Quantum particle production in the formation of naked Kasner-type singularities

The quantum production of scalar massless particles cannot prevent the formation of thread-like naked singularities.     

Repulsive gravity near naked singularities and point massive particles

We summarize the parallel session B4: ‘Analytic approximations, perturbation theory, effective field theory methods and their applications’ and the joint session B2/B4: ‘Approximate solutions to Einstein equations: Methods and Applications’, of the GR20 & Amaldi10 conference in Warsaw, July 2013. The contributed talks reported significant advances on various areas of research in gravity.     

The nature of singularities

Conclusions We have established, under reasonable conditions, that singularities must be either curvature singularities or primordial singularities. There is still the possibility that the Cauchy data for, say, a gravitational collapse might be compatible with or might necessitate a quasi-regular singularity that, though technically primordial, lies entirely to the future of the data-surface. Until this is ruled out, we cannot be sure that classical relativity does give curvature singularities in physically reasonable situations.The methods examined here are concerned only with whether the Riemann tensor is bounded, and so they can say nothing on the crucial question ofhow badly the Riemann tensor may be unbounded. Upper limits on the behavior on some geodesies have been set by Tipler [6], but more work needs to be done here. One would like to know whether the curvature could fail to be, say,L ¹; but to answer this we should have to use quite different methods based on integration overM rather than the behavior along curves.A revised version of material presented at the Singularities Symposium of the 8th International Conference on General Relativity and Gravitation, August 1977.     

The possible existence of Hs in nature from a geochemical point of view

A hypothesis of the existence of a long-lived isotope ²⁷¹Hs in natural molybdenites and osmirides is considered from a geochemical point of view. It is shown that the presence of Hs in these minerals can be explained only by making an additional ad hoc assumption on the existence of an isobaric pair of ²⁷¹Bh-²⁷¹Hs. This assumption could be tested by mass-spectrometric measurements of U, Pb, Kr, Xe, and Zr isotopic shifts.     

Existence of naked singularities in spherical symmetry

Existence conditions for naked singularities in spherical symmetry will be proved for arbitrary Misner–Sharp masses which fulfil the weak energy condition.     

On the occurrence of naked singularities in general relativity

It is shown that spherically symmetric collapse can lead to singularities which arenot hidden within black holes.Work supported by the Deutsche Forschungsgemeinschaft.     

Yet another point of view on the nature of quark condensates

Some questions associated with the nature and role of quark condensates are considered by using the example of two simple models where the interaction has a four-quark form. It is shown that, basically, quark condensates are weakly sensitive to the form of interaction.     

The Principle Underlying Quantum Mechanics

The present article reports on the finding of the principle behind quantum mechanics. The principle, referred to as genuine fortuitousness, implies that the basic event, a click in a counter, comes without any cause and thus as a discontinuity in spacetime. From this principle, the formalism of quantum mechanics emerges with a radically new content, no longer dealing with things (atoms, particles, or fields) to be measured. Instead, quantum mechanics is recognized as the theory of distributions of uncaused clicks that form patterns laid down by spacetime symmetry and is thereby revealed as a subject of unexpected simplicity and beauty. The departure from usual quantum mechanics is strikingly borne out by the absence of Planck's constant from the theory. The elimination of indeterminate particles as cause for the clicks, which the principle of genuine fortuitousness implies, is analogous to the elimination of the ether implied by the principle of relativity.     

Quantum Mechanics from Focusing and Symmetry

A foundation of quantum mechanics based on the concepts of focusing and symmetry is proposed. Focusing is connected to c-variables—inaccessible conceptually derived variables; several examples of such variables are given. The focus is then on a maximal accessible parameter, a function of the common c-variable. Symmetry is introduced via a group acting on the c-variable. From this, the Hilbert space is constructed and state vectors and operators are given a definite interpretation. The Born formula is proved from weak assumptions, and from this the usual rules of quantum mechanics are derived. Several paradoxes and other issues of quantum theory are discussed.     

Geometry from the spectral point of view

In this Letter, we develop geometry from a spectral point of view, the geometric data being encoded by a triple (A. H. D.) of an algebraA represented in a Hilbert spaceH with selfadjoint operatorD. This point of view is dictated by the general framework of noncommutative geometry and allows us to use geometric ideas in many situations beyond Riemannian geometry.

This paper is dedicated to the memory of J. Schwinger     

On the nature of the nearest singularities of the free energy in the neighborhood of a critical point

Algebraic functions are used to provide an example of multiple-valued functions which coincide with a model (single-valued) free energy on one sheet of the Riemann surface in the neighborhood of a critical point. For the case of homogeneous free energies andα=α′=0, there are enough conditions to determine the behavior of the nearest singularities (branch points) to the critical point of the algebraic function. If no other singularities are present these branch points would represent the spinodal line. The particular exponents of the two-dimensional Ising model are used to provide a specific example.     

Relating the Quantum Mechanics of Discrete Systems to Standard Canonical Quantum Mechanics

Standard canonical quantum mechanics makes much use of operators whose spectra cover the set of real numbers, such as the coordinates of space, or the values of the momenta. Discrete quantum mechanics uses only strictly discrete operators. We show how one can transform systems with pairs of integer-valued, commuting operators $P_i$ and $Q_i$ , to systems with real-valued canonical coordinates $q_i$ and their associated momentum operators $p_i$ . The discrete system could be entirely deterministic while the corresponding (p, q) system could still be typically quantum mechanical.     

Quantum Mechanics of H-Atom from Path Integrals

The quantum mechanical Coulomb problem in two and three dimensions is solved completely in terms of path integrals. We derive the integral representations for the Green's functions in configuration space and recover the wave functions from factorized residues.     

On the occurrence of naked singularities in general relativity. II

It is shown that naked shell crossing singularities can occur in the gravitational collapse of a spherically symmetric ball of perfect fluid for a large family of equations of state in which the pressure has an (arbitrarily large) upper bound, and, moreover, that this behaviour is stable with respect to spherically symmetric perturbations of the initial data, as well as with respect to perturbations of the equation of state.Work supported by the Deutsche Forschungsgemeinschaft.