Questions tagged [causality]
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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What exactly is different about the slice of space and lightcone concept in special relativity?
In Sean Carroll's book on GR, in the very first chapter about SR, he mentions how the difference between Newtonian concepts of space and time, and the view put forward in SR is how there is an "...
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Is every symmetric causal isomorphism between distinguishing spacetimes a conformal diffeomorphism?
For this question let us consider spacetimes which are time-oriented and distinguishing (or stronger).
Some bijections between such spacetimes are known to be conformal diffeomorphisms because they ...
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In the Twin Paradox, can one twin travel backwards in time?
In the Twin Paradox, if the travelling twin, Betty, instead of returning to her brother Albert at home, continues her journey after a period of rest, why is causality not violated due to her brother, ...
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Does General Relativity allow sudden gravitational source changes?
When I was taught General Relativity as a student, many years ago, I was told that there was no way to create a gravitational "surprise", where the source strength of some system changed ...
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Microcausality in Fermions
We can show that for the Dirac field, the anti-commutator between the field and its adjoint vanishes for space-like separated points. However, for causality we need to show that the commutator instead ...
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Can you see same event at two times?
It may happen that my setup is based on a misunderstanding of GR:
Imagine you have a clock on your wrist - your proper time device upto an initial $\tau_0$, and you live in the spacetime $(M,g)$ and ...
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Why deforming a null geodesic leads to timelike geodesic?
Wald at page #232 wrote
For timelike geodesics conjugate points signal when a timelike geodesic can be varied to yield a curve of greater length between two points $p$ and $q$.
He then said we can ...
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Definition of Black Hole
Wald and other literature defines the definition of Black Hole as
$$B=M-J^{-}(\mathscr{I}^+)$$
where M is spacetime, $\mathscr{I}^+$ is future null infinity and $J^-$ is causal past.
The idea is to ...
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Partial Differential Equations (PDEs) in 2+1 Spacetime with Gradient of the Time Derivative
I have a set of 2 variables $f_1,f_2$, on the Domain of 1+1 spacetime $\{t,x\}$ and a set of PDEs with multiple terms of mixed 2nd-order partial-differentials.
$$\partial_t{f_1} = F_1(f_1,f_2, \...
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Why doesn't the Coulomb gauge imply instantaneous interactions? [duplicate]
As I understand it the Coulomb gauge is always valid so that one can take
$$\nabla \cdot \mathbf{A}=0\tag{1}$$
together with Maxwell's equations and not predict anything that is inconsistent with ...
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Why causality issues are used to justify the impossility of interactions that are faster than the speed of light? [closed]
It is frequently happening that causality issues, i.e. inversing the causes and consequences, are used to justify the impossibility of superluminal movements and data transmission.
However similar ...
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Why gradient of a timelike coordinate is a timelike vector?
First of all, How do you differentiate between timelike coordinates and spacelike coordinates ?
My understanding is that if we are given a metric tensor, a coordinate will be timelike if $dx^{2}$ has ...
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Quantum entanglement and space like separation of entangled particles [duplicate]
Suppose we have 2 entangled particles who are not in the light cone of each other(they are space-like separated).Suppose that you have a observer named Earth who is inside the lightcones of both ...
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Does nature work exclusively on the cause-effect principle?
Does nature work exclusively on the principle of cause-effect or are there situations in which the principle is violated?
Is randomness in probabilistic process truly fundamental or just a reflection ...
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Max speed in discrete space
Say that light moves N pixels/sec - does it imply that max speed for matter is <= (N-1) pixels/sec?
Does it imply and light will always outrun Rindler observer (constant acceleration in flat space) ...
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Does decreasing $r$ coordinate represent Black Hole?
I am studying Kerr metric in Boyer Lindquist coordinates $(t,r,\theta,\phi)$ which represent Kerr Black Hole. It has three regions to consider: $M_{1}$ is outside the outer horizon, $M_{2}$ is within ...
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Tunneling time controversy, recent experiments
In reference 1 it is claimed a superluminal tunneling time was measured in hydrogen. Here the authors make an unambiguous superluminal claim.
But this article by Quanta magazine says that in reference ...
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Question on the plausibility of a time-travel-related energy paradox [closed]
if an object or person were to travel back in time, their mass-energy would disappear from the present and reappear in the past. This would imply:
A net creation of energy at the moment of ...
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Object perceived to be traveling faster then light [duplicate]
Consider an object with a worldline $$x = -vt+x_0$$ and an observer at $$x=0$$ such that the object is moving towards the observer with velocity $v$. From each point $(x,\frac{x_0-x}{v})$ in the ...
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Proving that the order of the events is invariant [closed]
Text of the exercise:
Event B is a consequence of event A. Using Lorentz transformations, prove that there is no inertial frame for which Event B happens before event A.
I wanted for someone to say ...
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Causality in QFT. Klein-Gordon field
The Causality in QFT is said not be violated by showing field operators in Klein Gordon field commute outside the light cone. This is necessary because If I here measure a observable A and my friend ...
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Schwarzschild spacetime metric unchanged under a time-reversal
Does time-reversal assumption imply (even without deriving the metric) that, from POV of stationery observer relative to the star, particle/light trajectory from A-B will have the same momentum (speed/...
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Energy–momentum bookkeeping on a self-intersecting timelike world-line
Consider a classical, finite-mass traveller in 3 + 1-dimensional general relativity who follows a smooth closed timelike curve (CTC). After a proper time $\Delta\tau$ the world-line returns to its ...
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Can local operators annihilate vacuum state?
It is a statement about local relativistic QFT that I hear from Juan's 2015 TASI lecture on Entanglement Entropy. I can vaguely understand this statement, since say usual second-quantization ...
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Trouble understanding proof of the cluster decomposition principle
The proof of the cluster decomposition principle in Streater and Wightman begins with the definitions of $F_1,F_2$ as follows:
The $\mathscr W$ are Wightman functions of some arbitrary fields, and ...
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