Questions tagged [causality]

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Causality, branch cut choice and analytic continuation of Euclidean 2-pt. correlator in 2D CFT

In 2D CFT, the Euclidean two point correlator of a primary operator $\mathcal{O}$ with conformal weights $h$, $\bar{h}$ is given by $$ \begin{align} \langle\mathcal{O}(z,\bar{z})\mathcal{O}(0,0)\...
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How is causality encoded in string theory?

How is causality encoded in string theory? There is a superficially similar thread, Causality in String Theory, which however asks a quite different question.
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experiment proposal to validate microcausality

I've been wondering about microcausality for some time now (a recent question of mine regarding the topic) and i'm wondering if its possible to devise an experiment to detect potential violations I ...
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162 views

What does the time reversibility of the laws of physics mean for causality?

Does the fact that the fundamental laws are symmetric with respect to direction of time show that causation does not exist? Since causality always requires the cause to precede the effect, but laws of ...
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375 views

How does one determine if a spacetime is globally hyperbolic?

A spacetime $M$ is said to be globally hyperbolic if it is strongly causal and if the sets $J^+(p)\cap J^-(q)$, for all $p,q\in M$, are compact. (For more information, see the Wiki article on causal ...
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Why can apparent horizon be computed based on its local geometry?

Why can apparent horizon be computed based on its local geometry? In the paper titled Black Holes, Geometric Flows, and the Penrose Inequality in General Relativity by Hubert L. Bray, has been written:...
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Axiomatization of SR: can we replace light rays with timelike world-lines?

If I eliminate a lot of details and just sketch the general ideas, then a common way of presenting SR is this: Axiom 1: Clocks exist. Axiom 2: Light rays exist. This is the approach followed in, e.g....
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The point of holedness

In general relativity there is a vaguely defined notion of a spacetime having "holes", with many different definitions. Many of those were cast off when it was realized that Minkowski space also has ...
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General theorems on tachyon propagation?

I was reading the quite nice answer of QMechanic on the topic of compact support tachyon fields not propagating faster than light, but this case is a rather simple one, free scalar field in flat space....
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68 views

How to realize explicitly an $SO^+(1,3)$ Lorentz transformation of $(x-y)$ to $(y-x)$ for space-like separation?

Consider two spacetime points $x, y$ which are space-like separated. How can one realize explicitly a proper, orthochronous Lorentz transformation between two frames such that $x-y$ becomes $y-x$? ...
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Graviton propagator, and Gauss-Bonnet gravity

Let's say we consider Einstein's Lagrangian from GR. In linearized gravity, we would expand the Ricci scalar to quadratic order in the perturbation parameter to find the propagator. My question is as ...
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Timelike, spacelike etc. for higher-order tensors

Vectors $V^\mu$ in relativity can be classified into those which are timelike, spacelike and null. A similar classification is available for tensors: A tensor $$T^{\mu_1\mu_2...\mu_p}_{\phantom{\mu_1\...
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How does one find the Vaidya black hole event horizon?

As for a definition, there are quite precise ones for what an event horizon is. One can define it as the boundary of the causal past of future null infinity, i.e., $\mathcal{H}=\partial J^-(\mathscr{I}...
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89 views

In a globally-hyperbolic spacetime, does every pair of elements have overlapping light cones?

Suppose we have a spacetime $(M,g)$, and denote by $J^+(p)$ the set of points that lie in the causal future of $p$, i.e. $x \in J^+(p)$ iff there is a future-directed timelike curve $\gamma: [0,1]\...
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Analytic cotinuation between Minkowskian and Euclidean space, and causality

We can flip between Minkowkian and Euclidean signature by Wick rotation, and it is a well defined operation, provided there are no non - trivial singularities. Now, Unitarity in Minkowskian space ...
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260 views

Causality and wick rotation

What is the connection between causality and wick rotation? I came across implication of this connection multiple times but can't find a rigorous explanation. For example in the answer to Wick ...
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160 views

Is the vanishing commutator of observables outside the light cone only a necessary or also a sufficient condition for causality?

