How is theory of relativity mathematically build up?

I am a senior secondary student.I find it difficult to go into the details of theory of relativity.How can I approach it? Do I have to begin with metrics and tensors?|||I haven't read Ellis's book, but I have read Rindler's and I strongly recommend it. Rindler does a great job of giving the reader an intuitive view of things and presents some pretty interesting problems. If you like the mathematical side of GR, particularly geometry, you will like this book. He goes over the geometry of curved spaces in depth which is good if you want to understand the beauty that is GR. The SR section of the book is great. He derives the Lorentz transformations from scratch and based on Einsteins Relativity principle, and Einsteins law of light propagation. He also introduces 4-vectors which remove a lot of the tedium form SR calculations.





All in all a great book.|||The difficulty lies in finding a good exposition of tensors that a novice can relate to. In this case, a novice is someone who is familiar with multivariable calculus and linear algebra. If you have a good footing in these areas, I would recommend beginning with metrics and tensors, yes. Here is a good primer for tensors:





http://www-hep.physics.uiowa.edu/~vincen…





The easy way to conceive of the metric is element





gij = ∂E/∂xi dot ∂E/∂xj





where E is the Euclidean vector of interest. For example, in spherical coords:





|E%26gt; = rsin(θ)cos(φ)|x%26gt; + rsin(θ)sin(φ)|y%26gt; + rcos(θ)|z%26gt;





thus g11 = sin^2(θ)cos^2(φ) + sin^2(θ)sin^2(φ) + cos^2(θ) =





= sin^2(θ)(cos^2(φ) + sin^2(φ)) + cos^2(θ)





= sin^2(θ)(1) + cos^2(θ) = 1





etc.





From this point, group theory will be the next point of interest, in deterermining the properties of the poincare groups etc.





If all of this is above your head, you should be able to find the basics of SR in any college level introductory physics text. But until you become familiar with tensors, you won't be able to have a full working understanding of the mathematics behind relativity, GR in particular, just like no one could be expected to have a working knowledge of modern physics without knowing calculus.





If you aren't familiar with the mathematics, the book recommended above seems a good recommendation. If you are familiar, Ohanian's gravitation and spacetime is an excellent introductory text. Good luck.|||The simplest answer is it's built from Lorentz transformations. Understanding invariance is key to reference frames.





EDIT: Approaching relativity for the first time for most will feel overwhelming. This great mind, doing great things, with greatness... I shouldn't be so cynical, but relativity is simply a paradigm. Any approach will bring you to a deeper understanding. Depending on how thorough you intend to be, you could stop at knowing E=mc^2. I recommend wrestling with simple concepts. For instance, Lorentz transformations describe motion integrated with time. This is completely different from Galilean transformations, which are exceedingly easier, but less descriptive.|||Get the book by Ellis called "Flat and Curved Spacetimes". It may be out of print but it is worth getting. Ellis does a marvelous job of goping through the foundations of special (flat spacetime) and general relativity (Curved spacetime). Special relativity is done without resorting to tensor notation or the introduction of a metric tensor. By the time you get to the itroduction of those quantities, you'll have a good understanding of how these mathematical objects relate to the spacetime you are trying to describe.





In the mean time, start with special realtivity. The fundamental assumption in this theory is that two observers moving in unifomr motion relative to each other should see the laws of physics as the same. So, the equations that describe electromagnetism for instance, should be valid for both observers. A consequence is that light is always measured at 3x10^8 m/s regardless of the wheter or not the person making the measurement is moving with respect to the sourcve of the light. This couples space and time. It leads to the Lorentz transformations between uniformly moving observers. But the spacetime (space + time) is "flat" in the sense that you can use a pseudo-Euclidean measure of distance (distance ~ sqrt(x^2+y^2+z^2)).





This is a really rich theory and it paves the way for the general theory. The difference between special and general relativity is that any motion between observers is allowed in- not just uniform (constant speed) motions. So once you incorporate accelerations, you can talk about forces. You then define the Equivalence principle which basically says that if you are in an isolated system you can't tell teh difference between uniform acceleration and gravitational pull. Stated another way, if you are in a elevator car and you can't see out, the physics you'd experience would be unchanged if the car were standing onthe surface of the earth or being pulled along in space by a rocket acclereating at g (9.8 m/s^2). What this leads to are non-Euclidean spacetimes - non-flat - in which lines that are locally parallel can meet at some other point in the spacetime. Thus we say the space has curvature. This where the tensor machinery is most useful (although some folks prefer using differential forms). Gravity is then the cuirvature of spacetime caused by mass. Things "fall" toward masses bbecause they are following paths along the curved spacetime.





Anyway, start with Ellis' book. It'll set you up well for more advanced texts.