Reichenbachian Common Cause Systems Revisited

According to Reichenbach’s principle of common cause, positive statistical correlations for which no straightforward causal explanation is available should be explained by invoking the action of a hidden conjunctive common cause. Hofer-Szabó and Rédei’s notion of a Reichenbachian common cause system is meant to generalize Reichenbach’s conjunctive fork model to fit those cases in which two or more common causes cooperate in order to produce a positive statistical correlation. Such a generalization is proved to be unsatisfactory in the light of a probabilistic conception of causation. Accordingly, an alternative model for systems of multiple common causes is offered, which is capable of emulating the explanatory efficacy of Reichenbachian common cause systems, while overcoming their major conceptual shortcomings at the same time.     

Only Countable Reichenbachian Common Cause Systems Exist

In this paper we give a positive answer to a problem posed by Hofer-Szabó and Rédei (Int. J. Theor. Phys. 43:1819–1826, 2004) regarding the existence of infinite Reichenbachian common cause systems (RCCSs). An example of a countably infinite RCCS is presented. It is also determined that no RCCSs of greater cardinality exist.     

Reichenbachian Common Cause Systems of Arbitrary Finite Size Exist

A partition of a Boolean algebra Ω in a probability measure space (Ω, p) is called a Reichenbachian common cause system for the correlation between a pair A,B of events in Ω if any two elements in the partition behave like a Reichenbachian common cause and its complement; the cardinality of the index set I is called the size of the common cause system. It is shown that given any non-strict correlation in (Ω, p), and given any finite natural number n > 2, the probability space (Ω,p) can be embedded into a larger probability space in such a manner that the larger space contains a Reichenbachian common cause system of size n for the correlation.     

Exchangeability and Conditionally Identical Common Cause Systems

A pair (A, B) of events in a classical probability measure space (Ω, p) is called exchangeable iff p(A ) = p( B). Conditionally identical common cause system of size n for the correlation is an n-partition of Ω such that (i) any member of the partition screens the correlation off and (ii) for any member {C _i } _{i ∊ I} of the partition p(A|C _i ) = p(B|C _i ). The common cause system is called proper if p(A|C _i )≠(A|C _j ) for some i ≠ j. In the paper it is shown that exchangeable correlations be explained by proper conditionally identical common cause systems in the following sense. (i) Given a proper conditionally identical common cause system of size n for the two events A and B in Ω, then the pair (A, B) will be an exchangeable (positively) correlating pair. (ii) Given any exchangeable (positively) correlating pair of events in Ω and given any finite number n > 2, then the probability space can be embedded into a larger probability space in such a way that the larger space contains a proper conditionally identical common cause system of size n for the correlation.     

Reichenbach's Common Cause Definition on Hilbert Lattices

The Reichenbachian definition of the commoncause is formally generalized for the quantum case intwo different ways according to two possible definitionsof the conditional probability on a Hilbert lattice, and it is shown that, unlike in the classicalcase, neither of the two definitions isconsistent.     

The Limits of Common Cause Approach to EPR Correlation

It is often argued that no local common cause models of EPR correlation exist. However, Szabó and Rédei pointed out that such arguments have the tacit assumption that plural correlations have the same common causes. Furthermore, Szabó showed that for EPR correlation a local common cause model in his sense exists. One of his requirements is that common cause events are statistically independent of apparatus settings on each side. However, as Szabó knows, to meet this requirement does not entail that different combinations of common cause events (e.g. meet and join in lattice-theoretic terminology) are statistically independent of measurement settings. This further condition is formulated in two ways. First, the apparatus settings are completely independent of such combinations. Second, the apparatus settings on each side are independent of such combinations. Does a common cause model which meets the former and the latter respectively exist? This problem is considered. In particular, the latter version is Szabó’s and Rédei’s open problem. Negative answers are given to both versions.     

Common Cause Completability of Classical and Quantum Probability Spaces

It is shown that for a given set of correlations either in a classical or in a quantumprobability space both the classical and the quantum probability spaces areextendable in such a way that the extension contains common causes of thegiven correlations, where common cause is taken in the sense of Reichenbach'sdefinition. These results strongly restrict the possible ways of disprovingReichenbach's common cause principle and indicate that EPR-type quantumcorrelations might very well have a common cause explanation.     

Formal existence and uniqueness of the Reichenbachian common cause on Hilbert lattices

The Reichenbachian definition of the common cause for two correlating events is formally generalized for the quantum case in two different ways. It is shown that (1) in the first quantum case, unlike in the classical case, there exists a common cause for any two correlating events, and (2) the common cause is not unique either in the classical or in both quantum cases.     

Local Primitive Causality and the Common Cause Principle in Quantum Field Theory

If (V) is a net of local von Neumann algebras satisfying standard axioms of algebraic relativistic quantum field theory and V ₁ and V ₂ are spacelike separated spacetime regions, then the system ( (V ₁ ), (V ₂ ), ) is said to satisfy the Weak Reichenbach's Common Cause Principle iff for every pair of projections A (V ₁ ), B (V ₂ ) correlated in the normal state there exists a projection C belonging to a von Neumann algebra associated with a spacetime region V contained in the union of the backward light cones of V ₁ and V ₂ and disjoint from both V ₁ and V ₂ , a projection having the properties of a Reichenbachian common cause of the correlation between A and B. It is shown that if the net has the local primitive causality property then every local system ( (V ₁ ), (V ₂ ), ) with a locally normal and locally faithful state and suitable bounded V ₁ and V ₂ satisfies the Weak Reichenbach's Common Cause Principle.     

