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1.
We introduce a model with a set of experiments of which the probabilities of the outcomes coincide with the quantum probabilities for the spin measurements of a quantum spin-
particle. Product tests are defined which allow simultaneous measurements of incompatible observables, which leads to a discussion of the validity of the meet of two propositions as the algebraic model for conjunction in quantum logic. Although the entity possesses the same structure for the logic of its experimental propositions as a genuine spin-
quantum entity, the probability measure corresponding with the meet of propositions using the Hilbert space representation and quantum rules does not render the probability of the conjunction of the two propositions. Accordingly, some fundamental concepts of quantum logic, Piron-products, classical systems and the general problem of hidden variable theories for quantum theory are discussed. 相似文献
2.
Geoffrey Hemion 《International Journal of Theoretical Physics》1990,29(12):1335-1368
The role of probability theory in classical physics is examined. It is found that the probabilities for the outcomes of typical experiments depend strongly on the assumed behavior of given classical models at infinity. A discrete classical model is introduced and it is shown that the resulting probabilities are similar to those in the usual theory of quantum mechanics. 相似文献
3.
Sudzhit Basu 《Russian Physics Journal》1982,25(10):956-960
A unique linear rule of constructing quantum operators defined by the probability operator
for coordinates and momenta, is considered.
is assumed to be a normalized, positive definite operator, establishing a dynamical correspondence between the classical and quantum Poisson brackets. It is shown that such an operator exists in the case of a harmonic oscillator. The principal implications of the suggested rule of constructing the operators of physical quantities are determined, in comparison with the corresponding results of conventional quantum mechanics.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 89–93, October, 1982. 相似文献
4.
Kolmogorov's theory of probability is monotonic, meaning that the probability of A is less than or equal to the probability
of B whenever A entails B. A nonmonotonic theory of probability is obtained, if the greatest lower bound for probabilities
is set at −1 instead of 0, the value fixed by Kolmogorov's positivity axiom. The new theory retains Kolmogorov's other axioms,
and many important theorems still hold. It also has substantial applicability: it can accommodate probabilities for spin-
systems while preserving Boolean operations. That is to say, negative probabilities are here provided with a homely setting
in the quantum domain.
PACS : 03.65.-w, 03.65.Ta, 34.80.Nz. 相似文献
5.
Stanley Gudder 《International Journal of Theoretical Physics》1992,31(5):825-834
Symmetry groups and systems of covariance are investigated in the framework of quantum probability theory. It is shown that a measurementX can be represented by a positive operator-valued measure
on a sectorS of the amplitude space. Moreover,
provides a generalized system of covariance for the generalized unitary representation of a symmetry group. 相似文献
6.
C. Wetterich 《Annals of Physics》2010,325(12):2750-2786
We describe fermions in terms of a classical statistical ensemble. The states τ of this ensemble are characterized by a sequence of values one or zero or a corresponding set of two-level observables. Every classical probability distribution can be associated to a quantum state for fermions. If the time evolution of the classical probabilities pτ amounts to a rotation of the wave function , we infer the unitary time evolution of a quantum system of fermions according to a Schrödinger equation. We establish how such classical statistical ensembles can be mapped to Grassmann functional integrals. Quantum field theories for fermions arise for a suitable time evolution of classical probabilities for generalized Ising models. 相似文献
7.
C. Anastopoulos 《Foundations of Physics》2001,31(11):1545-1580
Quantum theory does not only predict probabilities, but also relative phases for any experiment, that involves measurements of an ensemble of systems at different moments of time. We argue, that any operational formulation of quantum theory needs an algebra of observables and an object that incorporates the information about relative phases and probabilities. The latter is the (de)coherence functional, introduced by the consistent histories approach to quantum theory. The acceptance of relative phases as a primitive ingredient of any quantum theory, liberates us from the need to use a Hilbert space and non-commutative observables. It is shown, that quantum phenomena are adequately described by a theory of relative phases and non-additive probabilities on the classical phase space. The only difference lies on the type of observables that correspond to sharp measurements. This class of theories does not suffer from the consequences of Bell's theorem (it is not a theory of Kolmogorov probabilities) and Kochen–Specker's theorem (it has distributive logic). We discuss its predictability properties, the meaning of the classical limit and attempt to see if it can be experimentally distinguished from standard quantum theory. Our construction is operational and statistical, in the spirit of Copenhagen, but makes plausible the existence of a realist, geometric theory for individual quantum systems. 相似文献
8.
