Decoherence and memory: SMM/DTT and relational quantum mechanics

01The question behind this comparison

Decoherence occurs when a system becomes correlated with degrees of freedom that are not controlled in a later experiment. Relative phases can remain present in the total state while disappearing from the reduced statistics available locally. A memory is a physical correlation that persists and can influence a later operation. These concepts overlap, but neither implies the other: an environment can decohere a system while retaining information that later returns to it.

SMM/DTT’s source memory gives this distinction a natural role. Inner work may store relations absent from the completed record, and later completion can reveal some of them. The relevant question is whether the discarded variables are merely bookkeeping or have operational consequences. A theory of retained records therefore benefits from multi-time interventions that distinguish irreversible loss, temporary inaccessibility and deliberately protected phase memory. ^{[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 makes decoherence meaningful relative to a system and the interactions available to it. A record may be stable for one observer while a larger controlled system still admits coherent operations on that record and its environment. DTT’s distinction between inner retention and outer access fits this structure when completion is explicitly indexed to a receiver and a test language.

The distinction becomes more demanding when observers later compare memories. It is not sufficient to say that each has a personal world; the physical model must predict their joint statistics under the actual comparison operation. A single source can offer a common mechanism for those statistics, but an absolute archive is an additional assertion beyond the relational interpretation. The overlap example illustrates the practical issue: an observer controlling only the qubit sees reduced purity, while one controlling the correlated environment may restore coherence. DTT can make this difference constructive by specifying access permissions as physical couplings, not merely epistemic labels. Its novelty would be a derived organization of accessible memory that explains when descriptions can be compressed to stable classical records. ^{[2] [3] [4]}

05Worked benchmark

Start with (|0⟩+|1⟩)|e⟩/√2 and let an interaction correlate the alternatives with normalized environment states |e₀⟩ and |e₁⟩. The reduced system state has diagonal entries 1/2 and off-diagonal entries γ/2, where γ=⟨e₁|e₀⟩. Its eigenvalues are (1±|γ|)/2 and its purity is [1+|γ|²]/2.

If |γ|=0.6, the purity is 0.68. If the environmental alternatives become orthogonal, purity falls to 1/2 and the system looks maximally mixed. A controlled reversal of the joint interaction can nevertheless restore the original pure state when all relevant degrees of freedom remain coherent. This is why a completed local archive cannot be identified with the full microscopic state. The entropy of its reduced description measures inaccessible correlations under a chosen partition; it is not, by itself, evidence that information has been fundamentally destroyed. ^{[3] [4]}

06What follows for the source programme

The practical value of a source-memory model is that it can predict when a simple one-time description fails. If every future intervention depends only on the retained density operator, an ordinary channel is enough. If different preparation histories with that same operator produce different responses, a larger memory or process tensor is required. The additional structure becomes explanatory when its organization constrains those responses, instead of merely storing a complete list of previously observed outcomes. ^{[3] [4]}

THE SAME QUESTION, DIFFERENT STARTING POINTS

The comparison at a glance

Continue on SMONAD

• Retained observations versus predictive states →

  Connects this comparison with the author’s underlying construction.

• Eliminating hidden variables creates memory →

  Connects this comparison with the author’s underlying construction.

• Toy models of projection-induced irreversibility →

  Connects this comparison with the author’s underlying construction.

• When memory can be represented by one time →

  Connects this comparison with the author’s underlying construction.

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

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