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A theory that describes how matter interacts dynamically with the geometry of space and time. It was first published by Einstein in 1915 and is currently used to study the structure and evolution of the universe, as well as having practical applications like GPS.

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Before Maxwell's equations, physics postulated what is now called Galilean relativity. In a vacuum, electromagnetic waves obeying Maxwell's equations propagate at speed $c:=\left(\mu_0\varepsilon_0\ri …
answered Mar 24 '16 by J.G.
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The mass-energy, radius, entropy, lifetime etc. are related with power laws whose exponents depend on not only $D$ but in some cases also the geometry. For example, which $p$ gives the entropy-energy …
answered Jun 3 '17 by J.G.
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I don't know where you read anyone implying all matrices are tensors, but you're right to define tensors by their transformation law. (As a very simple example of a matrix that's not a tensor in gener …
answered Jul 3 '17 by J.G.
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Note: technically, everywhere we've been using $\sqrt{g}$ it should be $\sqrt{|g|}$, but I'll let the former denote the latter in a slight abuse of notation like the rest of this page. gj255 has alre …
answered Jul 19 '18 by J.G.
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Physical theories contain parameters whose values must be empirically determined to make predictions. (For example, for electromagnetism you need the fine structure constant.) We therefore need the th …
answered Jan 17 '16 by J.G.
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By a five-dimensional extension of general relativity that unifies it with electromagnetism, you presumably mean Kaluza-Klein theory or something very similar. As explained here, K-K is indeed backgro …
answered Dec 2 '16 by J.G.
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In natural units $c=\hbar=1$, so velocity is dimensionless, length and time each have mass dimension $-1$ and acceleration has dimension $+1$, so force has dimension $2$. In $d$-dimensional spacetime …
answered May 30 '17 by J.G.
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We can show $-p_\mu u^\mu =mc^2$, with $m$ the rest mass. Thus our result is the rest energy. For $3$-velocity $v$ we have $u^0=\gamma c,\,u^i = \gamma v^i$ so $u_\mu u^\mu = \gamma^2 (c^2 - v^2) = c^ …
answered Jun 19 '18 by J.G.
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We'll work with $\mu_0=1$. From the Lagrangian density $-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}-A_\nu j^\nu=-\frac{1}{2}\partial_\mu A_\nu F^{\mu\nu}-A_\nu j^\nu$ and the definition $F_{\mu\nu}=\partial_\mu …
answered Mar 13 '17 by J.G.
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The point of general relativity is that the laws of physics look the same regardless of the coordinates chosen (as long as s diffeomorphism relates the old coordinate system to the new one). This mean …
answered Jul 3 '18 by J.G.
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The closest thing in mainstream theoretical physics is "closed timelike curves", paths along which you can travel and thereby return to the same place and time as you started, provided your velocity v …
answered Jul 1 '17 by J.G.
5
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If you want to compare Maxwell's EM with GR, note they're respectively obtainable from extending a global $U(1)$ variance to a local one and Lorentz invariance to invariance under general coordinate t …
answered Dec 24 '18 by J.G.
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If we were discussing electromagnetic forces, you might be asking whether electromagnetism causes the forces or vice versa. To make this less of a chicken-egg question, I'd assume "electromagnetism" h …
answered Apr 17 '16 by J.G.
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Since $g_{ab}g^{cb}=\delta_a^c$ is the identity matrix, taking the trace gives $g_{ab}g^{ab}=D$ in a $D$-dimensional spacetime.
answered Jan 4 '18 by J.G.
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The $4\times 4$ tensor is symmetric, so the $6$ entries below the leading diagonal are equal to the $6$ above it. Therefore, there are only $4^2-6=4+6=10$ DOFs before we consider Bianchi; the sum $4+6 …
answered Apr 6 '18 by J.G.

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