ADDENDUM TO “THE RELATIVISTIC COVARIANCE OF THE B-CYCLIC RELATIONS”

In a previous paper [Found. Phys. Lett. 10, 383–391 (1997)] we proved that the Evans–Vigier definitions of B ⁽⁰⁾ and B ⁽³⁾ may be related not with magnetic fields but with a 4-vector field. In the present Addendum it is shown that the terms used in the B-cyclic theorem proposed by M. Evans and J.-P. Vigier may have various transformation properties with respect to Lorentz transformations. The fact whether theB ⁽³⁾ field is a part of a bivector (which is equivalent to antisymmetric second-rank tensor) or a part of a 4-vector depends on the phase factors in the definition of positive- and negative-frequency solutions of the (B, E) transverse field. This is closely connected to our considerations of the Bargmann–Wightman–Wigner (Gelfand–Tsetlin–Sokolik) constructs and with Ahluwalia's recent consideration of the phase factor related to gravity. The physical relevance of proposed constructs is discussed.     

On the Consequences of Retaining the General Validity of Locality in Physical Theory

The empirical validity of the locality (LOC) principle of relativity is used to argue in favour of a local hidden variable theory (HVT) for individual quantum processes. It is shown that such a HVT may reproduce the statistical predictions of quantum mechanics (QM), provided the reproducibility of initial hidden variable states is limited. This means that in a HVT limits should be set to the validity of the notion of counterfactual definiteness (CFD). This is supported by the empirical evidence that past, present, and future are basically distinct. Our argumentation is contrasted with a recent one by Stapp resulting in the opposite conclusion, i.e. nonlocality or the existence of faster-than-light influences. We argue that Stapps argumentation still depends in an implicit, but crucial, way on both the notions of hidden variables and of CFD. In addition, some implications of our results for the debate between Bohr and Einstein, Podolsky and Rosen are discussed.     

Simple quantum cosmology: vacuum energy and initial state

A static non-singular 10-dimensional closed Friedmann universe of Planck size, filled with a perfect fluid with equation of state p = – , can arise spontaneously by a quantum fluctuation from nothing in 11-dimensional spacetime. A quantum transition from this state can initiate the inflationary quantum cosmology outlined in [Gen. Relativ. Gravit. 33, 1415 (2001)]. With no fine-tuning, that cosmology predicts about 60 e-folds of inflation and a vacuum energy density depending only on the number of extra space dimensions (seven), G,, c and the ratio between the strength of gravity and the strength of the strong force. The fraction of the total energy in the universe represented by this vacuum energy depends on the Hubble constant H₀. Estimates of H₀ from WMAP, SDSS, the Hubble Key Project, and Sunyaev-Zeldovich and X-ray flux measurements range from 60 to 72 km s^–1 Mpc^–1. Using a mid-range value of H₀ = 65 km s^–1 Mpc^–1, the model in [Gen. Relativ. Gravit. 33, 1415 (2001)] predicts 0.7.     

Coexistence and Joint Measurability in Quantum Mechanics

This talk is a survey of the question of joint measurability of coexistent observables and it is based on the monograph Operational Quantum Physics (Busch et al., Springer-Verlag, Berlin, 1997) and on the papers (Lahti et al., Journal of Mathematical Physics 39, 6364–6371, 1998; Lahti and Pulmannova, Reports on Mathematical Physics 39, 339–351, 1997; 47, 199–212, 2001).     

The Green's Causal Functions of Bilocal Fields

On concrete examples it is demonstrated that in quantum field theory with three universal constants c, h, and k suggested in [1], the limiting value k ^–1 = 0 corresponding to local theory is a bifurcation point: the Green's causal function for finite k bifurcates into . The natural carrier of the latter is the Euclidean space-time R ₄, and its continuation from R ₄ to R _3,1 is regular. The former is singular at zero point and on the light cone and hence is rejected.     

A simplified form for the Hamiltonian and Lagrangian of the spin-independent gravitational two-body system

In general, the gravitational two-body Hamiltonian, to orderc ^–2, containsGP ²,G (P · r)², andG ² terms. We have previously shown [4–6] that a proper choice of coordinate system enables one to eliminate theG (P · r)² term. We now show that, making use of energy conservation, and coordinate transformations, we can eliminate either of the remaining two terms. In particular, we are able to write down a Hamiltonian and a Lagrangian that contain no mixed potential and kinetic terms.Laboratoire associé au Centre National de la Recherche Scientifique.     

