A quantum logical alternative "Either non-measure preservation Or unitary evolution" exists in the framework of Schroedinger's theory. This explains irreversibility and allows to describe both time-symmetric and time-asymmetric processes in Hermitian quantum theory. The CPT and Noether's theorems remain valid in chronotopology. The Bohr-Einstein controversy, Wigner's conjecture and the Poincaré's non-recurrence are naturally explained. Extended numerical calculations correctly predict the CP- and T-symmetry violation coefficients |η2π0|, |ηπ±|, |ημ±|, |ηe±|, [Formula: see text] and their phase angles: arg (η)=ϕ2π0, ϕπ±, ϕμ±, ϕe± for the K0, [Formula: see text]-decays. A relationship is discovered between the mixing factor and the relevant matrix elements. The ratio "matter/antimatter" appears as temperature dependent in the Universe, antimatter decays prevailing at around T≥ 1024 Kelvin.
A quantum logical alternative "Either non-measure preservation Or unitary evolution" exists in the framework of Schroedinger's theory. This explains irreversibility and allows to describe both time-symmetric and time-asymmetric processes in Hermitian quantum theory. The CPT and Noether's theorems remain valid in chronotopology. The Bohr-Einstein controversy, Wigner's conjecture and the Poincaré's non-recurrence are naturally explained. Extended numerical calculations correctly predict the CP- and T-symmetry violation coefficients |η2π0|, |ηπ±|, |ημ±|, |ηe±|, [Formula: see text] and their phase angles: arg (η)=ϕ2π0, ϕπ±, ϕμ±, ϕe± for the K0, [Formula: see text]-decays. A relationship is discovered between the mixing factor and the relevant matrix elements. The ratio "matter/antimatter" appears as temperature dependent in the Universe, antimatter decays prevailing at around T≥ 1024 Kelvin.
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 fundamental equations of quantum mechanics are time-symmetric, yet measurements generate irreversible records and a one-way causal structure at macroscopic scales. The Quantum Time-Symmetric Interpretation (QTSI) explains this contrast as emergent rather than fundamental. Isolated quantum systems are described by a two-component temporal bispinor containing both forwardand backward-evolving amplitudes, coupled through a pseudo-Hermitian SU(1,1) Hamiltonian. Their coupling is governed by a mixing parameter Δ that depends on a macroscopic amplification fraction φ = N m /N t , where N t is the total number of relevant microscopic events and N m is the number that trigger irreversible macroscopic records. The associated retrocausal coherence time τ_RC = ħ/|Δ(φ)| is the characteristic timescale on which ψ+ and ψ− mix. As φ increases, τ_RC grows, temporal interference requires progressively longer times to form, and in the limit φ → 1 it becomes physically inaccessible. Δ vanishes, the two temporal sectors decouple dynamically, time symmetry is broken, and the system enters the irreversible classical regime. Standard quantum mechanics is recovered in this limit. The Born rule emerges naturally as ψ− → 0, since |ψ+ + ψ−|² reduces to |ψ+|² without any additional postulate. QTSI is a locally causal, ontologically realist, no-signaling interpretation: Bell correlations arise from time-symmetric global boundary conditions rather than nonlocal influences. Observable deviations from standard quantum mechanics are predicted in weakly monitored interferometric regimes, including the visibility formula V(φ) = V₀[1−exp(−T_av(1−φ)Δ₀/ħ)] — which decreases with monitoring fraction φ and reduces to V ≈ V₀(1−φ) for T_avΔ₀/ħ ≫ 1 — and a new three-slit signature in which the Fourier spectrum of the intensity pattern contains phase-coherent sum-phase peaks absent in standard quantum mechanics, whose Fourier amplitude scales as (1−φ) with the monitoring fraction.
We reconsider the model of quantum mechanics violation in the K0−K0 system, due to Ellis, Hagelin, Nanopoulos, and Srednicki, in which CP- and CPT-violating signatures arise from the evolution of pure states into mixed states. We present a formalism for computing time-dependent asymmetries in this model and show that present data constrains its parameters significantly. In the future, this model will be put to very stringent tests at a ø-factory. We present the theory of these tests and show the relation between particular ø-decay correlations and the parameters of quantum mechanics violation.
We establish the precise connection between the theoretical T, CP, CPT asymmetries, in terms of transition probabilities between the neutral meson B d states, and the experimental asymmetries, in terms of the double decay rate intensities for Flavour-CP eigenstate decay products in a B-Factory of entangled states. Genuine asymmetry parameters in the time distribution of the asymmetries are identified and their measurability analysed, disentangling genuine and possible fake terms. The nine asymmetry parameters – three different observables for each one of the three symmetries – are expressed in terms of the ingredients of the Weisskopf-Wigner dynamical description of the entangled B d -meson states and we obtain a global fit to their values from the BaBar Collaboration experimental results. The possible fake terms are all compatible with zero. The information content of the nine asymmetry parameters is indeed different. The non-vanishing and are impressive separate direct evidence of Time-Reversal-Violation and CP-Violation in these transitions (and compatible with Standard Model expectations). A 2σ effect for the Re(θ) parameter responsible of CPT-Violation appears; interpreted as an upper limit, it leads to eV at 95% C.L. for the diagonal flavour terms of the mass matrix. Finally, we consider scenarios where, in the presence of quantum gravity fluctuations (space-time foam), the CPT operator may be ill-defined. Its perturbative treatment leads to a modification of the Einstein-Podolsky-Rosen correlation of the neutral meson system by adding an Entanglement-weakening term of the wrong exchange symmetry, the ω -effect. The analysis is extended to identify how to probe the complex ω when the connection between the Intensities for the two time-ordered decays ( f, g ) and ( g, f ) is lost ( f flavour and g CP eigenstate decay channels), and how the ω -effect is disentangled from CPT violation in the evolution Hamiltonian.