Horst-Heino von Borzeszkowski

Entropy identity and equilibrium conditions in relativistic thermodynamics

Starting out with the balance equations for energy-momentum, spin, particle and entropy density, an approach is considered which represents a framework for special- and general-relativistic continuum thermodynamics. A general entropy density 4-vector, containing particle, energy-momentum, and spin density contributions, is introduced. This makes possible, firstly, to test special entropy density 4-vectors used by other authors with respect to their generality and validity and, secondly, to determine entropy supply and entropy production. Using this entropy density 4-vector, material-independent equilibrium conditions are discussed. While in literature, generally thermodynamic equilibrium is determined by introducing a variety of conditions by hand, the present approach proceeds as follows: For a comparatively wide class of space–time geometries, the necessary equilibrium conditions of vanishing entropy supply and vanishing entropy production are exploited. Because these necessary equilibrium conditions do not determine the equilibrium, supplementary conditions are added systematically motivated by the requirement that also all parts of the necessary conditions have to be fixed in equilibrium.

The Weyl-Cartan Space Problem in Purely Affine Theory

According to Poincaré, only the “epistemological sum of geometry and physics is measurable”. Of course, there are requirements of measurement to be imposed on geometry because otherwise the theory resting on this geometry cannot be physically interpreted. In particular, the Weyl-Cartan space problem must be solved, i.e., it must be guaranteed that the comparison of distances is compatible with the Levi-Civita transport. In the present paper, we discuss these requirements of measurement and show that in the (purely affine) Einstein-Schrödinger unified field theory the solution of the Weyl-Cartan space problem simultaneously determines the matter via Einsteins equations. Here the affine field Γikl represents Poincarés sum, and the solution of the space problem means its splitting in a metrical space and in matter fields, where the latter are given by the torsion tensor Γi[kl].

Comment on the Article “Relativistic Non-Equilibrium Thermodynamics Revisited”

Abstract There are two problematic items in García-Colín and Sandoval-Villalbazos approach to “relativistic non-equilibrium thermodynamics” (L.S. García- Colín and A. Sandoval-Villalbazo, J. Non-Equilib. Thermodyn. 31, 2006, pp. 11–22). The paper does not follow the fundamentals of relativity theory; according to them, the energy-momentum tensor (EMT) has to include all energies of the considered system. Secondly, strange thermodynamic consequences result by using the presuppositions made by the authors. The paper is critically discussed and some shortcomings are elucidated.

Classical gravity and quantum matter fields in unified field theory

The Einstein-Schrödinger purely affine field theory of the non-symmetric field provides canonical field equations without constraints. These equations imply the Heisenberg-Pauli commutation rules of quantum field theory. In the Schrödinger gauging of the Einstein field coordinatesUkli=Γkli−δliΓkmm, this unified geometric field theory becomes a model of the coupling between a quantized Maxwellian field in a medium and classical gravity. Therefore, independently of the question as to the physical truth of this model, its analysis performed in the present paper demonstrates that, in the framework of a quantized unified field theory, gravity can appear as a genuinely classical field.

Reference systems and gravitation

It is shown how the formalism of the tetrad theory of gravitation used by Treder (1967a, b, 1970) follows from the more general fibre bundle formalism. This is of interest in the study of the relations between tetrad theories and the general theory of relativity. In particular, the breaking of the principle of general relativity and the interpretation of tetrad fields as reference systems are considered in greater detail.

On the behaviour of test matter in the vicinity of singularities

The eikonal approximation of the Klein-Gordon equation in a Riemannian space is considered; this leads to the equations of timelike geodesics. It is shown that, in the vicinity of focal points, the eikonal limit is not valid for test matter focused by gravity. Therefore, first, in the vicinity of singularities considered in the so-called singularity theorems such test matter must be described by their (quantum) field equations and, second, there is no direct physical interpretation of incomplete timelike geodesics.

On the compatibility of spinor field equations with regard to generalisations of Weyl's lemma

Generalisations of Weyls lemma are discussed. In order to secure the compatibility of the spinor field equations, the generalisations may not be arbitrary. It is shown that a contracted Weyl lemma must be valid. This lemma ‘saves’ the duality between the Lorentz covariant and the Einstein covariant representation of the equation of continuity. The meaning of Weyls lemma and its generalisations is discussed in terms of the fibre bundle theory.

On Matter and Metric in Affine Theory of Gravity

The affine theory was conceived as a geometric model, wherein the connection field is the primary structure of the space-time. According to the program lying on the basis of this theory, metric and some sort of matter are somehow to be deduced from the connection field. In the present paper, we point out classical ways to a realization of this program. It is shown that, even in that case where the introduction of the metric seems to exclude the coupling of gravity to matter, the situation is not so hopeless as one may assume. In particular, for a symmetric Einstein tensor, it is answered the old question as to a self-consistent introduction of a metric and a metrical energy-momentum tensor controversially debated by Einstein, Eddington, and Weyl.

Quantum mechanics and the physical reality concept

The difference between the measurement bases of classical and quantum mechanics is often interpreted as a loss of reality arising in quantum mechanics. In this paper it is shown that this apparent loss occurs only if one believes that refined everyday experience determines the Euclidean space as the real space, instead of considering this space, both in classical and quantum mechanics, as a theoretical construction needed for measurement and representing one part of a dualistic space conception. From this point of view, Einsteins program of a unified field theory can be interpreted as the attempt to find a physical theory that is less dualistic. However, if one rgards this dualism as resulting from the requirements of measurements, one can hope for a weakening of the dualism but not expect to remove it completely.

Interference and interaction in Schrödinger's wave mechanics

Reminiscing on the fact that E. Schrödinger was rooted in the same physical tradition as M. Planck and A. Einstein, some aspects of his attitude to quantum mechanics are discussed. In particular, it is demonstrated that the quantum-mechanical paradoxes assumed by Einstein and Schrödinger should not exist, but that otherwise the epistemological problem of physical reality raised in this context by Einstein and Schrödinger is fundamental for our understanding of quantum theory. The nonexistence of such paradoxes just shows that quantum-mechanical effects are due to interference and not to interaction. This line of argument leads consequently to quantum field theories with second quantization, and accordingly quantum theory based both on Plancks constant h and on Democrituss atomism.