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arXiv:quant-ph/0012003 · The European Physical Journal D

Entangled quantum clocks for measuring proper-time difference

Won-Young Hwang, Doyeol Ahn, Sung Woo Hwang, Yeong Deok Han

Published Apr 1, 2002• 12 citations
arXivHTMLPDF
DOI
10.1140/epjd/e20020065

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Time as Record: Proper Time, Psychological Time, and Onto-Physical Entanglement: A CPT-Coherence Framework for Distinct Temporal Readout Regimes

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Time is not a single operational object. Laboratory time, relativistic proper time, biological timing, psychological duration, and coherence-depth structure play different roles and are accessed by different readout systems. This paper develops a theoretical framework for distinguishing these temporal regimes while identifying a common structural feature: each becomes physically or experientially meaningful only through a system capable of generating stable records of change. The starting point is quantum proper-time readout in optical ion clocks. In relativistic quantum clock experiments, proper time is not merely an external scalar parameter; it is inferred from an internal phase record whose visibility can be degraded when clock identity becomes entangled with motional history. Such systems provide a controlled physical example of time-as-record: the clock records elapsed proper time only insofar as its internal identity remains coherent under admissible evolution. We use this clock setting to introduce a broader distinction among four temporal objects: tlab, tprop, tpsych, TC. Here tlab is laboratory coordinate time, tprop is relativistic proper time recorded by physical clocks, tpsych is psychological time generated by cognitive and embodied record processes, and TC is the CPT-Coherence structural coordinate organizing admissibility, trace access, and stable observable descent. These quantities are not identical. The central thesis is not that psychological time is quantum proper time, nor that optical clocks measure consciousness or coherence depth. The thesis is narrower: proper time and psychological time are categorically distinct but structurally comparable as readout regimes. Within CPT-Coherence Theory, this comparison is organized by Onto-Physical Entanglement: what a system is cannot be separated from how it remains coherent under admissible transformation. In the clock case, identity persistence is measured by phase coherence and Ramsey visibility. In the cognitive case, psychological duration is modeled as a higher-level record produced by attention, interoception, memory, arousal, prediction, and event segmentation. The proposed object is not a single inner clock, but a cognitive readout functional: Reccog : embodied cognitive state history → (duration, ordering, temporal confidence, felt passage). This permits a disciplined analogy: proper time is physical clock-readout; psychological time is cognitive record-readout; coherence depth is the structural admissibility coordinate of the theory. The paper formulates a temporal-readout taxonomy, introduces record-stability witnesses for both physical and psychological timing, and specifies failure conditions that prevent the framework from collapsing into metaphor. The result is a falsifiable perspective: if psychological duration is a record-stability phenomenon, then distortions of subjective time should correlate not only with estimated duration, but also with measurable changes in attention, bodily-state integration, memory ordering, confidence, and event-boundary structure. Thus, the physics of proper-time readout does not explain psychological time directly; it supplies a rigorous model of how time becomes a record for an embedded system.

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The theory of relativity associates a proper time with each moving object via its world line. In quantum theory however, such well-defined trajectories are forbidden. After introducing a general characterisation of quantum clocks, we demonstrate that, in the weak-field, low-velocity limit, all ``good'' quantum clocks experience time dilation as dictated by general relativity when their state of motion is classical (i.e. Gaussian). For nonclassical states of motion, on the other hand, we find that quantum interference effects may give rise to a significant discrepancy between the proper time and the time measured by the clock. The universality of this discrepancy implies that it is not simply a systematic error, but rather a quantum modification to the proper time itself. We also show how the clock's delocalisation leads to a larger uncertainty in the time it measures – a consequence of the unavoidable entanglement between the clock time and its center-of-mass degrees of freedom. We demonstrate how this lost precision can be recovered by performing a measurement of the clock's state of motion alongside its time reading.
The theory of relativity associates a proper time with each moving object via its world line. In quantum theory however, such well-defined trajectories are forbidden. After introducing a general characterisation of quantum clocks, we demonstrate that, in the weak-field, low-velocity limit, all ``good'' quantum clocks experience time dilation as dictated by general relativity when their state of motion is classical (i.e. Gaussian). For nonclassical states of motion, on the other hand, we find that quantum interference effects may give rise to a significant discrepancy between the proper time and the time measured by the clock. The universality of this discrepancy implies that it is not simply a systematic error, but rather a quantum modification to the proper time itself. We also show how the clock's delocalisation leads to a larger uncertainty in the time it measures – a consequence of the unavoidable entanglement between the clock time and its center-of-mass degrees of freedom. We demonstrate how this lost precision can be recovered by performing a measurement of the clock's state of motion alongside its time reading.
Time is not a single operational object. Laboratory time, relativistic proper time, biological timing, psychological duration, and coherence-depth structure play different roles and are accessed by different readout systems. This paper develops a theoretical framework for distinguishing these temporal regimes while identifying a common structural feature: each becomes physically or experientially meaningful only through a system capable of generating stable records of change. The starting point is quantum proper-time readout in optical ion clocks. In relativistic quantum clock experiments, proper time is not merely an external scalar parameter; it is inferred from an internal phase record whose visibility can be degraded when clock identity becomes entangled with motional history. Such systems provide a controlled physical example of time-as-record: the clock records elapsed proper time only insofar as its internal identity remains coherent under admissible evolution. We use this clock setting to introduce a broader distinction among four temporal objects: tlab, tprop, tpsych, TC. Here tlab is laboratory coordinate time, tprop is relativistic proper time recorded by physical clocks, tpsych is psychological time generated by cognitive and embodied record processes, and TC is the CPT-Coherence structural coordinate organizing admissibility, trace access, and stable observable descent. These quantities are not identical. The central thesis is not that psychological time is quantum proper time, nor that optical clocks measure consciousness or coherence depth. The thesis is narrower: proper time and psychological time are categorically distinct but structurally comparable as readout regimes. Within CPT-Coherence Theory, this comparison is organized by Onto-Physical Entanglement: what a system is cannot be separated from how it remains coherent under admissible transformation. In the clock case, identity persistence is measured by phase coherence and Ramsey visibility. In the cognitive case, psychological duration is modeled as a higher-level record produced by attention, interoception, memory, arousal, prediction, and event segmentation. The proposed object is not a single inner clock, but a cognitive readout functional: Reccog : embodied cognitive state history → (duration, ordering, temporal confidence, felt passage). This permits a disciplined analogy: proper time is physical clock-readout; psychological time is cognitive record-readout; coherence depth is the structural admissibility coordinate of the theory. The paper formulates a temporal-readout taxonomy, introduces record-stability witnesses for both physical and psychological timing, and specifies failure conditions that prevent the framework from collapsing into metaphor. The result is a falsifiable perspective: if psychological duration is a record-stability phenomenon, then distortions of subjective time should correlate not only with estimated duration, but also with measurable changes in attention, bodily-state integration, memory ordering, confidence, and event-boundary structure. Thus, the physics of proper-time readout does not explain psychological time directly; it supplies a rigorous model of how time becomes a record for an embedded system.