Scale relativity and quantization of the planetary system around the pulsar PSR B1257 + 12

The theory of scale relativity suggests that, at very large time scales, classical laws should be replaced by a non-deterministic, quantum-like description. The theory gives up individual, localized trajectories, but it yields the probability density of families of virtual trajectories, as deduced from a generalized Schrödinger equation. In this paper, we compare the system of three planets recently discovered around the pulsar PSR B1257 + 12 to the predictions of the theory. We expect the planet periods to be quantized according to the formula , where is a multiple of 144 km/s (as determined from the Solar System and from galactic and extragalactic data). The observed periods confirm the theory with a remarkably high precision (relative differences of some 10 4) and in a highly significant way (probability 3 × 10 5), allowing us to successfully check second and third order terms. We