Foundations of Physics, Vol . 28, No. 2, 1998 A New Variational Principle for the Fundamental Equations of Classical Physics Vieri Benci 1 and Donato Fortunato 2 Received February 19, 1997 In this paper we introduce a variational principle from which the fundamental equations of classical physics can be deduced. This principle permits a sort of unification of the gravitational and the electromagnetic fields. The basic point of this variational principle is that the world-line of a material point is parametrized by a parameter a which carries some physical information , namely it is related to the rest mass and to the charge . In particular, the (inertial) rest mass will not be a property of a material point , but it will be a constant of the motion which is determined by the initial conditions. In this framework the equality between the inertial and gravitational mass can be deduced. 1. INTRODUCTION In this paper, we introduce a new variational principle for the fundamental equations of the classical physics. Using this principle, we obtain a sort of unification of the gravitational and the electromagnetic fields. Moreover, the (inertial) rest mass will not be a property of a material point, but it will be a constant of the motion which is determined by the initial conditions. Also it turns out to be equal to the gravitational mass. The basic point of this variational principle is that the world-line of a material point is parametrized by a parameter r which carries some physi- cal information, namely it is related to the rest mass and to the charge. The graph of a world-line is a curve in a 5-dimensional space: 4 dimensions for the spacetime and one for r. Thus, this approach recalls the Kaluza theory: (1) however, it is quite different, since the curves in our 5-dimen- sional space are not regarded as geodesics of a 5-dimensional metric. 333 0015-9018/98/0200-0333$15.00/0 Ñ 1998 Plenum Publishing Corporation 1 Dipartmento di Matematica Applicata, Universita Á di Pisa, Pisa, Italy. 2 Dipartmento di Matematica Applicata, Universita Á di Bari, Bari, Italy.