Is it possible to understand GR and SR on your own ?

[Monsterboy]

Is it possible to read and understand General and Special relativity on your own (by studying from the right textbooks),without a degree in physics? I know the basic stuff in calculus ,algebra ,geometry and Newtonian physics etc ...how will i know whether i am upto it?

 

[micromass]

Yes, it is possible. I know some people who self-studied it and who had a very solid grasp on the material, you can even find such people on this forum. However, it is very important to have some kind of "mentor" to guide you. Because what will happen if you get stuck? Who will tell you whether your grasp is solid enough? Who will tell you what textbooks to study? Sure, self-studying works, but doing it completely alone is very very difficult.

 

[Monsterboy]

Who will tell you what textbooks to study?

I am sure you or some others in here can name some textbooks right?

However, it is very important to have some kind of "mentor" to guide you. Because what will happen if you get stuck? Who will tell you whether your grasp is solid enough?

How much can PF help ? i can ask doubts here i assume ,will i end up asking thousands of doubts?. Will MIT open courseware and some courses on Coursera help?

If you are learning it during a college degree ,how long does it take? like a year for GR and another for SR ?

 

[micromass]

I am sure you or some others in here can name some textbooks right?

A textbook is very personal though, certainly for self study. Not everyone will find my selection of textbooks useful or good. You need somebody who knows you well and can suggest you based on your learning style.

How much can PF help ? i can ask doubts here i assume ,will i end up asking thousands of doubts?

Perhaps. But PF can only do so much.

Will MIT open courseware and some courses on Coursera help?

I have found them very useless personally. But again, this is a personal thing.

If you are learning it during a college degree ,how long does it take? like a year for GR and another for SR ?

Depends how rigorous you want it. If you want to know the math behind it rigorously, then you'll need some more time.

 

[Monsterboy]

A textbook is very personal though, certainly for self study. Not everyone will find my selection of textbooks useful or good. You need somebody who knows you well and can suggest you based on your learning style.

Isn't there some standard textbooks that nearly everyone who has understood it has read ? Can you list a few of them?

Perhaps. But PF can only do so much.

Perhaps ,i should wait for responses from people who actually did it on their own.

I have found them very useless personally. But again, this is a personal thing.

I did take some courses on other topics ,they do mention sometimes that it's not going to be enough.

The problem is i don't know anyone personally who has a background in physics.

 

[mjordan2nd]

Isn't there some standard textbooks that nearly everyone who has understood it has read ? Can you list a few of them?

http://math.ucr.edu/home/baez/physics/Administrivia/rel_booklist.html

 

[phinds]

Keep in mind that SR and GR are not even in the same league as each other in terms of full understanding. SR only requires high school algebra and not much of that. GR requires lots of advanced math (several courses worth) and my understanding is it's very hard stuff. The math you listed won't touch it.

 

[Monsterboy]

Keep in mind that SR and GR are not even in the same league as each other in terms of full understanding. SR only requires high school algebra and not much of that. GR requires lots of advanced math (several courses worth) and my understanding is it's very hard stuff. The math you listed won't touch it.

I recently signed up in
Educator.com through PF (there was an offer ) can you at least tell me which courses on math that I need to take ? I know it won't be enough but I need to start some where right ?

 

[phinds]

I recently signed up in
Educator.com through PF (there was an offer ) can you at least tell me which courses on math that I need to take ? I know it won't be enough but I need to start some where right ?

I don't know the list but it has been laid out in a number of posts on this forum so a forum search will probably turn it up, or perhaps a more knowledgeable member here will respond.

 

[wabbit]

For GR in terms of maths I think the key (and the one difficult) thing you need is differential geometry. The course should mention metrics, connections, curvature, etc.
Prior to that some (but not much) grounding in differential equations is a must, and of course linear algebra (nothing fancy needed there, but vector spaces, matrices, etc.).

I believe some GR textbooks include most of the math you need in a narrow form directed to precisely what is used, so that could be a way to get there without going through learning the maths in full. I can't think of one right now but other posters might.

Edit : I see another poster pointed you to a book list by Baez. I haven't looked at it but if it's from Baez it should be good - sounds to me like a great place to start.

 

[Fredrik]

Honestly, I think that for a person who hasn't studied any math at the university level, GR is just too difficult a subject. To really know GR, you must know differential geometry, and while I think it would be possible to write a good book on differential geometry that skips the proofs of the theorems that require knowledge of topology, I don't think such a book exists. So you have to know topology just to begin studying differential geometry. This is something that takes months of full-time studies, even for someone who has already studied analysis at the university level.

If you're willing to spend a year or two studying, then you should start with linear algebra and calculus. Then you can try Lee's books on topological manifolds, smooth manifolds and Riemannian manifolds, in that order. But there's a good chance that you will find it too difficult to take the step from calculus to Lee, so you might want to throw in an intermediate step or two. People usually study a book on real analysis before topology.

I think you should forget about GR for now and focus on SR. Start with "Spacetime physics" by Taylor & Wheeler. I haven't read it, but it's supposed to be the easiest intro to SR. So I don't think there's a lot of math in it. The best intro to SR I know is in the first three chapters of "A first course in general relativity" by Schutz. (Yes it's a GR book, but the first chapters are about SR). Unfortunately I think you need to know some linear algebra first.

 

[mjordan2nd]

I'm curious as to why so many are saying that knowing differential geometry/topology is necessary before studying GR. Plenty of books walk you through all you need starting from calc/odes/linear algebra. I suppose you might not gain as deep of an understanding, but you can certainly start doing GR problems without having taken a formal differential geometry course. At least that was my experience.

 

[Fredrik]

I'm curious as to why so many are saying that knowing differential geometry/topology is necessary before studying GR. Plenty of books walk you through all you need starting from calc/odes/linear algebra. I suppose you might not gain as deep of an understanding, but you can certainly start doing GR problems without having taken a formal differential geometry course. At least that was my experience.

Yes, you can start, and maybe even finish. This will give you a fair understanding of the physics. I didn't find this approach satisfying. I read a little in Schutz and d'Inverno at first, and found it very frustrating. I eventually settled on studying Wald and Spivak at the same time. (Schutz, d'Inverno and Wald are GR books. Wald is the only one of them that takes the math seriously. Spivak was the best book on differential geometry at the time. Lee is the best choice now).

My recommendation isn't to study differential geometry before GR, but to study them both at the same time.

I realize that a lot of people don't feel the same need as I do to actually understand the math. For such a person, it's reasonable to study Schutz without any math knowledge beyond the basics of calculus and linear algebra.