General and Special Relativity Duke it Out

As it turns out, relativity is a pretty tricky theory to try and wrap around your finger. Who would have guessed? If you’ve been thinking about our astronaut twins from yesterday, then I imagine you’ve been doing a lot of head-scratching. Does general relativity cause Scott Kelly to age faster in space, or does special relativity and a slower-ticking clock take the cake?

Buckle your seatbelt, because it’s time for the answer, and it’s a bumpy ride. Let’s imagine for a minute that we’re having a cup of coffee somewhere way out in the middle of space in a place so remote that there is next to no gravity. Looking back at a clock on Earth – using the telescope that just happens to be at the ready in this particular coffee shop – we would see time ticking by very slowly because Earth’s gravity was causing it to slow down. This is Einstein’s theory of general relativity.

While we’re looking at Earth, we happen to see the International Space Station (ISS) float by. From our viewpoint, it looks like it’s crawling over the planet when really it's a few hundred miles above the Earth’s surface. The space station’s altitude varies occasionally, but on this day, it’s orbiting at an altitude of 264 miles (425 km) above the surface. In space terms that’s not far from the Earth’s surface, but it is far enough that the ISS isn’t feeling as much of a pull from gravity as people on the ground feel. Therefore, back at the coffee shop, we see time moving slightly faster on the space station than we do back on Earth.

Now we know how time looks from very far away. But what about here on Earth? We’re concerned with how Scott Kelly, the astronaut on the ISS, will experience time compared to his twin brother on Earth. To do that, we have to consider both the general relativity, which wants to speed up the passage of time, and special relativity, which wants to slow down the passage of time thanks to the speed at which the ISS zips around the Earth. (Remember, special relativity kicks in more and more as an object’s speed increases.) The question becomes: Which type of relativity – general or special – has a stronger effect on the ISS? A lot of math is involved in finding the answer, but as it turns out, the ISS, with its orbital speed of just over 17,000 mph, is moving fast enough for special relativity to win! Scott is aging more slowly than his brother.

Were the ISS at a much higher altitude, where gravity’s pull is significantly less, and travelling a bit slower, like Global Positioning System (GPS) satellites do, then we would see the opposite. General relativity would win out and time would tick by a little faster than it does at home. Because astronauts stay relatively close to the Earth, however, they take advantage of a fortuitous mix of general and special relativity and age a little slower than their counterparts on Earth.

How much less, then, will Scott have aged when compared to his twin brother Mark once Scott returns to Earth? Only a matter of milliseconds. For the younger of the twins, though, that might be just enough for bragging rights.

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