Sum rules describing perfect screening at equilibrium in a classical plasma are extended to the time-displaced structure function of an inhomogeneous one-component plasma. We find that there are long-wavelength modes which oscillate undamped with a single frequency
,
being an angular average of the squared plasma frequency at infinity. Our results are derived heuristically, allowing also for quantum effects, from linear response theory, and rigorously from the classical BBGKY hierarchy under some reasonable assumptions on the spatial decay of correlations. Special cases are investigated, in particular plasmas bounded by walls of varied shapes.This laboratory is associated with the CNRS. 相似文献
9.
Charis Anastopoulos 《International Journal of Theoretical Physics》2003,42(6):1229-1256
We argue that the complex numbers are an irreducible object of quantum probability: this can be seen in the measurements of geometric phases that have no classical probabilistic analogue. Having the complex phases as primitive ingredient implies that we need to accept nonadditive probabilities. This has the desirable consequence of removing constraints of standard theorems about the possibility of describing quantum theory with commutative variables. Motivated by the formalism of consistent histories and keeping an analogy with the theory of stochastic processes, we develop a (statistical) theory of quantum processes: they are characterized by the introduction of a density matrix on phase space paths (it thus includes phase information) and fully reproduces quantum mechanical predictions. We can write quantum differential equations (in analogy to Langevin equation) that could be interpreted as referring to individual quantum systems. We describe the reconstruction theorem by which a quantum process can yield the standard Hilbert space structure if the Markov property is imposed. We discuss the relevance of our results for the interpretation of quantum theory (a sample space is possible if probabilities are nonadditive) and quantum gravity (the Hilbert space arises here after the consideration of a background causal structure). 相似文献
10.
11.
Eduard Prugovečki 《Foundations of Physics Letters》1989,2(2):163-190
A second-quantized bundleE, called the quantum gravitational bundle, is constructed from graviton bundles in accordance with outlined general principles for geometro-stochastic second quantization, and quantum gravitational frame fields are introduced in it. The gravitational bundleE is the carrier of a semiclassical connection
that can be used as a stepping stone in the construction of a second-quantized gravitational connection. The geometro-stochastic quantum propagations governed by such connections can be expressed in terms of path integrals over causal stochastic paths which embody stochastic parallel transport under free-fall conditions. Their epistemic implications for the quantum theory of measurement are discussed.1. Supported in part by the NSERC Research Grant No. A5206. 相似文献
12.
Jeffrey Bub 《Foundations of Physics》1976,6(5):511-525
Bell's problem of the possibility of a local hidden variable theory of quantum phenomena is considered in the context of the general problem of representing the statistical states of a quantum mechanical system by measures on a classical probability space, and Bell's result is presented as a generalization of Maczynski's theorem for maximal magnitudes. The proof of this generalization is shown to depend on the impossibility of recovering the quantum statistics for sequential probabilities in a classical representation without introducing a randomization process for the hidden variables. Hidden variable theories that exclude such a randomization process are termed strict, and it is shown that the class of local hidden variable theories is included in the class of strict theories. A counterargument by Freedman and Wigner is evaluated with reference to Clauser's extension of a hidden variable model proposed by Bell. 相似文献
13.
Recently, A. A. Kirillov introduced an important notion of classical and quantum family algebras. Here the criterion of commutativity is given. The quantum eigenvalues of
are computed. 相似文献
14.
Vladimir N. Chernega Olga V. Man’ko Vladimir I. Man’ko 《Journal of Russian Laser Research》2018,39(2):128-139
We construct the quantum density matrix of a spin-1/2 state for three given probability distributions describing positions of three classical coins and associate its matrix elements with the Triada of Malevich’s squares. We present the superposition principle of spin-1/2 states in the form of a nonlinear addition rule for these classical coin probabilities. We illustrate the obtained formulas by the statement “God does not play dice – God plays coins.” 相似文献
15.
Hans-Karl Janssen 《Zeitschrift für Physik B Condensed Matter》1976,23(4):377-380
From the path probability density for nonlinear stochastic processes a Lagrangean for classical field dynamics is derived. This formulation provides a convenient approach to the mode coupling equations and the renormalization group theory of critical dynamics. An application is given for the time-dependent isotropic Heisenberg ferromagnet. The dynamical exponent
is derived aboveT
c for all dimensionsd>2. 相似文献
16.
