The way I think I understand it, even if we had some “element 0” like in mass effect to keep a starship from reaching unmanageable mass while accelerating, faster than light travel still wouldn’t be possible because you’d be violating causality somehow, but every explanation I’ve read on why leaves me bamboozled.
In: 608
In 3D, when you’re standing still, time is flowing by and you’re not moving through space. When you’re moving, time is still flowing by at the same rate, and you are moving through space.
In 4D spacetime, this isn’t the right picture. In 4D, you’re always moving at the same rate in a 4D direction. Your 4D velocity is constant all the time. If you are standing still in space, that means all your motion is happening in the time dimension. If you start moving through space, then the direction of your 4D arrow isn’t fully pointed along the time dimension, now it also points in one or more space dimensions a tiny bit. This means that your overall 4D velocity has not changed, but now some component of it is in the space direction and the rest in the time direction.
This is the reason you can’t travel faster than light: If it were possible to point your 4D velocity vector completely in the space direction such that the time component were zero, you would be traveling AT the speed of light, not faster. (You can’t actually do this because it takes an infinite amount of energy to point the 4D velocity vector completely into the space dimensions for any object that has mass. But if you could, you’d be going c.)
So it turns out that the total 4D velocity is an invariant for all things at all times. In order to go faster than c in a space direction, you’d have to increase the 4D velocity, which means changing an invariant, a thing that cannot change.
Too hard? Let’s make it simpler.
Imagine a 2D person in a sheet of paper. Paper person has a 2D matchstick one inch long. When they point the stick in some direction in the paper, the stick (and paper person) moves in that direction at a rate of one inch per second. So they just zoom around the paper all day, pointing the stick in some direction they want to go, and it moves them along. (When they get to the edge, they just wrap around to the other side of the paper. They don’t really know when this happens because it all just looks flat to them.)
One day, paper person discovers they can push the matchstick up out of the surface of the paper a little bit. When this happens, the component of the matchstick along the paper still makes them zoom around (think of this as the shadow of the matchstick that falls on the paper, which paper person can’t distinguish from the matchstick itself). And the component of the matchstick perpendicular to the paper moves the entire sheet up or down in that direction at the speed of that component.
So now imagine the matchstick is pointing at a 45 degree angle to the paper. Paper person is moving at reduced speed in the paper, and the entire paper is moving up at the same speed. How fast is paper person moving? Well, if you do the math, still one inch per second. No matter what direction the matchstick points, they’re always moving through 3D at an inch per second.
To paper person, they can’t really tell when the entire sheet is moving up or down, they only perceive their motion relative to the paper. If they point the matchstick completely up, they stop moving at all in the paper, and now the entire paper is moving up at an inch per second.
The question you’re asking is: Why can’t the paper person ever move faster than an inch per second? Because the matchstick is only one inch long. No matter the direction of the matchstick, the combination of movement in all the directions is always and forever going to be one inch per second.
Latest Answers