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*ok, i realize this is probably a really simple/dumb question, so I should explain that I don't have any formal learning in any math. my last math class was years ago in grade 11, and it was basic algebra. everything else I know is on a need to know basis (when i see a symbol i don't know, formula i don't understand and is necessary for whatever I'm reading, I find out what it is)... so I probably skipped over some basic things... i know it's not good, but my career path is not science, i like learning about these things just for fun so I didn't bother to learn some things i probably should have.*

i only know the concepts of SR and the very basic formulas (time contraction, etc.). figure i'd learn the basics then get into the harder stuff... anyway, i recently decided to try and get into the harder stuff (harder for me at least lol hard=numbers, I've dyscalculia) and got "a first course in general relativity" by schutz.

i only know the concepts of SR and the very basic formulas (time contraction, etc.). figure i'd learn the basics then get into the harder stuff... anyway, i recently decided to try and get into the harder stuff (harder for me at least lol hard=numbers, I've dyscalculia) and got "a first course in general relativity" by schutz.

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I'm having trouble understanding the reasoning on page 11 ("1.6 invariance of intervals"). it comes after a spacetime diagram of a light-ray being reflected and how it is seen from the point of view of 2 observers (the slope of the ray is the same for both obviously, and what changes is t and x).

then it gives the formula: ( http://aycu28.webshots.com/image/13067/2004495092710270588_rs.jpg ) . (the formula also equals 0 because v=1=c). ok, so far so good, i get that.

then it talks about how those coordinates are linear combinations of their counterparts, and how ?s^2 (s with the bar on top ... the first part of pic. 1, before "=") is a quadratic function of the unbarred coordinate increments. ok.

this is where it loses me:

**1)**"we can therefore conclude that ( http://aycu16.webshots.com/image/13015/2001170268022097477_rs.jpg ) for some numbers {M; a,b (<-greek letters)=0,...,3}, which may be a function of v, the relative velocity of the two frames"

can anyone explain step by step how they arrive at this and what it stands for? ... I'm guessing I'm missing something very basic here. but I'm pretty good at figuring out stuff by one example and extrapolating the concept... just need the words to explain what the hell is going on up there.

**problem 2)**"and that if ?s^2=0 then ( http://aycu28.webshots.com/image/11867/2003091507785314037_rs.jpg )" ... this is probably the dumber question, but where did the ?r come from? r is usually radius, but i don't see how that would apply here..

again, sorry if this is newb stuff, but this is my first attempt at getting into the math of it all.

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