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12

The rubber-sheet analogy is often used to "explain" the basics of GR to beginners, but actually it has nothing to do with real gravity. It acts much more like a scalar field (the up/down freedom degree) - and there were several attempts to build a scalar gravity. But the correct description turned out to be tensorial and purely geometrical. GR has 10 ...


9

The source of gravity is not mass, but stress-energy-momentum, so you are correct that the energy converted in this process already has gravity and that that gravity is only rearranged The change in the gravitational field needs time to propagate, though, and this does indeed happen at the speed of light.


5

To add to Hindsight's great answer: one of the reasons that the analogy fails is the same reason why Nordström's Scalar Theory of Gravitation fails: Waves on rubber sheets are described by linear wave equations; at least in the small amplitude limit. However, by analogy with Maxwell's equations, waves in gravitation should bear energy. But we are also ...


3

The first reason is that your "distance" between geodesics is measured by a parallely propagated direction $\partial/\partial \phi$. If you take a look at the sphere, the difference $\Delta \phi$ does not correspond to the distance between the points on the geodesics. The distance between them would be measured by arc-lengths of great circles. But you are ...


3

The other forces are also just the result of "spacetime bending", just in a different way. There is no fundamental difference in the description of the other forces through gauge theories and gravity through relativity.1 The reason why it is often said that it is different is that our usual methods of quantizing a theory fail when applied to gravity. But to ...


2

That's a very nice answer by ACuriousMind. I would like to add something, though. GR is actually not like other gauge theories in some of its aspects (apart from having lots of similarities). For starters, it is background-independent and highly non-linear. In ordinary QFT we usually deal with perturbative expansions, which make sence only for weak-coupled ...


1

Start with the lower expression: $$ (c/2)\eta^{bc}\eta^{ae}\partial_{a}\left(g_{be,c} + g_{ce,b} - g_{bc,e}\right) - (c/2)\eta^{ae}\eta^{bc}\partial_{c}\left(g_{be,a} + g_{ae,b} - g_{ba,e}\right).\\ = \frac{c}{2}\eta^{bc}\eta^{ae}\left(g_{be,ca} + g_{ce,ba} - g_{bc,ea}-g_{be,ac} - g_{ae,bc} + g_{ba,ec}\right)\\ =\frac{c}{2}\eta^{bc}\eta^{ae}\left(g_{ce,ba} - ...


1

Force is a classical concept that is useful in modeling the mesoscopic world, i.e the world of classical thermodynamics, mechanics and electrodynamics. Exchanged particles are quantum mechanical concepts which mainly work in small atomic size dimensions. There is continuity in physics going from mesoscopic to the microscopic frameworks, and continuity ...



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