The theory of relativity is so called because the way time, mass, and length are measured depends on what the observer measures as moving compared (relative) to themselves. For the “Twin Paradox” we evaluated how the passage of time and length changes from both Terra’s and Stella’s perspective. Specifically, we saw that we will measure time slowing down for someone traveling with a velocity relative to us as well as see their length shorten in the direction they are moving, and their mass to increase. (The observer will always measure their passage of time, and measurements of length and mass to be the same.)

While these observations are experimentally confirmed, more than just relative velocity can affect the measurement of time, length, and mass. That is why special relativity is called special: it’s the special case where we only concern ourselves with the effects of relative velocity. General relativity is a more complete description because it includes the effects of gravity. In addition to the effects of special relativity, general relativity shows that the passage of time slows as gravity (the gravitational field) increases. This slowing down of the passage of time in both special and general relativity is referred to as time dilation.

Time dilation was a major plot point of the 2014 movie Interstellar. In this movie (no spoilers, I promise!), explorers traveled through a wormhole that took them to another galaxy. One of the planets they visited was covered with water and orbited just outside of a black hole called Gargantua. Because black holes have some of the most extreme gravity in the universe, seven years passed on Earth for every hour spent on the water planet. This had heartrending implications for the explorers reuniting with their loved ones.

We’ve seen Stella travel into the future due to special relativity in this lesson and the explorers in the Interstellar movie travel into the future due to general relativity. That begs the question, “Is it possible to travel back in time?” The answer is no, and it helps to look at the equation for time dilation from special relativity to understand why (for general relativity, there is no known way to go back in time either but it’s more complicated). We won’t be calculating any numbers. Instead, we will be figuring out the “story” the equation tells. In order to travel back in time, we must find a condition where time slows down so much it runs backward; that is, we will need to have negative time in our equation.

Time dilation for special relativity (as shown in this lesson) is:

t_move = t_rest times square root of 1 - (v/c)²

where t_move is the passage of time for something that is moving with velocity v, t_rest is the passage of time for an observer at rest, and c is the speed of light. Since time always passes at the same rate for an observer at rest, we must find the condition when t_move is negative. t_move becomes smaller and smaller as v gets closer to c, but once v becomes greater than c (which can’t happen anyway), t_move becomes an imaginary number (a number that involves the square root of a negative number). You can’t travel back in time due to the effects of special relativity!

All of this material may seem outside of our everyday experience, but it really isn’t. The effects due to special and general relativity need to be taken into account any time you make use of GPS navigation. The Global Positioning System (GPS) is composed of about 30 satellites in orbit around the Earth so that at least 4 are visible at any given place on the planet. Each satellite carries a very accurate atomic clock and transmits radio waves carrying information on their location and the time. Your navigation system receives this information from at least 3 satellites and uses the time it took the signals to reach you from each satellite to calculate how far away they are. Your GPS receiver uses triangulation to determine the only one point where these distances are possible: your location on Earth. But, as we have learned, the clocks on the satellite will run differently than clocks on Earth. Special relativity shows that the clocks will run a little slow because of their velocity while orbiting the Earth. General relativity shows that the clocks will run a little fast because they are in a lower gravitational field than clocks on Earth’s surface. Adding both of these effects together produces a 38-microsecond gain per day for the satellites’ time compared to the clocks on the Earth. While this change in time is very small, it would result an error of 6 miles (10 km) every day. Without making corrections to the satellite’s time due to both special and general relativity, the GPS system would be useless!

If you want to learn more about relativity and time, please see these other TED-Ed lessons on relativity:
-The fundamentals of space-time: Part 1 – Andrew Pontzen and Tom Whyntie
-The fundamentals of space-time: Part 2 – Andrew Pontzen and Tom Whyntie
-The fundamentals of space-time: Part 3 – Andrew Pontzen and Tom Whyntie
-Is time travel possible? – Colin Stuart

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