Einstein Case Research Articles

The role of quantum group invariance in nonextensive quantum statistical mechanics

We discuss the consequences of introducing quantum group invariance in nonextensive quantum statistical mechanics. In particular, we show that in the Tsallis formalism the simplest quantum group invariant density matrix leads to a thermodynamics equivalent to the Bose–Einstein case in the Boltzmann–Gibbs formulation.

Quantum group invariant, nonextensive quantum statistical mechanics

We study the consequences of introducing quantum group invariance in the formalism of nonextensive quantum statistical mechanics. We find that the corresponding thermodynamical system is equivalent to a Bose–Einstein gas in the Boltzmann–Gibbs formalism with a higher critical temperature than the standard Bose–Einstein case.

Warped products with special Riemannian curvature

We study the geometry of particular classes of Riemannian manifolds obtained as warped products. We focus on the case of constant curvature which is completely classified and on the Einstein case. This study provides nontrivial instances of Einstein manifolds which are warped product of Einstein factors.

Probability relations involving several subsystems

We consider the question of factorizability in tensor product spaces, and argue that the correlations associated with entangled states are even more problematic in the general case involving any tensor product of Hilbert spaces, than in the Einstein, Podolsky, and Rosen case with only two [1].

Neighbours of Einstein's equations: Connections and curvatures

Once the action for Einstein's equations is rewritten as a functional of an SO(3,C) connection and a conformal factor of the metric, it admits a family of ``neighbours'' having the same number of degrees of freedom and a precisely defined metric tensor. This paper analyzes the relation between the Riemann tensor of that metric and the curvature tensor of the SO(3) connection. The relation is in general very complicated. The Einstein case is distinguished by the fact that two natural SO(3) metrics on the GL(3) fibers coincide. In the general case the theory is bimetric on the fibers.

On the quantum cross sections in dilute gases

The quantal cross section Q(N)qm for collision in dilute gases is given for any order N, where previously in the literature only values up to N=4 were to be found. The quantum-statistical character of Q(N)qm is discussed and calculations are presented for Q(1) through Q(6) for Boltzmann, Fermi–Dirac, and Bose–Einstein cases for 3He–4He, 3He–3He, and 4He–4He using extensive tables of phase shifts.

Struggling with Causality: Einstein's Case

The ArgumentEinstein's concept of causality as analyzed in this paper is a thick concept comprised of: (a) regularity; (b) locality; (c) symmetry considerations leading to conservation laws; (d) mutuality of causal interaction. The main theses are: 1. Since (b)–(d) are not elements of Hume's concept of causality, Einstein's concept, the concept embedded in the theory of relativity, is manifestly non–Humean. 2. On a Humean conception, Newtonian mechanics is a paradigmatically causal theory. Einstein, however, regarded this theory as causally deficient, for it fails to comply with both (b) and (d). Special relativity was (partly) motivated by the wish to correct the first of these failures; general relativity the second. 3. Ironically, general relativity, based on the thick concept of causality, opens the way for a conventionalist understanding of that concept. 4. With regard to human freedom, Einstein professed to be a Spinozist. However, he suggested a version of soft determinism, not found in Spinoza.

Gravity theories with action densities bounded from below

We discuss ways of constructing theories of gravity where the action density is bounded from below. This property can make the euclidean path integral better defined than in the standard Einstein case. For a class of action densities which depend (non-linearly) on the scalar curvature, such models are at the classical level equivalent to scalar-tensor theories of gravity with scalar potentials that imply a stable vacuum (which can be flat space) and where there is the possibility of an inflationary phase, as well as other interesting features. Scalars with such types of potentials appear naturally in some Kaluza-Klein and other theories. When integrating out the scalars in such theories, we could end up with the models discussed here.

Solutions to the Reissner-Nordström, Kerr, and Kerr-Newman problems in fourth-order conformal Weyl gravity.

We continue our study of the general structure of fourth-order conformal Weyl gravity which we are exploring as a possible theory of gravity, and in this paper we present three new exact solutions to the theory which we have found. First we present the complete and exact solution to the Reissner-Nordstr\"om problem associated with a static, spherically symmetric point electric and/or magnetic charge coupled to fourth-order conformal Weyl gravity. We find that, unlike the familiar second-order Einstein case where the modification to the Schwarzschild metric is in the form of a term which behaves like $\frac{1}{{r}^{2}}$, in the fourth-order case the modification is found to behave like $\frac{1}{r}$, i.e., just like the Newtonian potential term itself. Additionally, we present two further exact solutions to the theory which we have found, namely, those associated with the fourth-order Kerr and Kerr-Newman problems in which a stationary, axially symmetric rotating system with or without electric and/or magnetic charge is coupled to gravity.

Cosmic strings in Riemann-Cartan spacetimes

The author introduces a Riemann-Cartan gravitational theory which is conformally invariant and includes a dynamic torsion field along with a scalar field. When he breaks the conformal invariance, the scalar field is fixed and a torsion field remains. This process is then analysed in the geometry of a cosmic string. He finds that, as in Einstein's theory, the resulting Riemannian geometry is flat although the topology is conical in nature. He also finds a torsion field which is singular on the string and decreases with increasing distance from it. Because of the presence of this field, particle and photon motion is different from the Einstein case. This suggests the possibility that the development of galaxies could have been influenced by this field.

Relativistic effects in the motion of artificial satellites: The oblateness of the central body I

The motion of artificial satellites in the gravitational field of an oblate body is discussed in the post — Newtonian framework using the technique of canonical Lie transformations. Two Lie transformations are used to derive explicit results for the longperiodic and secular perturbations for satellite orbits in the Einstein case.

Comment on the Brans-Dicke-Bianchi type-III vacuum solution

We wish to point out that the Brans-Dicke-Bianchi type-III vacuum solution recently given by Tiwari and Singh (1984) is not new. Moreover, the solution given has no correct Einstein limit, contrary to what is claimed by these authors. The Ellis-MacCallum vacuum solution in the Einstein case can be obtained from the Brans-Dicke solution first given by Lorenz-Petzold (1984a).

Causal stochastic interpretation of Fermi—Dirac statistics in terms of distinguishable non-locally correlated particles

Like in the Bose—Einstein case, Fermi—Dirac statistics are shown to correspond to subquantal, causal, space—time behaviour of distinguishable particles correlated by actions-at-a-distance. This justifies the introduction of the non-local hidden parameters introduced by Bohm and Vigier in the stochastic interpretation of quantum mechanics.

Prescribed sources and gauge conditions

Arbitrary, nonconserved, external sources may be coupled to gauge fields. The conservation identities on the field equations then become gauge-fixing conditions on the gauge-breaking terms needed to implement this approach. The stability of co-ordinate choices under source variations is discussed in the Einstein case.