Is there a way to learn general relativity WITHOUT those concepts? My curriculum made sure to introduce all that before going into GR, didn’t know that wasn’t common. Guess that was my point of confusion.
Comment on Manifolds
kogasa@programming.dev 5 days agoManifolds and differential forms are foundational concepts of differential topology, and connections are a foundational concept of differential geometry. They are mathematical building blocks used in modern physics, essentially enabling the transfer of multivariable calculus to arbitrary curved surfaces. I think the joke is that physics students don’t typically learn the details of these building blocks, rather just the relevant results, and get confused when they’re emphasized.
Droggelbecher@lemmy.world 5 days ago
kogasa@programming.dev 5 days ago
Not really, you need to have a basic understanding at least
Droggelbecher@lemmy.world 5 days ago
That’s what I thought, which is why I don’t get the meme. Who is it talking about? Who has learned about GR but gets confused by manifolds? How else would they have learned GR?
someacnt@sh.itjust.works 5 days ago
I do not recall well, but connections are sections of a suitable bundle, right? I have to eventually learn this but eh, seems too tedious.
kogasa@programming.dev 5 days ago
You might be thinking of a [connection of an affine bundle](en.wikipedia.org/wiki/Connection_(affine_bundle). You could learn it through classes (math grad programs usually have a sequence including general topology, differential topology/smooth manifolds, and differential geometry) or just read some books to get the parts you need to know.
psud@aussie.zone 5 days ago
You lost a bracket in your link
niktemadur@lemmy.world 5 days ago
The geometry of the cosmos itself. Tracing good ol’ fashioned circles and triangles with the full extent of the visible universe and even beyond. This stuff blows my mind, even just the mere fact that we’re doing it, let alone the fact that we’re getting such incredible, counter-intuitive results.
Picture yourself having a time machine, going back to visit Euclid or Pythagoras, or even Kepler or Galileo, and blowing their mind with four words: The Geometry Of Spacetime.
Not only does time itself has a geometry, it must curve and contract to accommodate the absolute speed of light… nuts I tell ya.
Then there are at least four spatial dimensions, but there may be as many as eleven. To think that Copernicus thought epicycles were weird, wait till he gets a load of THIS!