The author, who was Schrödinger's assistant during his last years in Vienna, gives an account of Schrödinger's views and activities during that time which lead him to a different approach to research on the relations between gravitation and quantum phenomena. Various features of past research are outlined in nontechnical terms. A heuristic argument is presented for the role of the zero-point energy of massive particles in counteracting gravitational collapse and the formation of horizons. Arguments are presented for the view that (...) progress in describing extreme gravitational phenomena can be achieved by the new outlook obtained from the introduction of the analog of Maxwell's vacuum displacement term with a quasiconstant parameter, rather than from renormalization of special processes, even if this is successful. The results can be expected to be in accord with Schrödinger's conjectures.A physical interpretation for the change of sign of the differential invariant of Karlhede, Lindström, and Åman at the horizon is suggested.Some important historical details about Schrödinger are touched upon. (shrink)

The prediction of general relativity on the gravitational collapse of matter ending in a point is viewed as an absurdity of the kind to be expected in any consistent physical theory due to ultimate conflicts of the axioms of geometry with the properties of physical objects. The necessity to introduce a probability interpretation for the solution of partial differential equations in space time for quantum theory points to similar roots. It is pointed out that quantum theory in the very small (...) is not going to eliminate the problem, but macroscopic quantum effects in the large, modifying the properties of the horizon, may achieve it. Solutions such as wormholes allow as much empirical evidence as any science fiction. The present approach considers successive modifications of the field equations and equations of motion of gravitational theory by admixture of terms with higher derivatives. The rigorous application of a gauge principle combines Einstein's equations with the tensor analog of Maxwell's equations which are of third order for the metric. It is speculated that the natural presence of torsion in such a gauge theory is related to matter sources. (shrink)

The requirement to present Dirac's Large Number Hypothesis in one system of units in which the resulting modifications to Einstein's theory are exhibited, led to the construction of generalizations of General Relativity based rigorously on the geometry of semisimple groups. The foundations of such a theory are discussed and some of their possible interpretations are presented.

Following a heuristic modification of the principle of inertia and the principle of equivalence, a higher-dimensional metric theory is constructed on the manifold of the SO(3, 2) De Sitter group which allows us to treat structureless and spinning particles on the same footing. A dimensional analysis of the physical magnitudes is performed.