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So, I guess the name for this particular online identity I'm using here is Pseudo-Riemann. The name comes from the fact that the spacetime we live in is described by a pseudo-Riemannian manifold. Here is a quick deconstruction of that jargon:
Bernhard Riemann was a 19th centuary mathematican and a student of Carl Friedrich Gauss. He invented the notion of manifolds, which are mathematical objects that describe certain kinds of spaces, namely those that on small scales resemble the flat Euclidean geoemtry we all learned in school. But on large scales (when you "zoom out") they can be curved and interconnected in interesting ways. "Riemannian manifolds" basically describe pure space: they have the property that the length of all possible paths are strictly positive, which is what we would expect (if you go in any direction, the path you take is longer than zero). But general relativity tells us that we can think of the universe as a four dimensional manifold - three dimensions of space and one of time. To describe time we need pseudo-Riemannian manifolds, which have the property that paths within them can have zero length or even negative length. In fact we alyways move on these negative length paths, because those represent paths that move forward in time. Paths with positive length are called "space-like" and represent events in space-time that do not lie in each others past or future. (In fact in fact it is pure convention which kind is positive and which is negative - what matters is that space and time have opposite signs). Paths of zero length are the ones that light rays take.
I can not possibly do these concepts justice in such a short blog post, so this explanation was probably more confusing than anything else. If you would like to learn more I can recommend the book "Spacetime and Geometry" by Sean Carrol. I'm thinking about maybe doing some sort of online interactive course about these things. Probably won't happen but we'll see. Let me know if you would be interested.
Anyway, this should tell you that I am very interested in physics. And also other stuff. But this is all I'm revealing today.
Oh yeah, pronouns are he/him.
Posted 2021-06-07
2022-01-06 | Wow!!!
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