Explaining the Unobserved—Why Quantum Mechanics Ain’t Only About Information

A remarkable theorem by Clifton et al [Found Phys. 33(11), 1561–1591 (2003)] (CBH) characterizes quantum theory in terms of information-theoretic principles. According to Bub [Stud. Hist. Phil. Mod. Phys. 35 B, 241–266 (2004); Found. Phys. 35(4), 541–560 (2005)] the philosophical significance of the theorem is that quantum theory should be regarded as a “principle” theory about (quantum) information rather than a “constructive” theory about the dynamics of quantum systems. Here we criticize Bub’s principle approach arguing that if the mathematical formalism of quantum mechanics remains intact then there is no escape route from solving the measurement problem by constructive theories. We further propose a (Wigner-type) thought experiment that we argue demonstrates that quantum mechanics on the information-theoretic approach is incomplete.     

A Remark on Lp-Boundedness of Wave Operators¶for Two Dimensional Schrödinger Operators

Let H=−Δ+V be a two dimensional Schr?dinger operator with a real potential V(x) satisfying the decay condition , δ > 6. Let H ₀=−Δ. We show that the wave operators are bounded in L ^p (R ²) under the condition that H has no zero resonances or bound states. In this paper the condition , imposed in a previous paper (K. Yajima, Commun. Math. Phys. 208, 125–152 (1999)), is removed. Received: 13 September 2001 / Accepted: 15 October 2001     

Nonradiative decay of the low-lying nuclear isomer 229m Th(3.5 eV) in a metal

A new nonradiative decay channel for the anomalously low-lying isomeric level 3/2⁺ (3.5±1.0 eV) of the ²²⁹Th nucleus in a metal via the conduction electrons is examined. The lifetime of the isomer in a metal is calculated. An explanation is given for the experimental results of S. B. Utter et al., Phys. Rev. Lett. 82, 505 (1999), where the optical radiation spectrum of the indicated isomer was investigated. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 6, 367–370 (25 September 1999)     

A unified quantum theory of mechanics and thermodynamics. Part IIb. Stable equilibrium states

Part IIb presents some of the most important theorems for stable equilibrium states that can be deduced from the four postulates of the unified theory presented in Part I. It is shown for the first time that the canonical and grand canonical distributions are the only distributions that are stable. Moreover, it is shown that reversible adiabatic processes exist which cannot be described by the dynamical equation of quantum mechanics. A number of conditions are discussed that must be satisfied by the general equation of motion which is yet to be discovered.Part I of this paper appeared inFound. Phys. 6(1), 15 (1976). Part IIa appeared inFound. Phys. 6(2), 127 (1976). The numbering of the sections, equations, and references in this part of the paper continues from those in Part IIa.     

Spectrum of the Metric Operator of a Simple -Symmetric Model

In papers (Krejčiřík D. et al.: J. Phys. A: Math. Gen.: 39(32), 10143–10153 (2006); Krejčiřík D., Tater M.: J. Phys. A: Math. Theor. 41(24), 244 (2008)) a new very simple -symmetric model was introduced and closed formula for the metric operator was found. We use an alternative integral form of this metric operator to study the spectrum of the metric.     

Contribution of strings to the observed variability of extragalactic sources of radiation

The mechanism for the fast variability introduced in the observed luminosity of compact extragalactic sources of radiation by the diffraction of electromagnetic radiation by cosmic strings is studied. Cosmic strings at cosmological distances can produce not only the observed variability but also a large increase in the observed luminosity of quasars. Curves of the variation of the luminosity are obtained and the characteristic times of the oscillations of the luminosity are presented for a string with density 10¹⁶ g/cm. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 6, 385–390 (25 September 1996)     

Gauge theory onR×S 3 topology

A model for gauge theories over a compact Lie group is described using R × S³ as background space. The U(1) and SU(2) gauge theories are considered as particular examples, and a comparison with other results is given. Our results differ from those of Carmeli and MalinFound. Phys. 16, 791 (1986);17, 193 (1987)] by a supplementary term in the curvature tensor due to the noncommutativity of derivatives used on R × S³ space. Some observations about supersymmetry and gravity on R × S³ space are also given.     

On Consistency of the Quantum-Like Representation Algorithm

In this paper we continue to study so-called “inverse Born’s rule problem”: to construct a representation of probabilistic data of any origin by a complex probability amplitude which matches Born’s rule. The corresponding algorithm—quantum-like representation algorithm (QLRA)—was recently proposed by A. Khrennikov (Found. Phys. 35(10):1655–1693, 2005; Physica E 29:226–236, 2005; Dokl. Akad. Nauk 404(1):33–36, 2005; J. Math. Phys. 46(6):062111–062124, 2005; Europhys. Lett. 69(5):678–684, 2005). Formally QLRA depends on the order of conditioning. For two observables (of any origin, e.g., physical or biological) a and b, b|a- and a|b conditional probabilities produce two representations, say in Hilbert spaces H ^b|a and H ^a|b . In this paper we prove that under “natural assumptions” (which hold, e.g., for quantum observables represented by operators with nondegenerate spectra) these two representations are unitary equivalent. This result proves the consistency of QLRA.     

