Questions tagged [causality]

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34 views

Problem with infinitesimal factor in the expression for $G^{+}(x,y,E)$

In my book on QFT (Lancaster & Blundell) they give the following expression for the Green's function: $$G^{+}(x,y,E) = \sum \frac{i\phi _{n}(x)\phi ^{*}_{n}(y)}{E-E_{n}}.$$ However, they then ...
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1answer
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Where did the boundary conditions go in the frequency-space solution to the Green's function for a damped harmonic oscillator?

In differential equations, Green's functions are only defined given boundary conditions. In fact, you need two of them for a second order differential equation. In a lot of physics lecture notes, a ...
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1answer
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What does it mean that gravity is '“local”? [closed]

What is "local" defined to be? Why don't larger systems affect smaller ones? ie. Don't we need to consider the gravitational pull from all other objects in the universe? Is this "...
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The problem of time [closed]

It seems common in physics to treat time as a dimension somewhat like the spatial x, y, or z. And according to this idea everything that ever was or will be is already laid out in a block. Nothing new ...
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0answers
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If there was a solid bar of diamond between here and Proxima Centauri [duplicate]

Or maybe not diamond, but imagine some substance that was crystalline, the hardest substance and the least ductile, which retained a perfect shape under enormous pressures. My question is, if you ...
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2answers
83 views

What does it mean when one says that a vector field is spacelike, timelike, or null separated?

In Goldstein Classical Mechanics Chapter 7 (3rd edition, page 287), the authors classify vector fields as follows: Name Time Portion Space Portion (Magnitude$)^2$ Type Coordinate $ct$ $\mathbf{r}$ $...
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3answers
73 views

Does the idea of non-contact force violate the law of logic or mathematics?

I saw that some forces like gravity and electromagnetism, are called 'non-contact force'. For example, in case of repel and attract magnetic forces, what does 'non-contact force' mean? If the meaning ...
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3answers
696 views

Can Lagrangian have a potential term proportional to the quadratic or higher of velocity?

In general, classical Lagrangian $L(q,\dot q)=\frac{m}{2} \dot q^2-U(q,\dot q)$ has a $\dot q$-dependence. For example, potential term $U(q,\dot q)$ of the charged particle is given as follows:$U(q,\...
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0answers
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Has it been proven that causality means the S-matrix is analytic?

In books like 'the analytic S-matrix' they give justification that causality implies analyticity however they also said it hasn't been explicitly proven. This book was written a while ago, has it been ...
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1answer
49 views

Near a white hole, what do lightcones look like?

In the vicinity of a Schwarzchild black hole, spacetime looks like this (at least according to a quick google search). Here, the centre of the black hole is supposed to be at $x=0$ and the event ...
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1answer
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How does the null cone relate to the Minkowski diagram?

I appreciate, this may be self explanatory or a silly question. I have seen derivations for the Minkowski diagram (Penrose) and don't understand if the null cone is just the $\mathbb{R}^2$ case or if ...
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1answer
45 views

Black hole, ingoing light-like and causality

In Kruskal-Szekerers coordinates, for example, I've noticed that ingoing light-like trajectories, in the interval $ 0<r<r_s$, are decreasing in time $t$ so they travel in the past for an ...
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1answer
47 views

Does faster than light lead to closed timelike curves?

If some signal can be sent to a spacelike interval then is it possible in some reference frame to have a close timelike curve? Novikov claims so in this paper. The argument lies below eq$7$ but ...
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28 views

Entanglement entropy with a local operator insertion

According to several papers discussing the behavior of entanglement entropy (EE) with a local quench or a local operator insertion (cf. https://arxiv.org/pdf/1911.04797.pdf), if the operator was ...
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2answers
49 views

Does the effect of field travels faster than light? [duplicate]

As I was going through some work of my college level courses of fundamental physics, the formula caught my attention $F={G}\frac{Mm}{r^s}$. "r" seems can be any value; there would still be ...
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2answers
47 views

Is space and time consecutive in physics, like frames in cameras? [duplicate]

Is time consecutive in physics? Here is my deeper explanation of what I mean. Are frames for example in a camera a good metaphor with the concept that time also has "frames" in the space of ...
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0answers
28 views

Does microcausality plus the time-slice property imply local primitive causality?

