Questions tagged [locality]

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How do Lieb-Robinson Bounds talk about locality without the position operator?

So we know when one goes from QM to QFT Lieb Robinson bounds become micro causality. But micro causality is a statement on the commutators assuming they are space-like, time-like or light-like. ...
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Locality in Bell Experiments

I have a question about experiments that show a violation of Bell's inequalities. It's said that these experiments disprove local realism. However, immediately before the final measurement of the 2 ...
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Conserved charge at null infinity associated with Large gauge transformation

I am reading Strominger's lecture notes "Lectures on the infrared structure of gravity and gauge theory" (https://arxiv.org/abs/1703.05448). At some point, following (I guess) the authors of ...
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How are we able to use quantum field theory to study systems?

I've been trying to understand the concept of locality in QFT, and I was reading this paper by Edward Witten, where he explains (on pg 13) that the state space cannot be factored into a tensor product ...
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Must all field theories depend on the spatial derivate of the fields?

For instance, if I have encountered \begin{equation} \label{eqq2} \frac{\partial \mathcal{L}}{\partial (\partial_i \phi)} = 0 \end{equation} This tells us that $\mathcal{L}$ cannot depend on $\...
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Locality of interactions and their high energy behavior

In a classic Georgi review of EFT, I have read the following quote The result of eliminating heavy particles is inevitably a nonrenormalizable theory, in which the nontrivial effects of the heavy ...
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Why does one work with the Lagrangian density in field theory?

Why is it necessary to introduce the Lagrangian density (integral of the Lagrangian over volume) when describing the dynamics of fields? Is there a specific reason for that or just for convenience?
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On the Bell's Theorem / Bell-type Inequalities and the Kochen-Specker Theorem

It appears to me that the Kochen-Specker theorem, if not Gleason’s theorem already, seals the fate of realism / value definiteness (with possibly the additional assumption of non-contextuality, ...
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Interpretations for Interaction-free measurements

So I read several papers on IFM by Vaidman, Dicke, and many others, In all of them I think the Pilot wave theory is able to adequately justify the observations, but then I came across several papers ...
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Are all physically realistic Hamiltonians local?

My understanding of modern physics is that physicists think that, fundamentally, physical laws are local. For system A to interact with system B, they either need to be very close to each other or ...
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How did the local hidden variable theory resolve the EPR paradox?

I'm trying to understand the motivation for local hidden variable theory. The EPR paradox considers the following thought experiment, where we can express a state $|\psi \rangle \in H_{Alice} \otimes ...
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Is Electrostatics Local?

We can solve uniquely for the electrostatic potential $\phi(x)$ of some given charge distribution if we set the boundary condition that $$\lim_{|x|\to\infty}\phi(x) = 0$$ (or whatever boundary ...
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Conformal Field Theory and Vertex Operator Algebra

I am trying to understand CFT from the viewpoint of both math(in particular using VOA) and physics. Now, in Math, we use the VOA to make sense of fields corresponding to certain states. We define for ...
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Global conservation + Lorentz invariance = local conservation?

On the page 83 of "Quantum Field Theory Lectures of Sidney Coleman", Coleman showed an interesting example: It seems that global conservation law and local conservation law can be related. ...
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What does local gauge invariance have to do with locality?

This concept is just being introduced to me in my QFT course, and my instructor mentioned that if a scalar field $\phi$ has $U(1)$ symmetry, then you can make a suitable gauge transformation $\phi \...
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Is QFT "more" non-local than QM, at least mathematically?

Could physics still be local? Here's what I mean: The Schrodinger/Dirac equations allow for quantum entanglement, right? So in that sense they are non-local physically. But they are mathematically ...
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How constraint to first-order derivative in Lagrangian is a consequence of demand to get local theory?

In Physics From Symmetry Section 4.2 Restriction, the Author said that It is sometimes claimed that the constraint to first-order derivatives is a consequence of our demand to get a local theory, but ...
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Are infinitesimal dilatation transformations local?

In quantum field theories, a local transformation of a scalar field $\phi(x)$ is a transformation that involves the field and its derivatives at same point. See for instance Weinberg's QFT textbok, ...
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Are anyons non local?

Studying anyonic statistics in 2 dimensions, I naturally thought to ask the question of whether anyons are non local, since as we braid one around another, no matter the distance between the two, one ...
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Many worlds is nonlocal too after all according to some physicists?

Not a physicist but I have understood that MWI is unique in that it preserves local dynamics. There is a wavefunction - not in spacetime but in some more abstract space. But the worlds with spacetime ...
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Meaning of 'Local' density in Liouville's theorem

Liouville's theorem is commonly stated as $$\frac{d\rho}{dt} = \frac{\partial{\rho}}{\partial{t}} + [\rho, H]$$ Where, $H$ is Hamiltonian of the system, $\rho$ is the density, $[...]$ is the usual ...
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Many Worlds locality and EPR experiment

I've read in Sean Carroll's book (Something Deeply Hidden) that the Many-Worlds interpretation of quantum mechanics might be the only way to avoid instantaneous effects of entanglement, by having the ...
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In Cosmology, what does it mean to be 'local'?

I'm trying to make a point that there is curvature of spacetime from the metric expansion that contributes to the dynamics of a galaxy. This curvature would be in addition to the curvature caused by ...
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Why should the split property hold in AQFT?

