In the grand body of the universe and even our own solar system the speed of light is incredibly slow on the cosmic scale. Why does it have this speed limit ? It is theoretically possible to go faster than light ? Or is light just the fastest thing we have observed thus far ?
In: 1092
Try watching this video: https://youtu.be/qdycfWfAtsM
Time and space are not separate. If they were, then time would be unchanged no matter how fast you moved through it, and you could accelerate to any speed without limit except for fuel. But they are actually two aspects of one thing, called spacetime. So when you change how you move in one (space) then the way you move in the other (time) also changes to match, keeping overall spacetime the same.
Think of a horizontal line and a vertical line that cross in the middle, drawn on a piece of paper. The two lines are clearly distinct, so they seem separate in that sense, like time and space. But if you rotate the piece of paper, the two lines both change away from horizontal and vertical. And if you rotate them far enough, then they swap places: the line that was vertical becomes the horizontal one and vice versa. But the piece of paper stays exactly how it was, just rotated 90 degrees.
The same is true of space and time, but there’s a wrinkle: the geometry of spacetime is a bit different from the piece of paper. On the piece of paper, you can calculate the distance between two points by giving them X and Y coordinates and then use the Pythagorean theorem. Spacetime geometry is governed by an equation called the Minkowski metric, which actually is just a version of the Pythagorean theorem – but one where you subtract the square of the time dimension instead of adding it, and that changes the math. Accelerating in space is equivalent to a ‘hyperbolic rotation’ in spacetime. We’re familiar with circular rotation, where you come back around to the same orientation after 360 degrees. But in spacetime, you can rotate a line infinitely in one direction and it never comes back to facing the same direction. (Again, the video helps make sense of this.) This is why the speed of light is a limit: no matter how much you accelerate (‘rotating toward’ the speed of light) away from where you started, you never reach it: it’s always infinitely far away, in that sense.
The Minkowski metric divides spacetime into two domains: one where the distance in time is greater than the distance in space (this is called being timelike), and another where the distance in space is greater than the distance in time (called spacelike). The speed of light is the dividing line between the two: It’s the line where the distance in space and the distance in time are exactly equal. Because of the math of hyperbolic rotations, any observer who starts one one side of that line stays on that side, permanently: they can never accelerate enough to cross it, because they would have to do so for an infinite amount.
There’s also an interesting theory that this explains quantum mechanics: that QM is where our timelike world view comes into contact with spacelike phenomena. In this theory, tachyons (faster than light particles) are real and mediate thing like quantum entanglement, and in fact all the weirdness of quantum physics is down to the way ordinary phenomena like causality look utterly transformed across the divide created by the speed of light.
That was a lot. I hope it helps.
Latest Answers