Simultaneity and completed records: SMM/DTT and The two-state vector formalism

01The question behind the comparison

Two events being available in one record does not imply that they happened simultaneously. A photograph can combine light emitted at different times; an archive can collect reports made in different places; a later observer can compare events that were never in causal contact. DTT’s outer completion is most naturally understood first as availability of a record. Identifying it with a universal simultaneous present would be a further physical claim, requiring a synchronization rule and an account of its relation to relativity.

Relativistic simultaneity is defined relative to a chosen inertial frame for spatially separated events. Local coincidence is different: two clocks meeting at one event can compare readings without convention about distant simultaneity. A source-based theory may contain a deeper ordering, but if that order selects an observable preferred frame it has physical consequences. If it never affects any observable, it functions as underlying explanatory structure. Keeping these alternatives distinct prevents a metaphysical unity of source from silently becoming an absolute laboratory time.

The six nested inner levels concern the formation of accessible relations and do not automatically supply six hypersurfaces or a seventh global slice. Nesting is a dependency structure. A completion relation might instead form a partial order, allowing some records to be incomparable until a later interaction combines them. Such a construction could preserve the difference between local causal precedence and frame-dependent order at a distance. The positive DTT question is then how a common source produces a consistent network of local records without requiring every observer to share one instantaneous world-picture.

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

The two-state formalism uses preparation, intermediate measurement and final selection in a specified protocol. These stages can be causally ordered without assigning every distant event a universal time. DTT’s outer completion can be compared with a final retained record, but the record’s completeness does not make all events summarized in it simultaneous. This distinction is essential in relativistic experiments.

A useful DTT model would define local instruments and show how their jointly retained outcomes remain consistent across admissible descriptions of the protocol. If a postselected ensemble is used, the later information identifying successful runs must be included in the account of access. An observer who lacks that information has different conditional knowledge, not a different earlier event generated by personal awareness. The comparison therefore links completion with operational availability while resisting an unwarranted global present. The six nested inner levels become relevant if they determine the allowed record network or its quantum correlations; they do not by themselves choose a simultaneity convention for spatially separated measurements. ^[1]

05Worked example: what follows and what does not

In an inertial frame, let two events be simultaneous and separated by distance L along x: Δt = 0 and Δx = L. A second frame moving at speed v assigns Δt′ = −γvL/c², with γ = 1/√(1−v²/c²). Unless v or L vanishes, the events are not simultaneous in that frame. Their eventual inclusion in the same notebook does not change this result. For timelike-related events, however, all inertial frames preserve their causal order. A DTT record relation should therefore distinguish causal ancestry from the order imposed by a particular display or coordinate system.

06What this comparison contributes

This yields a useful design principle for comparisons: shared source, shared information and shared simultaneity are three different claims. The first concerns ontology, the second communication or correlated access, and the third spacetime conventions or structure. A rigorous completion theory could explain why local observers agree when their records overlap while legitimately disagreeing about distant simultaneity. That would connect unity with the observed plurality of perspectives in a mathematically meaningful way.

THE SAME QUESTION, DIFFERENT STARTING POINTS

The comparison at a glance

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