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11
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1answer
166 views

Explaining causal completion axiom in Haag-Kastler axioms?

There are several variants of the Haag-Kastler axioms for algebraic quantum field theory. Usually one associates an algebra $\mathcal{A}(O)$ to each open region $O$ of spacetime. An often-suggested ...
6
votes
1answer
203 views

Delocalization in the square root version of Klein-Gordon equation

In this Wikipedia article a relativistic wave equation is derived using the Hamiltonian $$H=\sqrt{\textbf{p}^2 c^2 + m^2 c^4}$$ Substituting this into the Schrödinger equation gives the square root ...
4
votes
1answer
224 views

Closed timelike curves in the spin-2 gravity formalism

Let's say we take some topologically trivial CTC spacetime, like the Gödel metric: $$ds^2 = -dt^2 - 2e^{\sqrt{2}\Omega y} dt dx - \frac{1}{2}e^{\sqrt{2}\Omega y} dx^2 + dy^2 + dz^2$$ And then I ...
3
votes
1answer
62 views

Are closed timelike curves generic feature of ANEC-violating stress-energy tensor?

Kip Thorne has shown that in order to create closed timelike curves (CTCs), one needs stress-energy tensor $T^{\mu\nu}$ that violates averaged null energy condition (ANEC). Will $T^{\mu\nu}$ with ...
2
votes
1answer
132 views

Locality defined in terms of the Lagrangian density

I've been reading through Matthew Schwartz's book "Quantum Field Theory and the Standard Model" and in chapter 24 there is a section on locality (section 24.4). In it he defines locality in terms of ...
1
vote
1answer
71 views

Schwarzschild equation physical meaning

When you pass an event horizon of a black hole according to the Schwarzschild equation time and space swap the physical meaning. So you can no longer move away from a black hole, in similar way as you ...
1
vote
1answer
48 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 ...
1
vote
1answer
177 views

If a point r lies in the boundary of the chronological future of another point p, why does the chronological future of r belong to that of p?

I am studying the global causality of the spacetime. Here, I come across a problem. Suppose a point $r\in \partial I^+(p)$. $I^+(p)$ is the chronological future of a different point $p$ in ...
0
votes
1answer
10 views

A media in which the electrical displacement vector is not causal

I recently did an electrodynamics homework problem in which we showed that in a certain model (Lorentz-Drude), where the permittivity of free space $\epsilon$ was dependent upon the angular frequency ...
0
votes
1answer
56 views

Why is spatial conformal infinity a point

One property of spatial infinity is that all spacelike geodesics end at it. Since spacelike geodesics can have different directions, I do not understand why spatial infinity is a point. It looks more ...
0
votes
1answer
44 views

Can you recover the values of spacetime intervals $s^2$ from given causal relations between events?

Given a suitable set $\mathcal S$ of events together with their (pairwise) causal relations, i.e. for each pair of distinct events $\mathsf A, \mathsf B \in \mathcal S$ the assignment whether ...
9
votes
0answers
85 views

Can one classify partial differential equations according to the causality properties of their solutions (and if yes, then how)?

Recently, I bumped into this interesting comment by Valter Moretti which made me wonder about the following, more general question (to which I suspect the answer is affirmative): Can we easily tell, ...
5
votes
0answers
139 views

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 ...
4
votes
0answers
201 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 ...
4
votes
0answers
73 views

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 ...
4
votes
0answers
118 views

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 ...
3
votes
0answers
96 views

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 ...
2
votes
0answers
30 views

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 ...
2
votes
0answers
74 views

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 ...
2
votes
0answers
212 views

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 ...
2
votes
0answers
95 views

If $S$ is a closed achronal set in a spacetime, any timelike curve starting at a point in $I^+[S]$ and ending at a point in $I^-[S]$ interset $S$?

Suppose $S$ is an achronal set in a spacetime $M$. And $S$ is closed. At the same time, any null geodesic of $M$ intersects $S$. Then, why does any timelike curve from $I^+[S]$ to $I^-[S]$ intersect ...
1
vote
0answers
61 views

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?
1
vote
0answers
94 views

Is it possible to assign a physical radius to a black hole?

The Schwarzschild metric is given by: $$c^2d\tau^2 = \left(1-\frac{r_s}{r}\right)c^2 dt^2-\left(1-\frac{r_s}{r}\right)^{-1}dr^2 - r^2 \left(d\theta^2 + \sin^2 \theta \, d\varphi^2\right).$$ The ...
1
vote
0answers
169 views

Big Bang, Heat Death, and cause and effect

If the Universe has two 'end points', one being the Big Bang, and the other being heat death, is there anything in the laws of physics which forbid a random fluctuation in the heat death state from ...
1
vote
0answers
134 views

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 ...
0
votes
0answers
52 views

How to get anti-commuting rule from the view of field?

I was reading the 1951 Lectures on Advanced Quantum Mechanics and I found something really disturbing. That's the anti-commuting rule mentioned on Page 40 at last. Though it was named as Quantum ...
0
votes
0answers
26 views

Linkal causality in special relativity

I have a slight variation of the barn / ladder paradox, where there is a ladder too long to fit into a barn at rest, but when moving at a sufficient speed, it is length contracted with regards to the ...
0
votes
0answers
36 views

Can an event occur before or after the other one depending on what frame of reference we are in?

Two buses moving relative to each other with 30% the speed of light (4 light-min apart). Now by some mysterious way bus 1 comes to the knowledge that after 3 min-bus 2 time bus 2 is going to explode. ...
0
votes
0answers
53 views

Third law of motion when action and reaction are separated by some time

For every action there is an equal and opposite reaction. I have used this law only when bodies are in contact with each other which means for every action reaction is produced at same instant of ...
0
votes
0answers
19 views

Can we say a certain yes to having probability independence for some events?

Mathematically it is just a question of assumption of proof to say that $P(A|B)=P(A)$ if A is independent from B. However, in real life is it possible to assume $P(A|B)=P(A)$ instead of ...
0
votes
0answers
58 views

Penrose diagram for Schwarzschild metric

Can someone show me a procedure (I mean a complete series of mathematical passages) to derive the Penrose diagram for Schwarzschild metric? I don't want to do that passing through the Kruskal-Szekeres ...
0
votes
0answers
222 views

Is the principle of least action fully equivalent to the Euler-Lagrange equations?

I am citing from Landau and Lifschitz, this statement that will seem to you well-known, trivial, etc: "Between these positions, (i.e. $q_1$ and $q_2$) the system moves then in such a way that the ...
0
votes
0answers
114 views

Does causality alone resolve the mathematical ambiguity of expressing physical systems?

Newton's 2nd law of motion is most often written in the differential form $\sum F = {dp \over dt} $ but can also be expressed in an integral form $ p = \int\sum F dt $ Each form of expressing ...
0
votes
0answers
105 views

What is wrong in following arguments about connection of local gauge invariance and causality?

There is a question and corresponding downvoting of my answer, so I decided to ask this question. There is my answer on it: "...The most theories of free fields are invariant under global gauge ...
0
votes
0answers
344 views

Hardy's Theorem

https://perimeterinstitute.ca/psi_portal/sites/perimeterinstitute.ca.psi_portal/files/hardyphysrevlett.68.2981.pdf Some researchers in Bohmian Mechanics have hoped to make the theory Lorentz ...