Attempt to Resolve the EPR-Bell Paradox via Reichenbach's Concept of Common Cause

Reichenbach's common cause principle claims that if there is correlation betweentwo events and none of them is directly causally influenced by the other, thenthere must exist a third event that can, as a common cause, account for thecorrelation. The EPR-Bell paradox consists in the problem that we observecorrelations between spatially separated events in the EPR experiments whichdo not admit common-cause-type explanation, and it must therefore be concludedthat, contrary to relativity theory, in the realm of quantum physics there existsaction at a distance, or at least superluminal causal propagation is possible; thatis, either relativity theory or Reichenbach's common cause principle fails.By means of closer analyses of the concept of common cause and a more precisereformulation of the EPR experimental scenario, I sharpen the conclusion wecan draw from the violation of Bell's inequalities.     

The Phase Diagrams for 11 Binary Alkali Halide Systems Having Common Anion

The quasiregular model is improved. Using the thermodynamic condition of phase equilibrium we obtain the equations of solid-liquid phase equilibrium curves. The phase diagrams for 11 binary alkali halide systeme having common anion have been obtained. The eutectic point of each phase diagram ie also calculated. The results show that the agreement of theoretical curves with the experimental reeults ie good (except the system CsBr-NaBr).     

Enhanced Charging in Common Environments Compared to Independent Environments for Two-Level Systems

The charging process of a quantum battery (i.e., a two-level system) is studied in two scenarios, that is, a quantum battery and a charger are coupled to the common reservoir environments or coupled to their respective independent environments. In the common reservoir scenario, it is shown that the optimal charging process can be realized by increasing the number of environments and setting the same coupling strength between battery-reservoirs and charger-reservoirs. In the independent reservoir scenario, however, it is shown that decreasing either the number of reservoir environments or the coupling strength would enhance the charging performance. These results demonstrate that the charging performance of quantum batteries can be significantly improved by constructing common environments. This may be of help to the realization of the quantum battery with optimal charging performance in multiple environments.     

Theoretical Calculation of the Eutectic Point for 27 Binary Alkali Halide Systems Having Common Ions

We suppose that the excess enthalpy and entropy may be expanded as polynomials in the mole fractions, and determine the equations of the liquid-solid phase equilibrium curves of a binary system according to thermodynamic theory. For the 27 binary alkali halide systems having the phase diagram with an eutectic point, we calculate the values of the eutectic point (T_o, X_Bo). These results agree well with the experimental values.     

Common Coherence Witnesses and Common Coherent States

We show the properties and characterization of coherence witnesses. We show methods for constructing coherence witnesses for an arbitrary coherent state. We investigate the problem of finding common coherence witnesses for certain class of states. We show that finitely many different witnesses W1,W2,⋯,Wn can detect some common coherent states if and only if ∑i=1ntiWi is still a witnesses for any nonnegative numbers ti(i=1,2,⋯,n). We show coherent states play the role of high-level witnesses. Thus, the common state problem is changed into the question of when different high-level witnesses (coherent states) can detect the same coherence witnesses. Moreover, we show a coherent state and its robust state have no common coherence witness and give a general way to construct optimal coherence witnesses for any comparable states.     

共光路共模块自适应光学系统中赝相位共轭器件应用分析

研究了角反射器阵列形成赝相位共轭波的能力,计算了其对泽尼克多项式表示的各阶像差的保真度,分析了在共光路共模块自适应光学系统中角反射器阵列与哈特曼－夏克波前传感器二者之间单元数目,位置匹配方面的问题,对失配所带来的误差进行了计算。     

Common Information Components Analysis

Wyner’s common information is a measure that quantifies and assesses the commonality between two random variables. Based on this, we introduce a novel two-step procedure to construct features from data, referred to as Common Information Components Analysis (CICA). The first step can be interpreted as an extraction of Wyner’s common information. The second step is a form of back-projection of the common information onto the original variables, leading to the extracted features. A free parameter γ controls the complexity of the extracted features. We establish that, in the case of Gaussian statistics, CICA precisely reduces to Canonical Correlation Analysis (CCA), where the parameter γ determines the number of CCA components that are extracted. In this sense, we establish a novel rigorous connection between information measures and CCA, and CICA is a strict generalization of the latter. It is shown that CICA has several desirable features, including a natural extension to beyond just two data sets.     

Classical Systems, Standard Quantum Systems, and Mixed Quantum Systems in Hilbert Space

Traditionally, there has been a clear distinction between classical systems and quantum systems, particularly in the mathematical theories used to describe them. In our recent work on macroscopic quantum systems, this distinction has become blurred, making a unified mathematical formulation desirable, so as to show up both the similarities and the fundamental differences between quantum and classical systems. This paper serves this purpose, with explicit formulations and a number of examples in the form of superconducting circuit systems. We introduce three classes of physical systems with finite degrees of freedom: classical, standard quantum, and mixed quantum, and present a unified Hilbert space treatment of all three types of system. We consider the classical/quantum divide and the relationship between standard quantum and mixed quantum systems, illustrating the latter with a derivation of a superselection rule in superconducting systems.     

某些力学系统与电路系统的相似性

1力学与电路理论中定理的相似性 牛顿第二定律与电容的伏安关系是极其相似的 牛顿第二定律 F外=mdv质/dt 电容的伏安关系 Is=CdUc/dt 其中F外与电源Is对应,m与C对应,v质与Uc对应.