Existence of hidden variables having only upper probabilities

We prove the existence of hidden variables, or, what we call generalized common causes, for finite sequences of pairwise correlated random variables that do not have a joint probability distribution. The hidden variables constructed have upper probability distributions that are nonmonotonic. The theorem applies directly to quantum mechanical correlations that do not satisfy the Bell inequalities.It is a pleasure to dedicate this paper to Karl Popper in celebration of this 90th birthday. The first author has known Popper for more than three decades, and has profited much from their discussion of many different topics, among which have been the foundations of probability and the foundations of quantum mechanics, both central to the present paper.     

Quantum probabilities,Kolmogorov probabilities,and informational probabilities

The relations between quantum probabilities, Kolmogorov probabilities, and informational probabilities are studied against the background offered by the concept of a quantum mechanical probability tree built in previous work. It is shown that the quantum mechanical transformation theory goes beyond the Kolmogorov concept of probabilities. It is furthermore shown that the quantum mechanical concept of probability is of the same essence as the informational one. The analyses that produce these conclusions bring forth the first lines of a general mathematical representation of the emergence and circulation of patterns of any kind.     

Identical particles, projectors and probabilities

In this Letter we reanalyze the old problem of the probability interpretation of the wave function in the case of identical particles. It is shown that, although the construction of observable single particle position (or momentum) operators is not easy nor natural, it is possible to bypass the problem through the construction of projectors that make probability computations completely systematic, easy to understand and adequate to the spirit of Quantum Mechanics.     

Environment-assisted invariance,entanglement, and probabilities in quantum physics

I introduce environment-assisted invariance or envariance-a symmetry exhibited by correlated quantum systems and related to causality-and describe how it can be used to understand the nature of ignorance and, hence, the origin and interpretation of Born's rule for quantum probabilities.     

Lifetimes,branching ratios,and transition probabilities in Mo I

The radiative lifetimes of 56 levels in Mo I have been measured by the method of laser-induced fluorescence from sputtered metal vapor. Emission branching ratios have been measured for these levels to determine transition probabilities for 570 Mo I transitions in the wavelength range 2944–9767 Å. The uncertainty in the transition probability of stronger branches is typically less than 5%.     

Non-isospectral Hamiltonians, intertwining operators and hidden hermiticity

We have recently proposed a strategy to produce, starting from a given Hamiltonian h₁ and a certain operator x for which [h₁,xx†]=0 and x†x is invertible, a second Hamiltonian h₂ with the same eigenvalues as h₁ and whose eigenvectors are related to those of h₁ by x†. Here we extend this procedure to build up a second Hamiltonian, whose eigenvalues are different from those of h₁, and whose eigenvectors are still related as before. This new procedure is also extended to crypto-hermitian Hamiltonians.     

Single-case probabilities

The propensity interpretation of probability, bred by Popper in 1957(K. R. Popper, in Observation and Interpretation in the Philosophy of Physics,S. Körner, ed. (Butterworth, London, 1957, and Dover, New York, 1962), p. 65; reprinted in Popper Selections,D. W. Miller, ed. (Princeton University Press, Princeton, 1985), p. 199) from pure frequency stock, is the only extant objectivist account that provides any proper understanding of single-case probabilities as well as of probabilities in ensembles and in the long run. In Sec. 1 of this paper I recall salient points of the frequency interpretations of von Mises and of Popper himself, and in Sec. 2 I filter out from Popper's numerous expositions of the propensity interpretation its most interesting and fertile strain. I then go on to assess it. First I defend it, in Sec. 3, against recent criticisms(P. Humphreys, Philos. Rev.94,557 (1985); P. Milne, Erkenntnis25,129 (1986)) to the effect that conditional [or relative] probabilities, unlike absolute probabilities, can only rarely be made sense of as propensities. I then challenge its predominance, in Sec. 4, by outlining a rival theory: an irreproachably objectivist theory of probability, fully applicable to the single case, that interprets physical probabilities asinstantaneous frequencies.     

Lifetimes,branching ratios and transition probabilities in molybdenum I

The radiative lifetimes of 14 excited levels in Mo I have been measured by time-resolved laser fluorescence spectroscopy. Emission branching ratios for the decay of these levels have been measured to determine absolute transition probabilities for 135 lines in the wavelength range 2600–6800Å. The transition probabilities are compared with earlier values. Erroneous J assignments in the literature are corrected.     

Weak objectification,joint probabilities,and Bell inequalities in quantum mechanics

The weak objectification of physical properties is shown to yield the same probabilistic implications as strong objectification and can therefore be refuted on the basis of suitable interference experiments. An alternative test of hypothetical objectification statements, as they occur in the EPR experiment, is based on joint probabilities and the ensuing Bell inequalities. Quantum mechanics turns out to be partially compatible with Bell's inequalities even in cases where weak objectification is excluded by interference.     

Uncovering hidden nodes and hidden links in complex dynamic networks

Inferring network structures from available data has attracted much interest in network science; however, in many realistic networks, only some of the nodes are perceptible while others are hidden, making it a challenging task. In this work, we develop a method for reconstructing the network with hidden nodes and links, taking account of fast-varying noise and time-delay interactions. By calculating the correlations of available data with different derivative orders for multiple pairs of accessi...     

Mielnik and cantoni transition probabilities

It is shown that when a Mielnik transition probability space is given, Cantoni transition probabilities can also be defined on it. A condition is given under which these transition probabilities are equal.     

Quantum probabilities,operators of state preparation,and the principle of superposition

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.     

Transition probabilities, oscillator strengths and lifetimes for singly ionized magnesium

The electric dipole transition probabilities, oscillator strengths and lifetimes have been calculated using the weakest bound electron potential model theory (WBEPMT) for singly ionized magnesium. In the calculations both multiplet and fine structure transitions are studied. We have employed both the numerical Coulomb approximation (NCA) method and numerical non-relativistic Hartree-Fock (NRHF) wave functions for expectation values of radii. The calculated oscillator strengths and lifetimes have been compared with MCHF results given by Fischer et al. (2006). A good agreement has been obtained with the MCHF results. Moreover, some new transition probabilities, oscillator strengths and lifetime values, not existing in the data bases for highly excited levels in singly ionized magnesium, have been obtained using this method.     

POVMs and hidden variables

Recent results by Paul Busch and Adán Cabello claim to show that by appealing to POVMs, non-contextual hidden variables can be ruled out in two dimensions. While the results of Busch and Cabello are mathematically correct, interpretive problems render them problematic as no hidden variable proofs.     

Towards gauge unified,supersymmetric hidden strong dynamics

We consider a class of models with extra complex scalars that are charged under both the Standard Model and a hidden strongly coupled S U(N)h gauge sector and discuss the seenarios in which the new scalars are identified as the messenger fields that mediate the spontaneously broken supersymmetries from the hidden sector to the visible sector.The new scalars are embedded into 5-plets and 10-plets of an S(/(5)v gauge group that potentially unifies the Standard Model gauge groups.The Higgs bosons remain as elementary particles.In the supersymmetrized version of this class of models,vector-like fermions whose left-handed components are superpartners of the new scalars are introduced.Owing to the hidden strong force,the new low-energy scalars hadronize before decaying and thus evade the common direct searches of the supersymmetric squarks.This can be seen as a gauge mediation seenario with the scalar messenger fields forming low-energy bound states.We also discuss the possibility that in the tower of bound states formed under hidden strong dynamics(of at least the TeV scale),there exist a dark matter candidate and the collider signatures(e.g.diphoton,diboson,or dijet)of models that may show up in the near future.