In algebraic quantum field theory, one assigns complex unital $*$-algebras (or von Neumann algebras) $\mathfrak{A}(O)$ to open regions $O$ of Minkowski spacetime. I am reading an article by Chris ...
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Thought experiment in relativistic quantum mechanics?

Background Consider the following thought experiment in the setting of relativistic quantum mechanics (not QFT). I have a particle in superposition of the position basis: $$ H | \psi \rangle = E | \...
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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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Locality of the Turbulent Energy Cascade

Locality appears to be an omnipresent feature of physics, including within turbulent fluid dynamics. In 1941 Kolmogorov postulated that the turbulent energy cascade is driven by scale-local ...
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Please explain the meaning of below statement

Newtons second law is a local law. (In the book,it says that it means that it applies to a particle at a particular instant without taking into consideration any history of the particle or its motion.)...
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The conditions under which a stress tensor $T^{\mu\nu}$ exists

I used to believe that the existence of the stress tensor in a QFT has to do with translation invariance: "If a theory is translation invariant, then one can construct a conserved $T^{\mu\nu}$ by ...
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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 ...
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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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How is the non-local nature of quantum entanglement explained?

From what I understand, Einstein tried to introduce real but hidden variables to remove the apparent non-local nature of quantum entanglement, but Bell's inequality showed local realism isn't possible....
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On the computation of functionals in QFT

Using the Gaussian (path)-integral $$ \int \mathcal{D}\eta e^{i\int_{t_i}^{t_f} dt \eta(t) O(t) \eta(t)} = N [\operatorname{det} O(t)]^{-1/2} $$ my book claims that we can compute the following ...
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Why can't light travel three days into the future then transmit that information back to us prior to us arriving at that position? [closed]

Example: If a football game between the Pittsburgh Steelers @ Tennessee Titans will happen in 3 days Sunday 10/25/2020 at 1pm, why can't light leave today 10/22/2020 and go to where the Earth will be ...
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What is the main reason for the locality of Einstein's equivalence principle?

Einstein's equivalence principle (EEP) states: "Locally, a free-fall frame in a gravitational field is equivalent to an inertial frame in space in the absence of a gravitational field". ...
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Non-analytic functions and non-local Lagrangians

Infinite sums of increasingly higher-order derivatives, when present in Lagrangians, are typically taken as a sign of nonlocality. This is supposed to rule out fractional, negative and exotic (for ...
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Why Locality meant jointly observable?

Tobias Osborne's lecture around 20:00, he mentioned that the ideal of "Locality" could be expressed as such If $x-y$ were space-like, then for all observable $A_{j,x}$ and $A_{k,y}$ were ...
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Lattice differentiation and Locality

Assume we define the locality of a theory in the following way: Assume we have a theory of real scalars, so this theory is non local if the action has terms like $$\int d^dx\,\phi(x)V(x-y)\phi(y).$$ ...
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Rewriting the equation governing local transport into $\nabla (\ln(\sigma)) \cdot \nabla U_0 =− \nabla ^2(U_0)$

A paper concerning local sheet conductivity and sheet current density says the equation governing local transport $$\nabla \cdot \vec{j} = − \nabla\cdot(\sigma \nabla U) = 0,$$ where U denotes the ...
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What is a "quasi-local" charge?

Could someone please tell me what is a quasi-local charge? For instance, why are Brown-York charges called quasi-local?
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Why quantum mechanics doesn’t break locality in entanglement but hidden variables theories will?

What makes it so that quantum mechanics doesn’t break locality in entanglement yet hidden variable theories will? In Bell‘s inequality said that hidden variables theories need to break locality in ...
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QFTs without Lagrangian

I have been reading other questions in this site, but I have not found answers to all my questions about theories without Lagrangians. What do we mean exactly when we say that they do not have a ...
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What is locality?

In QFT and statistical mechanics, one is usually interested in studying integrals of the form: $$Z(\phi) =\int d\mu_{C}(\phi')e^{-V(\phi+\phi')}$$ where $\mu_{C}$ is Gaussian measure with mean zero ...
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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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Particle picture in position space in quantum field theory

When I operate $a^{\dagger}_k$ on vacuum, $|0\rangle$, I get a particle created in momentum space with a 4-momentum equal to $(\omega_k, \vec{k})$ where $\omega_k=\sqrt{m^2+\vec{k}^2}$ here I'm only ...
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Is wave function collapse non-local or local?

Imagine a particle in a very large box which takes years to travel from one end to the other. Alice and Bob are outside the box, on opposing ends. Each can remove their side of the box to check if the ...
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Local fields vs particles

I have heard it said that Richard Feynman was a proponent of a particle approach to QFT while Julian Schwinger preferred a local fields description. What is meant by “local fields”? Surely when one ...
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Euclidean view in curved manifold

Let's suppose I am an ant who lives in a 2D curved space. Locally the world seems 2d-euclidean to me, but it is not if I consider a large portion of space. Now let's consider a human being who lives ...
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Why is there no gauge-invariant local operator in GR?

I have a hard time understanding why the bulk locality is a question. I know some operator which depends on a particular coordinate $x$, $O(x)$, and its correlation function like $ \langle O(x)O(y) \...
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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 ...
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