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Can you recommend a book/resource that explains this from first principles and introduces the math involved as well? The books I've read either exclude math alt

Can you recommend a book/resource that explains this from first principles and introduces the math involved as well? The books I've read either exclude math altogether or if they don't, they assume that reader already knows and understands all the math that is required for this.

spaceseaman 9y ago
You would be interested in this book https://en.wikipedia.org/wiki/The_Road_to_Reality https://en.wikipedia.org/wiki/The_Road_to_Reality It is quite long and dense but explains the math from first princples like you want.
raattgift 9y ago
Just about any standard textbook on General Relativity will cover the content of my comment in the first chapter or so. I like Carroll's [ https://www.preposterousuniverse.com/spacetimeandgeometry/ https://www.preposterousuniverse.com/spacetimeandgeometry/ ] and indeed, you get to deal with intervals and worldlines in chapter 1. It assumes you know or are ready to learn some differential calculus and how to read a formula with an integral but it (maybe a bit steeply) teaches tensors (and some aspects of vectors and scalars) across the first couple of chapters. Carroll provides some (quasi-)samples under the "Lecture Notes" tab, but the book itself has benefited from editing. He also supplies links to alternatives that can be had for free-as-in-beer.
SAI_Peregrinus 9y ago
The classic text is "Grativation" by Misner, Thorne, and Wheeler. It's very dense, but very thorough. The other classic is "General Relativity" by Wald. They don't really include the math background though, for that you need texts on multivariable calculus.
reubenswartz 9y ago
Check out "Why Does E=MC^2". (I wish I understood it better. I think some of what raattgift was saying is related to the deeper issues, which the book does raise, and which I paraphrased at a very high level.) https://smile.amazon.com/dp/B002TJLF7W/ https://smile.amazon.com/dp/B002TJLF7W/

spaceseaman 9y ago

You would be interested in this book https://en.wikipedia.org/wiki/The_Road_to_Reality https://en.wikipedia.org/wiki/The_Road_to_Reality It is quite long and dense but explains the math from first princples like you want.

raattgift 9y ago

Just about any standard textbook on General Relativity will cover the content of my comment in the first chapter or so. I like Carroll's [ https://www.preposterousuniverse.com/spacetimeandgeometry/ https://www.preposterousuniverse.com/spacetimeandgeometry/ ] and indeed, you get to deal with intervals and worldlines in chapter 1. It assumes you know or are ready to learn some differential calculus and how to read a formula with an integral but it (maybe a bit steeply) teaches tensors (and some aspects of vectors and scalars) across the first couple of chapters. Carroll provides some (quasi-)samples under the "Lecture Notes" tab, but the book itself has benefited from editing. He also supplies links to alternatives that can be had for free-as-in-beer.

SAI_Peregrinus 9y ago

The classic text is "Grativation" by Misner, Thorne, and Wheeler. It's very dense, but very thorough. The other classic is "General Relativity" by Wald. They don't really include the math background though, for that you need texts on multivariable calculus.

reubenswartz 9y ago

Check out "Why Does E=MC^2". (I wish I understood it better. I think some of what raattgift was saying is related to the deeper issues, which the book does raise, and which I paraphrased at a very high level.) https://smile.amazon.com/dp/B002TJLF7W/ https://smile.amazon.com/dp/B002TJLF7W/