Time reversal and temporal asymmetry: SMM/DTT and The two-state vector formalism

01The question behind the comparison

Reversing time in a physical theory means more than replacing a displayed t by −t. One must transform quantities such as velocities, momenta and angular momenta appropriately, and specify how the dynamics and boundary conditions behave. A process can obey a reversible law while occurring in an asymmetric state. DTT’s passage from inner generation to outer completion could represent a fundamental asymmetry, an effective loss of access, or a boundary-conditioned orientation. These are alternatives with different consequences, so a useful comparison does not treat the word irreversible as sufficient explanation.

A completed record is typically stable because many microscopic degrees of freedom support it. That stability need not make the total evolution noninvertible. If a system becomes correlated with an environment and the environment is ignored, the reduced description can lose visible coherence even when the joint dynamics preserves information. Reversing the reduced evolution is then difficult because the discarded correlations are needed. This offers a natural language for a completion interface, provided its environment and resource budget are included rather than absorbed into a metaphysical label.

The six nested levels can distinguish different forms of reversibility. An inner operation may be mathematically invertible, while an observer cannot access its inverse after completion. A higher level may retain enough information to reverse a lower operation, while the outer record omits that information. This hierarchy would support a precise account of apparent irreversibility. It would differ from a fundamental destructive update, which changes the theory’s allowed trajectories themselves. Both are intelligible, but only a specified model determines which description applies.

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 makes preparation and successful final selection enter a symmetric conditional description. It does not imply that the practical act of recording outcomes can be reversed by exchanging their names. DTT can contribute an explicit model of how the retained outcome becomes available, including the memory and environment that the conditional formula leaves outside its compact notation.

The comparison is particularly useful when discussing apparent retrocausality. Changing the selected final ensemble changes conditional statements about earlier outcomes; it does not by itself change the unconditioned earlier record available to an experimenter. A DTT completion model must preserve this distinction unless it proposes a quantitatively different law. The six nested levels would then need to determine the actual instrument and its probabilities, not just reinterpret a final boundary as inner time flowing backwards. The constructive achievement would be a unified account of coherent evolution, selection and irreversible record access. That is a substantive research direction even if the resulting statistics remain exactly those of ordinary quantum mechanics. ^[1]

05Worked example: what follows and what does not

Start with a qubit in (|0⟩ + |1⟩)/√2 and an environment in |e⟩. Let an interaction produce (|0⟩|e₀⟩ + |1⟩|e₁⟩)/√2, where the environment states are orthogonal. The qubit alone is then described by a diagonal density matrix with probabilities one half, because tracing over the environment removes the off-diagonal terms. The joint state remains pure. An inverse joint unitary can in principle restore the original superposition, whereas operations on the qubit alone generally cannot. This is an example of lost local access, not a proof that the universe has erased information. A physical DTT completion law can be compared with this explicit distinction.

06What this comparison contributes

An account of temporal asymmetry is strongest when it identifies the operation whose inverse fails, the information needed for reversal, and the observer for whom that information is unavailable. These questions also keep metaphysical becoming distinct from laboratory reversibility. A theory may affirm genuinely new actual events while retaining reversible equations for measurable correlations; whether that combination is coherent depends on its ontology and its rule for records, not on an isolated slogan about quantum mechanics.

THE SAME QUESTION, DIFFERENT STARTING POINTS

The comparison at a glance

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