Inner time and outer time: SMM/DTT and The two-state vector formalism

01The question behind the comparison

The distinction between producing an event and having a record of it is the most useful entry into dual time. A measurement apparatus can undergo internal changes before a stable pointer value becomes available. Calling these two descriptions inner and outer is initially an explanatory distinction. The stronger DTT claim is that spatially articulated objects themselves emerge through such production, so the apparatus is already part of the resulting world rather than the ultimate source. The philosophical attraction is that becoming is placed in the constitution of events, not added afterwards to an already complete spatial inventory.

A clear account therefore separates three orders. Dependence orders the nested operations required for completion. Succession orders the accessible records. Duration compares changes with a physical clock. These orders need not coincide simply because the same symbol t appears in their description. Two operations may depend on one another without having separately measurable durations. Conversely, records may be separated by unequal clock intervals despite containing the same number of abstract updates. This distinction protects DTT from concealing a conventional external clock inside the word generation.

A constructive interpretation of the six levels treats later capabilities as presupposing earlier ones: a retained contrast can support a relation, and a sufficiently organized set of relations can support a spatial readout. That is a possible functional architecture, not a claim that any arbitrary six operations automatically make a universe. The explanatory burden is to identify operations, retained memory and a completion condition together. When those ingredients are specified, inner time can acquire content through which partial histories it distinguishes and outer time through which records it exposes.

02The single-source and nested-time proposal

SMM begins with one nonspatial generative source. DTT distinguishes its inner production from the outer order in which completed results become accessible. The six inner levels are nested functional dependencies within that production; the seventh denotes outer completion. They are not six independent clocks, six spatial directions, or six simultaneously occupied temporal axes. This distinction makes the framework more specific than a general claim that everything changes: it asks how a world of persistent relations can be generated before its spatial representation is taken for granted. ^[2]

03The comparator’s explanatory structure

The two-state description conditions quantum probabilities on both an earlier preparation and a later successful selection. For an intermediate ideal projective measurement with projectors Pk, the ABL probability is proportional to |⟨f|Pk|i⟩|², normalized by the sum over outcomes. This is a precise boundary-conditioned rule. It does not introduce two independently readable clocks.

For example, prepare a qubit in |0⟩, later select |+⟩, and measure the z basis in between. The only nonzero intermediate contribution is k = 0, so its conditional probability is one. Measuring the x basis instead gives certainty for the plus outcome within the successfully selected ensemble. The difference concerns the specified measurement context. It does not mean that both incompatible outcomes existed as one ordinary classical record. The formalism’s time symmetry is a useful comparator for DTT’s production/completion distinction, but identifying postselection with ontological creation would require an additional argument and careful accounting of failed selections. ^[1]

04The precise agreement and difference

DTT’s inner and outer time refer to production and completion; the two-state formalism’s dual description refers to preparation and postselection around an intermediate quantum event. A later successful selection is not the same thing as the creation of an outer world. It is a condition defining a subset of experimental runs. Equating the two would confuse a physical boundary condition with an ontological claim about how events become actual.

There is nevertheless a useful bridge. A DTT completion instrument might specify which outcomes are retained, and its conditional probabilities could be compared with an ABL calculation for the same preparation, measurement and final selection. The comparison must include failed completions or rejected selections in the full probability accounting. Otherwise apparent unusual probabilities may be ordinary selection effects. The distinctive DTT question is why a particular completion instrument is generated by the source rather than chosen externally. The two-state formalism provides a sharp benchmark for that question while leaving the six nested levels and the origin of measured duration unexplained. ^[1]

05Worked example: what follows and what does not

Consider an idealized detector with a two-step preparation followed by registration. Its internal path is blank → armed → latched, while the public display changes only at the last transition. If the detector can be delayed while armed, the public record count remains unchanged even though the physical clock advances. Thus a completion count and a clock interval are independent measurements. If a proposed source law fixes their ratio without adjusting the detector separately, that is a substantive relation. If one simply defines a second time to be twice the first, the relation is a convention. The example is intentionally modest: it identifies what a dual-time mechanism must add beyond a two-stage description, without claiming that a laboratory detector is the Single Monad.

06What this comparison contributes

This makes the comparison answerable in a precise way. A framework may agree that events possess an internal explanatory structure while denying that this structure is temporal in the same sense as measured duration. It may also agree about record order while disagreeing about whether unrecorded possibilities already exist. The productive DTT contribution is to connect these questions through completion. Its strongest mathematical development would specify which differences among inner histories survive as different outer correlations, and which are unobservable descriptions of the same process.

THE SAME QUESTION, DIFFERENT STARTING POINTS

The comparison at a glance

Continue on SMONAD

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