From time operator to chronons

Asao Arai

Pavol Šiška

Photoelectric Effect in a Discrete-Time (Chronon) Framework

Denis Waldemar Sánchez Michel

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.

Asao Arai

Zhiyong Wang, Cai-Dong Xiong

Erasmo Recami, Michel Zamboni‐Rached, Ignazio Francesco Licata

Aim of this paper is trying to show the possible significance, and usefulness, of various non-selfadjoint operators for suitable Observables in non-relativistic and relativistic quantum mechanics, and in quantum electrodynamics: More specifically, this work starts dealing with: (i) the hermitian (but not selfadjoint) Time operator in non-relativistic quantum mechanics and in quantum electrodynamics; with (ii) idem, with the introduction of Time and Space operators; and with (iii) the problem of the four-position and four-momentum operators, each one with its hermitian and anti-hermitian parts, for relativistic spin-zero particles. Afterwards, other physical applications of non-selfadjoint (and even non-hermitian) operators are briefly discussed. We mention how non-hermitian operators can indeed be used in physics [as it was done, elsewhere, for describing Unstable States]; and some considerations are added on the cases of the nuclear optical potential, of quantum dissipation, and in particular of an approach to the measurement problem in QM in terms of a "chronon". [This chapter is largely based on work developed, along the years, in collaboration with V.S.Olkhovsky, and, in smaller parts, with P.Smrz, with R.H.A.Farias, and with S.P.Maydanyuk]. PACS numbers: 03.65.Ta; 03.65.-w; 03.65.Pm; 03.70.+k; 03.65.Xp; 03.65.Yz; 11.10.St; 11.10.-z; 11.90.+t; 02.00.00; 03.00.00; 24.10.Ht; 03.65.Yz; 21.60.-u; 11.10.Ef; 03.65.Fd; 02.40.Dr; 98.80.Jk. Keywords: time operator, space-time operator, non-selfadjoint operators, non-hermitian operators, bilinear operators, time operator for discrete energy spectra, time-energy uncertainty relations, Klein-Gordon equation, chronon, quantum dissipation, decoherence, nuclear optical model, cosmology, projective relativity.