The problem of the validity and interpretation of the energy-time uncertainty relation is briefly reviewed and reformulated in a systematic way. The Bohr-Einsteinphoton-box gedanken experiment is seen to illustrate the complementarity of energy andevent time. A more recent experiment with amplitude-modulated Mößbauer quanta yields evidence for the genuine quantum indeterminacy of event time. In this way, event time arises as a quantum observable.

An axiomatic framework for describing general space-time models is presented. Space-time models to which irreducible propositional systems belong as causal logics are quantum (q) theoretically interpretable and their event spaces are Hilbert spaces. Such aq space-time is proposed via a “canonical” quantization. As a basic assumption, the time t and the radial coordinate r of aq particle satisfy the canonical commutation relation [t,r]=±i $h =$ . The two cases will be considered simultaneously. In that case the event space is the (...) Hilbert space L2(ℝ3). Unitary symmetries consist of Poincaré-like symmetries (translations, rotations, and inversion) and of gauge-like symmetries. Space inversion implies time inversion. Thisq space-time reveals a confinement phenomenon: Theq particle is “confined” in an $h =$ size region of Minkowski space $\mathbb{M}^4$ at any time. One particle mechanics overq space-time provides mass eigenvalue equations for elementary particles. Prugovečki's stochasticq mechanics andq space-time offer a natural way for introducing and interpreting consistently such aq space-time andq particles existing in it. The mass eigenstates ofq particles generate Prugovečki's extended elementary particles. When $h =$ →0, these particles shrink to point particles and $\mathbb{M}^4$ is recovered as the classical (c) limit ofq space-time. Conceptual considerations favor the case [t,r]=+i $h =$ , and applications in hadron physics give the fit $h =$ ⋍2/5 fermi/GeV. (shrink)

The physical concept of locality is first analyzed in the special relativistic quantum regime, and compared with that of microcausality and the local commutativity of quantum fields. Its extrapolation to quantum general relativity on quantum bundles over curved spacetime is then described. It is shown that the resulting formulation of quantum-geometric locality based on the concept of local quantum frame incorporating a fundamental length embodies the key geometric and topological aspects of this concept. Taken in conjunction with the strong equivalence (...) principle and the path-integral formulation of quantum propagation, quantum-geometric locality leads in a natural manner to the formulation of quantum-geometric propagation in curved spacetime. Its extrapolation to geometric quantum gravity formulated over quantum spacetime is described and analyzed. (shrink)

Dirac's equation is reviewed and found to be based on nonrelativistic ideas of probability. A 4-space formulation is proposed that is completely Lorentzinvariant, using probability distributions in space-time with the particle's proper time as a parameter for the evolution of the wave function. This leads to a new wave equation which implies that the proper mass of a particle is an observable, and is sharp only in stationary states. The model has a built-in arrow of time, which is associated with (...) a restriction to positive-energy solutions. The usual solution for a Coulomb field is retained, though it now implies a slightly different charge distribution. The conventional nonstationary solutions become invalid. The new formulation appears to offer a resolution of difficulties that have been associated with Dirac's equation. It also predicts the occurrence of virtual pairs at a level that may be experimentally testable, and suggests a mechanism for self-cancellation of the vacuum energy. (shrink)