Computer Science
Scientific paper
Jul 1998
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998csf.....9.1115p&link_type=abstract
Chaos Solitons Fractals, Vol. 9, No. 7, p. 1115 - 1142
Computer Science
7
Relativity Theory: Energies
Scientific paper
The author derives some relations in the framework of Nottale's theory of scale relativity. He uses the formal tool of this theory, namely a complex derivative operator associated to a complex velocity. He points out the possibility to recover some differential relations given by the correspondence principle. Then, the author compares the complex equations that he obtained with their well-known classical counterparts. The original result, with respect to the 'scale-covariance' statements, is the following: energy is not a pure quadratic expression in terms velocities, as in classical mechanics; it contains also a term of velocity divergence, which is present intrinsically in its expression. Then, he infers the Dirac and Pauli equations from the energy formulas. The author finds that the 'form' of the equations of motion also changes, they contain an additional term of current, which is absent in the classical equations.
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