Macroscopic quantum-type potentials in scale relativity

TL;DR

This paper explores how scale relativity and fractal space-time concepts introduce quantum-like potentials that could influence biological systems, with implications for understanding self-organization and multi-scale processes.

Contribution

It reviews the application of scale relativity theory to biology, highlighting the role of quantum-type potentials arising from fractal space-time in biological phenomena.

Findings

Quantum-type potentials may influence biological processes.

Fractal space-time could underpin self-organization in biology.

Potential links between physical phenomena and biological structures.

Abstract

We review in this paper the use of the theory of scale relativity and fractal space-time as a tool particularly well adapted to the possible development of a future genuine theoretical systems biology. We emphasize in particular the concept of quantum-type potentials, since in many situations the effect of the fractality of space -- or of the underlying medium -- amounts to the addition of such a potential energy to the classical equations of motion. Various equivalent representations -- geodesic, quantum, fluid mechanical, stochastic -- of these equations are given, as well as several forms of generalized quantum potentials. Examples of their possible intervention in high critical temperature superconductivity and in turbulence are also described, since some biological processes may be analog in some aspects to these physical phenomena. These potential energy extra contributions could have emerged in biology from the very fractal nature of the medium, or from an evolutive advantage, since they involve spontaneous properties of self-organization, morphogenesis structuration and multi-scale integration.