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Trivially no. Consider two such sets in a flat space-time with the same number of events. Each event in the second set is associated with an event in the first event such that taking the earliest event in each set to define the origin of a frame of reference the 4-vectors of position of events in the second set are twice the four vectors of position of the ...


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You can only recover conformally related spacetimes from its null geodesics, that is, the class of spacetimes related by the transformation $g_{\mu\nu} \rightarrow \Omega^2(x) g_{\mu\nu}$ which possess a different matter content


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Not quite. Galilean relativity, which has absolute time, is definitely causal; you can't have future events influence past ones because all observers agree on all times. However, it is interesting how much relativity you can get with incomplete axioms. There's a derivation on page 38 here that shows you can get the Lorentz transformations, but with a ...


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Based on this post: Is causality a formalised concept in physics and the content within, the issue of causality seems to me to be a philosophical as much as a physical question. So I would guess there is no clearcut answer to your question. Have a read, see what you think, and see will you end up as confused as everybody else seems to be regarding the ...


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If you want to make a flat space theory for a topologically trivial manifold you can do it in the standard ways if your metric was very very close to the Minkowski metric. Yours is not. So for instance you aren't going to be able to ignore higher order terms in $h$ since in one of the $y$ directions your $h$ blows up. You can still compute an $h$ field by ...


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Taking from Peskin & Schroeder p.14: They then calculate it asymptotically, and refer to: Gradshteyn and Ryzhik (1980), #3.914 for an exact solution Searching that reference, we come across: #3.914, 6: (Available here) Where $K_2$ is the modified Bessel function.


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We know that the theory of cosmic censorship prevents singularities from existing without an event horizon that hides them from the Universe. Actually, we don't. Don't forget that cosmic censorship is just a hypothesis. It isn't a rigorous well-tested theory like General relativity. See this on the Wikipedia Cosmic censorship article: "The hypothesis ...


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I agree with your definition of locality (probably not surprising :)). Causality I would say is the statement that an event in the future should not affect an event in the past. We can formulate this in classical physics terms. Causality is necessary in order for there to be a well defined initial value problem: I should be able to choose an initial time ...


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Causality means that if something happens before in one reference frame of your choice, it happens before in any other existing reference frame in the universe. Locality means that if two events are space-like separated then it exists at least one reference frame where they happen at the same time; if two events are time-like separated, then it exists at ...


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To reach the Lienard-Wiechert potentials or to prove Feynman's equation (exposed in his lectures without proof), it's necessary to begin with the so-called retarded potentials expressed here conveniently by the following. \begin{equation} \phi\left(\mathbf{r},t\right)=\dfrac{1}{4\pi\varepsilon_{o}}\iiint ...


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To add to ACuriousMind's answer on the Liénard-Weichert potentials, you can put these formulas into an even more wonderfully descriptive form since you can derive Feynman's formula from them for the radiation from a moving charge: $$\vec{E} = ...


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The force does not change instantaneously, the correct way the electromagnetic field of (and thus the force exerted by) a moving electric charge is given by the Liénard-Wiechert potential, where one can see that the effect of the charge does not travel faster than light.


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The force is not propagated instantly. It takes time for the information to get from one point to another. You can treat that as an instant if you are working with small enough distances and velocities, but it's not. If you'll ever study field theory you'll meet retarded potentials that are just this: the field propagates at the speed of light and it's no ...



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