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What is the basic assumption(s) required to explore general relativity?

For example, if one merely assumes that the speed of light $c$ is the same for all observers, and the laws of physics are the same for all observers, then it's possible using a mix of algebra and some calculus to derive every SR result from time dilation to length contraction, $E = mc^2$, and so on.

What is the basic premise of general relativity? I assume that all of SR is included but is there anything else?

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2 Answers 2

The basic premise behind general relativity is the equivalence principle, the idea that an object moving in an accelerating (non-inertial) reference frame is indistinguishable from one moving under the influence of a gravitational field.

(As an aside, Einstein's original proofs of time dilation, length contraction, even $E=mc^2$ don't involve any calculus - they are quite simple and elegant. GR on the other hand is rather calculus-intensive)

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E = mc^2 without calculus? Looks like I need to work on my SR again then... –  frogeyedpeas Jun 5 '13 at 2:19
    
Yeah, you definitely don't need calculus for $E=mc^2$. Even the algebra is very simple. (In fact, off the top of my head, I can't think of anything in SR short of accelerations that needs calculus.) –  Mike Jun 5 '13 at 2:27
    
I used the method of taking derivatives of mass, and substituting it into expression for force, and using chain rule to convert dt into v dx... and then integrate –  frogeyedpeas Jun 5 '13 at 2:31
    
Look here: youtube.com/watch?v=hW7DW9NIO9M for a nice, easy-to-follow derivation. –  Zen Jun 5 '13 at 3:00
    
The Doppler factor (1+v^2/2c^2) that follows after "for our purposes" is an approximation that comes from a Taylor expansion of the exact factor. And Taylor expansion comes from calculus. –  jld Jun 5 '13 at 3:50

What is the basic premise of general relativity?

It just might be general covariance even if the content of that phrase is controversial. For example:

Einstein offered the principle of general covariance as the fundamental physical principle of his general theory of relativity and as responsible for extending the principle of relativity to accelerated motion. This view was disputed almost immediately with the counter-claim that the principle was no relativity principle and was physically vacuous. The disagreement persists today.

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