Einstein’s special theory of relativity teaches us that time is relative. But what does it mean that time is relative? How can we live in a universe where no one can agree on when events begin, when they end, and how long they last? The infamous “twin paradox” shows what life is like in a truly relativistic world.
Simply put, Relativity tells us that moving clocks run slowly. It’s a phenomenon called time dilation, and it’s a cold, hard fact of the universe. Einstein had to introduce the concept to save something he thought was much more fundamental: the universality of physical laws. If we want the laws of physics – which also means the experience of physics – to be the same regardless of your frame of reference, the perspectives must change for observers at different speeds.
Special relativity says that a clock attached to a moving object will run at a slower rate than a stationary clock. And what goes for mobile clocks goes for everything else; physics, chemistry and biology all operate at a slower pace in moving frames of reference.
Related: How does time work?
It is very difficult to measure this effect on a human scale, because it only manifests itself significantly as one approaches the speed of light. It is still measurable. In 1971, physicists Joseph Hafele and Richard Keating installed atomic clocks on jet planes and sent them flying around the world. When the clocks returned, they were out of sync with a ground clock by exactly the amount predicted by special relativity.
To explore all the implications of this idea, let’s start with some hypothetical twins, Alice and Bob. As long as they stay close to each other, their clocks will stay in sync and they will age at the same rate. But if Bob were to get on a rocket and cruise around the galaxy at a speed close to light, things would be a little different.
For Bob, maybe a few months or a few years have passed on his journey. But depending on how fast it went, it could have taken decades, if not centuries, for Alice.
The real paradox
As puzzling as this tale is, it is not a paradox. This is exactly what the physics of special relativity requires: different observers in the universe will have different calculations of the passage of time depending on their speed.
So here is the real paradox. Nothing is different for Bob when he travels. It’s not like he’s moving in slow motion or anything. Everything seems completely normal – so normal, in fact, that until he accelerates, he can’t even tell he’s moving at all.
It was the crucial thought experiment that helped Einstein develop special relativity. If you’re moving at exactly the same speed (no accelerations or decelerations), it’s impossible to tell if you’re the one moving, or if you stay still and the rest of the universe moves.
Have you ever been in a car and you see the car next to you backing up, and for a moment you think you’re moving forward? Your mind relies on outside cues to help you know if you’re moving.
So, from Bob’s point of view, he stands perfectly still, and it’s Alice (and everyone Earth) who moves away from him. Yes, it seems unlikely, but from a physics perspective, Bob can’t tell the difference. In Bob’s calculations, his clock is running normally, and Alice’s clock should be running slowly. So when they meet again, she should be younger than him, because not so much time has passed for her.
But Alice says exactly the same thing about Bob, because according to her, she’s the one standing still and he’s the one moving.
Who is right, Alice or Bob? This is the real paradox.
A certain point of view
We can solve the twin paradox by looking at the big picture. It is true that as long as Bob is flying at a constant speed, he and Alice will fundamentally disagree about the flow of time, and both perspectives will be valid. But in order for them to compare notes, Bob must return to Earth. In other words, he has to slow down, stop, turn around, reaccelerate, and come home.
This act of turning around has a major impact on Bob’s time calculation. He will do something that will take him away from his particular frame of reference. And he will be able to tell that he does this not by looking at the outside universe but by making observations inside his rocket – for example, the vibrations of the engines and the pushing of his body against the ground during deceleration.
Because of this asymmetry, Bob’s perspective is no longer as valid as Alice’s, and he can no longer pretend he is still as the universe moves around him. When he finally returns to Earth, he will know that he was the traveling twin and that he was the one who traveled at near light speed.
The math of special relativity tells us how much Alice and Bob will age in their own frames of reference, and that same math demonstrates that they will eventually agree on the numbers in the end.
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