Global Positioning System Test of the Local Position Invariance of Planck’s Constant

Publicly available clock correction data from the Global Positioning System was analyzed and used in combination with the results of terrestrial clock comparison experiments to confirm the local position invariance (LPI) of Planck’s constant within the context of general relativity. The results indicate that $h$ is invariant within a limit of $|{\beta }_h|<0.007$, where ${\beta }_h$ is a dimensionless parameter that represents the extent of LPI violation.

Figure 1

Changes in IGS-published clock corrections every 15 min for satellite 18 on 6/10/10, plotted against distance from the Earth’s center. The uncertainty in the ordinate is $\sigma$, as published in the SP3 files. The least-squares linear fit has a small slope $m$.

Figure 2

Daily and filtered values of ${\beta }_f$ for 1 yr for (a) satellite 2, (b) satellite 18, (c) satellite 32. Satellite 2 had the least annual oscillation; satellite 32 had the greatest range in ${\beta }_f$. (d) Combined probability distribution of filtered ${\beta }_f$ for 7 satellites for 1 yr.