The use of relativity within GPS navigation systems is crucial for compensating for the effects of time dilation due to both special relativity and general relativity. Without accounting for these effects, the accuracy of GPS positioning would significantly degrade.
First, let's consider the effect of special relativity on GPS satellites. The satellites in the GPS constellation are in motion relative to observers on Earth's surface. According to special relativity, time dilation occurs when objects are in relative motion. Therefore, the atomic clocks aboard GPS satellites, which are used to provide precise timing information, experience time dilation compared to clocks on the Earth's surface.
Due to the high velocities of the satellites (approximately 14,000 kilometers per hour), time dilation effects become significant. If not accounted for, the time discrepancy between the satellite clocks and the Earth-based clocks would result in inaccurate positioning calculations. However, the GPS system's algorithms take into account the time dilation predicted by special relativity. The satellite clocks are adjusted to compensate for the time dilation effect, ensuring that they remain synchronized with the clocks on Earth's surface.
Next, let's consider the effect of general relativity on GPS satellites. The satellites are also subject to a weaker gravitational field in their orbit compared to the Earth's surface. According to general relativity, time dilation occurs in the presence of a stronger gravitational field. Therefore, the atomic clocks in the satellites, being in a weaker gravitational field, experience time passing more quickly compared to clocks on the Earth's surface.
To account for this effect, the satellite clocks are adjusted once again. The clocks on the satellites are intentionally made to run slightly faster than clocks on Earth. By doing so, the effects of general relativity's gravitational time dilation are compensated for, and the clocks remain synchronized with the clocks on Earth's surface.
By carefully accounting for both the time dilation effects predicted by special relativity (due to relative motion) and general relativity (due to gravitational fields), the GPS navigation system can provide accurate positioning and timing information.
It's worth noting that the corrections for relativity in GPS are relatively small but are essential to ensure the precision of the system. The success of GPS navigation in everyday life is a practical demonstration of the validity and applicability of Einstein's theories of relativity.