The tag has no usage guidance.

learn more… | top users | synonyms

1
vote
1answer
184 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 ...
1
vote
0answers
58 views

Path integral (sum over paths where $v>c$) [on hold]

The path integral formalism is used to get for example the propagator of particles. In this formalism we integrate over all mathematically possible paths (and weight them with the non-relativistic ...
11
votes
1answer
167 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 ...
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 ...
6
votes
1answer
204 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 ...
26
votes
2answers
3k views

Definitions: 'locality' vs 'causality'

I'm having trouble unambiguously interpreting many answers here due to the fact that the terms locality and causality are sometimes used interchangeably, while other times seem to mean very different ...
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 ...
9
votes
4answers
846 views

Where does movement come from? [closed]

When you put a body in motion, where does that movement come from? Ok, you will say things like "acceleration", but where does that acceleration come from? Then you might say "a force is creating the ...
9
votes
6answers
1k views

What is the physical definition of causality?

Maxwell's equations give a physical relationship between the electric and magnetic fields $\vec E$, $\vec B$ at the same time, which some interpret as changes in one causes changes in the other etc. I ...
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 ...
6
votes
5answers
133 views

Can the mass within the event horizon of a black hole interact gravitationally with the mass outside the event horizon?

If so, gravitons and their fields, unlike photons, must be able to cross the event horizon freely in both directions. If not, the observed mass of a black hole must depend only on the particles ...
4
votes
1answer
48 views

anticausal group velocity?

https://en.wikipedia.org/wiki/Anomalous_dispersion claims: Recently, it has become possible to create gases in which the group velocity is not only larger than the speed of light, but even ...
1
vote
3answers
212 views

How can an action be dependent on both its past and future?

Is it true that whenever an action takes place it is dependent on both its past and future? I mean if we already know that whatever we are doing is dependent on future as much as it is dependent on ...
1
vote
3answers
120 views

What would happen if you went back in time to get a random number?

For example, you go to a website that generates a random number. You get the number 8. What would happen if you went back in time a few minutes, and repeated the same actions. Would you get the same ...
2
votes
1answer
99 views

Particle here at a given time, in another galaxy a second later… Really?

I read "The Quantum Universe (Cox & Forshaw)" that a particle can be measured at a given position at a given time, and in another galaxy one second later. The probability of such event may be ...
20
votes
2answers
2k views

What do physicists mean by “information”?

On the question why certain velocities (i.e. phase velocity) can be greater than the speed of light, people will say something like: since no matter or "information" is transferred, therefore the ...
4
votes
2answers
152 views

When does causal separation imply no spacelike separation?

(See here for notation.) In Minkowski space, if $p\prec q$, then there is no spacelike curve $c:[0,1]\to \mathbb{R}^{n-1,1}$ with $c(0)=p$ and $c(1)=q$. This is obvious from a spacetime diagram. Here ...
4
votes
0answers
202 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 ...
86
votes
9answers
10k views

How fast does gravity propagate?

A thought experiment: Imagine the Sun is suddenly removed. We wouldn't notice a difference for 8 minutes, because that's how long light takes to get from the Sun's surface to Earth. However, what ...
3
votes
1answer
451 views

Are some gravitational wavelengths forbidden by causality?

Consider a gravitational wave in linearized gravity $d_{\mu \nu}(X_{\eta}) = D_{\mu \nu} e^{i X_{\eta} K^{\eta}}$ with $K^{\eta} = (-\omega t, \textbf{k})$. Let $d=| \textbf{D}|$ the scalar maximum ...
19
votes
3answers
3k views

In superluminal phase velocities, what is it that is traveling faster than light?

I understand that information cannot be transmitted at a velocity greater than speed of light. I think of this in terms of the radio broadcast: the station sends out carrier frequencies $\omega_c$ but ...
10
votes
4answers
2k views

The Lagrangian in Scalar Field Theory

This is perhaps a naive question, but why do we write down the Lagrangian $$\mathcal{L}=\frac{1}{2}\eta^{\mu\nu}\partial_{\mu}\phi\partial_{\nu}\phi - \frac{1}{2}m^2\phi^2$$ as the simplest ...
7
votes
3answers
188 views
3
votes
1answer
84 views

Signal travels with speed greater than light breaks causality

Signal can't travel at speed greater than light speed in vacuum which is a assumption of special relativity. But if a signal travels at speed greater than $c$ then it will violate causality. I tried ...
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 ...
1
vote
2answers
109 views

How is locality preserved in quantum mechanics?

I was reading this post: http://motls.blogspot.com/2015/06/locality-nonlocality-and-anti-quantum.html Specifically here: "There is no nonlocality. There is no action at a distance. There is no doubt ...
66
votes
10answers
7k views

Quantum Entanglement - What's the big deal?

