Kostik's latest activity
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Kostik replied to the thread A Dirac's "GTR" Eq (27.4): how momentum ##p^\mu## varies.It's not clear that the argument above (27.3) for ##p^0## applies for ##p^1##. The integral $$\int_V p^0 dx^1 dx^2 dx^3$$ is the mass... -
Kostik replied to the thread A Dirac's "GTR" Eq (27.4): how momentum ##p^\mu## varies.Heck, no. Dirac says that if ##b^\mu \propto p^\mu \propto u^\mu##, then at ##x=z(\lambda)##: $$z^\mu (\lambda) + b^\mu (x) = z^\mu...
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Kostik replied to the thread A Dirac's "GTR" Eq (27.4): how momentum ##p^\mu## varies.Dirac infers (27.4) but doesn't derive it. I was looking to derive (27.4).
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Kostik posted the thread A Dirac's "GTR" Eq (27.4): how momentum ##p^\mu## varies in Special and General Relativity.In Dirac's "General Theory of Relativity", chapters 26-30, he builds up various action principles from which Einstein's equation...
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Kostik replied to the thread A Does the EP imply that a free-falling observer follows a geodesic?.Never mind, it's obvious. In an inertial reference frame, a "free-falling particle" is simply one not acted upon by any forces, hence...
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Kostik reacted to PAllen's post in the thread A Covariant form of Maxwell's (inhomogeneous) equations (in GR) with
Like.
The main discussion is in and around box 16.1, p. 390 of my edition. -
Kostik posted the thread A Does the EP imply that a free-falling observer follows a geodesic? in Special and General Relativity.From https://www.astro.gla.ac.uk/users/norman/lectures/GR/part4-screen.pdf: "It is possibly not obvious, but the Strong EP also tells...
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Kostik replied to the thread A Covariant form of Maxwell's (inhomogeneous) equations (in GR).Could you kindly give a reference within MTW?
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Kostik replied to the thread A Covariant form of Maxwell's (inhomogeneous) equations (in GR).Dirac seems to think the ##\partial \rightarrow \nabla## rule is self-evident. He says in chapter 10 (p. 19), “The laws of physics must...
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Kostik replied to the thread A Covariant form of Maxwell's (inhomogeneous) equations (in GR).When I try to "follow my nose", I get: $${F^{\mu\nu}}_{;\nu}={F^{\mu\nu}}_{,\nu} + \Gamma^\mu_{\alpha\nu}F^{\alpha\nu} +...
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Kostik replied to the thread A Covariant form of Maxwell's (inhomogeneous) equations (in GR).Actually, Dirac does not "impose" the change ##\partial\rightarrow\nabla##; in fact, my derivation of the covariant statement of the...
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Kostik posted the thread A Covariant form of Maxwell's (inhomogeneous) equations (in GR) in Special and General Relativity.Background: In flat spacetime (special relativity), Maxwell's homogeneous equations $$\text{curl} \textbf{ E}=-\frac{d\textbf{B}}{dt}...
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Kostik reacted to PAllen's post in the thread A Error in Landau-Lifshitz Vol 2, Fig. 20, page 310 with Like.
I don’t have L-L, but am generally familiar with Lemaître coordinates (a personal favorite to use). The outgoing null geodesics exterior...
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Kostik replied to the thread A Error in Landau-Lifshitz Vol 2, Fig. 20, page 310.Yes, I am sure. Here is my work. My ##\rho## is Landau's ##R##. Also, it's clear because the angle formed by the light cone gets more...
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Kostik replied to the thread A Error in Landau-Lifshitz Vol 2, Fig. 20, page 310.I should have provided a picture from the L-L text:
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