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In short: The particle horizon is the extent of our current past light cone, and the event horizon is the extent of our future light cone at $t=\infty$. It is important to be clear that these horizons are horizons only to an observer at this place in Space and Time. They do not mark physical boundaries between different regions in Space; rather, they ...

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"Is this causality condition equivalent to Lorentz invariance?" No. Lorentz invariance ensures that points in spacetime that are spacelike (timelike) separated in one frame stay spacelike (timelike) in all inertial frames. Causality, in this context, is the notion that an event can not have effect at any spacelike separated point in spacetime. "Now the ...

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It would take less than 8 mins. It depends on elasticity of space time fabric. Consider Put a marble on a cloth and then observe how much it descends and curves cloth. Now, suddenly remove marble The time taken by cloth to regain its original position, so that it ends point feel no curvature, clearly depends on elasticity of fabric and amount of depth it had ...

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Causality requires that $\chi(t) \propto \Theta(t)$, where $\Theta(t)$ is the Heaviside step function. In other words, $\chi(t-t') = 0$ for $t'>t$, so that only past influences from times $t'\leq t$ affect the system response at time $t$. This leads to constraints on $\chi(\omega)$ viewed as a function of complex frequency: it must be analytic in the ...

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If quantum mechanics is probabilistic, there is no reason for a particle to be in one place and not the other, but particles do make up their minds... but how? This topic is obscured by common confusions about what quantum mechanics entails. There are several different explanations of what is happening in reality, if anything, to bring about the ...

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In fact, for Quantum Mechanics Nature is intrinsically probabilistic: there is no law describing with probability $1$ a single event. In accordance with Copenhagen interpretation of the quantum formalism this must not be considered as a limitation to our knowledge, but it is simply the manner as things exist in Nature, it is an ontological claim. In this ...

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Quantum mechanics is uncertain, but it's not probabilistic. There are some very important differences between the two terms. In quantum mechanics nature limits our knowledge about which particular outcome a future measurement will have, but the possible outcomes of given initial conditions and their expectation values are perfectly deterministic (and ...

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Globally hyperbolic refers to the fact that hyperbolic equations always have locally a well defined Cauchy problem, that is, a unique development given initial conditions. Which means that, given a matter field at a time $t_1$, there exists a unique solution of that field at a time $t_2$. It is boosted up to globally hyperbolic if that property holds ...

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You would receive the photo as long as the light of the photografer taking the photo reaches you (just few seconds of delay between the 2 ), so basically you would receive the same data again, so the photographer sending the photo is no more reliable than the subject's light itself. Receiving the photo makes no stronger guarantee of subject being still there ...

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The Ellis-Bronnikov wormhole, with topology $\mathbb{R}^2 \times S^2$ and metric $$ds^2 = - dt^2 + dl^2 + (b^2 + l^2) d\Omega^2$$ violates the ANEC and possesses no closed timelike curves (nor can it be made to develop any since the topological handle is between two different spacetimes and not the same one), as can be seen by ...

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