Kent's final-measurement interpretation of quantum mechanics posits a single late-time measurement on the universe's quantum state whose Born-rule outcome selects, from something like a strongly decoherent set of histories, the one history that is actualized; an event occurs only if it leaves effective records in that final measurement. Adlam (2023, published 2026) argued heuristically that this selection mechanism explains the electromagnetic, thermodynamic, coarse-graining, fork, record, and cosmological asymmetries without a special low-entropy initial state, while explicitly acknowledging that the arguments are only heuristic. The open problem is to turn this account into a quantitative theory: define a formal measure of the robustness of generalized records and compute the probability that records survive to the final measurement; compute the Born-rule selection weightings over histories and derive — or refute — the dominance of entropy-increasing, record-forming histories without circular appeal to Landauer's principle or an assumed entropy gradient; model how dispersed microscopic records yield observable macroscopic records and forks; and assess whether expanding cosmologies are genuinely favored by the record-preservation constraint. No work constructing these models is known in the literature to date; the quantitative, non-circular core remains open.

Background

Physics exhibits several distinct temporal asymmetries: the thermodynamic asymmetry (entropy reliably increases), the electromagnetic asymmetry (waves are emitted and disperse but almost never converge onto a single absorber), the coarse-graining asymmetry (coarse-grained dynamics predicts forward but does not retrodict), the fork asymmetry (correlated events typically share a common cause in the past rather than a common effect in the future), the record asymmetry (detailed, reliable records exist of the past but not the future), and the cosmological asymmetry (the universe expands). The standard explanation is the past hypothesis: the postulate that the universe began in a specially low-entropy macrostate, from which the other asymmetries are derived. This explanation presupposes the time-evolution paradigm, in which the universe is a system evolving from an initial state and the initial state is the only place left to insert an asymmetry.

Kent's final-measurement interpretation of quantum mechanics (Kent 2014, 2015, 2017) offers a structurally different starting point. It is a realist, one-world, Lorentz-invariant proposal in which the universal quantum state evolves unitarily and, at the end of time, a single final measurement is posited whose outcome, selected with the ordinary Born-rule probabilities, fixes the real content of the world. The beables — the definite physical quantities, such as stress-energy tensor components at spacetime points — are computed as conditional expectation values given the selected outcome. In Kent's slogan, an event occurs if and only if it leaves effective records in the final measurement; where no end of time exists, the relevant probability distribution is defined by a limit as t→∞t\to\infty.

The mechanism relies on decoherence — the rapid spread of quantum correlations into the environment, which suppresses interference between macroscopically distinct alternatives — and on the consistent-histories formalism, in which a history is a chain of time-indexed projection operators and probabilities are assigned to sets of histories whose mutual interference terms vanish. A set of histories is strongly decoherent (Gell-Mann and Hartle 1995) when, at each step, subsequent projections are chosen from operators commuting with the generalized records of the history up to that point; generalized records are sets of orthogonal projections distinguishing the histories, whose physical picture is something like a photon or neutrino carrying the distinguishing information off to infinity and never interacting again. The final measurement therefore plausibly selects from something like a strongly decoherent set of histories, and this requirement is temporally asymmetric: it demands records oriented toward the final measurement.

Adlam (2023) argued heuristically that this selection mechanism by itself explains the observed temporal asymmetries and their alignment: histories in which events typically produce many widely dispersed, robust records — emission rather than convergent absorption, entropy increase, forward forks, forward records — are the histories most likely to belong to a strongly decoherent set, so the final measurement should select such a history, with no special low-entropy initial state required. The thermodynamic step cannot, however, simply invoke Landauer's principle (erasing one bit in an environment at temperature TT dissipates at least kTln⁡2kT\ln 2 of energy), because standard derivations of that principle presuppose an entropy-increasing universe (Ladyman et al. 2007; Maroney 2010), which would beg the question; Adlam instead links record dispersal to entropy via Maroney's characterization of entropy increase as the developed microscopic correlations becoming inaccessible to future evolution, but concedes the whole argument is informal. The paper explicitly contrasts its heuristic status with the quantitative development of past-hypothesis studies, offers only a toy counting argument for the conjecture that expanding cosmologies are favored because they allow records to persist (big-crunch-type recollapse would destroy them), and declares the general-relativistic extension — a final measurement on a Wheeler–DeWitt state (the wave function of the universe in canonical quantum gravity, which assigns amplitudes to entire spatial geometries rather than to configurations in a fixed spacetime) selecting between different spacetime geometries — beyond its scope, noting it would amount to constructing a novel theory of quantum gravity.

Problem Statement

Construct an explicit quantitative model — within Kent's final-measurement framework as fixed by its published postulates, or in a controlled, explicitly specified generalization of it — that replaces Adlam's heuristic selection arguments with calculation. The model must deliver, jointly and consistently:

  1. Record robustness and survival: a formal, computable measure of the robustness of a generalized record of an event, and a computation, for a realistic or controlled model system, of the probability that at least one record of each event in a candidate history survives undisturbed until the late-time final measurement (equivalently, is carried by a system that never interacts again).

