A new conception of time is presented in the framework of the quantum generalized stochastic and infinitely divisible fields. A non-unitary evolution operator lacking the continuous group property is derived from a time-reversal-invariant field theory in Minkowski's space. It describes the arrow of time on the quantum level. By quantizing the field action integral the usual evolution operator is obtained as a particular case. Quantum processes violating the T-symmetry are possible in the present theory. It is also explained why Born's interpretation of the wave function is necessary. The Feynman path integral is obtained as the limit of a series of similar integrals with finitely additive measures. This form of the Feynman integral does not conflict on the quantum level Heisenberg's Uncertainty Principle.
A new conception of time is presented in the framework of the quantum generalized stochastic and infinitely divisible fields. A non-unitary evolution operator lacking the continuous group property is derived from a time-reversal-invariant field theory in Minkowski's space. It describes the arrow of time on the quantum level. By quantizing the field action integral the usual evolution operator is obtained as a particular case. Quantum processes violating the T-symmetry are possible in the present theory. It is also explained why Born's interpretation of the wave function is necessary. The Feynman path integral is obtained as the limit of a series of similar integrals with finitely additive measures. This form of the Feynman integral does not conflict on the quantum level Heisenberg's Uncertainty Principle.
A new, physical definition of the time elements is mathematically given. Their union constitutes a disconnected time topological space, [Formula: see text]. Based on the properties of this time–space and using the theory of random quantum fields previously developed, a nonunitary evolution operator, [Formula: see text], is derived. [Formula: see text] breaks down into two disjunct, spontaneously renormalized evolution operators by quantizing the random field action integral: one operator is unitary, [Formula: see text], and the other non-measure-preserving, [Formula: see text]. [Formula: see text] coincides, apart from the renormalization, with the evolution operator of the standard QFT. U ump (τ) breaks time symmetry in QFT. It reconciles the time reversal invariance of the basic equations of quantum theory with the irreversibility of the macroscopic, and some microscopic, phenomena. It provides a basis for the CP violation in the neutral K0 meson decay. Functional integrals arising in the theory have in the limit countably additive measures.
The principles of a random quantum theory (R-QT) which is alternatively time-asymmetric or time-symmetric if the quantization is Fermi–Dirac or Bose–Enstein, respectively are presented. Bohr's quantization rule is applied on the field-action integral. A time topological space, [Formula: see text], is mathematically defined in which the paradoxes in standard quantum theory are solved. The time "quantum", is created as a regular, positive into-map of an observed observable's change resulting from a fundamental interaction process. [Formula: see text] is constructed as the union of time elements and can be embedded disconnectedly in the continuous Newtonian universal time, [Formula: see text]. Six axioms are formulated characterizing the space–time and R-QT. The disconnectedness of the (κ×λκ)-fold time-space, [Formula: see text], imparts a kind of disconnectedness to the κ×λκ-fold space–times, [Formula: see text], and induces the chrono-topology. In chrono-topology the unitary, U, or non-measure preserving, R, dynamics, is implemented by means of a time evolution, "complex" operator, [Formula: see text]. It breaks down by means of Bohr quantization into: [Formula: see text][Formula: see text] coincides formally — apart from the spontaneous renormalization — with the time evolution operator in the standard QFT. [Formula: see text] is a novum and produces the Maxwell–Boltzmann energy level distribution in a non-Euclidean QFT. Compatibility between time-reversal invariance of the standard QT equations and irreversibility of some phenomena both in microcosmos and macrocosmos is obtained. The [Formula: see text]-evolution leads to a time's arrow on quantum-scale systems.
