Questions tagged [locality]

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136
votes
11answers
18k 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 ...
108
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9answers
19k views

Why is quantum entanglement considered to be an active link between particles?

From everything I've read about quantum mechanics and quantum entanglement phenomena, it's not obvious to me why quantum entanglement is considered to be an active link. That is, it's stated every ...
92
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10answers
13k 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 ...
36
votes
2answers
6k 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 ...
34
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5answers
2k views

Can the Hubble constant be measured locally?

The Hubble constant, which roughly gauges the extent to which space is being stretched, can be determined from astronomical measurements of galactic velocities (via redshifts) and positions (via ...
33
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5answers
7k views

Why are infinite order Lagrangians called 'non-local'?

And in what sense are they 'non-local'?
27
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10answers
9k views

How do we know quantum entanglement works no matter the distance?

It is said quantum entanglement works regardless of distance. 2 particles can be entangled and information is shared instantaneously, even if they are lightyears away from each other. But how do we ...
27
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5answers
3k views

What combinations of realism, non-locality, and contextuality are ruled out in quantum theory?

Bell's inequality theorem, along with experimental evidence, shows that we cannot have both realism and locality. While I don't fully understand it, Leggett's inequality takes this a step further and ...
20
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5answers
21k views

Bell's theorem for dummies, how does it work?

I've been reading up on theoretical physics for a few years now and I feel like I am starting to get an understanding of particle physics, at least as much as you can from Wikipedia pages. One thing ...
19
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2answers
1k views

Locality in the scattering amplitude

Early in this talk by Nima Arkani-Hamed, he describes what locality means for scattering amplitudes. "Locality tells you that the only poles in the scattering amplitude occur when the sum of a subset ...
18
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3answers
825 views

Uncertainty principle - momentum so precise that uncertainty of position is outside light-cone?

Thought experiment: what happens if we measure momentum of a particle so precisely, that the uncertainty of its position becomes absurd? For example, what if the uncertainty of the position exceeds 1 ...
17
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1answer
872 views

Is string theory local?

By locality I mean something like the Atiyah-Segal axioms for Riemannian cobordisms (see e.g. http://ncatlab.org/nlab/show/FQFT). I.e. to any (spacelike) hypersurface in the target we associate a ...
16
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6answers
3k views

Quantum entanglement and spooky action at a distance

When quantum entanglement is explained in "layman's terms", it seems (to me) that the first premise, that we have to accept on faith, is that a particle doesn't have a certain property (the particle ...
15
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2answers
2k views

Locality in QFT vs “non-local” in QM

In quantum mechanics (QM), teacher always emphasizes on the "weird" parts, like EPR paradox, Bell inequality and so on. The Bell inequality tells us that QM is either nonlocal or non-realistic or both....
15
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1answer
13k views

How to understand locality and non-locality in Quantum Mechanics?

What actually is the definition of locality and non-locality? Does non-locality in Quantum Mechanics mean however far you separate 2 entangled atoms in space, the 2 atoms can still influence each ...
13
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3answers
796 views

Can someone clarify whether the recent experiment closing all remaining loopholes to Bell's Theorem really shut the door on local realism for good?

I saw this recent article on Phys.org that purports to close all remaining loopholes that previous experiments on violations of Bell's inequality left open. My question is, does this really close the ...
13
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5answers
671 views

Why must the field equations be differential?

In Landau–Lifshitz's Course of Theoretical Physics, Vol. 2 (‘Classical Fields Theory’), Ch. IV, § 27, there is an explanation why the field equations should be linear differential equations. It goes ...
12
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3answers
2k views

Bell's theorem and why nonlocality is problematic

I generally hear it assumed that Bell's inequality implies violation of counterfactual definiteness, because locality is considered sacrosanct. I understand of course that measurable violations of ...
12
votes
1answer
462 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 ...
11
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4answers
2k views

Do electrostatic fields really obey “action at a distance”?

In an electromagnetic theory class, my professor introduced the concept of "action at a distance in physics". He said that: If two charges are at some very large distance, and if any one of the ...
11
votes
1answer
966 views

Is this field redefinition for free scalar field theory non-local?

The action of free scalar field theory is as follows: $$ S=\int d^4 x \frac{\dot{\phi}^2}{2}-\frac{\phi(m^2-\nabla^2)\phi}{2}. $$ I have been thinking to redefine field as $$\phi'(x)=\sqrt{m^2-\nabla^...
10
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1answer
558 views

Assumptions of the Coleman-Mandula Theorem

In the original paper All Possible Symmetries of the S-Matrix, by S. Coleman and J. Mandula, they prove their famous 'no go' theorem regarding the possible extensions of Poincaré symmetry. The ...
10
votes
1answer
278 views

Why don't we have logarithms or exponentials of the fields in the Lagrangians?

All the Lagrangian densities I have seen have always been polynomials of the fields. Is this a coincidence or is there a reason which forbids, say, Lagrangians with logarithms or exponentials of the ...
10
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1answer
398 views

Yang and Mills' (and others') justification for local gauge invariance

In most physics textbooks, local gauge invariance is simply postulated---you start with a global symmetry, e.g. the global phase, then allow it to depend on the spacetime point, make the necessary ...
9
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5answers
938 views

Does local mean infinitesimally small?

I have studied General Relativity and there is one thing that I have trouble comprehending. What does local really mean? I will give some examples: The Hessian The Hessian is a way to compute the ...
9
votes
3answers
310 views

How exactly does the proof of Bell's theorem fail if you remove the locality assumption?

