Decoherence and memory: SMM/DTT and Everett many-worlds interpretation

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

Everett’s relative-state formulation applies unitary quantum evolution to the apparatus and observer as well as to the measured system. Correlated components of their joint state encode different relative outcomes. Modern decoherence-based accounts use effectively stable environmental records to explain why these components behave as autonomous branches for practical observation. Their language of worlds is an interpretation of this branching structure, not an additional term in the Schrödinger equation.

Its main contrast with a completion account is the status of the alternatives. Everett keeps all components in the universal state; a DTT model must specify whether completion releases a relative record, selects one outcome by an additional rule, or discards information through an explicitly open channel. Each option has a different relationship to unitarity. Mere sequential generation of a superposition does not make it Everettian, and describing observed definiteness does not by itself disprove relative-state quantum mechanics. Both accounts still need justified probability assignments for repeated records. ^[2]

04The decisive comparison

Everett uses decoherence to explain why distinct record branches become effectively independent while preserving the coherence of the total state. A DTT source memory that retains the phase discarded by local observation can implement precisely that situation. Outer completion then marks the stabilization and accessibility of a record, not necessarily the physical destruction of other components.

The interpretational fork concerns what a completed world contains. If DTT asserts one absolute record sequence, it must supplement decoherence with a rule selecting that sequence or a different ontology of the total state. If it treats each accessible record as relative to its branch, it can share Everett’s unitary mechanism while offering a proposed origin for the record architecture. The overlap calculation does not decide between them because the same reduced density operator occurs in both descriptions. The possibility of recoherence matters only when a specified theory actually removes it. A careful comparison thus uses memory to sharpen the global-state question and uses experiments to constrain concrete loss laws, without claiming that ordinary decoherence uniquely establishes either many worlds or a single completed archive. ^{[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 →

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• 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.