Time reversal and temporal asymmetry: SMM/DTT and McTaggart’s A-series and B-series

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

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 A-series describes an event’s passage through tensed positions, while physical time reversal transforms a dynamical history. These are different operations. Reversing a solution does not make the same event simultaneously past and future, and rejecting McTaggart’s argument does not establish that a Hamiltonian is time-reversal invariant. DTT’s completion language needs to keep the logical and dynamical questions separate.

An inner update might be invertible even though its completed output is described as irreversibly actual. This is coherent only if the ontology of actuality is distinguished from the recoverability of a physical state. If completion instead destroys accessible correlations, the model should identify whether the destruction is fundamental or due to restriction to a subsystem. McTaggart’s analysis then asks what the resulting asymmetry means for passage. The useful DTT contribution is a precise account of inverse operations and retained records; the philosophical claim that such operations constitute becoming requires an additional argument. Neither a reversed movie nor a new name for time can settle both issues at once. ^[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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