How to determine an effective potential for a variable cosmological term

It is shown that if a variable cosmological term in the present Universe is described by a scalar field with minimal coupling to gravity and with some phenomenological self-interaction potential V(ϕ), then this potential can be unambiguously determined from the following observational data: either from the behavior of density perturbations in dustlike matter component as a function of redshift (given the Hubble constant additionally), or from the luminosity distance as a function of redshift (given the present density of dustlike matter in terms of the critical value). Pis’ma Zh. éksp. Teor. Fiz. 68, No. 10, 721–726 (25 November 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Taking aberrations into account in experiments testing the relativistic theory of the Doppler effect

The interpretation of experimental results [L. A. Pobedonostsev, Sov. Phys. Tech. Phys. 34, 303 (1989)] on a test of the relativistic formula for the Doppler effect and the mistaken conclusion drawn by one author of the experiment that the special theory of relativity (STR) is unsound [L. A. Pobedonostsev, Galilean Electrodyn. 6(6), 117 (1995)] are criticized. It is suggested that the construction of the slit collimator be altered so as to take into account the aberration of light. Zh. Tekh. Fiz. 69, 124–126 (February 1999) Deceased.     

The relativistic statistical theory and Kaniadakis entropy: an approach through a molecular chaos hypothesis

We have investigated the proof of the H theorem within a manifestly covariant approach by considering the relativistic statistical theory developed in [G. Kaniadakis, Phys. Rev. E 66, 056125 (2002); G. Kaniadakis, Phys. Rev. E 72, 036108 (2005)]. As it happens in the nonrelativistic limit, the molecular chaos hypothesis is slightly extended within the Kaniadakis formalism. It is shown that the collisional equilibrium states (null entropy source term) are described by a κ power law generalization of the exponential Juttner distribution, e.g., , with θ=α(x)+β_μp^μ, where α(x) is a scalar, β_μ is a four-vector, and p^μ is the four-momentum. As a simple example, we calculate the relativistic κ power law for a dilute charged gas under the action of an electromagnetic field F^μν. All standard results are readly recovered in the particular limit κ→0.     

Possibility of the levitation of droplets in the atmosphere when they are charged by induction in an electric field under nonuniform evaporation conditions

The behavior of droplets in the atmosphere in an electric field has important bearing on the theory of thunderstorms. One of the possible mechanisms by which droplets become charged—the induction mechanism in the presence of nonuniform evaporation—is investigated in greater detail on the basis of recent experimental results (V. A. Saranin, Zh. Tekh. Fiz. 65(6), 21 (1995) [Tech. Phys. 40, 332 (1995)]). Zh. Tekh. Fiz. 68, 16–21 (February 1998)     

Multipole solutions of the wave equation

The wave equation is solved by the operator separation method proposed in V. V. Zashkvara and N. N. Tyndyk, Zh. Tekh. Fiz. 61(4), 148 (1991) [Sov. Phys. Tech. Phys. 36, 456 (1991)]. Solutions describing the evolution of circular-multipole fields are obtained in a cylindrical coordinate system. Zh. Tekh. Fiz. 68, 9–14 (June 1998) Deceased.     

Stability of Global Solution for the Relativistic Enskog Equation near Vacuum

The Cauchy problem of the relativistic Enskog equation with near-vacuum data is considered in this paper. Under the same assumption as that in Jiang (J. Stat. Phys. 127:805–812, 2007) for the relativistic Enskog equation, we obtain the uniform L ^∞-stability of the solution. What’s more important, is that for two new types of the scattering cross section σ, we give the global existence and L ¹(x,v)-stability for mild solution when the initial data lies in the space L ¹(x,v). As a corollary, we have a BV-type estimate. It is worth mentioning that the stability results in this paper can be applied to the case in Jiang (J. Stat. Phys. 127:805–812, 2007).     

The correction-to-scaling exponent in dilute systems

The leading correction-to-scaling exponent ω for the three-dimensional (3D) dilute Ising model is calculated in the framework of the field theoretic renormalization group approach. Both in the minimal subtraction scheme and in the massive field theory (resummed four-loop expansion) excellent agreement with recent Monte Carlo calculations (H. G. Ballesteros et al., Phys. Rev. B 58, 2740 (1998)) is achieved. The expression of ω as a series in a expansion up to O(ɛ²) does not permit a reliable estimate for d=3. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 10, 698–702 (25 May 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Thomae Formula for General Cyclic Covers of $${{\mathbb {CP}}^1}$$

Let X be a general cyclic cover of \mathbbCP¹{\mathbb{CP}^{1}} ramified at m points, λ₁... λ _m . we define a class of non-positive divisors on X of degree g −1 supported in the pre images of the branch points on X, such that the Riemann theta function does not vanish on their image in J(X). We generalize the results of Bershadsky and Radul (Commun Math Phys 116:689–700, 1988), Nakayashiki (Publ Res Inst Math Sci 33(6):987–1015, 1997) and Enolskii and Grava (Lett Math Phys 76(2–3):187–214, 2006) and prove that up to a certain determinant of the non-standard periods of X, the value of the Riemann theta function at these divisors raised to a high enough power is a polynomial in the branch point of the curve X. Our approach is based on a refinement of Accola’s results for 3 cyclic sheeted cover (Accola, in Trans Am Math Soc 283:423–449, 1984) and a generalization of Nakayashiki’s approach explained in Nakayashiki (Publ Res Inst Math Sci 33(6):987–1015, 1997) for general cyclic covers.     

