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I found the Weinberg passage, but to quote it I need to do it in an answer (too long). So here it goes. We have seen in this chapter that the nonvanishing of the tensor $R_{\lambda \mu \nu \kappa}$ is the true expression of the presence of a gravitational field. We also saw in Chapter 1 that Gauss was led to introduce the Gaussian curvature $K = -R/2$ as ...

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This is the relative strength of interactions of elementary particles: strong 1 electromagnetic 1/137 weak 10^-6 gravity 6x10^-39 A free neutron decays through the weak interaction with a lifetime of 14.7 minutes. The gravitational interaction is 10^-33 times weaker than the weak. In the lifetime computations this would be squared .Even if baryon ...

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There is no %100 proof in science; at least not for good science. It's always a question of being the most accurate / descriptive / useful theory. For example, Newtonian gravity is 'true' to the extent that it is very effective in a huge diversity of situations. General Relativity (GR) includes all of the accuracies of Newtonian Gravity, and then also ...

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There's a very real phenomenon called 'Gravitational Lensing', in which light is bent from its original trajectory by a massive enough cluster of matter (which curves the space-time around it). Moreover, it's bent by a different amount than predicted by a simply application of Newtonian ideas, as kindly pointed out by Rob Jeffries. Is this evidence enough? ...

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