One consequence of dropping the (heretofore unjustified) "reduction postulate" of orthodox quantum mechanics is that even if one measures the values of a complete set of commuting operators belonging to a system at any particular time, one cannot calculate the probability of a state of the system very far in the future or in the past. Quantum cosmology is affected by this.
One consequence of dropping the (heretofore unjustified) "reduction postulate" of orthodox quantum mechanics is that even if one measures the values of a complete set of commuting operators belonging to a system at any particular time, one cannot calculate the probability of a state of the system very far in the future or in the past. Quantum cosmology is affected by this.
It is well known, that the causal Schrödinger evolution of a quantum state is not compatible with the reduction postulate, even when decoherence is taken into account. The violation of the causal evolution, introduced by the standard reduction postulate distinguishes certain systems (as the measurement devices), whose states are very close to statistical mixtures (as the ones resulting from the process of decoherence). In these systems, this violation has not any observable effect. In arbitrary quantum systems, the transition from the initial density matrix to a diagonal matrix predicted by the standard reduction postulate, would lead to a complete breakdown of the Schrödinger evolution, and consequently would destroy all the predictive power of quantum mechanics. What we show here, is that there is a modified version of the postulate that allows to treat all the quantum mechanical systems on equal footing. The standard reduction postulate may be considered as a good approximation, useful for practical purposes, of this modified version which is consistent with the Schrödinger evolution and via decoherence with the experimental results. Within this approach, the physical role played by the reduction postulate is as a tool for the computation of relative probabilities and consequently for the determination of the probabilities of consistent histories.
A well-known, classical conundrum, which is related to conditional probability, has heretofore only been used for games and puzzles.It is shown here, both empirically and formally, that the counterintuitive phenomenon in question has consequences that are far more profound, especially for physics.A simple card game the reader can play at home demonstrates the counterintuitive phenomenon, and shows how it gives rise to hidden variables.These variables are "hidden" in the sense that they belong to the past and no longer exist.A formal proof shows that the results are due to the duration of what can be thought of as a gambler's bet, without loss of generalization.The bet is over when it is won or lost, analogous to the collapse of a wave function.In the meantime, new and empowering information does not change the original probabilities.A related thought experiment involving a pregnant woman demonstrates that macroscopic systems do not always have states that are completely intrinsic.Rather, the state of a macroscopic system may depend upon how the experiment is set up and how the system is measured even though no wave functions are involved.This obviously mitigates the chasm between the quantum mechanical and the classical.
In classical probability theory, the best predictor of a future observation of a random variable X, is its expected value EP[X] when no other information is available When information consisting in the observation of another random variable Y is available, then the best predictor of X is another random variable EP[X∣Y]. It is the purpose of this note to explore the analogue of this in the case of quantum mechanics. We shall see that exactly as in classical prediction theory, when the result of an observation is taken into account by means of a non-commutative conditional expectation, some of the usual paradoxes cease to be such.
The χ-spectral framework developed in this work proposes a unified operator-geometric foundation for physical law, integrating quantum measurement, modular state reduction, spectral geometry, and gravitational curvature into a single postulated structure. Physical measurement is formulated as an intrinsic operator-spectral transition generated by the bounded observable M_χ(k) = Φ_χ(k) + B_χ(k) + R_χ(k), which combines phase geometry, boundary tension, and χ-spectral curvature into a non-singular measurement mechanism. Probability amplitudes P_n(k) = |<e_n(k), Ψ_χ>_χ|^2 follow from the postulated χ-inner product structure, reproducing the Born rule within the framework — not as an independent axiom, but as a consequence of the postulated positive-definite inner product geometry. A central claim of the χ-spectral framework is the postulated compatibility between ZEBTS-SUPER gravitational dynamics and quantum mechanics. Gravitational curvature R_χ(k) enters the measurement operator M_χ(k) as a bounded geometric observable, postulated to ensure ultraviolet stability, finite expectation values, and unitarity across all scale layers. Collapse dynamics are formulated as bounded modular projections, postulated to guarantee non-perturbative, divergence-free state reduction. Decoherence is modeled as a structural spectral gradient D_χ(k) = M_χ(k+1) - M_χ(k), providing a proposed geometric mechanism for coherence loss without environmental reservoirs. The scale-layer commutator C_χ(k) = [M_χ(k+1), M_χ(k)] encodes contextuality and order-dependence as structural consequences of χ-operator geometry. Together, these results demonstrate that quantum dynamics, gravitational curvature, measurement theory, and modular collapse are postulated to be compatible and mutually reinforcing within the χ-spectral operator framework. The theory is designed to achieve mathematical closure: all physical observables are postulated to remain bounded, all transitions are postulated to remain unitary, and quantum-gravitational consistency is proposed as a consequence of χ-spectral geometry. The framework is a system of postulates whose scientific value lies in its falsifiable predictions (§7), not in proven closure.
In relativistic mechanics the time-like vector characterize the motion in spacetime with speed faster than the speed of light in vacuum c in which the line element ds2=c2dt2-dx2-dx2-dz2 is less than zero (where is infinitesimal change in time, and are infinitesimal change in space), thus the time in relativistic mechanics can instantaneously flow [1], however in quantum mechanics although the time is treated as unobservable parameter (without any Hermitian observable operator have engine-value equivalent to time) any two physical quantity described by two non-commuting observable operatorsand fulfill , the knowledge of one immediately produce the knowledge of the other [2], thus in quantum mechanics if two particles interacted in finite temporal epoch and then separated in space the gaining of knowledge by the local measurement of physical quantity runs on one them (for example the measurement of spin direction of one particle using Stern-Gerlach experiment) immediately produce the knowledge of the complementary physical quantity of the other particle (for example the opposite spin direction of the other particle), this simply called quantum entanglement the concept that so much advanced after publication of the Jon Bell’s 1964 celebrated paper [3] in which he illustrated that we can add parameters to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, and then he conclude “there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously so that such a theory could not be Lorentz invariant”. The question now what these signals that can propagate instantaneously? The answer in this paper will be the time signals field which is defined for each constituent matter particle M and at each space point P as the measure of the total length of all occupation and leaving epochs of P by M which is representing a sequence function compactly supported only at the space point occupied by it and indexed by the number of occupation epochs of P by M, thus the flow of this time signal field from the far future to near future through the present to the near past to the far past inferable by the flow of matter particles constituting the system(such as sun, moon earth and clocks hands). Thus the present will represent in this paper a local absolute feature of time signals field defined at each space point as the set of all occupation epochs of it by matter particle, however the past and future will represent relativistic non-local features of the time signal field defined at each space point as a set of all leaving epochs between each two sequential occupation epochs, so the future after one occupation epoch is representing a past of the next one. Thus according to current representation of time, the two Mc-Taggard’s A and B series of time [4] will exist together as temporal set and then the time is real, the A-series in current theory is a set of all occupation and leaving epochs of space point by the matter particle that is consisting of the present, past and future epochs, and the B-series is the set of all leaving epochs of space points between each two sequential occupation epochs which are taking position before or after the discrete occupation epochs between them and then before or after each other.