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 The two-state vector formalism
The ABL rule is symmetric in the use of preparation and final selection, while an ordinary laboratory record has an asymmetric history of preparation, interaction and storage. 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
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 ABL rule is symmetric in the use of preparation and final selection, while an ordinary laboratory record has an asymmetric history of preparation, interaction and storage. DTT’s dual arrows can clarify this difference between a boundary-conditioned description and an actual record-producing procedure. Symmetry of a probability formula does not make the laboratory’s memory resources symmetric.
A DTT model might assign inner generation to the coherent process and outer completion to the retained outcome, but postselection would still be a separate condition on which outcomes enter the analysis. If a future selection changes the conditional probability of an earlier measurement, that is not automatically an influence that can send a message into the past. The full unselected statistics and the availability of the selection information must be tracked. The useful contribution is a transparent account of how a time-symmetric amplitude description coexists with asymmetric accessibility. The six nested levels become relevant only if they determine a specific completion instrument or memory law rather than repeat the two-boundary terminology. [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 | The two-state vector formalism |
|---|---|---|
| Explanatory starting point | The proposed generative arrow leads toward completion, while the record arrow depends on what later states retain about earlier events. | Earlier preparation and later selection define conditional quantum statistics in a specified protocol. |
| Key distinction | A completed record needs inherited correlations and memory resources; its existence alone does not prove microscopic time-reversal violation. | The ABL rule is symmetric in the use of preparation and final selection, while an ordinary laboratory record has an asymmetric history of preparation, interaction and storage. |
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.
- A DTT model might assign inner generation to the coherent process and outer completion to the retained outcome, but postselection would still be a separate condition on which outcomes enter the analysis.
- 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.
- Y. Aharonov, P. G. Bergmann and J. L. Lebowitz, Time Symmetry in the Quantum Process of Measurement (1964) ↗Original pre/postselection probability rule; neither hidden six-level dynamics nor controllable backwards signalling follows from it.
- 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