Bearing in mind I am a layman - with no background in physics - please could someone explain what the "big deal" is with quantum entanglement? I used to think I understood it - that 2 particles, say ...
-1
votes
1answer
87 views

Is causality in quantum physics also always valid?

For different observers the laws of causality are the same. So the cause and the effect are clear for all observers in any space or time. But is this still valid in quantum mechanics?
0
votes
1answer
66 views

Time Travel possibility and Paradoxes of The Past [duplicate]

can one travel back in time and if not so, what laws prevent time travel to the past. this is quite a challenge to understand.
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
1answer
40 views

Precise definition of “Observable Universe” and its alternatives

The Observable Universe is generally said to contain all space that could "in principle" have had a causal impact on Earth, but the exact limits of the "in principle" causal interaction go ...
0
votes
1answer
95 views

What is the meaning of the particle horizon in conformal diagrams?

I'm reading "Physical Foundations of Cosmology" (Mukhanov) and in Chapter 2.3 conformal diagrams get introduced. They seem to be a (graphical) tool to understand the causal structure of the universe. ...
1
vote
1answer
90 views

Relationship between locality, causality, and free theories

This text on QFT defines a free theory as that in which dynamics of the field for each degree of freedom evolves independently from all the other. In principle we have an infinite degrees of freedom, ...
1
vote
1answer
55 views

response function and Fourier transform

A response function defined as the kernel of the following integral: $\rho(t) = \int_{-\infty}^t \chi(t,t') E(t')dt'$ (1), where $\chi(t,t')$ is the response function. Physically, it relates ...
1
vote
3answers
252 views

Does quantum mechanics break causality? [duplicate]

If quantum mechanics is probabilistic, there is no reason for a particle to be in one place and not the other, but particles do make up their minds... but how?
0
votes
1answer
150 views

Intuitive meaning of Globally Hyperbolic

I am been studying differential geometry and spacetime and I keep coming across the term globally hyperbolic. I am having a hard time coming up with an intuitive understanding of this idea. What is an ...
5
votes
4answers
538 views

How can we know, today, that there's something from 100 light-years from here?

In my understanding, to take a picture of something that is 100 light-years from here, our "camera" would have to travel 100 years at light speed, take the picture, send to us, and 100 years later we ...
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 ...
1
vote
0answers
26 views

Can a solid object inside the black hole event horizon avoid the singularity? [duplicate]

I will ask this as a simple lay man. Let's consider an astronomical black hole that was creating by in falling matter on a neutron star. As neutron star get heavier it gets smaller and a Schwarzschild ...
6
votes
2answers
2k views

Is time going backwards beyond the event horizon of a black hole?

For an outside observer the time seems to stop at the event horizon. My intuition suggests, that if it stops there, then it must go backwards inside. Is this the case? This question is a followup ...
22
votes
1answer
1k views

Causality and how it fits in with relativity

I was talking to my teacher the other day about Einstein's spacetime and there's one thing he couldn't explain about the nature of Cause. I may be being stupid or just unable to comprehend, thanks for ...
0
votes
2answers
118 views

Is causality a total order?

I've read that it is physically not possible to violate causality defined as a total order on the spacetime graph. So I was wondering if at least causality can be broked down to a partial order and if ...
0
votes
0answers
37 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. ...
1
vote
3answers
253 views

How can the past, the present and the future coexist at the same time? [closed]

We all heard it many times, the theory of Time suggest it is parallel rather than being linear. This leaves the door opened for alternate realities and well, immortality. However, even after reading ...
1
vote
3answers
95 views

Where is the event horizon in a black hole?

At the beginning I thought that the event horizon coincides with the surfaces, but then making a new name when you could just call it surface would seem a bit pointless. Then where is the event ...
2
votes
1answer
286 views

Huggins Displacement Theory and Retrocausality

I was looking at the Wikipedia entries on Time Travel and the Grandfather paradox and noticed a paragraph on the so-called Huggins Displacement Theory. I haven't been able to find the source although ...
0
votes
1answer
76 views

Quantum Mechanics and Causality

Causality coupled with special relativity states that no particle can travel faster than light. Interpreting in terms of quantum mechanics, it means that dirac delta wave-function at x=a, can't ...
1
vote
1answer
74 views

Numerical relativity in causally pathological spacetimes

To perform numerical relativity simulations one almost universally adopts the so called "3+1" approach: spacetime is divided up into spacelike slices, each representing a "moment in time". After some ...
2
votes
1answer
65 views

A rope between Earth and Moon - Length and Speed of Light [duplicate]

An earlier question was asked on what would happen if a rope was attached between Moon and Earth, but the question was more about the impacts in terms of geology. We keep the same experiment setup : ...
1
vote
1answer
102 views

Can we prove absolutely that FTL = causality violation

I've been wondering about this for a long time. Given that special relativity is normally true, can we still prove that causality violation must occur if FTL is found? All proofs I can find, depend on ...