The equal-time commutator of observables in QFT has to vanish outside the light cone in order to ensure causality. Mathematically spoken, $[ \bar{\psi}(x)\Gamma_1\psi(x),\bar{\psi}(y)\Gamma_2\psi(y)]|...
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How exactly analyticity of S-matrix comes from causality principle?

Recently I've read that analyticity of S-matrix ($S(k)$, where $k$ corresponds to momentum, may be analytically extended into complex values of momentum) comes from causality principle. How to prove ...
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Does nonlocal theory violate causality?

Let's talk about two kinds of nonlocal theories. The first one frequently derives from integrating out part of the degrees of freedom to obtain a kind of effective theory. Probably, we get an integral ...
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37 views

Causal past of future null-like infinity for a black hole

I can't understand following statement from Carroll book [Future] event horizon can be equivalently defined as the boundary of $J^-(\mathcal{I}^+)$, causal past of future null infinity. I made use ...
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105 views

Spacelike, timelike, lightlike vectors and the light-cone structure

Consider a semi-Riemannian manifold which of these statements is false: All vectors on the light-cone are light-like, all vectors in the interior of the light-cone are time-like and all vectors in ...
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1answer
78 views

What is the mathematical meaning of locality?

I have read on the Principle of locality Wikipedia page that: "The special theory of relativity limits the speed at which all such influences can travel to the speed of light, c. Therefore, the ...
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129 views

Constraints vs Boundary Conditions

I have a very broad question about how the mathematical framework that classical theories of physics utilize to solve problems. The question is: What are the intrinsic differences between the ...
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35 views

Penrose diagram and coordinate transformation

I am looking at the Minkowski line element in spherical coordinates $$ \mathrm{d}s^2 = - \mathrm{d}t^2 + \mathrm{d}r^2 + r^2 \mathrm{d}\theta^2 + r^2 \sin^2(\theta) \mathrm{d}\phi^2$$ and want to ...
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Rindler's trap door experiment with a rod (or a tank, or a pile of fragile matter) of finite hight

About 60 years ago a thought experiment was proposed which is widely referenced, e.g. as "Man falling into grate variation" of "The ladder paradox" or, perhaps more poignantly, "The tank paradox": ...
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Hausdorff property in Minkowski spacetime

In the 4-dimensional Minkowski spacetime, for a given point $x = (x^0,x^1,x^2,x^3)$, its timelike future/past set is defined as, $$ I^{\pm}(x) = \{y =(y^0,...,y^3) \in \mathbb{R}^4 : \eta_{\mu \nu}(y-...
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Locality and relativity - a paradox?

The equations of nature are supposed to exhibit locality in the sense that the action depends on fields and their derivatives. i.e. comparing the values of fields at local points. But two points on a ...
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226 views

Feynman propagator for Dirac fields and $i\epsilon$ prescription for analytic continuation

The analytic continuation from Euclidean space to Minkowski spacetime is perturbatively well (uniquely) defined to all orders for the Feynman propagator for Dirac fields with the so called "$i\epsilon$...
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143 views

At what critical Reynolds number does vortex shedding begin?

In: "Fluid Dynamics", Chapter 3 (Turbulence), Section 26, Landau and Lifchitz analyze the problem of the stability of a steady flow past a body of finite size. The fluid is assumed to be ...
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1answer
100 views

Causal ordering on spacetimes

On any spacetime $(M,g)$ we can form the causal ordering $\leq$, where for any two points $a,b \in M$ we have that $a \leq b$ iff there exists some future directed, non-spacelike curve from $a$ to $b$....
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160 views

Lorentzian path integral for string theory and causality

Is the Lorentzian path integral in string theory well defined, as opposed to the usual Euclidian path integral that is commonly used for simplicity? The path integral is roughly $$\sum_{\mathbf{\...
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159 views

Malament theorem in curved spacetime?

Malament's theorem roughly assert that given a very general theory of a point particle, characterized by some operator $P_D$ such that for a region of space $D$ at a given time $t$, $P_D | \Psi \...
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333 views

Reconciling the causality of QFT and the Feynman propagator

Unlike the retarded propagator, the Feynman propagator $\Delta_F(x-x^\prime)$ is given by $$\Delta_F(x-x^\prime)=\int\frac{d^3\textbf{p}}{(2\pi)^32E_\textbf{p}}\Theta(t-t^\prime)e^{-ip\cdot(x-x^\prime)...
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238 views

Causality in CPT symmetry analogue of free electron laser (stimulated absorbtion)?

