Delayed choice and quantum erasure: SMM/DTT and Bohmian 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. ^{[3] [4]}

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

Bohmian mechanics supplements a wavefunction with an actual configuration, ordinarily particle positions. The Schrödinger equation guides the wavefunction, and a velocity law guides the configuration. When configurations follow the quantum-equilibrium distribution, the theory reproduces the usual quantum statistics in its applicable domain. Apparatus outcomes are ultimately configurations too, so measurement is treated as a physical interaction rather than a separate primitive collapse.

This is an instructive comparison for SMM because it provides an explicit account of definite observed events while retaining an additional, nonclassical level of description. But a Bohmian particle follows a trajectory in a configuration space whose geometry is supplied. The Single Monad proposal instead seeks to explain how spatial and particle records arise at all. The challenge is therefore not to rename a guiding wave as inner time. It is to show what variables replace the configuration, how records obey the equilibrium statistics, and whether the replacement adds an observable consequence. ^[2]

04The decisive comparison

Bohmian accounts of quantum erasure include actual detector and marker configurations guided by their joint wavefunction. The final coincidence classes depend on the entire apparatus interaction, so a simple story in which the observed fringe identifies one pre-existing path can be misleading. DTT likewise should not equate a private source-address sequence with an experimentally reconstructed particle history.

The productive correspondence is that a definite earlier detection can coexist with a later sorting of correlations whose phase information was retained in a larger state. Neither model needs to alter the stored detector bit. The difference concerns the hidden dynamics that yields the sorting: Bohmian guidance is explicit, while a source model must specify memory, measurement context and its readout. The benchmark’s cancellation of complementary fringes is therefore essential. It prevents either hidden-variable language or completion language from suggesting a usable signal into the past. DTT could add explanatory depth by deriving the physical organization of that retained correlation from one nonspatial process, but the eraser result alone cannot establish that deeper generative ontology. ^{[2] [3] [4]}

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. ^{[3] [4]}

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. ^{[3] [4]}

THE SAME QUESTION, DIFFERENT STARTING POINTS

The comparison at a glance

Continue on SMONAD

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• SMM/DTT research claim map: results, assumptions and open targets →

  Places the comparison alongside the programme’s published results, assumptions and open targets.