Masters Thesis

GPS test of the local position invariance of Planck's constant

Publicly available data on satellite positions and clock corrections for the Global Positioning System was analyzed and used in combination with the results of prior terrestrial clock comparison experiments to confirm the time dilation of general relativity for atomic and cryogenic resonator clocks. A model for testing local position invariance (LPI) in the context of general relativity was developed and used to confirm that Planck's constant $h$ is invariant within a limit of $0.007$, where $\beta_h$ is a dimensionless parameter that represents the extent of its LPI violation. The model assumes that general relativity is correct for macroscopic gravitational effects, while looking for LPI violations of non-gravitational phenomena. It is widely believed that it is meaningless to measure variations of fundamental constants with dimensions, such as $h$, and that it is only meaningful to look for variations in dimensionless fundamental constants such as the fine-structure constant $\alpha$. It is shown that when a system of units is carefully defined, variations of $h$ and the electric charge $e$ would be observable. Any variation of dimensionless constants such as $\alpha$ must arise from the variation of a quantity with dimensions. This finding is independent of the choice of units, including Planck units.\beta_h

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