Single-particle interference: SMM/DTT and QBism

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

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 regards the phase-dependent detection probabilities as an agent’s expectations for actions involving preparation, phase control and detection. It does not demand a story assigning a hidden path to each trial. DTT seeks exactly such a deeper generative account, though that account need not be a classical path story. Both approaches accept that a change of phase in the apparatus changes the probabilities an informed observer should use.

The comparison is useful because it separates an explanatory model from the data it organizes. An agent can rationally use a DTT-generated instrument without accepting every metaphysical interpretation of its source. Conversely, subjective probabilities do not permit choosing arbitrary fringe shapes: the quantum structure constrains the assignments. For the source programme to add physics, a constraint on coherent memory or completion must determine some relation that ordinary apparatus modelling leaves adjustable. An independently predicted visibility-versus-delay curve would be such a relation. Merely recasting the same probability as either a source frequency or an agent expectation changes its interpretation without supplying a new experimental result. ^{[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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