Mathematical treatment of Special Relativity

[WiFO215]

Does anyone know of any book that treats special relativity from a mathematical standpoint? I want to learn SR before starting to read Schutz/ Hartle/ Carrol.

 

[Landau]

https://www.amazon.com/dp/1852334266/?tag=pfamazon01-20 is written for (second year) mathematics students.

 

[WiFO215]

I looked through that book. Can't make out just by browsing whether I will like it or not. Will give it a read and get back to you. Have you read it? What is your opinion on it?

 

[Landau]

I'm sorry, I haven't read it myself, only browsed though it. Are you a mathematics/physics student? Do you know SR from a phycisists' point of view?

 

[qspeechc]

Ok, I did some research and I found https://www.amazon.com/dp/9810202547/?tag=pfamazon01-20, but I haven't read it.

 

[Landau]

Sounds interesting, but very hard to find!

There's also https://www.amazon.com/dp/0387940421/?tag=pfamazon01-20.

 

[George Jones]

There also is

https://www.amazon.com/dp/1441931023/?tag=pfamazon01-20.

Does anyone know of any book that treats special relativity from a mathematical standpoint? I want to learn SR before starting to read Schutz/ Hartle/ Carrol.

I echo what Landau wrote. By "mathematical," do you mean "quantitative, but still from a physics point of view," or do you mean "written in a style suitable for a mathematics course?"

 

[WiFO215]

Ok, I did some research and I found https://www.amazon.com/dp/9810202547/?tag=pfamazon01-20, but I haven't read it.

Looks like a very rare book. I can't find it selling anywhere near me. I can't seem to find a preview either.

EDIT: http://www.worldscibooks.com/physics/1125.html
The contents page looks like what I'm looking for, approx. a 100 page solid exposition before GR.

 

[WiFO215]

I'm sorry, I haven't read it myself, only browsed though it. Are you a mathematics/physics student? Do you know SR from a phycisists' point of view?

There also is

https://www.amazon.com/dp/1441931023/?tag=pfamazon01-20.I echo what Landau wrote. By "mathematical," do you mean "quantitative, but still from a physics point of view," or do you mean "written in a style suitable for a mathematics course?"

Thanks guys. I'm looking for a math treatment, from the perspective of linear algebra, geometry and the like.
Naber's book looks a little too advanced for the present.

 

[Fredrik]

"https://www.amazon.com/dp/0387940421/?tag=pfamazon01-20", by Anadijiban Das.

I haven't read it, so I don't really have an opinion about it. But it's getting good reviews. Kind of expensive though.

 

[Landau]

@Fredrik: I already mentioned that book in post #6 ;) Haven't read it either, but looks promising (based on Google preview).

 

[Fredrik]

I thought I had clicked all the links, but I must have missed that one. Naber's book looks really nice, especially the stuff about spinors. I might have to get that one myself.

 

[Fredrik]

Does anyone know of any book that treats special relativity from a mathematical standpoint? I want to learn SR before starting to read Schutz/ Hartle/ Carrol.

I just noticed what exactly you're asking here. Schutz's GR book contains one of the best introductions to SR, so I think you should probably start with that one.

 

[Fredrik]

Does anyone know a book that includes a statement and proof of the Currie-Jordan-Sudarshan no-interaction theorem?

 

[WiFO215]

I just noticed what exactly you're asking here. Schutz's GR book contains one of the best introductions to SR, so I think you should probably start with that one.

Okay. I shall look through it. I'm going through Woodhouse's book now. It's okay. Not to my taste. I'm going to have to use Schutz anyway.

 

[WiFO215]

Schutz is okay, but I'd like to know if there are better. Schutz isn't a math oriented style. Does anyone have any other suggestions?

 

[Fredrik]

I'm thinking very seriously about writing one, but if you don't have a time machine...

If you do, then please bring back a copy for me too so I don't have to write it.

