In this article
- The question behind the comparison
- The single-source and nested-time proposal
- The comparator’s explanatory structure
- The precise agreement and difference
- Worked example: what follows and what does not
- What this comparison contributes
Dual arrows of time: SMM/DTT and McTaggart’s A-series and B-series
McTaggart’s earlier/later relation distinguishes orientation without supplying a physical explanation of an arrow. His tensed ordering concerns passage, whereas DTT’s dual-arrow language can distinguish the functional direction toward completion from the historical direction of retained records. The comparison develops this distinction through a worked example and explains its implications for SMM/DTT’s nested generation, completed records and account of the observable world.
01The question behind the comparison
An arrow of time is an asymmetry with a specified meaning. A causal arrow concerns permitted influence; a thermodynamic arrow concerns typical entropy change; a psychological arrow concerns memory and anticipation. SMM/DTT adds a proposed generative orientation: production is organized toward completion, after which a result can participate in later records. These orientations can support one another, but their agreement is an explanatory question. A growing archive by itself says nothing about the entropy of the entire universe, and a time-symmetric microscopic law can still support asymmetric records when supplied with asymmetric conditions.
The phrase dual arrows is most useful when it names the relation between inner completion and outer succession. The inner orientation is functional: unfinished and finished configurations have different roles. The outer orientation is historical: a retained result can constrain later access. They need not be opposite vectors drawn on a plane. Drawing two arrows can obscure the real issue if no criterion identifies what reverses when an arrow is reversed. For example, reversing a movie reverses the displayed order, whereas unmaking its records would also require reversing changes in the storage device and environment.
The six nested levels locate completion inside a structured process. Nesting can explain why some operations depend on earlier achievements, but nesting alone does not establish irreversible dynamics. A perfectly reversible circuit also contains dependencies. A physical arrow can arise when a subsystem loses access to correlations, when a boundary state selects one orientation, or when a genuine noninvertible law is posited. These alternatives have different implications for energy, probability conservation and the possibility of recovering a previous state. DTT becomes sharper when it chooses between them in a particular model.
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 relation distinguishes orientation without supplying a physical explanation of an arrow. His tensed ordering concerns passage, whereas DTT’s dual-arrow language can distinguish the functional direction toward completion from the historical direction of retained records. The three notions should not be collapsed. Entropy could increase in a sequence described entirely with B-relations, and an A-theorist could imagine a world with a different thermodynamic history.
DTT adds a potentially useful mechanism when unfinished states cannot yet participate in later records but completed states can. This yields an asymmetric accessibility relation even before a thermodynamic interpretation is chosen. McTaggart’s challenge returns if this accessibility is described as itself becoming actual in an unexplained higher time. The constructive response is to define the relation within the model and state separately whether it constitutes objective passage. The comparison thus separates a demonstrable asymmetry of record dependence from a philosophical claim about the reality of becoming. Either can be investigated without pretending that it automatically proves the other. [1]
05Worked example: what follows and what does not
Take a memory initially in a known state 0 and a fair bit X. A reversible copy maps (X,0) to (X,X). Before copying, the two devices are uncorrelated; afterwards they share one bit of mutual information. No information has been erased in this ideal operation. The record points toward the earlier value because of the initially blank memory and the chosen interaction. Restoring only the memory to 0 is a different operation, with a thermodynamic cost under the usual erasure assumptions. This simple distinction shows how a record arrow can depend on preparation without proving a fundamental violation of time-reversal symmetry. It also shows why a source-memory budget belongs inside any physical completion model.
06What this comparison contributes
The promising connection is a derivation of aligned orientations from a shared source law and admissible boundary conditions. An inner stage count would then acquire meaning through its relation to records and entropy production, not through the appearance of an arrow in a diagram. The conceptual gain is already useful: it prevents the familiar experience of passage, the ordering of causes and the irreversible loss of accessible information from being silently treated as the same phenomenon.
THE SAME QUESTION, DIFFERENT STARTING POINTS
The comparison at a glance
| Question | SMM/DTT | McTaggart’s A-series and B-series |
|---|---|---|
| Explanatory starting point | The proposed generative arrow leads toward completion, while the record arrow depends on what later states retain about earlier events. | Tensed positions and fixed earlier/later relations classify events without specifying their physical production. |
| Key distinction | A completed record needs inherited correlations and memory resources; its existence alone does not prove microscopic time-reversal violation. | McTaggart’s earlier/later relation distinguishes orientation without supplying a physical explanation of an arrow. |
KEEP THE CONNECTION
Key ideas
- The proposed generative arrow leads toward completion, while the record arrow depends on what later states retain about earlier events.
- DTT adds a potentially useful mechanism when unfinished states cannot yet participate in later records but completed states can.
- A completed record needs inherited correlations and memory resources; its existence alone does not prove microscopic time-reversal violation.
Continue on SMONAD
- Temporal asymmetry: reading the published model →
Connects this comparison with the author’s discussion of arrows.
- Publication record: Dual-Time Topological Geometry and the Emergence of Temporal Asymmetry in Non-Equilibrium Dynamics →
Connects this comparison with the author’s discussion of arrows.
- The Principle of Ever-renewed Creation →
Connects this comparison with the author’s discussion of arrows.
- Renewal and persistence: why a changing world can keep a history →
Connects this comparison with the author’s discussion of arrows.
- Time Chest →
Connects this comparison with the author’s discussion of arrows.
Sources and further reading
References support the comparator and the specific mathematical or interpretive claims indicated. SMM/DTT connections are developed in the analysis above.
- J. E. McTaggart, The Unreality of Time (1908) ↗Primary philosophical argument: A/B ordering and the regress problem; our record examples are independent illustrations.
- Mohamed Haj Yousef, The duality-of-time postulate, SMONAD ↗Author’s presentation of SMM/DTT; source ontology and nested inner generation distinguished from outer completion.
How these comparisons distinguish premises, results and physical claims