Stochastic and quantum space-time metrics and the weak-field limit

In this review we present a simple method of introducing stochastic and quantum metrics into gravitational theory at short distances in terms of small fluctuations around a classical background space-time. We consider only residual effects due to the stochastic (or quantum) theory of gravity and use a perturbative stochastization (or quantization) method. By using the general covariance and correspondence principles, we reconstruct the theory of gravitational, mechanical, electromagnetic, and quantum mechanical processes and tensor algebra in the space-time with stochastic and quantum metrics. Some consequences of the theory are also considered, in particular, it indicates that the value of the fundamental lengthl lies in the interval 10^–23l10^–22 cm.     

Review: Gas of Wormholes: A Possible Ground State of Quantum Gravity

In order to gain insight into the possible Ground State of Quantized Einstein's Gravity, we have derived a variational calculation of the energy of the quantum gravitational field in an open space, as measured by an asymptotic observer living in an asymptotically flat space-time. We find that for Quantum Gravity (QG) it is energetically favourable to perform its quantum fluctuations not upon flat space-time but around a "gas" of wormholes of mass m _p, the Planck mass (m _p 10¹⁹ GeV) and average distance l _p, the Planck length a _p(a _p 10^–33 cm). As a result, assuming such configuration to be a good approximation to the true Ground State of Quantum Gravity, space-time, the arena of physical reality, turns out to be well described by Wheeler's quantum foam and adequately modeled by a space-time lattice with lattice constant l _p, the Planck lattice.     

Local quantum statistics in arbitrary curved space-time

A local quantum statistics based on a finite temperature field theory in an arbitrary Riemann space-time is considered. The expressions have been derived for the partition functions, the grand thermodynamic potential and the particle distributions 〈n _k〉 of massive scalar gas and fermion gas in arbitrary space-time. It is shown that the chemical potential depends on the geometry of manifold.     

Space-Time Fluctuations Induced by D-Branes and Their Effects on Neutrino Oscillations

Neutrino oscillations are analyzed in the Ellis-Mavromatos-Nanopoulos-Volkov (ENMV) model, where the quantum gravitational fluctuations of the space-time background are described by virtual D branes. Such fluctuations may induce neutrino oscillations if a violation of the equivalence principle or a tiny violation of the Lorentz invariance is imposed. In this framework, the oscillation length of neutrinos turns out to be proportional to E ^–2 M, where E is the neutrino energy and M is the energy which is the scale characterizing the topological fluctuations in the vacuum.     

The gravitational field in the wave zone I. The radiating terms of the metric tensor

We consider an asymptotically flat space-time generated by a perfect fluid source of compact spatial support. Using the de Donder gauge conditions, the Einstein equations are reduced to a new form of Poisson-type equations. A formal iterative scheme is set up to solve these equations by expanding the components of the metric tensor in powers ofc ^–1. The coefficient of each power ofc ^–1 depends on the asymptotically retarded timeu andx, y, z and satisfies a Poisson-type equation. Assuming asymptotic flatness the solution is carried out in the first orders. The results are explicit expressions of the metric up to orderc ^–4 in terms of the source functions. These expressions hold over all space-time. A further expansion in powers ofr ^–1 gives the first terms of the metric that contribute to gravitational radiation.     

Security proof of counterfactual quantum cryptography against general intercept-resend attacks and its vulnerability

Counterfactual quantum cryptography,recently proposed by Noh,is featured with no transmission of signal particles.This exhibits evident security advantages,such as its immunity to the well-known photon-number-splitting attack.In this paper,the theoretical security of counterfactual quantum cryptography protocol against the general interceptresend attacks is proved by bounding the information of an eavesdropper Eve more tightly than in Yin’s proposal [Phys.Rev.A 82 042335(2010)].It is also shown that practical counterfactual quantum cryptography implementations may be vulnerable when equipped with imperfect apparatuses,by proving that a negative key rate can be achieved when Eve launches a time-shift attack based on imperfect detector efficiency.     

Classical and Quantum Coherent States

p-Mechanics is a consistent physical theory which describes both quantum and classical mechanics simultaneously (V. V. Kisil, p-Mechanics as a physical theory. An Introduction, E-print:arXiv:quant-ph/0212101, 2002; International Journal of Theoretical Physics 41(1), 63–77, 2002). We continue the development of p-mechanics by introducing the concept of states. The set of coherent states we introduce allows us to evaluate classical observables at any point of phase space and simultaneously to evaluate quantum probability amplitudes. The example of the forced harmonic oscillator is used to demonstrate these concepts.     

