Relativity: Where to start?

[Guest raines]

Until recently, I had never been very interested in science or math.

 

Now I am.

 

I picked up a couple of books that looked interesting to me, and I'm currently trying my best to understand the basics of general relativity, special relativity, and superstring theory.

 

However, I feel that I might be approaching concepts that are too advanced for me, and am wondering where I should begin.

 

As far as prerequisite learning goes, I've just completed pre-calculus and physics, both of which were gifted courses.

 

The books I'm reading, as aforementioned, are Zero: The Biography of a Dangerous Idea by Charles Seife, and The Elegant Universe by Brian Greene

[□h=-16πT]

Ok well those books are ok if you just want to know the theory side of the big theories in modern physics, but that's boring. If you want to get into the interesting side of GR etc, i.e. the maths, then you should get a couple of books on the calculus of many and single dimensions, abstract algebra (set and group theory, linear algebra etc.) and differential geometry. Those prerequisites will suffice for any introductory course in general relaltivity. As for superstring theory and the like, generally a post grad/grad course, you'll need an education in complex analysis and spinor algebra/calculus. As a basis for all advanced physics you need a fairly decent knowledge of classical mechanics.

 

A good book I have on single dimensional calculus and a bit of multi-D is "The Calculus Tutoting Book"- C&R Ash. A damn good mathematics book for university physics courses is "Mathematical Methods for Physics and Engineering"- Riley et al, which gives a fairly detailed exposition of most of the topics i mentioned above, plus more. As for differential geometry I have "Geometrical Methods of Mathematical Physics"- B. Schutz, an excellent book demanding very few prerequisites and that covers all aspects of differential geometry, from Riemann to Cartan. The universal text for general relativity is "Gravitation"- Misner et al, a big book with a hefty price tag. I learnt GR/SR at university level from "A first course in general relativity"- B. Schutz, which covers the differential geometry required for basic GR before going into the physics.

[CanadaAotS]

If you want to get into the interesting side of GR etc, i.e. the maths

 

the math is the interesting part? lol...

[ydoaPs]

i like both the ideas and the math. i am not at the right level for the maths yet, but i am starting. when i get some more money, i am going to get some more math books(that is after i buy some stabities).

[brad89]

I thought relativity was the belief that energy and matter are a relation of the same stuff. I knew there was more to it, but is that really true or not?

[ydoaPs]

basically, everything is relative, but c. what you are talking about is probably [imath]E^2=(mc^2)^2+({\rho}c)^2[/imath]

[□h=-16πT]

the math is the interesting part? lol...

 

Yes, I find it is. It's better than being told that such and such happens as a result of GR without being given any justification.

[□h=-16πT]

I thought relativity was the belief that energy and matter are a relation of the same stuff. I knew there was more to it, but is that really true or not?

 

Well special relativity starts off pretty basic and then develops into the idea of mass-energy equivalence. SR deals with inertial frames in a flat Euclidean space-time; GR with the geometry of curved space-time.

[Tom Mattson]

If you want to learn relativity then the place to begin is the following link:

 

http://www.physics.nyu.edu/hogg/sr/sr.pdf

 

The first 4 chapters assume knowledge of basic physics and precalculus mathematics. Chapter 5 assumes that you know how to do simple matrix operations, and Chapter 6 uses a minimal amount basic calculus.

[Tom Mattson]

Just a few other small comments.

 

Ok well those books are ok if you just want to know the theory side of the big theories in modern physics' date=' but that's boring. If you want to get into the interesting side of GR etc, i.e. the maths,

[/quote']

 

I agree with your sentiment. To me there is nothing less interesting than being told a bunch of statements that appear to be completely logically disjointed. The only nit I have to pick here is that the math is the theory side of physics. That's precisely what theoretical physicists do. Books such as The Elegant Universe do not present theory at all, but rather qualitative interpretations of the concepts of a theory.

 

I thought relativity was the belief that energy and matter are a relation of the same stuff.

 

To really get to "what relativity is" you should go back to its postulates. Special Relativity is founded on the two beliefs that:

 

1. The laws of physics are the same for any two inertial observers.

2. The speed of light is independent of the motion of its source.

 

What you state above is a derived consequence of this foundation.

 

I knew there was more to it' date=' but is that really true or not?

[/quote']

 

All available experimental evidence says "yes".

 

basically' date=' everything is relative, but c.

[/quote']

 

Not exactly. In relativity there are a number of quantities that are not relative. We call them "Lorentz scalars" or "rank-0 Lorentz tensors". For instance the 4D "dot product" of any two 4-vectors results in a Lorentz invariant. An example is the 4-momentum contracted with itself:

 

[math]

p_{\mu}p^{\mu}=m^2

[/math]

 

Hence "m" (the mass of the particle) is not relative.

[□h=-16πT]

That's what I meant by theory, just couldn't think of another way of putting it. Thanks for pointing that out.

[revprez]

the math is the interesting part? lol...

 

Yes, because the math exposes the theory.

 

Rev Prez

[Saint]

Yes, I find it is. It's better than being told that such and such happens as a result of GR without being given any justification.

 

As much as you'd like it to be, math is not a justification. It's tool for modelling. If GR makes no sense to you conceptually (without math), that should tell you something.

[swansont]

As much as you'd like it to be, math is not a justification. It's tool for modelling. If GR makes no sense to you conceptually (without math), that should tell you something.

 

Yes: "GR is difficult."

[Tom Mattson]

As much as you'd like it to be, math is not a justification.

 

It is justification for statements that begin with, "SR predicts that..."

 

I can't even count the number of arguments against relativity I've seen by people who think they've found a paradox in the theory, when in truth the person simply does not know what the theory says.