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Temporal Variation of the Fundamental Physical Quantities in a Static Universe

The standard interpretation of the observed redshifted spectra and luminosities towards distant astrophysical objects is that the universe is expanding, an inference which is found to be consistent with other cosmological probes as well. Clearly, only the interpretation of {\it dimensionless} quantities does not depend on the physical unit system as opposed to {\it dimensional} quantities whose dynamics does depend on the arbitrarily chosen system of units. All that redshift or luminosity measurements really indicate is that cosmological scales expand {\it relative} to local scales. An alternative choice of a ruler could be the distance between two remote galaxies, in which case local distances have to decrease with time (with respect to the ruler) for consistency with redshift measurements. In the latter choice, microscopic scales such as the Compton wavelength, or the Planck length, decrease with time, and consequently fundamental `constants' such as the Planck constant, speed of light, Newton gravitational constant, and particle masses, are spacetime-dependent. To illustrate this fundamental indeterminacy we construct an alternative interpretation to the expanding model that is characterized by a static metric with time-dependent fundamental physical quantities. The two alternative descriptions, are referred to as the `expanding' and `static' space perspectives, respectively. Cosmological inflation, recombination, and all other early universe processes are unaltered; the `expanding' and `static' perspectives are associated with exactly the same cosmological model.