Yu. M. Lomsadze 《Russian Physics Journal》1979,22(6):622-629
It is shown that the theorem of the first part of this cycle of papers necessarily, by virtue of only the fundamental principles of quantum theory, implies the existence of two fundamentally different types of evolution of isolated quantum macrosystems, i.e., the S and PS evolutions of pure states. As for isolated quantum microsystems, they can only S-evolve. The paper considers the fundamental specific singularities of PS evolution, which follow strictly from the theorem itself, as well as its corollary, proved in the first part [1] of this cycle of papers, also only on the basis of the fundamental principles of quantum theory. These singularities consist in the fact that, regardless of the commutativity of any observable
of a system described by a vector in physical Hilbert space with the S-operator of this system, the probability distribution of this observable
during measurement (with an appropriate instrument ), providing complete information about the characteristic of the system, is not conserved during the process of PS evolution. Nor is even the expectation of the result of measurement of the observable
conserved with time.Paper presented at a session of the Department of Nuclear Physics, Academy of Sciences of the USSR (Moscow, February, 1978).Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 63–72, June, 1979.The author is indebted to Prof. S. N. Sokolov (Institute of High-Energy Physics, Serpukhov) for his invaluable discussion of the Everett concept. 相似文献
17.
We study the fractional decomposition of the quantum enveloping affine algebras
and
with vanishing central charge in the limit
. This decomposition is based on the bosonic representation and can be related to fractional supersymmetry and k-fermionic spin. The quantum affine algebras and the classical ones are equivalent in the fermionic realization. 相似文献
18.
O. Jedrkiewicz R. Loudon J. Jeffers 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2006,39(1):129-140
Previous work on the retrodictive theory of direct
detection is extended to cover the homodyne detection of coherent optical
signal states
and
. The retrodictive input state probabilities are obtained by
the application of Bayes' theorem to the corresponding predictive
distributions, based on the probability operator measure (POM) elements for
the homodyne process. Results are derived for the retrodictive information
on the complex amplitude of the signal field obtainable from the difference
photocount statistics of both 4-port and 8-port balanced homodyne detection
schemes. The local oscillator is usually assumed much stronger than the
signal but the case of equal strengths in 4-port detection is also
considered. The calculated probability distributions and error rates are
illustrated numerically for values of signal and local oscillator strengths
that extend from the classical to the quantum regimes. 相似文献
19.
Mioara Mugur-Schachter 《International Journal of Theoretical Physics》1992,31(9):1715-1751
An integrated view concerning the probabilistic organization of quantum mechanics is first obtained by systematic confrontation of the Kolmogorov formulation of the abstract theory of probabilities with the quantum mechanical representationand its factual counterparts. Because these factual counterparts possess a peculiar space-time structure stemming from the operations by which the observer produces the studied states (operations of state preparation) and the qualifications of these (operations of measurement), the approach brings forth probability-trees, complex constructs with treelike space-time support. Though it is strictly entailed by confrontation with the abstract theory of probabilities as it now stands, the construct of a quantum mechanical probability treetransgresses this theory. It indicates the possibility of an extended abstract theory of probabilities: Quantum mechanics appears to be neither a normal probabilistic theory nor an abnormal one, but a pioneering particular realization of afuture extended abstract theory of probabilities. The integrated perception of the probabilistic organization of quantum mechanics removes the current identifications of spectral decompositions of one state vector, with superpositions of several state vectors. This leads to the definition of operators of state preparation and of the calculus with these and to a clear understanding of the physical significance of the principle of superposition. Furthermore, a complement to the quantum theory of measurements is obtained. 相似文献
20.
Recently, Schmid and Spekkens studied the quantum contextuality in terms of state discrimination. By dealing with the minimum error discrimination of two quantum states with identical prior probabilities, they reported that quantum contextual advantage exists. Meanwhile, if one notes a striking observation that the selection of prior probability can affect the quantum properties of the system, it is necessary to verify whether the quantum contextual advantage depends on the prior probabilities of the given states. In this paper, we consider the minimum error discrimination of two states with arbitrary prior probabilities, in which both states are pure or mixed. We show that the quantum contextual advantage in state discrimination may depend on the prior probabilities of the given states. In particular, even though the quantum contextual advantage always exists in the state discrimination of two nonorthogonal states with nonzero prior probabilities, the quantum contextual advantage depends on prior probabilities in the state discrimination of two states. 相似文献