Temporal dilation due to special relativity has a significant impact on the Global Positioning System (GPS). The GPS is a satellite-based navigation system that relies on precise timing to calculate accurate position information. The system uses a network of satellites orbiting the Earth to transmit signals that are received by GPS receivers on the ground.
However, because the satellites are in motion relative to observers on the Earth's surface, the principles of special relativity come into play. According to special relativity, time appears to pass differently for objects in relative motion. In this case, the satellites are moving at high speeds relative to observers on the ground.
The time dilation effect means that clocks on the satellites will appear to run slightly faster relative to clocks on the Earth's surface. This is because the satellites are moving at significant velocities, and as a result, experience time dilation. The time difference might be small but can accumulate over time.
If the time difference between the clocks on the satellites and the clocks on the ground was not accounted for, it would lead to errors in the GPS system. The positions calculated by the GPS receivers would gradually become less accurate. For example, errors could accumulate and cause discrepancies of several meters or more.
To compensate for this effect, the GPS system incorporates relativistic corrections. The atomic clocks aboard the satellites are programmed to run slightly slower to match the expected time dilation effect. Additionally, the GPS receivers on the ground apply corrections to account for the time difference between the satellite clocks and the receiver's clock.
By accounting for the relativistic time dilation, the GPS system can maintain the necessary accuracy for position calculations. Without the consideration of this effect, the GPS system would suffer from significant errors in determining locations. Therefore, special relativity's temporal dilation plays a crucial role in ensuring the precision and functionality of the GPS system.