Dynamical time versus system time in quantum mechanics

Valia Allori

D. Arsenović, Nikola Burić, Dragomir M Davidović +1 more

Properties of an operator representing the dynamical time in the extended parameterization invariant formulation of quantum mechanics are studied. It is shown that this time operator is given by a positive operator measure analogously to the quantities that are known to represent various measurable time operators. The relation between the dynamical time of the extended formulation and the best known example of the system time operator, i.e., for the free one-dimensional particle, is obtained.

Erkki Brändas, Theodore E. Simos, George Maroulis

The old dilemma of quantum mechanics versus the theory of relativity is reconsidered via a first principles relativistically invariant theory. By analytic extension of quantum mechanics into the complex plane one may (i) include dynamical features such as time‐ and length‐scales and (ii) examine the possibility and flexibility of so‐called general Jordan block formations. The present viewpoint asks for a new perspective on the age‐old problem of quantum mechanics versus the theory of relativity. To bring these ideas together, we will establish the relation with the Klein‐Gordon‐Dirac relativistic theory and confirm some dynamical features of both the special and the general relativity theory.

Juan Gonzalo Muga, R. Sala Mayato, I. L. Egusquiza

Balázs, András

The symbol-matter problem of biological systems, posed clearly by H. H. Pattee, is followed up to its origin in a quantum mechanical framework. The two complementer descriptional mode (i.e. dynamical versus symbolic or quantum mechanical versus ''classical'') are defined as connected in a Copenhagen–type quasiclassical (h → 0) dynamics (internal time-dependent discrete projection operator formalism). The concept of natural symbol as constraint is described in the form of a quasiclassical wavefunction with classical measurement records as variables while the basic projectors are defined as a quasiclassical dynamical "bra" Hilbert vector acting on a quantum dynamical "ket" vector. The origin problem is touched necessarily upon, as a split between measurement record (so its quasiclassical wavefunction, natural symbol) and the quantum mechanical dynamical wavefunction. The concept of symmetry-restoring internal time process is introduced, following from compelling internal retrocausality of a time evolution (advocated several times elsewhere). While adopting basically the Copenhagen view, using some ideas of Everett and other aspects of non–orthodox formulations of quantum measurement, it is shown that the necessary imbedding of internal (-τ) time evolution into the split off external (+t) one and internal time ’’quantizations’’ (leading to a discrete total semigroup) results in a converging chain of quantum internal measurement transitions, similar to those introduced by H. P. Stapp in his symbolic (human mind-) model, ultimately leading to a model of an elementary, very special self-reproducing quantum automata, where the state transition functions are internally determined (programmed) from the very origin of their emergence. It is shown that only off-diagonal statistical matrix elements are to be used in the internal projectionally evoluting time–series (metabolism), ’’self’’-reproduction (diagonality) being the fixed point of the recursion of the internal state transitions of the proposed quantum mechanical automata model (’’metaphor’’).

Juan Gonzalo Muga, R. Sala Mayato, I. L. Egusquiza