Time-asymmetric evolution is derived from time-reversal invariant fundamental QFT-equations. Chrono-topology, the disconnected time topological space J4, is the playground for the generalized random and infinitely divisable quantum fields, a new development in time-asymmetry. Based on the properties of this time space and using the theory of random quantum fields previously developed a non-unitary, complexity evolution operator, C(J4), is derived. C(J4) breaks down, by Bohr- quantizing the field-action integral, alternatively into two, spontaneously renormal- ized parts: One, (unitary) Uu(r), implying U - processes and one (non-measure- preserving), Knmp(r), producing R - processes. Unmp(r), breaks time-symmetry and provides a basis for CP-violation in QFT and in particular in the K0-meson decay. Functional integrals arising in the theory have as a limit Feynman's path integral in accordance with the measure theoretical requirements. Irreversibility and time-symmetry are not incompatible (compare Boltzmann, Poincaré) in chrono-topology.
The laws of classical mechanics and quantum theory do not distinguish between the past and the future. But a lot of phenomena tell us that the "arrow of time" points only in one direction. For example, in biology we discover evolutionary processes leading to diversification and increasing complexity; it is a typical feature of such evolutionary processes that "forward" in time is possible but "backward" in time is impossible. At what level can phenomena like these be described? There is another problem in connection with time: within usual quantum theory, space-coordinates and time are not symmetrical to each other, which is in contrast to the basic results of special theory of relativity. In usual quantum theory coordinates are operators and play the role of statistical quantities; time however does not behave statistically and remains a simple parameter when we go from classical to quantum mechanics. For this reason there is no uncertainty relation for the time and energy within usual quantum theory which would agree in its physical content with that for the coordinates and momenta. The purpose of this paper is to show, on the basis of new aspects, that both one-sidedness of time and its uncertainty are charateristics at the fundamental level of quantum theory. We have extended usual quantum theory on the basis of space-time arguments. In this connection a time-operator appeared and there is in general temporal asymmetry at the microscopic level. The picture might be important in the description of phenomena with an "arrow of time", i.e., processes which belong to the physics of becoming. Furthermore, we have derived an uncertainty relation for the energy and time which agrees in its physical content with the uncertainty relation for the momentum and the coordinate; this relation is different from that of usual quantum theory. Within the frame of this physical picture all the concepts (diversity, natural selection, mutation), which are presently used in connection with the evolution of biological systems, are already established at the quantum mechanical level and, therefore, our theoretical picture might also be the foundation for the explanation of the phenomena at the biological (macro-molecular) level.
Abstract Based on the hypothesis that the (non-reversible) arrow of time is intrinsic in any system, no matter how small, the consequences are discussed. Within the framework of local quantum physics it is shown how such a semi-group action of time can consistently be extended to that of the group of spacetime translations in Minkowski space. In presence of massless excitations, however, there arise ambiguities in the theoretical extensions of the time translations to the past. The corresponding loss of quantum information on states upon time is determined. Finally, it is explained how the description of operations in classical terms combined with constraints imposed by the arrow of time leads to a quantum theoretical framework. These results suggest that the arrow of time is fundamental in nature and not merely a consequence of statistical effects on which the Second Law is based.
The formalism of Quantum Mechanics is based by definition on conserving probabilities and thus there is no room for the description of dissipative systems in Quantum Mechanics. The treatment of time-irreversible evolution (the arrow of time) is therefore ruled out by definition in Quantum Mechanics. In Quantum Field Theory it is, however, possible to describe time-irreversible evolution by resorting to the existence of infinitely many unitarily inequivalent representations of the canonical commutation relations (ccr). In this paper I review such a result by discussing the canonical quantization of the damped harmonic oscillator (dho), a prototype of dissipative systems. The irreversibility of time evolution is expressed as tunneling among the unitarily inequivalent representations. The exact action for the dho is derived in the path integral formalism of the quantum Brownian motion developed by Schwinger and by Feynman and Vernon. The doubling of the phase-space degrees of freedom for dissipative systems is related to quantum noise effects. Finally, the role of dissipation in the quantum model of the brain and the occurrence that the cosmological arrow of time, the thermodynamical one and the biological one point into the same direction are shortly mentioned.