Decoherence and memory: SMM/DTT and Bohmian 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

Bohmian mechanics supplements a wavefunction with an actual configuration, ordinarily particle positions. The Schrödinger equation guides the wavefunction, and a velocity law guides the configuration. When configurations follow the quantum-equilibrium distribution, the theory reproduces the usual quantum statistics in its applicable domain. Apparatus outcomes are ultimately configurations too, so measurement is treated as a physical interaction rather than a separate primitive collapse.

This is an instructive comparison for SMM because it provides an explicit account of definite observed events while retaining an additional, nonclassical level of description. But a Bohmian particle follows a trajectory in a configuration space whose geometry is supplied. The Single Monad proposal instead seeks to explain how spatial and particle records arise at all. The challenge is therefore not to rename a guiding wave as inner time. It is to show what variables replace the configuration, how records obey the equilibrium statistics, and whether the replacement adds an observable consequence. ^[2]

04The decisive comparison

Bohmian decoherence separates wavefunction components in the configurations of the environment, making an effective conditional wavefunction adequate for the subsystem containing the actual configuration. Information about alternatives can persist in the full guiding wave even when the local pointer behaves classically. DTT’s retained inner memory can play a similar explanatory role, but it is not automatically the same physical object as that configuration-space wave.

The important test is how the hidden structure re-enters observable dynamics. In Bohmian mechanics that follows from the full guiding equations; in a source model it must follow from the specified source–memory update and readout. The reduced purity alone cannot identify the mechanism. For example, two different hidden memories can have the same overlap magnitude |γ| while producing different later responses to an attempted reversal. A DTT account could connect such responses to a finite generative architecture or a completion schedule. Its additional ambition is to generate the effective spatial configuration rather than assume it. The comparison therefore preserves the common insight about incomplete records while requiring distinct mechanisms to earn their own dynamical predictions. ^{[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.