In this paper Bell derives his famous inequality using the assumtions of locality and realism. In order to understand how the locality assumption affects the derivation of the inequality, and why it ...
9
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2answers
1k views

Algebraic/Axiomatic QFT vs Topological QFT

Can anybody please tell me a good source investigating the relation between Algebraic/Axiomatic Quantum Field Theory (AQFT) and Topological Quantum Field Theory (TQFT)? Or is there none?
9
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4answers
2k views

Locality in Quantum Mechanics

We speak of locality or non-locality of an equation in QM, depending on whether it has no differential operators of order higher than two. My question is, how could one tell from looking at the ...
9
votes
2answers
448 views

Relation between Borchers class and the LSZ formula on S-matrix equivalence

It seems well known that different quantum fields can give rise to the same $S$-matrix. I know of two ways this is described. The first is through the Borchers class of relatively local fields, i.e. ...
9
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2answers
877 views

Tracking down the locality assumption in a CHSH inequality derivation

CHSH inequality requires both locality and realism. I will equate here realism with counterfactual definiteness. Now counterfactual definiteness tells us that given two different measurements on the ...
8
votes
1answer
3k views

Local versus non-local functionals

I'm new to field theory and I don't understand the difference between a "local" functional and a "non-local" functional. Explanations that I find resort to ambiguous definitions of locality and then ...
8
votes
1answer
593 views

Theories with non-vanishing commutators outside the lightcone

I'm reading Weinberg's new book on Quantum Mechanics, and in Chapter 8.7 "Time-Dependent Perturbation Theory" he derives the usual Dyson series for the $S$ matrix when the interaction Hamiltonian $V_I(...
8
votes
1answer
568 views

Lorentz invariance, energy-momentum conservation & the locality of interactions

I have been reading these notes ("Minkowski Spacetime: A Hundred Years Later", by Vesselin Petkov) 1, in which the author states (in the middle of the text on page 137) that "The only Lorentz ...
7
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2answers
2k views

Why is lagrangian density correct?

The textbooks I have available explain that due to the infinite degrees of freedom of a field, the relevant object in QFT is the lagrangian density. A lagrangian is then obtained for the field by ...
7
votes
2answers
1k views

Difference between locality and causality?

I ask this question as the two seem to be very closely related and are sometimes taken to be one and the same (in the notion of microcausality in QFT), which has left me confused as to what meaning of ...
7
votes
3answers
518 views

Don't these experiments suggest that locality has to be abandoned in the quantum realm?

First a quick recap because maybe my understanding/assumptions are flawed (you can jump to the question highlighted in bold below if you like to): Bell's inequalities require that an accurate(ly ...
7
votes
1answer
265 views

$\phi^{n}$ quantum scalar field theories where $n$ is not an integer

Consider a quantum scalar field theory with interaction terms of the form $\phi^{n}$, where $n$ is not an integer. Where are some examples of widely-studied quantum field theories which involve such ...
7
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2answers
328 views

Does Microcausality follow from Lorentz Invariance?

In a Lorentz Invariant theory, does microcausality automatically hold? In a free theory this is obvious. In an interacting theory I found some 'proof's in this paper: http://arxiv.org/abs/0709.1483 ...
7
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2answers
3k views

Commutation relations in QFT and the principle of locality

My question is, given two space-time points $x^{\mu}$ and $y^{\mu}$, if the events that occur at these points are simultaneous, i.e. $x^{0}=y^{0}$, are the two events necessarily space-like separated? ...
7
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1answer
795 views

How is the 'cluster decomposition principle' implemented in holographic theories?

Since holographic theories are non-local by definition, how is this principle implemented? Naively, it seems to me it is not, at least, in some sense. I would appreciate an explanation as simple ...
7
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1answer
535 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
291 views

Where is locality used in CHSH/Bell's inequality?

A very similar question is asked here, but I'm still confused :( From Bell, in a hidden variable model, $A = A(\lambda, a)=\pm 1$ is the observed spin of the first particle around axis $a$, and $B = ...
6
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1answer
199 views

How soon that a force affect another object?

Imagine this scenario: I have 2 objects in vacuum without any force exerted upon them not even a possible gravitational force between them. Now if one of them gets a gravitational or magnetic force, ...
6
votes
1answer
812 views

$U(1)$ abelian/axial/chiral anomaly in 4D

I am reading $U(1)$ abelian/axial/chiral anomaly in 3+1 dimensions using the path integral method (Fujikawa). Am I wrong in assuming that the anomaly can be cancelled by introducing a counter term in ...
6
votes
3answers
765 views

Non-local structure of field theory

Can someone explain what is non-local structure of field theory? I know you cannot have $\phi(x) \phi(y)$ term in Lagrangian which indicates the non-locality. However, why I cannot have the non-local ...
6
votes
2answers
689 views

How does locality decouple the UV and IR behaviour of a QFT?

I came a comment in this paper: Scattering Amplitudes and the positive grassmannian in the last paragraph of page 104 which says: "One of the most fundamental consequences of space-time locality is ...
5
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4answers
2k views

Assumptions in Bell's Theorem

It is often Stated that Bell's Theorem is equivalent to the statement: No theory of Local Hidden Variables can reproduce all of the predictions of quantum mechanics. I see nowhere in Bell's Theorem ...
5
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1answer
1k views

Definition of Local Function

Now a days I am studying Srednicki's QFT book. In its third chapter it is written that Any local function of φ(x) is a Lorentz scalar, [...] . Now my question is: What is a local function?
5
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1answer
2k views

What is known on violations of unitarity or locality?

Recently the amplituhedron become a hot topic. I realized that two of the central pillars that QFT is based on, unitarity and locality, are no longer playing an important part (due to gravitational ...
5
votes
2answers
1k views

What is a local operator in quantum mechanics?

In quantum mechanics, what exactly is meant by "local" operator? What about a "global" or a "non-local" operator? Are these the same? Can you also also help me understand what exactly is a local ...