Delayed choice and quantum erasure: SMM/DTT and relational 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. ^{[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

Relational quantum mechanics treats physical quantities and state assignments as relative to interactions between systems. An observer is any relevant physical system, not necessarily a conscious mind. What is definite relative to one system need not be represented by the same state relative to an external system that has not yet interacted with it. Communication and subsequent interactions are part of the physical account of how records are compared.

DTT’s separation of generation from accessible records can be formulated in this language when completion is indexed to a receiving system. A universal outer archive, by contrast, would add an observer-independent structure beyond Rovelli’s original proposal. Neither choice is settled merely by saying that observations occur. The useful comparison concerns exactly which system retains a record, which interactions make it accessible, and which consistency conditions connect descriptions. Relational quantum mechanics does not derive the six inner levels, while their presence alone does not decide whether completion should be universal or relational. ^[2]

04The decisive comparison

Relational quantum mechanics gives a particularly natural description of an eraser experiment in terms of which systems have interacted and which records are being compared. The signal detector has a local result; a later marker measurement establishes a relation that defines the relevant coincidence subset. DTT can identify outer completion with the availability of such a relational archive, provided the receiving systems and permitted tests are specified.

The common emphasis on records must not obscure the exact probability rule. A later receiver who knows the marker result uses a conditional distribution, while an earlier receiver without it uses the unconditioned distribution. Their different information does not constitute inconsistent physical predictions. If DTT posits one absolute completed history behind both assignments, that is additional ontology beyond the relational description. A useful model can show how both receivers obtain their proper distributions from the same source memory. Its novelty would concern the mechanism of access or the compatibility of records, not an unsupported claim that a change in an observer’s knowledge causes the past physical event to change. ^{[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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