I love the movie Interstellar but I have never fully understood how time dilation works. More recently reading “Project Hail Mary” this term came up again and I went on a Wikipedia binge trying to understand how it works.
How can time be different based on how fast you travel? Isn’t one second, one second everywhere? (I’m guessing not otherwise there would be no time dilation) but I just don’t understand what causes it or how to wrap my head around it
In: Physics
It certainly is tricky. You have to start by accepting that the universe does not always have to make sense. We humans are used to how certain things behave because we are quite big and quite slow. This does not mean that reality behaves the same way when something is really, really small or goes really, really fast.
There is a rule in physics called the principle of relativity. This states that there is no way to tell the difference between a thing standing still and a thing moving at a fixed speed from the inside. Like in an elevator: you feel it when the elevator speeds up or slows down (not fixed speed) but while it is traveling at a fixed speed, it is very hard to tell the difference between moving and not moving.
Okay, so given that this principle is true, imagine a light clock. This is a device with 2 mirrors facing each other and a photon bouncing up and down between them, forever. The clock is constructed so that every time the photon hits a mirror, one second has passed.
Now, someone puts that clock on a train and the train starts moving until it goes really, really fast, almost as fast as the speed of light. Remember that once it is moving at that speed, it is impossible to tell the difference INSIDE the train between moving and standing still. The photon just happily bounces up and down at 1 bounce per second.
Imagine standing on a platform watching that train go by in the distance. (imagine this is all possible). When you look inside of the train, you see the photon bouncing up and down, but also moving sideways through space (since the train is moving sideways). So from the perspective of the platform, the photon travels like this “/ / / “.
Pythagoras’ theorem tells us that the hypothenuse of a 90 degree triangle is a^2 +b^2 = c^2. So if the train is traveling at nearly the speed of light, in one second, the photon has traveled 1 light second vertically and one light second horizontally, so 1^2 + 1^2 = 2^2 or the square root of 2 or *1.41 light seconds per second.*
The photon covers a distance in 1 second that should have taken it 1.4 seconds. Remember that from the perspective inside train, the photon is just bouncing up and down like normal so it is traveling at 1 light second per second.
But how can a photon a) travel faster than the speed of light, and b) travel at different speeds at the same time? The answer to both questions is “it can’t”, so the only solution, no matter how unintuitive it seems to us, *is that a second simply takes longer when the train is moving.*
Again, this makes no sense to us who move at a few 100 km/hour but reality does not have to make sense. The conclusion is inescapable. Inside the train, a second still takes a second since it is defined by the photon bouncing, but outside the train looking in, we see that time in there moves slower. Just because the train is moving.
This effect is very real. GPS satellites have to compensate for this effect to remain accurate, for instance.
Latest Answers