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In Special Relativity, two events are said to be causally related or in causal contact if a signal could travel from one event to the other. Note that this does not require that an actual signal is transmitted. Indeed, this notion is valid in vacuum. Assume that in a given frame the spatial distance $\Delta r$ and time difference $\Delta t$ are such that \...

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Our current understanding of almost everything except gravity is based on relativistic quantum field theory (RQFT). This answer explains how tachyons are excluded by a general feature of RQFT. By tachyon, I mean a particle that travels faster than light. In the case of a classical point particle, that means the particle's worldline is spacelike. But our ...

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An important caveat: FTL implies time travel only if the FTL mechanism obeys the principle of relativity (that is if there is no "absolute" speed, only relative speed). All known physical laws obey this principle, and it dates back to Galileo, so this is a reasonable assumption. For simplicity let's consider an arbitrary FTL communication mechanism,...

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Indeterministic events don't violate anything. Every event is indeterministic, there is no determinism at all in reality. Indeterminism is nothing but the absence of determinism. It does not mean the absence or violation of causality. In reality, causes never determine their effects with absolute accuracy. Causes only determine the probability distribution ...

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Suppose there exists a point $p\in\mathcal{M}$ for which every past inextendible timelike curve through $p$ intersects $S$, but there exist an (inextendible) null curve through $p$ that does not intersect $S$. Then $p \in \tilde{D}^{+}(S)$, but $p \notin D^{+}(S)$.

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Fields extend through all of space so one can easily get confused talking about their lightcones. But as far as I can tell you are thinking about quantum field theories of two different types. Those in which $\left < \psi_f \right | U(0, t) \left | \psi_i \right > = 0$ whenever $\left | \psi_i \right >$ is a wave packet of compact support (call it ...

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There is a possibility that the "flow" of time may primarily be an analogy traceable to medieval water clocks: Einstein does appear to have consistently regarded time as a dimension comparable to the spatial ones, although the directionality of passage through it is limited to the familiar past-to-future one through its widely-accepted relation to ...

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