Relativity in Time Scale: Contraction of Mass and Planck’s Constant

All physical quantities can be expressed in terms of seconds or exponentials of seconds by using a time scale transformation method, a variant of the geometrized unit system. Since it is a fact that time slows down in a gravitational field by Schwarzshild’s gravitational time dilation factor (γg) due to general relativity and all physical quantities can be expressed as time in time scale transformation; in this article it is hypothesized that from the perspective of an observer at a point in a gravitational field, not only time or length but all other quantities are also scaled up/down by the gravitational time dilation factor at that point, with respect to their units in time scale. According to the hypothesis, for two observers at different points of a gravitational field where time flows γg times slower for one of them compared to the other, the observer with the shorter time perception measures the same mass, energy, momentum or charge quantities γg times smaller; Planck’s constant or action γg² times lower; the same frequency γg times higher; and the same Ricci curvature γg² times higher, compared to the observer with a longer time perception. Therefore, all physical quantities become relative to the observer; even the fundamental attributes of elementary particles (mass, charge, spin) might not be having predefined, invariant values, unless an interaction (measurement) with an observer in a gravitational field (a second entity) takes place. At first glance, such a claim seems contradictory to the fundamental conservation laws of physics. In fact, the conservation laws still hold from the perspective of the observer, as long as the gravitational time dilation factor for the observer’s position is constant. The hypothesis takes Einstein’s field equation for granted. Herein, it is theoretically demonstrated that physics still works consistently under this assumption and it provides testable predictions, alternative explanations for phenomenons like the nature of potential energy, expansion of universe, gravitatioal redshift and excessive gravitational lensing around the galaxies. For instance; expansion of universe can be interpretted as the result of a continuous increase in the time perception of the observer; the gravitational potential energy is not stored somewhere in the gravitational field, but as extra mass within the object itself; the observed excessive gravitational lensing might be a result of the time delay in our measurements and black holes have no interior. In the discussion, Pound-Rebka experiment and Hutchin’s work on the variations of Planck’s constant are assessed in the context of the hypothesis to present its strengths and discordances with the current understanding. The final objective of our work is to show that the hypothesis is self-consistent and worth to be tested experimentally.