The present and the becoming of the world: SMM/DTT and The thermal-time hypothesis

01The question behind the comparison

The present can mean an ontologically privileged reality, the event at which an observer is located, or the interval integrated into current experience. These meanings often overlap in ordinary speech but play different roles in a theory. SMM/DTT places outer completion at the transition between generative activity and accessible actuality. Its distinctive possibility is to explain the present through the constitution of records rather than take a moving instant as primitive. Whether this yields a universal present or only local completed events remains a further question.

A becoming theory must explain both novelty and continuity. If each completion is entirely independent, the world lacks inherited structure. If every completion is simply the unveiling of a fully fixed history, the theory may be closer to a block interpretation than its language suggests. DTT can articulate an intermediate construction in which lawful retained memory constrains new completions without making earlier physical tokens persist unchanged. The present would then be a dynamically sustained interface between inherited relations and newly accessible events. The proposal gains content through its memory rule.

The six inner levels belong within that interface. They are not six past moments traversed before reaching a seventh ordinary moment. Nesting expresses how the capacities required for a completed observable world depend on one another. A reader should therefore distinguish a symbolic diagram of completion from a physical claim about how long the present lasts. Neither the duration of conscious experience nor the resolution of an atomic clock follows from the number of nested roles. Those quantities require separate models of observers and physical clocks.

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

Connes and Rovelli propose that an algebra of observables together with a state can determine a temporal flow. In a finite faithful-state illustration, write K = −ln ρ and let observables transform as A(s) = exp(isK)Aexp(−isK). The parameter s is dimensionless. If ρ is a Gibbs state proportional to exp(−βH), then K differs from βH only by a scalar, so s can be related to ordinary Hamiltonian time by t = ℏβs in this convention.

This example explains both the power and the limitation of the comparison. Time need not be an independently supplied universal background, but the observable algebra and state are already doing essential work. A maximally mixed finite state gives a scalar K and hence trivial flow on that full matrix algebra. Different physical states can therefore select different flows. The thermal-time programme is not a claim that every microscopic event dissipates heat, nor does modular evolution alone constitute a thermodynamic arrow. DTT asks the further question of how the relevant state, algebra and accessible records are generated. ^[1]

04The precise agreement and difference

Thermal time provides a state-dependent flow, but a flow does not by itself select a privileged present. Every value of its parameter can label an event without one value being ontologically special. DTT’s outer completion therefore supplies a different kind of concept: the threshold at which a result becomes a usable record. A bridge between them needs both a flow and a rule for actuality or access.

A source-generated state could determine a modular clock while a completion condition determines which events the observer can register. This would make the experienced present an interface within an otherwise continuous flow. The model must explain why that interface occurs where it does and how it changes when the accessible state changes. The six inner levels may organize the prerequisites, but their existence is not a derivation of a universal now. The comparison identifies a productive division of labor: thermal time clarifies how temporal flow can arise from physical organization, while DTT investigates how organized production yields completed events within that flow. ^[1]

05Worked example: what follows and what does not

Imagine a ledger that records a sequence of transactions. At stage n it contains a stable history and a pending transaction whose validity depends on that history. At stage n+1 the transaction is accepted and can constrain later entries. The ledger’s current accepted state is a precise analogue of a completion boundary. Yet the analogy leaves open whether the future ledger already exists, whether old physical pages remain, and whether acceptance takes a definite duration. These are additional ontological or physical commitments. The example shows both the appeal and the limitation of identifying the present with completed accessibility.

06What this comparison contributes

The comparison becomes productive when it asks what a present does in the theory. Does it select what exists, what can cause later records, or what an observer can currently know? DTT has an unusually direct route to the second and third questions because completion and retention are central to its vocabulary. A successful account of the first would require a coherent ontology of uncompleted possibilities and of the past. This division allows philosophical ambition and operational precision to reinforce one another.

THE SAME QUESTION, DIFFERENT STARTING POINTS

The comparison at a glance

Continue on SMONAD

• What is Time? →

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• The Principle of Ever-renewed Creation →

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• Observer and record: making observation part of the model →

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• Duality of Time Theory →

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