While 2nd law of thermodynamics emphasizes past->future time direction, CPT theorem says that at least microscopic physics has some symmetry between past and future. For example the Feynman-...
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If microscopic dimensions were found in particle experiments, how do we determine whether it is spatial or temporal?

This is not a question asking why our universe is 1T+3D dimensional, and hence not about how the various models such as Itzhak Bars and F theory can incoporate multiple time into a model to describe ...
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Gauge Permitting c Magnetic Vector and Instant Electric Scalar Potentials?

The Lorenz gauge requires c propagation of both scalar and vector potentials. The Coulomb gauge requires instant "propagation" of these potentials but is stated in such a way as to permit c ...
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1answer
127 views

If there is a point in a past set, does its chronological future interset a future set?

This post concerns the causality of spacetime $\mathcal M$. A future set $F$ is defined to be the chronological future of some set $S\in \mathcal M$, ie., $F=I^+[S]$. Similiarly, a past set $P=I^-[S'...
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Amplitude for a string to propagate from one point to another

In Zwiebach’s book sections 12.6 and 12.7 interesting aspects of the wave function of the string are discussed. In order to introduce my question first recall what happens with the relativistic ...
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Why are the integral form of the GR equations problematic?

I have heard that working with the integral form of the GR equations is problematic - relative to determining a Greens function. Can someone explain the details as why?
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Testing Many-Worlds Interpretation (MWI) with a causality-violating configuration of “superluminal cables”

Suppose we managed to arrange a causality-violating transmission of data with hypothetical “superluminal cables” (SLC; see both links for respective descriptions) and expect, similarly to ideas ...
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3answers
311 views

Difference between action-at-a-distance and a field according to Maxwell?

My question is more on a historical note that involves Maxwell’s equations. Besides the information that I have obtained from textbooks, I am mainly getting it from History of Maxwell's Equations and ...
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1answer
280 views

Do string-wave functions always spread superluminally?

When one calculate the amplitude for a particle to propagate between two points, the results seems to violate causality. One book that makes some comments about this is Peskin & Schroeder, chapter ...
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1answer
637 views

In the Causal Set theory, what actually is a causal set?

The causal set theory is an approach to quantum gravity. But don't understand what it claims spacetime to be made of. What is a causal set? Is it a physical object or just a spacetime event? I read ...
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1answer
370 views

Is it proven experimentally that the speed of causality (light) is the maximum speed?

Is it possible to have an alternative theory which is consistent with experiments supporting GR, but which doesn't mandate a speed limit on causality? In other words, I understand there is ...
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1answer
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Difference between chronological future and domain of dependence

Given the following standard definitions of the two concepts, I fail to see how the chronological future differs from the future domain of dependence? Chronological future: The chronological future of ...
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Divergence of a vector which has explicit and implicit position dependence

I am doing EMT and I am trying to calculate the divergence of this current density given as, $$\vec{J}(\vec{r}', t_r) = \vec{J}(\vec{r}', t - \frac{|\vec{r}-\vec{r}'|}{c})$$ for $\vec{r} = (x,y,z)$ ...
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Would Doubly Special Relativity or Mach's Principle allow faster-than-light travel to occur without violating causality?

Doubly Special Relativity posits that the Planck length is the same in all reference frames. Mach's Principle posits inertia is produced by the combined mass of the universe. From my limited ...
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What is an equation which tells you if two points are time-like separated in curved spacetime?

I was thinking about how to tell if two points in a general spacetime are time-like separated. I think the only way of doing this is checking every path from $x$ to $y$ and seeing if one of the paths ...
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65 views

What is the null vector for a metric?

I am studying the Robertson Walker metric. I now understand what the geodesic looks like but what is a null vector of the geodesic? Is it just the tangent vector to the geodesic curve?
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What would the eternal black hole look like?

The white hole and black hole regions in a Kruskal diagram are said to be actually two different locations. Given the problems with white holes it might be a silly question but, hypothetically, what ...