Delayed choice and quantum erasure: SMM/DTT and objective collapse models

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

Objective collapse theories modify quantum dynamics so that sufficiently macroscopic alternatives are suppressed by a physical stochastic process. In GRW-type and continuous-spontaneous-localization families, the modification contains a rate and a spatial or mass-related structure. Amplification makes microscopic coherence relatively persistent while reducing macroscopic superpositions. These are dynamical proposals with measurable consequences, rather than interpretations that necessarily preserve every prediction of ordinary unitary quantum theory.

Outer completion in DTT is not automatically an objective collapse. A completion channel may simply expose a decohered record or condition on an ordinary outcome. It becomes a collapse proposal only when the state evolution changes in a specified way, with a probability law, energy accounting and a physical scale. Collapse models consequently provide a demanding comparison: they illustrate how an account of definite records can take quantitative risks. No bound on their parameters directly bounds an unspecified generative process; the two mechanisms must first be translated into comparable observable dynamics. ^[2]

04The decisive comparison

An objective collapse can destroy the coherence needed for an eraser to restore conditional fringes. Ordinary which-path entanglement need not do so, because measuring the marker in another basis can still reveal the phase correlations of the joint state. DTT completion has to specify which situation it creates. Publishing a local record is compatible with later erasure only when the relevant coherent correlations remain available under the stated operations.

This gives a concrete test of proposed completion laws. A rate depending on the lifetime or mass of the marker superposition would predict a visibility envelope for the sorted fringes, while the unsorted marginal must still obey the law’s causal constraints. The rate cannot be inferred from the word delayed or from six nested stages without a physical clock calibration. A source-memory account may instead predict recoverable coherence with a finite resource cost. The comparison therefore distinguishes irreversible collapse, environmental record spreading and restricted access to an inner archive. Each can reduce practical contrast, but their different response to a controlled reversal is where the mechanism acquires experimental content. ^{[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

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