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professor
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could soemone give me a site, or let me know of a book that gives the field equations in the context which Einstein presented them, along with his discussion of their implications?
professor said:i have read gravitation, tanks i will look at the other recomendations (the last looks like what I am looking for)- and ohh drat dident realize what thread i was in, i hope some more poeple find this (qm is atleast related so probably..)
- and ohh yes i began my learning of general calculus from my teachers college book in 7'th grade :) - I am only in tenth now, but i do know a thing or two about tensors.. curvature tensors is what I am looking for
professor said:well I am 15 now :P 16 in march :)
also- a tensor is a triple vector? - or a three dimensional vector (triple probably not the right word)
professor said:well I am 15 now :P 16 in march :)
also- a tensor is a triple vector? - or a three dimensional vector (triple probably not the right word)
professor said:well I am 15 now :P 16 in march :)
also- a tensor is a triple vector? - or a three dimensional vector (triple probably not the right word)
I wish I knew of a site. Lacking one you may want to see a derivation of them. I whipped this one up atprofessor said:could soemone give me a site, or let me know of a book that gives the field equations in the context which Einstein presented them, along with his discussion of their implications?
Thanks. Please note that I don't know how Einstein derived his equations. This is how I derived it based on Schutz's derivation as well as Chandrasekhar. I'd imagine that Einstein's wasn't that much different.professor said:edit: i just looked over the derivation website...thanks for that i had never seen how he (einstien) had come up with that before. I still am having problems with the idea of tensors in the first place... mabye ill post on calc forums for that, or hope my math teacher knows a thing or two about them... he probably will.
Huh!selfAdjoint said:A contravariant tensor of rank k is a multilinear function that takes k tangent vectors into a single vector.
A covariant tensor of rank k is a multilinear function that takes k tangent vectors into a coefficient number.
selfAdjoint said:A contravariant tensor of rank k is a multilinear function that takes k tangent vectors into a single vector. A covariant tensor of rank k is a multilinear function that takes k tangent vectors into a coefficient number.
Einstein's field equations are a set of ten partial differential equations that describe the relationship between the curvature of spacetime and the distribution of matter and energy within it. They are a fundamental part of Einstein's theory of general relativity and provide a mathematical framework for understanding gravity.
Einstein's field equations are important because they provide a more accurate and comprehensive understanding of gravity than Newton's law of gravitation. They have been extensively tested and have successfully predicted a wide range of astronomical phenomena, such as the bending of light by massive objects and the existence of black holes.
Solving Einstein's field equations is a complex task that requires a deep understanding of differential geometry and advanced mathematical techniques. It is typically done using computer simulations and numerical methods, rather than exact analytical solutions. However, there are simplified versions of the equations that can be solved with basic calculus skills.
Einstein's field equations have many real-world applications, particularly in the fields of astrophysics and cosmology. They are used to study the behavior of massive objects, such as planets, stars, and galaxies, and to make predictions about the evolution of the universe. They also have practical applications in fields like GPS technology, where they are used to correct for the effects of spacetime curvature on satellite signals.
No, Einstein's field equations cannot be proven in the same way that mathematical theorems can be proven. They are based on Einstein's theory of general relativity, which is a well-established and extensively tested scientific theory. However, like all scientific theories, it is subject to revision and refinement as new evidence and observations are gathered. So while the equations themselves cannot be proven, their predictions and implications can be tested and verified through experiments and observations.