Relativistic Notion of Mass and a Resolution of a Conflict Between Schopenhauer and Hegel

We discuss a mass change that has its origin in the action of forces on an object. This phenomenon, well-known in the context of quantum field theory (mass renormalization), can be discussed systematically in both classical and quantum mechanics in a framework given by Stückelberg. We employ this framework to resolve an interesting conflict of opinions between Schopenhauer and Hegel in the mid-19th century. We show that Hegel, Kant, and Schopenhauer demonstrated remarkable prescience in their views as seen from a modern perspective.     

Second Quantization of the Stueckelberg Relativistic Quantum Theory and Associated Gauge Fields

The gauge compensation fields induced by the differential operators of the Stueckelberg-Schrödinger equation are discussed, as well as the relation between these fields and the standard Maxwell fields; An action is constructed and the second quantization of the fields carried out using a constraint procedure. The properties of the second quantized matter fields are discussed.     

Eikonal Approximation to 5D Wave Equations and the 4D Space-Time Metric

We apply a method analogous to the eikonal approximation to the Maxwell wave equations in an inhomogeneous anisotropic medium and geodesic motion in a three dimensional Riemannian manifold, using a method which identifies the symplectic structure of the corresponding mechanics, to the five dimensional generalization of Maxwell theory required by the gauge invariance of Stueckelberg's covariant classical and quantum dynamics. In this way, we demonstrate, in the eikonal approximation, the existence of geodesic motion for the flow of mass in a four dimensional pseudo-Riemannian manifold. These results provide a foundation for the geometrical optics of the five dimensional radiation theory and establish a model in which there is mass flow along geodesics. We then discuss the interesting case of relativistic quantum theory in an anisotropic medium as well. In this case the eikonal approximation to the relativistic quantum mechanical current coincides with the geodesic flow governed by the pseudo-Riemannian metric obtained from the eikonal approximation to solutions of the Stueckelberg–Schrödinger equation. The locally symplectic structure which emerges is that of a generally covariant form of Stueckelberg's mechanics on this manifold.     

The application of novel extraction chromatographic materials to the characterization of radioactive waste solutions

A simple method for the separation and preconcentration of radiostrontium from acidic nuclear waste solutions for subsequent determination is described. The method involves passage of the waste solution, acidified to at least 2M with nitric acid, through an extraction chromatographic column consisting of a 1M solution of bis-4,4(5)[(t-butyl)cyclohexano]-18-crown-6 in 1-octanol sorbed on an inert polymeric substrate, which preferentially retains strontium. The strontium may then be stripped from the column with a small volume of either dilute (0.05M) nitric acid or water. Actinides present are removed quantitatively prior to strontium separation by passage of the sample through an actinide-specific extraction chromatographic column.Work performed under the auspices of the Office of Basic Energy Sciences, Division of Chemical Sciences, U. S. Department of Energy, under contract number W-31-109-ENG-38.     

Equilibrium relativistic mass distribution for indistinguishable events

A manifestly covariant relativistic statistical mechanics of a system of N indistinguishable events with motion in space-time parametrized by an invariant historical time is considered. The relativistic mass distribution for such a system is obtained from the equilibrium solution of the generalized relativistic Boltzmann equation by integration over angular and hyperangular variables. All the characteristic averages are calculated. Expressions for the pressure and the energy density are found, and the relativistic equation of state is obtained. Validity criteria are defined. The Galilean limit is considered; the theory is shown to pass over to the usual nonrelativistic statistical mechanics of indistinguishable particles. Anti-events are introduced; for an event-anti-event system the equation of state p, T ⁶ is found, which gives the value of the sound velocity c ² = 0.20, in agreement with the realistic equation of state suggested by Shuryak for hot hadronic matter.