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| bio | website | |
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| location | ||
| age | ||
| visits | member for | 2 years, 4 months |
| seen | 16 mins ago | |
| stats | profile views | 190 |
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1d |
answered | Points in Spacetime |
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1d |
answered | How to find distance of closest approach for a Schwarzschild geodesic? |
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May 10 |
comment |
What experiments have been proposed to discriminate between interpretations of quantum mechanics? If they are experimentally distinguishable, wouldn't they be competing theories rather than interpretations of one theory? |
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May 10 |
comment |
Why Can We Observe Space Curvature / Warping At All? @Archimedix To illustrate one straightforward difference, if you draw a triangle on a cylinder/curled-up-paper, the angles will add to $180$ degrees. The cylinder (intrinsically) flat. But if you draw a triangle on a sphere, they will not, and an ant crawling on its surface can tell just by measuring the angles. The sphere is curved. Imagine curvature as more warping, stretching, or contracting rather than crumpling. Although in more than $2$ dimensions, this gets more complicated. |
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May 10 |
revised |
Negative potential energy of gravity corrected sign. should just remember $e^\Phi$; would make things easier. |
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May 10 |
answered | Negative potential energy of gravity |
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May 10 |
comment |
Why can't you escape a black hole? This is very mistaken: "The 3 spacelike dimensions and 1 timelike dimension of normal space-time now become 3 timelike and 1 spacelike dimension." Spacetime is still Lorentzian beyond the horizon: its signature is still $(3,1)$. There is no event in spacetime whose tangent space is spanned by three timelike and one spacelike vectors! Also, I object to your use of 'topology'. |
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May 10 |
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Christoffel symbol for Schwarzschild metric @DavidZaslavsky alright, done. |
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May 10 |
answered | Christoffel symbol for Schwarzschild metric |
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May 10 |
comment |
Christoffel symbol for Schwarzschild metric What about it? $\partial_r g_{00} = -2M/r^2$, $\ldots$, $\partial_r g_{33} = 2r\sin^2\theta$. You should be able to do the rest yourself. Edit: Like I said previously, if you edit it what you're getting into your question, people will be willing to check it and correct it if need be, as long as you're showing an attempt to do it yourself. |
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May 10 |
comment |
Christoffel symbol for Schwarzschild metric Very well.It's a partial derivative. The metric components have no explicit $t$-dependence, so all $\partial_t(\ldots)$ are zero. You may be confusing this with the fact that most geodesic will have time-varying $r$, but the geometry is not dependent on the Schwarzschild $t$-coordinate at all. Edit: Rather, the $t$-dependence in the geodesics will come from the geodesic equation directly. |
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May 10 |
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Christoffel symbol for Schwarzschild metric let us continue this discussion in chat |
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May 10 |
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Christoffel symbol for Schwarzschild metric Since no components are dependent $t$, $\partial_t g_{ij} = 0$ for any $i,j$. Similarly $\partial_\phi g_{ij} = 0$, but not for $r$ or $\theta$. If you like, you can edit your question to show your attempt and people will try correct it if need be. |
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May 10 |
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Christoffel symbol for Schwarzschild metric Yup. Diagonal metrics are nice that way. |
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May 10 |
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Christoffel symbol for Schwarzschild metric Yes, just remember the Einstein summation convention when doing so. To be clear: the Schwarzschild metric is diagonal, in $-+++$ convention $g_{00} = -(1-2M/r)$, ..., $g_{33} = r^2\sin^2\theta$, the contravariant components $g^{mk}$ can be found through matrix inverse (so in this particular case they're just straight inverses because of diagonality). |
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May 10 |
comment |
Christoffel symbol for Schwarzschild metric I'm not sure what you're asking. $U^0 = t$, $U^1 = r$, $U^2 = \theta$, and $U^3 = \phi$ in the typical order with conventional coordinate labels in the Schwarzschild metric. Well, you can permute them any way you like, as long as you keep the metric tensor components consistent. |
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May 9 |
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I reached a result concerning displacement with quantized time intervals. Am I on to something? @Kurt: There are lots of ways of defining integrals, but the most straightforward one you'd want is the Riemann integral. This kind of formalization using limits is only ~150 years old, despite the result well-being known for a lot longer as David says. (The limit definition of derivative was by Cauchy, and is likewise younger than calculus.) |
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May 9 |
awarded | Citizen Patrol |
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May 9 |
revised |
Limit on velocity in Minkowski Spacetime geometry s/second/third/ |
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May 9 |
answered | Limit on velocity in Minkowski Spacetime geometry |
