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THE RIEMANNIAN SPACE-TIME OF LIVING PROCESSES
Jonathan Tennenbaum
In the 1930s and 1940s Vladimir Vernadsky and his collaborators put forward the conception, that living processes are characterized by a special type of space-time geometry, different from that of non-living processes.
Vernadsky pointed, on the one hand, to the overwhelming empirical evidence for what he called "the fundamental material-energetic distinction of living matter in the biosphere"; on the other hand, he emphasized Pasteur's discovery, of the pervasive property of optical dissymmetry (chirality) manifested by the material substrate of living processes. Following ideas of Pierre Curie, Vernadsky suggested that living organisms are governed by a different "geometrical state of space", not corresponding to ordinary euclidean geometry, but instead to a space-time geometry of the Riemannian type. Vernadsky noted, after discussions with mathematicians at the time, that the required form of Riemannian geometry had not yet been elaborated.
Unfortunately, very little substantial progress has been made, over the last 60 years, in answering this fundamental question raised by Vernadsky. This is partly due to an inadequate understanding -- including on the part of most mathematicians and physicists -- of the relevant geometrical conceptions of Bernhard Riemann; and partly to the lack of suitable experimental methods and methodologies for determining the characteristics of living processes in vivo. This is most important because, as Riemann and Vernadsky themselves emphasized, the required form of space-time geometry cannot be determined apriori, as a mathematical abstraction, but must be derived empirical, by measurements of living processes themselves.
Today, advances in the detection and theoretical analysis of biophoton emission of living cells, may open the way for a new approach to Vernadsky's hypothesis, concerning the space-time geometry of living processes. This is the subject of our talk, which will examine the conceptions of Vernadsky-Riemann on the background of modern developments in quantum biology, and suggest some directions for experimental investigation.
