Physical clocks and operational time: SMM/DTT and McTaggart’s A-series and B-series

01The question behind the comparison

A clock is a physical system whose changes provide a reproducible comparison with other changes. Its readings are not created by writing t in an equation. Oscillations, transitions and accumulated phases become clocks when a preparation, readout and calibration connect them with a measurable interval. SMM/DTT’s distinction between generative and observed time is therefore tested conceptually by asking what an embedded clock actually counts. If an outer clock is independent of the proposed inner dynamics, their ratio remains an additional assumption.

Operational time has several layers. A counter counts events. A phase tracks periodic evolution. A calibrated clock assigns units such as seconds. A relativistic clock measures proper time along its path. These descriptions can agree in a suitable regime while responding differently to noise, acceleration or changes in the underlying state. A generative theory must recover their agreement where established physics requires it. It should also explain why different clock technologies share the same spacetime dependence, rather than assigning each species its own completion rate.

The six nested levels are not six separate clocks that can be adjusted until a desired ratio appears. Their proposed role is to organize how a completed state becomes available. A successful clock law would derive a phase or counter response from that same source trajectory. Changing a refinement or branching parameter would then change geometry and timing in a linked way. If the oscillator frequency is retuned whenever the geometry changes, a numerical agreement demonstrates calibration freedom rather than a necessary physical relation. This is the decisive distinction between a constructive explanation and a convenient parametrization.

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

McTaggart distinguished tensed positions—past, present and future—from the relations earlier than and later than. His argument challenges the coherence of taking passage as a changing possession of incompatible temporal properties. For the comparison here, the distinction is a tool for asking what DTT’s completion adds to an ordered history. A sequence can be fully ordered without specifying which member is now present.

Consider a list of event labels A, B and C. The facts A precedes B and B precedes C do not change when a reader moves down the list. What changes is the reader’s relation to a particular entry. If a completion theory adds an objective change in actuality, it needs to say whether that change is another event, an irreducible feature of events, or a change in a meta-time. These alternatives expose the regress question without assuming that McTaggart’s conclusion is correct. His analysis is philosophical; it supplies no Hamiltonian, physical clock or information-processing mechanism. ^[1]

04The precise agreement and difference

McTaggart’s earlier/later ordering does not assign numerical durations. A clock adds a metric relation among changes, together with a physical procedure for reading it. DTT’s inner and outer counters therefore cannot be calibrated merely by calling one A-time and the other B-time. A tensed statement such as the clock reads noon now concerns the observer’s temporal relation to a reading, not the mechanism that produces the reading.

This separation gives DTT a concrete advantage if it can derive clocks from the same source dynamics that produces spatial records. It would explain more than an ordering of events. McTaggart’s categories remain useful because they ask whether the resulting numerical readings also establish passage or merely track relations in a history. They do not settle that issue. The productive result is a clock law with independently defined observables, followed by an explicit interpretation of the present. A ratio manufactured by rescaling an inner label answers neither the physical calibration question nor the philosophical problem of how a reading becomes present. ^[1]

05Worked example: what follows and what does not

An oscillator with angular frequency ω accumulates phase φ = ωτ. Its inferred interval is τ = φ/ω, once ω is independently calibrated. Suppose a source completes n records and a proposed inner counter reports u = 3n. An observed ratio u/n = 3 is exact, but it contains no seconds and says nothing about the oscillator phase. To conclude that a clock ratio is three, the source dynamics must establish how φ changes with n. Two models with φ = n and φ = 2n have the same record counts and different physical timing. This counterexample shows exactly why an additional transducer law matters.

06What this comparison contributes

A promising DTT explanation therefore uses clocks as outputs of the same theory that produces spatial relations. The result should be robust under changing the way a calculation is labelled and should state its domain of approximation. This operational standard does not diminish the philosophical distinction between production and observation; it gives that distinction a concrete route into physics. The most informative comparison asks which theory supplies the clock, which merely orders events, and which leaves the conversion from order to duration open.

THE SAME QUESTION, DIFFERENT STARTING POINTS

The comparison at a glance

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