Getting a real understanding of general relativity

[Ryan33H]

Hello,
I am new to this forum, but have read a lot of posts and it seems really cool. I am 38 and have a B.S. in mathematics (from many years ago).

I work in insurance, so I am pretty far removed from acedemia now. I have kept up my math studies as a hobby. After studying a lot of theoretical math, it has become really abstract and I am interested in learning how to apply it.

I would really like to learn about general relativity. Just to satisfy my own curiosity. I completed a year of undergraduate physics in my college years (calculus based), but except for pop sci books, that is my only real physics exposure. As far as math goes, I have completed analysis, abstract algebra, linear algebra (theoretical level), and Spivak's Calculus on Manifolds (in addition to a basic math major's requirements). I am well versed with my math up to this level.

The freshman physics I completed was interesting, but not challenging. Just some computational stuff. I would really appreciate any suggestions on where to take my studies into some real physics. Any suggestions about further math to study, but especially physics to get a real understanding of what is needed to explore general relativity would be awesome.

I have no intentions/illusions about becoming a physicist (just a hobby), but pop sci books don't really do it for me. Again, this is just a hobby, but I don't like to water down my studies. Any suggestions on study materials, especially ones with answers, so I know I am not incorrectly interpreting things would be great. Thanks in advance!

 

[phyzguy]

I have two suggestions. One, I really like Penrose's "The Road to Reality". With your math background, it should be a good way to re-introduce you to the ideas at a level above "pop-science". Second, it's hard to beat Misner, Thorne, and Wheeler's "Gravitation" for understanding GR. It's a huge volume and can be overwhelming, but it starts out slowly and builds from there. I think it is available online - at least I found an electronic copy.

 

[pervect]

Understanding special relativity will be essential - if you don't have SR as a base to build on, you won't get the sort of understanding of GR you're looking for. This will unavoidable entail learning some physics - the math part for understanding SR is fairly straightforwards, college algebra.

A book like Bondi's "Relativity and Common sense" might get you started on SR, but you'll probably need a more advanced book like Taylor & Wheeler's "Space-time physics" if you want to progress to GR.

In partciular, you'll want to understand the Lorentz interval, and the relativity of simultaneity.

After you have SR under your belt, it will be time to think about GR. There are some good books aimed at undergraduates nowadays, they'd be a good place to start. after you get SR under your belt. You could also take a look at some of the free things on the WWW, like Caroll's lecture notes and Baez's "The meaning of Einstein's equation" - they might not be everything you're looking for, but the price is right.

 

[Daverz]

For the physics background you'll need (Newtonian orbits, effective potential, Maxwell's equations, Laplace and wave equation), I recommend

French, Newtonian Mechanics
Schwartz, Principles of Electrodynamics
Taylor & Wheeler, Spacetime Physics, 1st ed (red paperback, ISBN: 071670336X)
Tevian Dray, The Geometry of Special Relativity

French starts out easy but gets advanced enough to include a good introduction to Newtonian orbits. I'm now recommending the Tevian Dray book because I'm unsure of the availability of the old red paperback 1st edition of Taylor and Wheeler's Spacetime Physics with the solutions in the back. If you can find that, working through the problems (with a minimum of peeking at the solutions) is the best way to learn SR.

https://www.amazon.com/gp/product/071670336X/?tag=pfamazon01-20

After that, there are some excellent intro GR books:

Ben Crowell's online GR book at http://www.lightandmatter.com
Hartle, Gravity
Cheng, Relativity, Gravitation and Cosmology: A Basic Introduction
Schutz, A First Course in General Relativity

 

[Ryan33H]

I have two suggestions. One, I really like Penrose's "The Road to Reality". With your math background, it should be a good way to re-introduce you to the ideas at a level above "pop-science". Second, it's hard to beat Misner, Thorne, and Wheeler's "Gravitation" for understanding GR. It's a huge volume and can be overwhelming, but it starts out slowly and builds from there. I think it is available online - at least I found an electronic copy.

Thanks! I was wondering about the Penrose book. I have been contemplating purchasing that, but I definitely will now.

 

[Ryan33H]

For the physics background you'll need (Newtonian orbits, effective potential, Maxwell's equations, Laplace and wave equation), I recommend

French, Newtonian Mechanics
Schwartz, Principles of Electrodynamics
Taylor & Wheeler, Spacetime Physics, 1st ed (red paperback, ISBN: 071670336X)
Tevian Dray, The Geometry of Special Relativity

French starts out easy but gets advanced enough to include a good introduction to Newtonian orbits. I'm now recommending the Tevian Dray book because I'm unsure of the availability of the old red paperback 1st edition of Taylor and Wheeler's Spacetime Physics with the solutions in the back. If you can find that, working through the problems (with a minimum of peeking at the solutions) is the best way to learn SR.

https://www.amazon.com/gp/product/071670336X/?tag=pfamazon01-20

After that, there are some excellent intro GR books:

Ben Crowell's online GR book at http://www.lightandmatter.com
Hartle, Gravity
Cheng, Relativity, Gravitation and Cosmology: A Basic Introduction
Schutz, A First Course in General Relativity

That is a great list and gives me a lot to work with. Thanks!

 

[Ryan33H]

Understanding special relativity will be essential - if you don't have SR as a base to build on, you won't get the sort of understanding of GR you're looking for. This will unavoidable entail learning some physics - the math part for understanding SR is fairly straightforwards, college algebra.

A book like Bondi's "Relativity and Common sense" might get you started on SR, but you'll probably need a more advanced book like Taylor & Wheeler's "Space-time physics" if you want to progress to GR.

In partciular, you'll want to understand the Lorentz interval, and the relativity of simultaneity.

After you have SR under your belt, it will be time to think about GR. There are some good books aimed at undergraduates nowadays, they'd be a good place to start. after you get SR under your belt. You could also take a look at some of the free things on the WWW, like Caroll's lecture notes and Baez's "The meaning of Einstein's equation" - they might not be everything you're looking for, but the price is right.

Thanks for the suggestions! The SR that is covered in my text from college is superficial at best. I will definitely take a look at those books.

 

[pervect]

Maxwell's equations will be helpful if one wants to draw analogies between gravity and electromagnetism. In a pinch one might do with just understanding partial differential equations in general. Usually Maxwell's equations are used to motivate understanding PDE's and vector calculus for physics students.

It's traditional to learn vector calculus (div, grad, curl - the language that Maxwell's equations are written in) before learning tensor methods. I'm not sure how much of an absolute requirement it is because basically all that gets replaced anyway. On the other hand, I'm not sure what roadblocks one will run into attempting to learn the tensor methods without being familiar with the undergraduate vector calculus methods. For instance, any motivational treatments that use examples from vector calculus methods will be lost.

I have a similar feeling on understanding Newtonian orbits, though I do think at a minimum one needs to be able to write the ordinary differential equation of a Newtonian orbit. The GR approach is going to be completely different, though, again a lot of it gets replaced. Basically the idea of Newton's laws generating a differential equation gets replaced with the geodesic equation which generates a differential equation.