟩+e^{iφ}|1⟩|m₁⟩)/√2, with orthogonal marker states. Ignoring the marker leaves the signal in an equal path mixture. Its balanced-recombiner output probability is 1/2, independent of φ. Measure the marker instead in the basis |m±⟩=(|m₀⟩±|m₁⟩)/√2. Each marker outcome occurs with probability 1/2.

Conditioned on the plus marker, the first signal output has probability cos²(φ/2); conditioned on the minus marker, it has sin²(φ/2). Averaging the two gives 1/2 again. At φ=0, the two sorted subsets are completely different, but the unsorted earlier data remain evenly distributed. A later selection can reveal this organization only when the marker result is communicated and the records are compared. The arithmetic explains why the effect offers no channel for controllable messaging into the past. ^{[2] [3]}

06What follows for the source programme

The contribution of a completion vocabulary is strongest when it distinguishes local detection, remote marking and the later comparison of their records. A source account can attach its hidden stages to that operational structure without claiming that a human decision recreates an earlier event. Any further prediction must survive the same unconditioned-versus-conditioned distinction; apparent retrocausal effects caused solely by sorting are already expected in ordinary quantum theory. ^{[2] [3]}

THE SAME QUESTION, DIFFERENT STARTING POINTS

The comparison at a glance

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