Why does relativity mean that mass changes with speed?

Everyone knows that relativity plays hell with time, and that it can do a number on space, but what about mass? Why do objects get more or less mass depending on their relative speed? We're going to give you a quick explanation of why running can make you gain weight. No, we don't think it's fair either.

At this point most people know, thanks to Einstein, that two people can experience their own version of time, and that their times vary depending on how fast they're moving relative to each other. If you were to clone yourself and send your clone on a rocket ship moving past you very fast, your clone would experience slower time relative to you. You would be stuck on some stationary place, your seconds ticking away, while watching your ingrate clone shaking their youthful ass on a rocket around the stars. Here's some consolation, though. That ass would be a little bit more massive than yours.


This is one of the many quirks of relativity. Once you mess with time and space, you mess with almost everything else as well. Some say that, since mass and energy are equivalent, making an object move faster increases its energy, which increases its mass. Actually, the idea of objects picking up mass with speed is more of a thought experiment that takes place on the very rocket ship we're watching.

Your clone gets lonely and clones themself. The two clones, exactly equal in mass and wearing the same clothing, get in a fight. They both attack with a flying jump kick, collide comically in mid-air, and come to a stop, their faces smashed against each other. From their perspective, this was a perfect example of the conservation of momentum. The conservation of momentum is a principle that states that overall, the momentum of a system has to stay the same. When you push something forward, you feel an equivalent push backward. The clones, each having a mass of, say, 100 kilograms, fly at each other at five meters a second - one flying to the left, and one flying to the right. That's an equivalent momentum flying in each direction, and it averages out to no momentum. When they collide they stop entirely, they keep the momentum of the system at zero. Momentum is conserved.

Or at least, it is conserved for the clones. After you've finished rolling on the floor, laughing and yelling, "You're not so pretty anymore," you realize that something is wrong. As they flew at each other, one clone was moving with the ship's motion, and one was moving against the ship's motion. And we've already learned that time doesn't work the same if people are going at different speeds relative to you. The clone moving against the motion of the rocket had to be experiencing slightly faster time compared to you, and the one moving with the rocket ship has to be experiencing slightly slower time compared to you. (Because of other quirks of relativity, they're not going across the same stretch of space, either.) And because of the motion of the rocket ship itself, the entire thing is working in a slightly different time system. This means that the perfect symmetry and the resulting conservation of momentum that the clones experienced doesn't apply to your perspective. To you, the clones either created or destroyed momentum.


Until you somehow measure their mass. That's when you realize that the twin that's moving faster, relative to you, is just a little bit more massive. The one that's moving slower relative to you, is just a little bit less massive. This difference in mass counterbalances the time and space distortions, and allows momentum to be conserved. The experiment can work from the perspective of the clones, as well. If they decided to each build rocket ships and ram each other at some speed comparable to the speed of light, and then bounce away like they're in bumper cars, they'd see each other moving in different time and over different distances after the collision, and only messing with mass would conserve momentum.

It sounds silly, but it has been observed experimentally. Electrons flying through cathode rays are a bit more massive than electrons at rest. Particles moving through accelerators are more massive than ones just sitting around. This slight difference in mass has been observed consistently since 1908. Of course, it can never make that much of a difference at the speeds at which humans move. But it is there. Relativity messes with our sense of the universe once again.


Top Image: Local Fitness

Via UVA Physics and Modern Physics.


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