Below, I try to wrap my head around the theory of relativity, and what the shape of space might look like:
In "Gravity and Spacetime" by Martin Gardner, the author tries to explain to me the concept of a 4-dimensional spacetime as best he can, and I do my very best to try and understand what he's saying. I understand the rules of Euclidian geometry, from highschool geometry, but the rest is all rather new. He goes over elliptic geometry and hyperbolic geometry, which are both based off of the postulate that "parallel lines never meet." He goes on from here, explaining a way to map space and time on a 3-dimensional axis (2-dimensions for space and 1 for time), and to explain how gravity works in Einstein's spacetime- that gravity is caused by the huge weight of planets/stars/celestial bodies in spacetime creating a well in the fabric of spacetime, in which other bodies that are traveling otherwise in a straight line get caught up in.
These theories and ideas are very interesting to me, although very hard to parse. I haven't had to think about geometry or math or graphs in a long time. These ideas of how space and time work together to influence our reality are very interesting and they give some sense to things that we take for granted- do parallel lines really never meet? What is gravity really and why is it a thing? I've seen the graphic of a large planet laying on a plane, displacing it slightly and how that causes gravity, but I had never read an actual explanation.
I can't really say whether I agree or disagree with these physics because I can't say I truly understand them, and all I know is that truly greater minds have done more with it and understand it way beyond my capability- perhaps all I can say is that with this brief glimpse, I have a greater interest in attempting to understand the idea of spacetime, and even the fact that spacetime is a model of reality and physics rather than just the idea that space and time are in fact things that exist.
My greatest source of confusion is when the author tries to say that actors in space and time might disagree when an event in time occurs or where it occurs in space, but can definitely agree in spacetime. I understand maybe that spacetime is 4 dimensional, but not how it relates to the non-euclidian geometry models we discussed earlier.
I also was interested to read about the mathematical descriptions and models for 4th, 5th, 6th, etc. dimensions, because I was under the impression that we hadn't even begun to comprehend what those could be!
On the subject of understanding the theory of relativity and space-time, these videos below helped:
I think the series is longer but this seems to cover the concepts introduced in that reading.
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