In quantum field theory, observables are associated with regions of spacetime. One of the basic principles of relativistic quantum field theory is microcausality, which says that observables ...
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2answers
78 views

Do wormholes really allow us to travel back in time?

Theories surrounding wormhole based time travel are annoying me tonight... So the way time works is relative, right? The closer you are to the frame of reference, the faster time moves. So, if we use ...
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1answer
42 views

Schwarzschild radius violation?

I have a puzzling question concerning the crossing of the Schwarzschild boundary. If a person (lets say in some large robust spaceship) flys quickly between 2 super-massive rotating black holes within ...
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1answer
32 views

Why consider spacetime trajectories that cut a $t=$constant at more than one points in the path integral of a relativistic particle?

Here is a picture from Padmanabhan's book on quantum field theory. Also described in the first part of this lecture within $17-25$ minutes. He says that a relativistic particle can follow a path like ...
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2answers
56 views

Possibility of having a spacetime trajectory that cuts the $t=$constant at more than one point

Can we have a spacetime trajectory like the blue curve (shown in the figure) inside the lightcone such that the trajectory cuts a $t={\rm constant}$ line at more than one point (three points in the ...
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1answer
55 views

Based on Newton's law of universal gravitation: How fast does any gravitational disturbance propagate?

Based on Newton's law of universal gravitation: How fast does any gravitational disturbance propagate?
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3answers
107 views

Why does $ds^2=0$ for a light signal's worldline in general relativity?

I know that in special relativity, the invariant interval $ds^2$ for a light signal's worldline is $$ds^2=\eta_{\mu\nu}dx^\mu dx^\nu=0$$ where the flat metric $\eta_{\mu\nu}=\text{diag}(-1,1,1,1)$. ...
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1answer
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How is causality preserved between observers in a cosmological setting?

Suppose that 2 observers are sending light signals to each other.If each of them are stationary in relation to a nearby galaxy, but each of these are separated by so great distance, they will be ...
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0answers
62 views

Does special relativity limit quantum field propagation?

For the classical Klein-Gordon field, the motion of a wavepacket is constrained slower than the speed of light for $m^2 >0$ and constrained to exactly the speed of light for $m = 0$ (the equation ...
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How much did Special Relativity evolve after Einstein's 1905 paper?

I know that the 4D coordinate system came afterward but it is hard to believe that Einstein and other physicists understood SR completely from 1905 on. One special question is, did Einstein himself ...
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2answers
271 views

Regarding the velocity of waves in even dimensions

A few years ago I asked on Reddit about the behavior of wave propagation in even and odd dimensions. I received this answer: "The answer lies in the solutions to the wave equations. Essentially, ...
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1answer
86 views

Penrose diagram for two black holes

There are well-known Penrose diagrams for black holes: And for collapsing star: Diagram for collapsing star is obtained by joining two Penrose diagrams: Is it possible to join diagrams for two ...
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1answer
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What exactly means “local”? How local (and memoryless) is “local”?

Local and memoryless are easily defined in quantized space and time: Local: What happens from one time step to the next in one "cell" of quantized space is only influenced by the state of ...
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2answers
80 views

How do the particles in a rigid body “know” when to accelerate?

In many cases, a force is applied to only a small part of a rigid body, yet all the particles of the body accelerate immediately. How do particles on which the force does not act directly "know&...
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Could a form of (temporally-limited non-superdeterministic) strong determinism resolve retrocausality in quantum theories?

It looks like "superdeterminism" is considered as a potential way to resolve EPR paradox/Bell's theorem/quantum theory. It seems "retrocausality" (or what could be or is called ...
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1answer
51 views

Equivalence Of Newton's Law and Leact action principle Without Math (Intuition): initial vs. boundary problem

First Let me write both the laws So Newton's law says that $$\mathbf{F}=m\mathbf{a}$$ and least action principle says that a particle occupy, at the instants $t_1$ and $t_2$, positions defined by two ...
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1answer
43 views

CTC, determinism and valuedness of Riemann tensor

What I understood is that By the math, the Riemann tensor is obtained by parallel-transporting a vector along a closed curve in the considered space, then apply Stoke's theorem. Now if physics is ...
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0answers
48 views

Methods to study the causal/light cone structure of General Relativity

I've been looking into causal set theory as an approach for quantum gravity, and my research has gotten me interested in the causal structure of spacetime. If I understand correctly, if one has ...
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0answers
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Killing vectors in Minkowsky Metric

So I was in the process to find the Killing vectors for the Minkowsky Metric and I stumbbled into a material that does a different procedure at the very end of the process, in comparisson to usual ...
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1answer
59 views

Is This Hypothesis Correct?

