Should I Study Special Relativity Before General Relativity for Cosmology?

[RyanH42]

Hi,I am ihigh school 12 grade I will be in collage 3 months later.I know simple calculus (derivatives and integral ).I watched Leonard Susskind Cosmology and Classical Physics Lectures.I want to learn cosmology and GR.My first question is Did I have to learn Specai Relativity before GR.
And Is there a cosmology or GR book(for my level ) which I can learn these things easily.
Thanks

 

[DEvens]

You can learn SR while you are learning GR. It's not the usual order, but it is possible. A lot of SR is very motivational for what is going on in GR.

It's quite a lot of math for high school level calculus. If you are the Sheldon Cooper type you might be able to do it. If you are just very bright it might be better to wait and do it in the usual order. Lots of differential equations and differential geometry between you and a basic understanding of GR.

When I was in grade 12 there was a book with a title something like "Relativity for T.C. Mits" but this book does not seem to be in print any more. I did find this one.

http://www.amazon.com/dp/1589880331/?tag=pfamazon01-20

T.C. Mits is "the celebrated man in the street." The math in the relativity book was just barely accessible to a grade 12 student who did well in calculus. I had to work pretty hard, but it was the first time I had seen relativity at all. Of course my first response was "That's not possible!" But it grows on you.

There are books at the not-much-math level that talk about cosmology. They come in different degrees of usefulness and fun. For example: Hawking has "A Brief History of Time" which is fun and very light on the math. Weinberg has "The First Three Minutes" which is still fun and has a little more math. You could get "Cosmos" by Sagan (either the book or the video series) with lots of interesting stuff, some cosmology but a lot of fun other stuff. And many very nice pictures.

When you start to chew into the math you could get Weinberg's "Gravitation and Cosmology." One chapter of this kept me very busy for four months in my fourth year of my BSc. Math heavy but still fun. And when you really start to chew on the math there are lots of other texts people are pleased with.

 

[RyanH42]

[QUOTE="DEvens, post: 5137075, member: 475460"]The math in the relativity book was just barely accessible to a grade 12 student who did well in calculus.[/QUOTE]
I found this comment on amazon

"I taught myself general relativity from this book and you can too! Feb. 21 2011
By John Nygate - Published on Amazon.com
Format: Paperback Verified Purchase

If you know high school maths and a bit of calculus, and are not scared of equations, this book is for you. (I got English A-levels grade A in math, further maths, physics, a long time ago, but that is all the formal training I have had.)

I agree with all those who give the book five stars.

Prof Leiber writes in short sentences with lots of white space which makes it easy to absorb the material.

It is all there, tensors, the lot!

I tried D'Inverno, but it was too much for me. With this book I taught myself general relativity in a couple of weeks, albeit, I had met tensors before in D'Inverno.

It is a pity more maths/physics books are not written like this."

The book is this http://www.amazon.com/dp/1589880447/?tag=pfamazon01-20
the comment about this book is amazing.I think you are talking about this book. Its out of stock but I can order it I guess.And I will order "The Education of T.C Mith What Modern Mathematics Means to You". too
I looked the ""The First Three Minutes" pdf and there's no math. I searched "Gravitation and Cosmology." too and I found the pdf.
Math is hard for me as you said.But the book is amazing.I want to read it but high school math is not enough I guess.

I will gonnna order these three books.I will going to read first "The Education of T.C Mith What Modern Mathematics Means to You". then "The Einstein Theory Relativity " then "Gravitation and Cosmology."

Thanks for Help

 

[lizzie96']

This webpage has some useful recommendations for relativity books, at a wide range of levels:

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

 

[ChrisVer]

Well if you are good with maths and abstractness then you won't have a problem studying GR without SR (GR is different to SR, and SR won't help you much in understanding GR's formalism- the opposite way is actually easier...it's the difference between going from a special case to describe the general one =almost impossible, to going from the general to the special one =many times possible).
But without mechanics it's difficult to understand what happens in nature.

SR is generally taught first for other reasons I guess. First of all its maths is not so difficult for a beginner, it is way more applicable in other fields (like particle physics), and somehow gets you in the idea of getting what relative actually means. On the other hand GR is different to that, you can just start from asking yourself how could I move on Earth in order to get the shortest path, and what you will actually build is General Relativity (for a 2D case since the Earth is a sphere)... you can even attempt answering this question without introducing tensors but the result will be very ugly, unreadable and un-intuitive.

 

[RyanH42]

I will going to study to understand basic math of GR.I know classical mechanics a liitle bit

 

[ChrisVer]

You could try the text
Lipschutz Differential Geometry...
It's good because it contains many examples, although I think it's difficult to give you the idea of what GR is... However it can give you the mathematical foundations to go further into GR (especially after Chapter 7, but since you are a beginner I'd recommend to go through all the previous ones). And you can find it online in pdf form...

 

[RyanH42]

thank you so much again this is great textbook

 

[DEvens]

[snippies]... you can even attempt answering this question without introducing tensors but the result will be very ugly, unreadable and un-intuitive.

Some place in one of the classic books about GR (maybe Misner, Thorne, and Wheeler's "Gravitation", but not sure) there is an example of doing this. It gives the distance between four places in Middle Earth as reconstructed from _Lord of the Rings_. And it asks if it can be concluded that Middle Earth exists on a flat surface or not. It also gives the formula to work this out. I tried several times but failed to be able to correctly enter the formula into a computer to evaluate it. And I also failed to correctly do the homework question to derive this formula without tensors.

So yes, ugly, unreadable, and un-intuitive is very accurate.

 

[ChrisVer]

Well, if you check Lipschutz you will find out that at first he doesn't introduce the metric when he introduces the first fundamental form ($ds^2$) or the 2nd fundamental form... Instead he puts some functions $E,F,G$ that count for the metric's components... In 2d surfaces this can work almost fine, and it somehow helps someone do the work without a priori needing tensor calculus... but in higher dimensional problems things get even worse - in nDimensions you will generally need $n+\frac{n^2-n}{2}= \frac{n(n+1)}{2}$ functions... in 4D this gives 10 functions.
Also coordinate transformations in >2D, outside the concept of tensors is a Legend-difficulty level game without a reason. (one can check equations 9.2 and 9.3 in the text where he tries to show the invariance of the 1st fundamental form).

 

[RyanH42]

I finished the first chapter.I didnt come metric part yet.So If I com that part I will going to understand better your idea.I will going to finish Lipschutz as fast as I can.This book is amazing.Today I want to finish second chapter.

 

[ChrisVer]

Take your time...

 

[RyanH42]

Yeah you are right.We learned chapter two and one in school.But applications are different and also hard.I have some problems about chapter one I will going to ask them in homework section..