Decoherence and memory: SMM/DTT and QBism

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

QBism interprets quantum probabilities as an agent’s personal expectations for the consequences of actions on the world. The quantum state belongs to that probability assignment rather than serving as a complete observer-independent description of the system. The Born rule acts as an additional normative constraint among an agent’s probability judgments. QBism does not deny an external world; it rejects an interpretation in which the state is simply a catalogue of its intrinsic properties.

The Single Monad Model has a much stronger ontological ambition: one source is intended to explain the production of physical multiplicity. A mathematical DTT model can still use an operational probability interface, but equating that interface with QBism would obscure this difference. The informative question is whether a proposed generative law imposes new, testable restrictions on the probabilities an agent should assign. If it does not, the two views can organize the same data while offering substantially different accounts of what the formalism means. ^[2]

04The decisive comparison

QBism interprets a reduced density operator as an agent’s probability assignment given the actions available to that agent. A decohered state therefore represents a change in the operational expectations, not direct proof that a hidden source has lost information. DTT adds an ontic account of where phase information might reside and how later completion could expose it. These descriptions can coexist at the level of experimental practice.

The comparison becomes concrete when access to an environment changes. An agent who gains control of a source-memory register should update the set of possible interventions and the corresponding probabilities; a DTT model should derive those probabilities from its joint dynamics. The overlap example quantifies why a mixed local assignment can be appropriate even when the total state is pure. Neither interpretation permits an arbitrary recovery of interference without the required physical operation. A source theory has additional explanatory value if it constrains the resources needed for recovery or predicts correlated errors in retained records. Otherwise its memory story is a possible realization of the same quantum interface, while QBism remains a different interpretation of the resulting assignments. ^{[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.