I have constructed a thought experiment regarding whether the future is deterministic or not. It goes like this: Let’s take an Observer 100 light years away from earth. Now presently, if he looks at ...
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1answer
60 views

Null vector space in Minkowski space

Let us consider a Minkowski space of the form: $$ds^2 = -dt^2 + dx^2 + dy^2 +dz^2.$$ What would the linearly independent null vectors of this space be? I am aware this is a trivial question but is ...
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1answer
276 views

What does a 4+1D wave look like at the light cone?

I need help making sense of a few comments from under this answer. I think it’s best if I reproduce the comments below: “The Green's function for the wave equation in even spatial dimensions is ...
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3answers
632 views

Are wormholes evidence for traversal of a higher dimension?

Warning, pop science coming.. please correct what I’m getting wrong. Einstein’s equations of relativity showed the potential for existence of wormholes that can connect different points in space time....
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2answers
238 views

Wouldn't a negative mass be going faster than $c$ according to our current models of relativity?

I heard that there are some physicists trying to figure out, out least hypothetically, how things with positive and negative mass may interact with each other. I'm really confused about how this can ...
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3answers
145 views

Causality: Why can't things move backwards in time, within past lightcone?

My question Why can't effects propagate backwards in time, within the backwards light cone of a cause? For example, when I turn on a flashlight, why doesn't the light travel backwards in time just ...
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0answers
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How to show time evolution operator obeys causality?

If we are given a time evolution function $K_t(\phi,\phi')$ which give the amplitude for a field starting in confiruation $\phi$ to go to configuration $\phi'$ after time t. What is the condition that ...
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1answer
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Why is the anti-commutation relation $\lbrace \psi_a(x), \bar{\psi}_b(y) \rbrace = 0$ enough to ensure causality?

In quantum field theory, it is crutial that two experiments can not effect each other at space-like seperation. Thus $[\mathcal{O}_1(x), \mathcal{O}_2(y)] = 0 $ if $(x-y)^2 < 0$. For the Klein-...
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1answer
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Causality and processes in QFT

We have virtual particles in quantum field theory (QFT). In general, they don't have the need to obey causality. My question is: Do the processes in QFT (electron self-energy, photon self-energy, ...
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1answer
80 views

Action at a distance in Quantum Field Theory

Definitely, I don't mean entanglement here: Suppose we have an electron and proton situating some distance apart, there is an electrostatic force between them, and this force is mediated by virtual ...
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5answers
209 views

What laws prevent massive particles to travel at the speed of light?

I and a few of my friends have come across an interesting question. Jackson talks about the case where photon has non-zero mass. By adding an extra term to the Lagrangian, he shows how Maxwell's ...
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2answers
68 views

Is a still object in 4D spacetime lightlike?

Every particle in the universe is moving in spacetime: a massive "still" one (in the 3D sense) is moving in a purely timelike direction, a massive "moving" one in a direction with ...
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3answers
161 views

Escape Velocity, Misattribution, and Black Holes

Escape velocity is the ballistic speed required to escape from a gravitational field to infinity, ignoring any third body dynamics. The operative word here being ballistic, meaning unpowered. ...
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2answers
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Another form of Black Hole Information Paradox?

Consider the Penrose Diagram of Collapsing Gravitational matter :                           Any radial light ray (say P) originating from $\mathscr{I}^{-}$ is bound to end up in the Black Hole. The ...
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2answers
193 views

Is general relativity the simplest possible theory of gravitation?

I can't find this, but i've seen that GR is the only possible theory of gravity if you assume causality and principle of equivalence?

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