Abstract
The nonadditive properties of mass make it desirable to abandon mass as a basis unit in physics and to replace it by a unit of the dimension of the quantum of action [h]. The ensuing four-unit system of action, charge, length, and time [h, q, l, t] interacts in a much more elucidating fashion with experiment and with the fundamental structure of physics. All space-time differential forms expressing fundamental laws of physics are forms of physical dimensions, h, h/q, or q. Their occurrence as periods (residues) of period integrals of forms makes h and q topological invariants in space-time and stresses in general the global nature of quantization. The coordinate dimensions [l] and [t] only come into play for the form-coefficients, the metric tensor, and their tensorial relatives. One thus obtains a very natural guidance for implementing the principle of general covariance, when coordinate-based descriptions are necessary. The consequences for the general theory of relativity are discussed.
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References
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Post, E.J. Physical dimensions and covariance. Found Phys 12, 169–195 (1982). https://doi.org/10.1007/BF00736847
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DOI: https://doi.org/10.1007/BF00736847