You're on a grass field, sitting on one of those riding lawnmower thingies, with a broken throttle. It's moving at a fixed speed of 1mph. You can't ever change its velocity. But you can steer it. If you are going precisely east-west, then it means you're not going north-south. The more you go north-south, the less you'll be going east-west. If you're going precisely north-south, it means you're not going east-west at all. One direction is traded against the other.

Pretty straightforward, right?

So here's the analogy: that grass field is a "dimension" in the same way that "spacetime" is a "dimension". The two "directions" of spacetime aren't "east-west" and "north-south", but "space" and "time". These are inherently traded against each other. The more you're moving through one, the less you're moving through the other.

So what about that constant-velocity rideable lawnmower? That's "c" -- the speed of light. You're always traveling at this velocity. If you are sitting still in space, then you are nonetheless moving through time. Your rate of movement through time is "c". But as soon as you start moving through space, it means you are moving less through time. This is exactly the same tradeoff as moving north-south vs. east-west. If you devote 100% of your "c" to moving in the direction of the "space" axis, then it means you're not moving on the "time" axis at all.

(This is basically all it means for something to be a "dimension": different axes that are traded against one another.)

This analogy can be used to understand quite precisely how movement relates to time dilation. (It also helped me understand e=mc^2. Why is "c" there? What does the speed of light have to do with the embodied energy of matter at rest? Answer: nothing is ever at rest; all static matter is moving through through time at the velocity of "c", and obviously that movement must have kinetic energy.) But it's not a completely perfect analogy. Weirder relativistic effects like length contraction and frame dragging need much weirder analogies.

From the perspective of an object accelerating, newtonian physics works totally intuitively. If you had a rocket that could accelerate at 1g indefinitely, you just go faster and faster and faster and you get to any destination you want (even far away!) pretty quickly. And it would be a rather comfortable trip! You'd have Earth-like gravity the whole way.

It's really only the observer's perspective that things get confusing. When an observer watches something accelerate, they see it never going faster than the speed of light, no matter how fast it "actually" goes.

The trick is time. Time for slow things passes faster than time for fast things. A clock on a very fast rocket ticks much more slowly than clocks on (relatively) stationary things. That's how the paradox is solved.

Let's say you wanted to visit the Andromeda galaxy, which is around 2,500,000 light years away. If you had a rocket that could travel at 1g indefinitely, you'd get there in a comfortable 29 years! However, observers on Earth would see the trip taking around 2,500,000 years.

If you'd like to play with these numbers yourself, feel free to check out this neat calculator (not made by me)

http://nathangeffen.webfactional.com/spacetravel/spacetravel...

Time might not even exist in and of itself.