Time as a Quantum Observable Near the Planck Scale: Maximally Symmetric Extensions, Physical Chronon States, and Temporal Decoherence

We develop a theoretical framework in which time is treated as a quantum observable near the Planck scale. The Salecker-Wigner-Peres (SWP) bound renders classical temporal definiteness operationally undefined below the Planck time t_P ≈ 5.39×10⁻⁴⁴ s. We address the Pauli objection using Galapon's maximally symmetric time operator on a dense physical domain, and argue that the domain condition is physically motivated by the SWP bound. We identify physical chronon states as regularised Gaussian wavepackets proven to belong to this domain. A random-walk model on the Planck temporal lattice leads to an order-of-magnitude temporal decoherence estimate τ ~ (m_P/m)² t_P, giving ~30 s for the free electron and ~9 μs for the proton. These predictions are distinguishable from Diósi-Penrose and CSL models by their m⁻² scaling in the temporal degree of freedom and may be testable with current attosecond interferometry and ion-trap platforms.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-05-14
DOI
https://doi.org/10.5281/zenodo.20188130
Primary Topic
Quantum Mechanics and Applications
Type
preprint
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preprint

Time as a Quantum Observable Near the Planck Scale: Maximally Symmetric Extensions, Physical Chronon States, and Temporal Decoherence

Denis Waldemar Sánchez Michel
Zenodo (CERN European Organization for Nuclear Research)
Quantum Mechanics and Applications
preprint

Time as a Quantum Observable Near the Planck Scale: Maximally Symmetric Extensions, Physical Chronon States, and Temporal Decoherence

Denis Waldemar Sánchez Michel
preprint en

Abstract

We develop a theoretical framework in which time is treated as a quantum observable near the Planck scale. The Salecker-Wigner-Peres (SWP) bound renders classical temporal definiteness operationally undefined below the Planck time t_P ≈ 5.39×10⁻⁴⁴ s. We address the Pauli objection using Galapon's maximally symmetric time operator on a dense physical domain, and argue that the domain condition is physically motivated by the SWP bound. We identify physical chronon states as regularised Gaussian wavepackets proven to belong to this domain. A random-walk model on the Planck temporal lattice leads to an order-of-magnitude temporal decoherence estimate τ ~ (m_P/m)² t_P, giving ~30 s for the free electron and ~9 μs for the proton. These predictions are distinguishable from Diósi-Penrose and CSL models by their m⁻² scaling in the temporal degree of freedom and may be testable with current attosecond interferometry and ion-trap platforms.

Zenodo (CERN European Organization for Nuclear Research)
Peace, Justice and strong institutions
Quantum Mechanics and Applications
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