 

[WiFO215]

See, what I find out of place is that after reading Linear Algebra, Analysis etc. from math textbooks, I find the treatment given in most physics books quite odd. Instead of simply calling vectors as part of some vector space, they have all these round-about definitions like "a vector is something that transforms properly". Why go into linear transformations and other mappings just to define the same thing??
They have all these weird connotations. A simple 4-D space that you might encounter all the time in an Algebra book is given some funny hokey name, "spacetime". Yeesh. They'll add "spacetime is curved" to sound more fancy. It's just a different metric, dammit! I'd find it so much easier if I could avoid all this weird stuff. This is why I'm looking for a book written on the math side.

 

[Landau]

I think Naber is the way to go. He says

Minkowski spacetime is a 4-dimensional real vector space M on which is defined a non-degenerate, symmetric, bilinear form g of index 1. The elements of M will be called events and g is referred to as a Lorentz inner product of M.

etc. so he clearly defines his math, and then explains how physicists (intuitively) think about them.

 

[Fredrik]

See, what I find out of place is that after reading Linear Algebra, Analysis etc. from math textbooks, I find the treatment given in most physics books quite odd. Instead of simply calling vectors as part of some vector space, they have all these round-about definitions like "a vector is something that transforms properly". Why go into linear transformations and other mappings just to define the same thing??

I agree. In fact, I don't think anyone hates that "definition" as passionately as I do. It's been about 15 years since I took classes where that definition was used, and I still get angry when I think about it. It's not just that it's a stupid and obsolete definition. It's also that the books I had to read back then as well as all the teachers I had always stated the definition in a way that doesn't make sense. Would it have killed them to say e.g. "an assignment of four functions v^\mu:M\rightarrow\mathbb R to each coordinate system..." instead of "something"??

But I have some good news for you. Schutz explains tensors really well, if I remember correctly. He defines them as multilinear functions, defines their components in a basis for the vector space (and it's dual space), and derives the formula for how the components associated with one basis are related to the components associated with another basis, i.e. how the components "transform".

So I still recommend that you read that part. When you get to the GR part, where he starts talking about differential geometry (manifolds, tangent spaces, and tensor fields), you will probably want to study a math text instead. (I know I did). This one is probably the best.

They have all these weird connotations. A simple 4-D space that you might encounter all the time in an Algebra book is given some funny hokey name, "spacetime". Yeesh.

This is actually very natural. I mean, it's the mathematical structure that we use to represent real-world concepts "space" and "time", so I think the name is very appropriate. Also, it's not just "a simple 4-D space", because even though the vector space structure is defined exactly the way we would do it for a Euclidean space, it doesn't have an inner product, and is equipped with a bilinear form that isn't positive definite instead.

They'll add "spacetime is curved" to sound more fancy. It's just a different metric, dammit! I'd find it so much easier if I could avoid all this weird stuff. This is why I'm looking for a book written on the math side.

There's a very good reason why the word "curved" is used, and you'll find the same terminology as well as an explanation of the terms in the best math books. (This one has to be the best).

 

[WiFO215]

But I have some good news for you. Schutz explains tensors really well, if I remember correctly. He defines them as multilinear functions, defines their components in a basis for the vector space (and it's dual space), and derives the formula for how the components associated with one basis are related to the components associated with another basis, i.e. how the components "transform".

Okay. So Schutz is good with the tensors and I'll read through it thoroughly later. But now, what I do to learn SR properly? Write that book of yours! Quickly! If that's not possible, give me some good suggestions. I'll just take your word for it that the notations serve some purpose.

@Landau,
The only reason why I'm hesitant to use books like Naber is the size. I'm looking for approx. 100 pages or less mathematical intro to SR, because 50-100 pages is the amount these GR books spend on it. I'm just looking for a substitute for those 100 pages.

 

[Fredrik]

I think your best option is probably to study Schutz and to use Naber when you want to look up a detail that you'd like to see presented in a different way. I doubt that you will find a single book that meets all your requirements.

And just to clarify, the Schutz book I'm talking about is A first course in general relativity, not that other one, which I haven't read.

 

[WiFO215]

Hi guys,
I found a combination to my liking. I am using the book by Carroll and supplementing it with Naber. I personally feel this is a good combo. Thanks for all your recommendations.

 

[Landau]

Have fun! :)

 

[WiFO215]

I've been seriously reading Schutz's treatment of tensors now and it is indeed very good. Am very pleased.