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A tensile pulse travels through the rope at the speed of sound. This speed depends on the density and the bulk modulus of the material - a rope strong enough to support its own weight would probably have a very high bulk modulus. The equation is $$v = \sqrt{\frac{K}{\rho}}$$ Where $K$ is the bulk modulus and $\rho$ the density.

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This is a perfectly good question; don't feel discouraged. Coming up with a notion of 'causality' that doesn't refer to any physical theory is pretty hard. I'll discuss it here in the context of general relativity (GR). The basic entities in GR are events; i.e. spacetime points $(t, x, y, z)$. Suppose we have two events $A$ and $B$ and that, according to ...

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As you correctly note, you need to prove $t_B > t_A$ is preserved by Lorentz transformations. It's not clear to me whether your final answer demonstrates this (since the sign of $x_b - x_a$ isn't totally obvious), but I think you're on the right track. I might have responded with the following argument. The invariant interval $$ds^2 = -dt^2 + dx^2 ... 1 The physical effects of gravitational wave (GW) is best understood in the transverse, traceless gauge. So, if a linearly polarized GW is propagating in the z-direction, it can have only h_{11}= - h_{22} and h_{12}= h_{21} as non-zero components which are orthogonal to the direction of propagation, along with the condition that the magnitudes of these ... 1 The state is "measured" in the sense you are imagining - that is, it becomes definite - at whatever time it becomes possible in principle to infer its having a particular measurement outcome. In your case, if the probe provides unambiguous information about the measurement result, the time of measurement will be found to have been delta-t back in time. This ... 0 If you're thinking in terms of waves, yes the mathematical formalism used in both cases are quite similar. Gravity does rid itself from the black hole, because the kind of wave (gravitational one) yielding gravitational radiation, what can be measured outside the event horizon. This gravitational irradiation moves on the speed of light. 1 Let's suppress some dimensions to simplify:$$\Delta s^2 = -(c\Delta t)^2 + \Delta x^2 $$This quantity$$\Delta s^2$$is preserved by changes of reference frame, just as in Galilean physics the quantity$$\Delta r^2 = \Delta x^2 + \Delta y^2  is preserved by rotations. Notice it is also the equation of a hyperbola. Thus, the effect of a frame shift is ...

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Let me answer my question. By the definition of conformal flatness, $\nabla_a\Omega|_{i^0}=0$, where $\Omega$ is the conformal factor, and $i^0$ is the spatial infinity. So the spatial infinity is singular, and I think that is the reason people think spatial infinity is a point.

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The world lines exists independent of the frame you choose. That is, Minkowski space-time is an affine space (like the euclidean space $\mathbb E^n$, not to be confused with $\mathbb R^n$) where there are no frames. Here you can "draw" world lines, and doesn't matter that there is none inertial frames yet. Then, when you select the frame you are actually ...

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Not exactly a swap, time becomes an imaginary number a square root of a negative number. "Formula The Schwarzschild radius is proportional to the mass with a proportionality constant involving the gravitational constant and the speed of light: $r_\mathrm{s} = \frac{2 G M}{c^2}$ where: rs is the Schwarzschild radius; G is the ...

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