The conventional wisdom (my favorite oxymoron) about Einstein’s theories is that, in our everyday lives, Newtonian physics is sufficient, without resorting to theories of relativity or quantum mechanics. If you ever use GPS to navigate on our roads (or streets or forests), however, this is no longer true. The current accuracy of our global GPS system is dependent on the practical application of Einstein's relativity theories. Of course, you can use GPS (or drop an apple on someone’s head) without knowing about either Einstein or Newton, but without Relativity Theory, that accuracy would not be possible. At Matt Parker’s YouTube channel, he reports the existence of an altitude at which positive and negative time distortions on a satellite cancel each other out. Parker made up a definition for this term, the "Time Dilatopause,” in an episode of his podcast here. My summary:
On satellites, time “runs faster” relative to earth time because of the lower gravity at that satellite's mean altitude from Earth. Simultaneously, time “runs slower” due to the satellite’s speed relative to objects at rest on Earth’s surface. In the case of geostationary satellites like those used in the global GPS system, the “slowdown” due to relative speed is 7.2 microseconds per day. The “speedup” due to the lower gravity is 38.4 microseconds per day. The “slowdown” is calculated with the formulas of Special Relativity; the overall correction is calculated with the formulas of General Relativity (which takes gravity into account while including the formulas of SR). 38.4 microseconds per day is the net speedup, which would be 45.6 were it not for the need to subtract the “Special Relativity slowdown” of 7.2 microseconds per day. It is thus the formulas of General relativity, used to adjust the speed of the clocks on the satellites, which gives GPS calculations their current accuracy. On your next GPS-guided journey, thank Einstein for making this accuracy possible.
It was Kevin Brown (see his free book, “Reflections on Relativity,” at https://www.mathpages.com/rr/rrtoc.htm) who worked out the altitude of the “Time Dilatopause” at about 1.5 times the Earth’s radius, lower than GPS satellites, which orbit at about 3,000 km. (Note that it would not be useful to orbit GPS satellites so close to Earth, as they would not be geosynchronous there.)
A native Australian comedian and nerd, who describes himself as a “stand-up mathematician,” Matt Parker’s website is standupmaths.com, where you’ll find a plethora of goodies. He’s the author of “Humble Pi: When Math Goes Wrong in the Real World.”
His podcast, “A Podcast of Unnecessary Detail,” is at http://festivalofthespokennerd.com/podcast.
Happy learning. Grow and have fun!
