Curator's Take
AI Commentary
This paper shows that an observer’s “internal” quantum clock can be built directly from the information gained when a measurement record is created, assigning each outcome a duration equal to its surprisal (the negative log of its Born probability). By linking the accumulated clock to Shannon and Rényi entropies, the authors provide a unified framework that ties together decoherence, record stability, and the long‑standing multiple‑clock problem, echoing recent efforts in quantum thermodynamics to treat information as a physical resource. If these ideas can be harnessed experimentally, they could reshape how we think about timing, error correction, and resource accounting in future quantum processors, although the approach currently rests on idealized conditioning assumptions that will need careful validation.
— Mark Eatherly
Summary
We develop a record-based account of internal time in quantum mechanics, where the formation of a stable record is represented as conditioning on actualized information, and along a history the accumulated record algebras are ordered by inclusion. If the duration of a realized outcome depends only on its conditional Born probability, composes additively under sequential conditioning, and is continuous and calibrated, then the actualization of each outcome contributes an internal duration equal to its surprisal, the negative logarithm of that probability, so that a certain outcome contributes no duration, whereas less likely outcomes contribute larger increments. The ensemble mean of the accumulated clock is the Shannon entropy of the record process, its moment-generating function is fixed by the Rényi entropy spectrum, and the realized clock admits a Doob decomposition into a predictable entropic compensator and a martingale of clock fluctuations, so that each increment is the information gain of the corresponding actualization. Records are characterized by graded criteria of distinguishability, decoherence, and stability. We also clarify the multiple-clock problem: in one fixed context, additivity of two surprisal clocks is equivalent to factorization of the Born distribution in that context, whereas for a pure bipartite state, additivity in every pair of local contexts is equivalent to rank-one factorization of the joint state and to the vanishing of all its $2\times2$ minors.