2026/03/15 by Vahid Kamali · 1 voice
Physics and Astronomy · #physics.gen-ph
paper · pdf · doi:10.1140/epjc/s10052-026-15481-x
We develop a Heisenberg-picture kinematical framework in which (i) time is treated as a quantum observable, admitting both a relational POVM construction for semibounded spectra and a fully self-adjoint realization on an enlarged (conjugate-energy) Hilbert space enabled by a gravitational conjugation symmetry Cg, and (ii) the generators of spacetime translations need not commute in curved backgrounds. The central postulate, [ xμ,Pν ]=iℏ gμν(x), makes the spacetime metric a metric operator defined by the symmetrized commutator. Jacobi identities close the algebra and imply an operator form of metric compatibility; in a worked FRW example we obtain [ P0,Pi ]=2iℏ N2(t) H(t) Pi, which reduces to 2iℏ H Pi in cosmic-time gauge N=1, exhibiting Hubble--controlled non-commuting ``translations.'' A key structural ingredient is the symmetry Cg: an antiunitary map that flips all translation generators, Pμ → -Θ PμΘ-1, while covariantly transforming the metric and Lorentz sectors, leaving the canonical commutators and the [P,P] algebra invariant. We discuss uncertainty relations and show how metric-operator fluctuations can rescale primordial amplitudes; an explicitly labeled toy propagation of such a rescaling to high-z halo abundances is given in Appendix~D.