Standard arguments against backward time travel typically rely on thermodynamic improbability orcausality paradoxes. In this note, we present a more fundamental barrier based on the operationaldefinition of internal time (clockability). We argue that, within systems capable of maintaining noncancelable internal registers, backward time travel is not merely dynamically forbidden, butoperationally ill-posed.Because clockability is defined by the irreversible accumulation of state differences, any operationintended to reverse the temporal coordinate would require the coherent erasure of the very registersthat define the system’s history. Such an operation forces the system outside its domain of validity,rendering the comparison between the “returned” system and any past state physically meaningless.This framework explains why time-reversal phenomena (e.g. spin echoes or recurrences) arerestricted to regimes lacking full clockability and establishes an informational no-go result formacroscopic temporal inversion.
This technical note introduces clockability as an operational criterion for assessing the validity of time-local descriptions in open quantum systems. While non-Markovian dynamics are commonly characterized through information backflow or violations of CP-divisibility, the structural conditions under which a temporal description remains operationally meaningful are rarely made explicit. This work reframes non-Markovianity not as a dynamical anomaly, but as a signal of local clockability breakdown: the failure of the environment to function as a stable register of persistent and locally accessible traces. Within this framework, CP-divisibility emerges as a sufficient condition for local clockability, whereas its violation marks the loss of applicability of time-local master equations rather than a failure of quantum dynamics itself. The note clarifies the relationship between divisibility-based and information-theoretic measures of non-Markovianity and motivates a hierarchical domain-of-validity analysis for temporal descriptions. No new physical mechanisms or mathematical formalisms are introduced. Instead, the work provides a diagnostic, information-theoretic perspective on when time-local representations (e.g., GKSL forms) are structurally justified, and when dynamical descriptions should be interpreted as non-local, history-dependent responses. This contribution is intended as a conceptual and methodological clarification relevant to quantum information theory, open quantum systems, and the operational foundations of time.
The concept of a global time is routinely employed across physics, from relativistic systems to quantum networks and distributed measurements. However, the operational conditions under which a global temporal ordering is physically meaningful are often left implicit. In this technical note, an operational criterion for the existence of a global time is provided, based on the comparability of internal temporal registers. While local time may be well defined in multiple subsystems, a global operational time exists if and only if their registers can be related through closed physical loops that allow verification of transitivity and stability. Classes of physically relevant systems are identified—such as entangled systems without classical comparison, distributed asynchronous networks, and regions separated by horizons—in which local clockability persists but global time becomes ill-posed. The result does not introduce new physics nor reinterpret existing theories, but clarifies the domain of validity of global temporal descriptions as an operational concept.
We establish two foundational results concerning time and irreversibility within an operational framework where physical measurements correspond to distinguishable, persistent record states. First, we prove that no physical clock can ground time as a fundamental parameter: any clock-induced ordering necessarily reduces to a preorder defined by reachability among record states via admissible transformations. Second, we prove that bounded recording capacity forces accessible irreversibility: any system capable of recording more distinct events than its accessible register capacity must exhibit non-invertible operations at the accessible level. These results are derived without assuming time, entropy, or thermodynamic principles as primitives. Together, they establish that temporal structure and irreversibility are not independent physical laws but emerge from operational constraints on physical memory and distinguishability. The framework is compatible with globally unitary microscopic dynamics while explaining effective irreversibility for bounded observers. We conclude that time is a representational index for record structure rather than an ontological primitive , establishing the necessary foundation for the failure of deterministic prediction addressed in companion work [3]
This technical note treats recent work on quantum signatures of proper time in optical ion clocks as an external stress reference for the Clockability cluster. The note does not propose a new theory of time, nor does it interpret quantum optical clocks as confirming Clockability. Instead, it distinguishes proper-time accumulation, physical clock readout, trace comparability, and temporal exportability as separate descriptive levels. Optical ion clocks are analyzed as temporal interfaces: finite physical architectures through which proper-time signatures become accessible under specific conditions of state preparation, motional structure, coherence, and readout. The aim is diagnostic only: to clarify how high-precision quantum-clock regimes make visible the distinction between local proper-time dynamics and the operational availability of temporal order.
We present a unified operational framework for the arrow of time grounded in irreversible information loss. While microscopic physical laws are time-reversal invariant, macroscopic irreversibility arises when systems overwrite metastable records. We show that recent reversible quantum-control experiments do not reverse time, but instead operate in regimes where no logically irreversible record is created. To formalize this, we introduce the **forgetting rate**
(Ξcr), a coarse-grained rate defined on physically selected metastable record states (e.g., pointer states, memory registers, or macroscopic configurations). Unlike standard entropy production, which is expressed in terms of microscopic transition asymmetry,
(Ξcr) captures the **rate of irreversible record overwriting**. In this formulation, entropy production obeys the lower bound
S˙irr≥kBΞcr,consistent with Landauer's principle but expressed at the level of record dynamics. Within this framework, thermodynamic, quantum-measurement, psychological, and cosmological arrows emerge as substrate-dependent manifestations of
Ξcr>0. Temporal asymmetry is therefore not a single global property, but a distributed feature of physical information-processing systems. The approach naturally explains the decoupling of arrows in composite systems and identifies experimentally accessible regimes where irreversibility can be locally suppressed. This work does not introduce a new microscopic law but provides a unifying, operational reformulation that connects information thermodynamics, decoherence theory, and memory dynamics through a single coarse-grained rate.
Abstract For decades, researchers have sought to understand how the irreversibility of the surrounding world emerges from the seemingly time-symmetric, fundamental laws of physics. Quantum mechanics conjectured a clue that final irreversibility is set by the measurement procedure and that the time-reversal requires complex conjugation of the wave function, which is overly complex to spontaneously appear in nature. Building on this Landau-Wigner conjecture, it became possible to demonstrate that time-reversal is exponentially improbable in a virgin nature and to design an algorithm artificially reversing a time arrow for a given quantum state on the IBM quantum computer. However, the implemented arrow-of-time reversal embraced only the known states initially disentangled from the thermodynamic reservoir. Here we develop a procedure for reversing the temporal evolution of an arbitrary unknown quantum state. This opens the route for general universal algorithms sending temporal evolution of an arbitrary system backward in time.