  2. Selection weightings, non-circularly: a computation of the Born-rule selection probabilities of the final measurement over the (approximately) strongly decoherent set of histories, establishing or refuting that histories exhibiting the observed aligned asymmetries — in particular a prevailing coarse-grained entropy gradient — carry the dominant selection weight. The derivation of entropy-gradient dominance may not presuppose a thermodynamic gradient, a specially tuned low-entropy initial or final macrostate, or Landauer-type principles derived under an assumed entropy-increasing background; any such input must be replaced by a non-circular argument or accompanied by an explicit domain-of-validity statement.

  3. Micro-to-macro mapping: a model of how dispersed microscopic generalized records yield approximately local, observable macroscopic records and forward forks, specifying under what conditions such aggregates are determinants (conditions necessary and sufficient for the recorded event) rather than merely partial records.

  4. Cosmological selection: using the same selection machinery, an assessment of the conjecture that expanding cosmologies are favored by the record-preservation constraint — in particular, whether any contracting or recollapsing branches could also satisfy record preservation. For this component an assessment means a stated verdict on the conjecture — favored, refuted, or undetermined — with reasoning drawn from the selection machinery; a full cosmological computation is not required, but the verdict must state whether any contracting or recollapsing branch could also satisfy record preservation.

The common objective uniting these components is a quantitative, non-circular final-measurement account of the temporal asymmetries, capable of supporting — or refuting — empirical discriminants against past-hypothesis-based predictions, such as the statistics of rare anti-thermodynamic fluctuations or temporal variation in record robustness. Explicitly excluded, per the source's own delimitation: constructing the full general-relativistic/Wheeler–DeWitt final-measurement theory, which the source describes as in effect a novel theory of quantum gravity; simplified or fixed-background models suffice provided their relation to the framework's postulates is stated.

References

  1. Emily Adlam, "Disappearing Without a Trace: The Arrows of Time in Kent's Solution to the Lorentzian Quantum Reality Problem", arXiv:2305.13201 (2023), DOI 10.48550/arXiv.2305.13201, https://arxiv.org/abs/2305.13201
  2. Emily Adlam, "Disappearing Without a Trace: The Arrows of Time in Kent's Solution to the Lorentzian Quantum Reality Problem", The British Journal for the Philosophy of Science 77(2), 373–398 (2026), DOI 10.1086/726085, https://doi.org/10.1086/726085
  3. Adrian Kent, "Solution to the Lorentzian quantum reality problem", Physical Review A 90, 012107 (2014), DOI 10.1103/PhysRevA.90.012107, https://doi.org/10.1103/PhysRevA.90.012107
  4. Adrian Kent, "Lorentzian quantum reality: postulates and toy models", Philosophical Transactions of the Royal Society A 373, 20140241 (2015), DOI 10.1098/rsta.2014.0241, https://doi.org/10.1098/rsta.2014.0241
  5. Adrian Kent, "Quantum reality via late-time photodetection", Physical Review A 96, 062121 (2017), DOI 10.1103/PhysRevA.96.062121, https://doi.org/10.1103/PhysRevA.96.062121
  6. Murray Gell-Mann and James B. Hartle, "Strong Decoherence", arXiv:gr-qc/9509054 (1995), https://arxiv.org/abs/gr-qc/9509054
  7. Owen J. E. Maroney, "Does a Computer Have an Arrow of Time?", Foundations of Physics 40, 205–238 (2010; published online December 2009), DOI 10.1007/s10701-009-9386-6, https://doi.org/10.1007/s10701-009-9386-6
  8. James Ladyman, Stuart Presnell, Anthony J. Short, and Berry Groisman, "The connection between logical and thermodynamic irreversibility", Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38(1), 58–79 (2007), DOI 10.1016/j.shpsb.2006.03.007, https://doi.org/10.1016/j.shpsb.2006.03.007
  9. Jeremy Butterfield and Brendan Marsh, "Non-locality and quasiclassical reality in Kent's formulation of relativistic quantum theory", Journal of Physics: Conference Series 1275, 012002 (2019), DOI 10.1088/1742-6596/1275/1/012002, arXiv:1902.01294, https://arxiv.org/abs/1902.01294
  10. Charis Anastopoulos, "Final States in Quantum Cosmology: Cosmic Acceleration as a Quantum Post-Selection Effect", arXiv:2401.07662 (2024), DOI 10.48550/arXiv.2401.07662, https://arxiv.org/abs/2401.07662
  11. Aram Ebtekar and Marcus Hutter, "Modeling the Arrows of Time with Causal Multibaker Maps", Entropy 26(9), 776 (2024), DOI 10.3390/e26090776, https://doi.org/10.3390/e26090776
  12. Emily Adlam, "Saving Science from Quantum Mechanics", Oxford University Press (2025), DOI 10.1093/9780197808887.001.0001, https://doi.org/10.1093/9780197808887.001.0001