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There are lots of foundations that persistently pay millions of dollars to exactly the same kind of research that you are doing and the same kind of researchers (those who yell that they made a revolution but there is no visible beef that makes sense), namely – among many and many others – The Templeton Foundation, FQXi, and most departments of philosophies ...


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Check out V.I. Arnold's Mathematical Methods of Classical Mechanics. This book is pretty terse and can have hard to follow notation. However, it is rigorous and contains mathematical explanations and proof of a wide array of topics in mechanics. It is also filled with very interesting examples. He introduces the concepts needed from differential geometry; ...


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The Particle Data Book, published by the Particle Data Group is probably the nearest to what you're asking for. The actual book is a massive tome costing a fortune. I'm not sure how much of and in what form it's online, but some intrepid Googling should find you most of what you want. As fqq points out the book is available from Phys. Rev. D vol. 86 Issue 1 ...


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For Mathematica the best I know is RGTC. I Used it a long time ago (briefly) for a calculation in IIA SUGRA in 10 dimensions. It calculate gravitational tensors, manages differential forms (also Lie algebra valued ones), calculates Hodge dualities, etc. Personal comment: If you are more intrepid (and FLOSS lover), there is a software called SAGE, which ...


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Your question and this answer are really better suited to the Meta, and I suspect a moderator will be along some time soon to migrate them. But while your question is still here ... An intuitive understanding of GR is extraordinarily difficult to attain. I've been studying GR (as an interested amateur not a pro) for a decade and I still make naive errors ...



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