Quantum-Like Model for Decision Making Process in?Two Players Game A Non-Kolmogorovian Model

In experiments of games, players frequently make choices which are regarded as irrational in game theory. In papers of Khrennikov (Information Dynamics in Cognitive, Psychological and Anomalous Phenomena. Fundamental Theories of Physics, Kluwer Academic, Norwell, 2004; Fuzzy Sets Syst. 155:4–17, 2005; Biosystems 84:225–241, 2006; Found. Phys. 35(10):1655–1693, 2005; in QP-PQ Quantum Probability and White Noise Analysis, vol. XXIV, pp. 105–117, 2009), it was pointed out that statistics collected in such the experiments have “quantum-like” properties, which can not be explained in classical probability theory. In this paper, we design a simple quantum-like model describing a decision-making process in a two-players game and try to explain a mechanism of the irrational behavior of players. Finally we discuss a mathematical frame of non-Kolmogorovian system in terms of liftings (Accardi and Ohya, in Appl. Math. Optim. 39:33–59, 1999).     

Drell–Yan process at Large Hadron Collider

Drell–Yan process at LHC, q[`(q)]? Z/g^* ? l⁺l^-q\bar {q}\to Z/\gamma ^\ast \to \ell ^+\ell ^-, is one of the benchmarks for confirmation of Standard Model at TeV energy scale. Since the theoretical prediction for the rate is precise and the final state is clean as well as relatively easy to measure, the process can be studied at the LHC even at relatively low luminosity. Importantly, the Drell–Yan process is an irreducible background to several searches of beyond Standard Model physics and hence the rates at LHC energies need to be measured accurately. In the present study, the methods for measurement of the Drell–Yan mass spectrum and the estimation of the cross-section have been developed for LHC operation at the centre-of-mass energy of 10 TeV and an integrated luminosity of 100 pb^− 1 in the context of CMS experiment.     

Properties of shock-compressed liquid krypton at pressures of up to 90 GPa

The following quantities of shock-compressed liquid krypton are measured behind a plane shock front at pressures up to 90 GPa: compressibility up to densities of 7 g/cm³, brightness (color) temperatures of 6000–24000 K, and electrical conductivities of 40–60000 (Ω·m)⁻¹. X-t diagram methods are used to estimate sound speeds of up to 5.5 km/s at pressures of 30–75 GPa. The optical absorption coefficients in the violet and red (30–300 cm⁻¹) are measured at pressures of 20–90 GPa from the rise in brightness of the shock front luminosity. The optical reflection coefficient of the shock front (∼13%) at a pressure of 76.1 GPa is measured for the first time. Zh. éksp. Teor. Fiz. 116, 551–562 (August 1999)     

On Geometric Problems Related to Brown-York and Liu-Yau Quasilocal Mass

We discuss some geometric problems related to the definitions of quasilocal mass proposed by Brown and York (Contemporary mathematics, vol 132, American Mathematical Society, Providence, pp 129–142, 1992; Phys Rev D (3) 47(4):1407–1419, 1993) and Liu and Yau (Phys Rev Lett 90(23):231102, 2003; J Am Math Soc 19(1):181–204, 2006). Our discussion consists of three parts. In the first part, we propose a new variational problem on compact manifolds with boundary, which is motivated by the study of Brown-York mass. We prove that critical points of this variation problem are exactly static metrics. In the second part, we derive a derivative formula for the Brown-York mass of a smooth family of closed two dimensional surfaces evolving in an ambient three dimensional manifold. As a by-product, we are able to write the ADM mass (Arnowitt et al. in Phys. Rev. (2), 122:997–1006, 1961) of an asymptotically flat 3-manifold as the sum of the Brown-York mass of a coordinate sphere S _r and an integral of the scalar curvature plus a geometrically constructed function Φ(x) in the asymptotic region outside S _r . In the third part, we prove that for any closed, spacelike, 2-surface Σ in the Minkowski space \mathbb R^3,1{\mathbb {R}^{3,1}} for which the Liu-Yau mass is defined, if Σ bounds a compact spacelike hypersurface in \mathbb R^3,1{\mathbb {R}^{3,1}} , then the Liu-Yau mass of Σ is strictly positive unless Σ lies on a hyperplane. We also show that the examples given by ó Murchadha et al. (Phys Rev Lett 92:259001, 2004) are special cases of this result.