Laurent Nottale

Macroscopic quantum-type potentials in theoretical systems biology.

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 systems theoretical 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—can be reduced to the addition of such a potential energy to the classical equations of motion. Various equivalent representations—geodesic, quantum-like, 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 similar in some aspects to these physical phenomena. These potential extra energy 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. Finally, some examples of applications of the theory to actual biological-like processes and functions are also provided.

NUMERICAL SIMULATION OF A MACRO-QUANTUM EXPERIMENT: OSCILLATING WAVE PACKET

We perform numerical simulations of a new proposal of laboratory experiment that would allow the transformation of a classical fluid into a quantum-type (super)fluid through the application of a generalized quantum potential. This quantum potential is simulated by using a real time retroactive loop involving a measurement of density, a calculation of the potential in function of the measured density, then an application of the calculated potential through a classical force. This general experimental concept is exemplified here by the case of a nonspreading oscillating wave packet in a harmonic oscillator potential. We find signatures of a quantum-like behavior which are stable against various perturbations. Finally, the feasability of a realization of this concept in an actual plasma experiment is analyzed.

A catalog of isolated galaxy pairs with accurate radial velocities

The present paper is devoted to the construction of a catalog of isolated galaxy pairs from the Uppsala Galaxy Catalog (UGC), using accurate radial velocities. The UGC lists 12 921 galaxies to δ > −2◦30′ and is complete to an apparent diameter of 1′. The criteria used to define the isolated galaxy pairs are based on velocity, interdistance, reciprocity and isolation information. A peculiar investigation has allowed to gather very accurate radial velocities for pair members, from high quality HI and optical measurements (median uncertainty on velocity differences 10 kms−1). Our final catalog contains 1005 galaxy pairs with ρ > 2.5, of which 509 have ρ > 5 (50% of the pairs, i.e. 8%of the UGC galaxies) and 273 are highly isolated with ρ > 10 (27% of the pairs, i.e. 4% of the UGC galaxies). Some global properties of the pair catalog are given.

Emergence of complex and spinor wave functions in scale relativity. II. Lorentz invariance and bi-spinors

Owing to the non-differentiable nature of the theory of Scale Relativity, the emergence of complex wave functions, then of spinors and bi-spinors occurs naturally in its framework. The wave function is here a manifestation of the velocity field of geodesics of a continuous and non-differentiable (therefore fractal) space-time. In a first paper (Paper I), we have presented the general argument which leads to this result using an elaborate and more detailed derivation than previously displayed. We have therefore been able to show how the complex wave function emerges naturally from the doubling of the velocity field and to revisit the derivation of the non-relativistic Schrodinger equation of motion. In the present paper (Paper II), we deal with relativistic motion and detail the natural emergence of the bi-spinors from such first principles of the theory. Moreover, while Lorentz invariance has been up to now inferred from mathematical results obtained in stochastic mechanics, we display here a new and deta...