The Maths of General Relativity (1/8) - Spacetime and Worldlines

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Recommends zamadatix · 2021-04 · on “Particle mystery: physicists confirm the muon is more magnetic than predicted”

An attempt at a true ELI5 is the bodies exist in what we know as spacetime, not as separate independent concepts of space and time which we perceive from our day to day experience, so we have to know a bit about the difference. Chiefly in spacetime everything always travels the same "speed" (c, the universal speed limit) and it's just a matter of how much of that speed appears as "traveling through space" and how much appears as "traveling through time". When 2 bodies warp spacetime it causes changes in the way each body's spacetime speed is distributed causing them to accelerate towards each other. The ELI15 version is think about vectors in our normal concept of 3D space first, if I told y

Recommends Vetch · 2022-01 · on “We need to reclaim our attention”

It's difficult to find material that's a series, rigorously demonstrated and advanced at the same time (there's lots excellent material that ticks either one or the other of those boxes). Here are some examples I subscribe to that come close: Covers Quantum Field Theory and General relativity in as approachable a manner as I imagine is possible while still going deep into detail: [LINK] Theoretical machine learning, Information theory and probabilistic inference : [LINK] Heavy emphasis on analysis and measure theory : [LINK] While ScienceClic's coverage of differential geometry topics is mostly a thin vertical slice of the subject, it covers it with incredible visualizations and pedagogical

Recommends psc · 2023-12 · on “New theory claims to unite Einstein's gravity with quantum mechanics”

ScienceClic on youtube has some really great videos, the first half of the string theory video [1] does a good job framing the conflict at a high level, string theory being one attempt to resolve the problem. It doesn't go into math but mentions that in the standard model, interactions are local, which for example means something like photon emission is instantaneous. When applied to gravity/gravitons, you get infinities in the math. This sort of makes sense to me, but I have yet to find anything that does an understandable job explaining how/why exactly the math breaks down. There's a series on the maths of general relativity [2] which I haven't completed but I'm hoping will provide a bit m