Abstract
The continuum form of the Gauss-Hertz principle is extended to include the time domain as well as space. The Schrödinger equation and general relativity are derived by this method. The equivalence of the principle is shown to that of the Hamiltonian method where the energy is the expression −[φ∇2φ+A·∇2 A], with φ being the difference between the acceleration potential and potential energy density, andA being the difference between the vector potentials of the acceleration field and the force field. The goal of Hertz to “demonstrate a third arrangement of the principles of mechanics...which starts with... time, space and mass” has apparently been achieved for relativity and for quantum mechanics, in addition to those classical equations previously found.
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Moore, R.L. Further extension of the Gauss-Hertz principle. Found Phys 8, 359–370 (1978). https://doi.org/10.1007/BF00708568
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DOI: https://doi.org/10.1007/BF00708568