The Metrological Non-Constructibility of Time in Canonical Quantum Gravity
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2026
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| author | KOJIMA, TERUHITO |
| author_facet | KOJIMA, TERUHITO |
| contents | <p>The Wheeler–DeWitt (WDW) equation, ˆHΨ = 0, plays a central role in canonical quantum<br>gravity but lacks an explicit time parameter. This feature is traditionally diagnosed as the “prob<br>lem of time.” In this paper, developed within the Sequential Time Theory (STT) program, we<br>argue that the absence of a time parameter is not an anomaly but an inevitable structural con<br>sequence of time metrology. We define physical closure independently of time-theoretic concepts<br>and show that for a physically closed universe, the global external time-derivative operator ∂t is<br>non-constructible under STT metrological premises. The proof demonstrates that linear global evo<br>lution requires a calibration map common across the physical state space, which a closed universe<br>fundamentally lacks. Furthermore, we position relational time programs (e.g., Page–Wootters) and<br>semiclassical approaches as non-competing cases; these frameworks successfully reconstruct inter<br>nal conditional dynamics without defining a global external time. The timelessness of the WDW<br>equation thus emerges as a structural metrological consequence of enforcing physical closure upon<br>a state-independent calibration.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19180881 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Metrological Non-Constructibility of Time in Canonical Quantum Gravity KOJIMA, TERUHITO Wheeler-DeWitt equation problem of time canonical quantum gravity metrology of time relational time philosophy of physics Sequential Time Theory <p>The Wheeler–DeWitt (WDW) equation, ˆHΨ = 0, plays a central role in canonical quantum<br>gravity but lacks an explicit time parameter. This feature is traditionally diagnosed as the “prob<br>lem of time.” In this paper, developed within the Sequential Time Theory (STT) program, we<br>argue that the absence of a time parameter is not an anomaly but an inevitable structural con<br>sequence of time metrology. We define physical closure independently of time-theoretic concepts<br>and show that for a physically closed universe, the global external time-derivative operator ∂t is<br>non-constructible under STT metrological premises. The proof demonstrates that linear global evo<br>lution requires a calibration map common across the physical state space, which a closed universe<br>fundamentally lacks. Furthermore, we position relational time programs (e.g., Page–Wootters) and<br>semiclassical approaches as non-competing cases; these frameworks successfully reconstruct inter<br>nal conditional dynamics without defining a global external time. The timelessness of the WDW<br>equation thus emerges as a structural metrological consequence of enforcing physical closure upon<br>a state-independent calibration.</p> |
| title | The Metrological Non-Constructibility of Time in Canonical Quantum Gravity |
| topic | Wheeler-DeWitt equation problem of time canonical quantum gravity metrology of time relational time philosophy of physics Sequential Time Theory |
| url | https://doi.org/10.5281/zenodo.19180881 |