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

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

Jul 1998

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998csf.....9.1043n&link_type=abstract

Chaos Solitons Fractals, Vol. 9, No. 7, p. 1043 - 1050

Mathematics

Probability

3

Pulsars: Planetary Systems, Quantum Effects: Planetary Systems, Planetary Systems: Periods, Planetary Systems: General Relativity

Scientific paper

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, the author compares the system of three planets around the pulsar PSR B1257+12 to the predictions of the theory. He expects the planet periods to be quantized according to the formula Tn = 2πGMPSR(√n2+n/2/ω˜0)3, where ω˜0 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 one to successfully check second and third order terms. The author finally predicts the periods of possible additional planets in this system, in particular T2 = 1.958 days.

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