Grammar Theory Based on Quantum Logic

Motivated by Ying' work on automata theory based on quantum logic (Ying, M. S. (2000). International Journal of Therotical Physics, 39(4): 985–996; 39(11): 2545–2557) and inspired by the close relationship between the automata theory and the theory of formal grammars, we have established a basic framework of grammar theory on quantum logic and shown that the set of l-valued quantum regular languages generated by l-valued quantum regular grammars coincides with the set of l-valued quantum languages recognized by l-valued quantum automata.     

LETTER: Neutrino Oscillations Induced by Gravitational Recoil Effects

Quantum gravitational fluctuations of the space-time background, described by virtual D branes, may induce the neutrino oscillations if a tiny violation of the Lorentz invariance (or a violation of the equivalence principle) is required. In this approach, the oscillation length of massless neutrinos turns out to be proportional to E ^–2 M, where E is the neutrino energy and M is the mass scale characterizing the topological fluctuations in the vacuum. Such a functional dependence on the energy is the same obtained in the framework of loop quantum gravity.     

Dual electromagnetism and magnetic monopoles

Dual electromagnetism (proposed some time ago) allows the fractional electric charges and the magnetic monopoles to exist simultaneously. In fact, the Dirac quantization condition can be numerically reduced (with some plausible assumptions) to the third component of the particle total weak isospin, which by definition is always quantized. The field angular momentum,L, of a static particle-magnetic monopole configuration is evaluated exactly; it is found that because the dual photon has a mass,M _c ,L generally depends onr, the separation between a particle and a monopole. However, sinceM _c - 130 GeV, atr > M _c ^–1 ,L is basically dominated by ordinary electromagnetism and as such very weakly dependent onr.     

Hartree–Fock versus quantum Monte Carlo study of persistent current in a one-dimensional ring with single scatterer

We calculate the persistent current of interacting spinless electrons in a one-dimensional ring containing a single δ barrier. We use the self-consistent Hartree–Fock method and the quantum Monte Carlo method which gives fully correlated solutions. Our Hartree–Fock method treats the non-local Fock term in a local approximation and also exactly (if the ring is not too large). Treating the Fock term exactly we attempt to support our previous Hartree–Fock result obtained in the local approximation, in particular the persistent current behaving like I∝L^-1-α, where L is the ring length and α>0 is the power depending only on the electron–electron interaction. Finally, we use the Hartree–Fock solutions as an input for our quantum Monte Carlo calculation. The Monte Carlo results exhibit only small quantitative differences from the Hartree–Fock results.     

Quantum and Classical Brackets

We describe p-mechanical (Kisil, V. V. (1996). Journal of Natural Geometry 9(1), 1–14; Kisil, V. V. (1999). Advances in Mathematics 147(1), 35–73; Prezhdo, O. V. and Kisil, V. V. (1997). Physical Review A 56(1), 162–175) brackets that generate quantum (commutator) and classical (Poisson) brackets in corresponding representations of the Heisenberg group. We do not use any kind of semiclassical approximation or limiting procedure for 0     

Spectroscopic Characterization of Eu(III) Complexes with New Monophosphorus Acid Derivatives of H<Subscript>4</Subscript>dota

The luminescence lifetimes of europium(III) complexes with new monophosphorus acid derivatives of H₄dota were measured by means of time-resolved laser-induced luminescence spectroscopy in H₂O and D₂O. The hydration numbers of these complexes were estimated using different empirical equations [Horrocks and Sudnick (1979) J. Am. Chem. Soc. 101 (1979) 334; Choppin and Barthelemy(1989) Inorg. Chem. 28, 3354–3357; Choppin and Bünzli Lanthanide probes in life, chemical and earth sciences. Theory and practice (1989); Kimura and Kato J. Alloys Comp. 275–277 (1998) 806; Parker (1999) J. Chem. Soc., Perkin Trans. 2, 493–503; Supkowski and Horroks (2002) Inorg. Chim. Acta. 340, 44–48]. It was shown that all the relationships gave similar results with a satisfactory precision. The hydration numbers of complexes of H₃do3a and H₄dota agreed with the literature values. One water molecule is coordinated in complexes of the new ligands. The results showed that the Choppin formula based on measurements only in H₂O can be satisfactorily used for estimation of the hydration numbers.     

Analysis of the Einstein-Podolsky-Rosen experiment by relativistic quantum logic

The EPR experiment is investigated within the abstract language of relativistic quantum physics (relativistic quantum logic). First we show that the principles of reality (R) and locality (L) contradict the validity principle (Q) of quantum physics. A reformulation of this argument is then given in terms of relativistic quantum logic which is based on the principlesR andQ. It is shown that the principleL must be replaced by a convenient relaxation ¯L, by which the contradiction can be eliminated. On the other hand this weak locality principle ¯L does not contradict Einstein causality and is thus in accordance with special relativity.