Time dilation is real! And anyone who uses a GPS, or the “My Location” option on Google Maps, is making direct use of the fact that time dilation is real.
The idea behind time dilation is just as you describe, where your perception of time is dependent on how fast you’re going, or how close to a very large object you are. Interstellar actually did a remarkably good job of discussing time dilation in general, especially given how counter-intuitive ideas to do with relativity can be.
In Interstellar, the major plot points surrounding time dilation are the difference between time passing in two different locations, where the astronauts sitting near the black hole felt time passing at a slower rate than their families back home on Earth. Similarly, when some of them head down to the water world, they feel time passing at a slower rate than the astronaut left on the spacecraft. Now, ignoring the exact numbers of this difference, which depends on things like how big the black hole is, how far you are from it, and how much movie magical math you’re willing to go for, this kind of time dilation does happen.
The principle is this: the deeper you find yourself in a strong gravitational field, the slower your clock will run, relative to someone who is not in as strong a gravitational field. This can be translated into meaning the closer you are to something large, the slower your clocks will run. However, it also means that if your two clocks are the same distance from two objects, one which has a much stronger gravitational pull than the other (say, a planet for one clock, and a black hole for the other), the clock around the more massive object (the black hole) will run slower, even though both clocks are the same distance away.
A GPS satellite, which orbits about 12,500 miles above the surface of the earth, is further away from the Earth than those of us who live on its surface, which means that our clocks on the surface will appear to progress more slowly, relative to the clock on the GPS. Unfortunately, we really need these two clocks to operate in sync with each other, or the location information you get back starts to be increasingly inaccurate, defeating the point of having the GPS in the first place. This effect can be mathematically calculated, so we can correct for this slight difference in clock speed by setting the GPS clock to run a little slower than normal. Just a little slower; this effect is only nanoseconds in size near the Earth.
But for a GPS, another form of time dilation is also in effect, because the fact that the satellite is in motion changes the clocks as well. This form of time dilation goes such that the faster you’re moving, the slower your clocks appear to move, relative to someone who is not moving. This effect gets more and more dramatic the closer to the speed of light you travel, so the offset in your clocks would get more severe.
A GPS satellite, which has to travel in a circle 12,500 miles above the Earth’s surface every 12 hours, is therefore going around 8,670 miles per hour. The speed of light is about 670,000,000 miles per hour, so our GPS is only going about 13 millionths of the speed of light. This is not a significant fraction of light speed, but it’s enough that we can calculate and measure the impact that it has on the onboard clocks on the GPS.
As it happens, the gravitational time dilation has a more significant impact on the clock than the speed of the GPS relative to us on the ground. While the speed-up due to gravity is partially canceled out by the slow-down imposed by its 8,670 mph speed, there’s still some residual extra speed on those clocks because they’re so far away from the most concentrated part of the Earth’s gravitational field. It’s this slightly diluted speed-up that’s calibrated into the clocks that we send up onto our satellites for the GPS network. (You’ll notice from the chart above that the space shuttle’s orbit was so close to the Earth that the gravitational effect wasn’t a big one, so the only clock-altering effect they were dealing with was due to their orbital speed around our planet.)
Anytime you pull your phone out to get directions to a restaurant, or to check how far you have left to walk, and your phone accurately figures out where you are, the GPS connection that underlies that software is relying on our understanding of relativity, and the time dilation the satellite is undergoing, to do its job properly.
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