Single-particle interference: SMM/DTT and Everett many-worlds interpretation

01The question behind this comparison

Single-particle interference is interference between alternative amplitudes contributing to one detection event. The particle number can be one while the quantum state has support on several paths. An interference pattern accumulates over many trials because the relative phase changes the probability of each individual detection; it does not require two particles to collide at the detector.

The SMM/DTT idea of sequential inner production offers a possible physical narrative for how alternative contributions belong to one completed event. Its useful mathematical content would be a coherent rule for combining those contributions before registration. A classical source that randomly chooses one path and retains only its label produces a mixture, not an interference pattern. Phase memory, a recombination operation and the measurement context therefore carry the decisive explanatory work. ^{[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

Everettian interference is possible while alternative components of the state remain coherent enough to recombine. Branches associated with robust macroscopic records ordinarily cease to interfere for practical purposes through decoherence, although the total dynamics remains unitary. DTT’s inner alternatives can match this behaviour if completion releases records only after the relevant amplitude combination, or if retained source coherence remains available for later reversal.

The sharp issue is whether the source retains one coherent state containing both path alternatives. If completion irreversibly chooses a path before recombination, the ideal interference pattern disappears unless an explicit replacement mechanism restores the cross term. Thus the experimentally relevant timing is the timing of a physical operation relative to recombination, not the verbal placement of an outer instant. Everett offers a clear account of why unrecorded alternatives interfere and stable records usually do not. DTT’s potential contribution is to derive the source architecture that protects or exposes those alternatives, with a resource-dependent prediction. A claim that one particle has one source does not select between these mechanisms. ^{[2] [3] [4]}

05Worked benchmark

Use an ideal balanced Mach–Zehnder interferometer. After the first beam splitter the path state is (|0⟩+|1⟩)/√2. A phase plate multiplies the second component by e^{iφ}. With a second balanced recombiner in the corresponding phase convention, the first output amplitude becomes (1+e^{iφ})/2. Its probability is cos²(φ/2), and the other output has probability sin²(φ/2).

For φ=0 every ideal trial reaches the first output; for φ=π none does; for φ=π/2 the outputs are equiprobable. If an environment records the paths in states with overlap γ, the interference term becomes Re(γe^{iφ}) and the visibility is |γ|. This calculation explains precisely what an inner-time mechanism must preserve: the relative phase and the coherence between alternatives. Changing the duration of private work while keeping these quantities and the registered phase fixed produces no new interference prediction. ^{[3] [4]}

06What follows for the source programme

The comparison rewards a model that identifies why a completion event combines amplitudes coherently, and why which-path information changes that combination. A finite-state simulation can exhibit the mechanism explicitly. Its result is an implementation of the interference law until independent restrictions on phase generation, memory capacity or recombination create a new testable relationship. A claimed fringe shift needs a formula tied to measured settings rather than an adjustable inner duration. ^{[3] [4]}

THE SAME QUESTION, DIFFERENT STARTING POINTS

The comparison at a glance

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