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The influence one event, process, or state, has on another event, process, or state, whereby the latter is at least partly dependent on the former.

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In the middle of some research, I reached a sort of confusion that I’d like to sort out. In flat space FTL is impossible, because in a Minkowski metric, $$\mathrm{d}s^2=c^2 \mathrm{d}t^2-\mathrm{d}x^2-...
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The spacetime $(M,g)$ is given locally at each point by the metric: $$g= -(dt + a \, d \phi)^2 + d\rho^2 + \kappa^2 \rho^2 \, d\phi^2 + dz^2 \ \text{where} \ \ a > 0$$ This is the spacetime of a ...
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It is noted in Peskin and Schroeder's QFT text that the momenta used in the evaluation of the field operator $\phi(x)$ are "on mass-shell": $p^2=m^2$. Specifically, this is in relation to ...
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We know that transitioning from classical mechanics to quantum mechanics, determinism breaks down. We also know that complexity and chaos theory have determinism in principle but we can't predict. My ...
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By causal/conformal structure I mean the context of Malament's 1977 theorem. If I understand correctly this means that any two spacetimes which agree about all of the future-directed continuous ...
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I have just read Jefimenko's notes on the causality violation it would pose to claim "varying electric fields give place to magnetic fields and viceversa" since both fields take place at the ...
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Assume $c=1$ I've been doing relativity by myself so I may be making some assumptions here that I would not have if my learning had been more extensive. One such assumption is that you can model the ...
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In Tong's lecture notes (http://www.damtp.cam.ac.uk/user/tong/qft.html) page 38, he calculates the following propagator: $$D(x-y) = \int \frac{d^3 p}{(2\pi)^3} \frac{1}{2E_\vec{p}} e^{-ip \cdot (x-y)}....
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I am studying Hawking's area theorem from the book the large scale structure of spacetime by Hawking and Ellis. At the end of page#318, it said: null geodesic generators of future infinity have no ...
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I have a question regarding the dimension of time. We all know that an event in spacetime is defined by a point $$ {x}^{u} = (ct, x, y, z) .$$ The only component that breaks the symmetry is $ct$, ...
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(Boyer-Lindquist coordinates and $ c = G =1 $ taken) As I know, line element in Kerr metric $ d s^2 = - \left( 1 - \frac{2Mr}{\rho^2} \right) d t^2 - \frac{4 M a r \sin^2 \theta}{\rho^2} d \phi d t + \...
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The typical definition of a causal net of observables in quantum theory is to consider, for the case of a (globally hyperbolic) spacetime $M$, the category of open sets $O(M)$ ordered by inclusion, in ...
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There are uniqueness theorems that classify Black holes according to its mass, angular momentum and charge. One of the theorem is Carter-Robinson theorem which has many assumptions and then it says ...
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For a non-interacting massive scalar field $\phi$ in an $n+1$ dimensional minkowskian spacetime, the field commutator between two event points is $$ [\phi(x),\phi(y)] = \int \frac{\mathrm{d}^n p}{(...
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According to Fermat's principle, light travels the fastest path from dot A to dot B. I wondered how light knows which path is the fastest, and found out that light actually goes all path, but non-...
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Consider the action integral, $S[\gamma] := \int L(\gamma(t),\dot{\gamma}(t),t)dt$. We can always re-write it in terms of an arbitrary curve parameter $\tau$ which need not coincide with time $t$: $$S[...
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Einstein says information cannot be transmitted faster than light. Say I set an alarm that ring at 9:00 am. I go to school, and wait until 9:00 am. Then I tell my friends that my alarm rang. If the ...
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Although title is more broad, and you are welcome to give examples, I will ask about why we accept certain things as acceptable in Einstein's thought experiments using a specific experiment: Consider ...
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I'm currently reading the introduction to Naber's The Geometry of Minkowski Spacetime, and in this post I'm writing down a few silly questions that keep popping into my head. I have near-zero formal ...
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I am not sure how to ask this question in a concise manner so I am sure somebody out there explained it but I cannot seem to find it. So I recently watched some videos explaining that $c$ not only ...
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I am going through the complex integral in peskin & Schroeder's intro to QFT (equation 2.54, deriving the Free Klein-Gordon Propagator): $$\langle0|[\phi(x),\phi(y)]|0\rangle=\int \frac{d^3p}{(2\...
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Usually, Penrose diagrams are marked with points and segments being named past/future timelike infinity $i^{-,+}$, past/future null infinity $\mathscr{I}^{-,+}$ and spacelike infinity $i^0$ -- see for ...
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I am following Peskin & Schroeder's QFT book. And on equation 2.51, we get an expression for the free Klein-Gordon propagator for timelike intervals $x^0-y^0=t$, $x-y=0$: $$D(x-y) \sim e^{-imt}\...
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Follow-up on this question about causality for Newton's second law. In $F=ma$, the $=$ sign signifies proportionality, not causality. It makes sense, as the equal sign is invertible, whereas causality ...
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I've recently read that what most people learned to think of as the 'speed of light' is actually the 'speed of causality', and that light just happens to travel at that speed (through free-space.) I'...
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