# Spacetime **Spacetime** is simply a four dimensional [Space](Space.md), contain three spatial dimensions and one time dimension. * If a photon could have a clock ticking with it, it would just remain frozen because nothing would be happening. * $c$ is the conversion factor between space and time. Light also happens to move at that speed, but that is not what is important. $c$ is the built in speed limit that characterizes the conversion between space and time in minkowski geometry. * $c$ is a speed limit, and it is *invariant*. Not matter who is measuring it, from any location, $c$ will be measured to the be the same. * There is no absolute notion of "simultaneity". Instead there is a future light cone, a past light cone and a set of "spacelike" points that you can't get to without going faster than the speed of light (we might more clearly call them "spacelike separated"). A light cone is the set of points that you can reach going at the speed of light. The light cones are the real structure built into spacetime. Give a specific point in space time, $p = (x, y, z, t)$, there are certain points that $p$ *cannot reach*! They are the points outside of the light cone extending from $p$. This is a constraint built into the structure of the universe. * When thinking about light cones, there are three types of paths a particle can take: 1. **Timelike** - moving mostly in the time dimension 2. **Spacelike** - moving mostly in space dimension 3. **Null / lightlike** * Note that in most / all current theories of physics we deem that spacelike paths are impossible - they would violate the laws of physics * Again, there is no such thing as "at the same time". There is such a thing as "at the same time" in a reference frame, in a coordinate system that is setup relative to an observer, but that is your choice, that is not built in to the framework of the universe. * But it is preferable to think *locally*. Rather than setting up a coordinate system that stretches across the entire universe, it is preferable to say "what does one observer see?". There is a temptation in relativity to talk about "how fast is a clock ticking from your point of view when you are far away and it is out there moving close to the speed of light?". Sean recommends un-asking that question. You can ask questions about what you see coming from that clock; what is the reading that you get from light rays going from the clock to you. Or you can ask about what a person standing next to the clock sees. These answers will of course be different. Now the whole point of relativity is that, to the observer moving next to the clock, they are not being effected at all! So they would see the clock moving at 1s/s. So rather than saying "clocks move faster when they are stationary, or they slow down when moving close to speed of light", we should say "clocks move at 1s/s all the time", and instead we can say "lets just compare clocks when they leave you and then they come back and are back at the same point in space" * --- Date: 20240611 Links to: Tags: References: * [The Biggest Ideas in the Universe | 6. Spacetime - YouTube](https://www.youtube.com/watch?v=Cg2tOUTE2F4)