17 votes
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Locality in QFT vs "non-local" in QM

The locality of a QFT refers to the operator algebra. The (non-) locality of Bell's theorem refers to the states (rays) of the Hilbert space. These are different notions of locality, and they coexist ...
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16 votes

What's wrong with the square root version of the Klein-Gordon equation?

Secondly, why is the first differential equation cumbersome to work with? It seems like it would in fact be easier to work with, since the operator under the square root could be expanded in terms of ...
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  • 2,645
13 votes
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What is the speed of Newtonian gravity?

So the fact that you don't see anything about the speed of gravity in Newton's equation is a bit of a clue; Newtonian gravitational interactions propagate instantaneously (ie. with infinite speed). If ...
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  • 902
13 votes

Are fermions intrinsically non-local?

So what people mean by 'non-local' varies from context to context and person to person. Wen has a very particular meaning to this. 1) In fermionization in $D=1+1$ the Jordan-Wigner fermions are, in ...
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  • 805
11 votes
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How to understand locality and non-locality in Quantum Mechanics?

The short answer is yes, in quantum mechanics quantum non-locality refers to the apparent instantaneous propagation of correlations between entangled systems, irrespective of their spatial separation. ...
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  • 9,843
8 votes
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Local versus non-local functionals

Yes, there are rigorous ways of defining locality in such contexts, but the precise terminology used unfortunately depends on both the context, and who is making the definition. Let me give an ...
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  • 54.8k
8 votes

Locality in QFT vs "non-local" in QM

Yes, QFT is a subset of QM theories – quantum field theories are theories whose observables are naturally constructed from field operators – so everything that holds for all QM theories holds for QFTs,...
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8 votes
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Non-local field redefinition and effects on path-integral measure

So, I would start by giving a precise definition of $\frac{\partial_\mu \pi}{\square}$, which is \begin{align} \frac{\partial_\mu \pi(x)}{\square}&=\square^{-1}_x\int d^4y\,\delta^{(4)}(x-y)\...
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  • 2,173
7 votes

Is there non-locality in the AdS/CFT?

You may find a small set of articles discussing non-commutative field theories, or dipole field theories, or field theories in the presence of a magnetic field. These types of field theories will ...
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  • 1,360
7 votes
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Why can't Faddeev-Popov ghosts be replaced with bosons?

Note that the inverse of $\Delta_{FP}$ is the Green function $G_{FP}(x,y)$ obeying: $$ \Delta_{FP}|_x G_{FP}(x,y)=\delta(x-y) $$ so, the action that you wrote down is non-local, should be of the ...
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  • 5,355
7 votes

What is a local operator in quantum mechanics?

If you are dealing with a multipartite state $\lvert\Psi\rangle$, then the distinction between local and non-local operations is an important one for example for the study of entanglement. Consider ...
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  • 12.5k
7 votes
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Functional Analytic Square Root of Hamiltonian Alternative to Dirac

I think that the problem is that the square root of the Laplacian is a non-local operator and non-locality is usully regarded as a bad thing in physics. The long range nature shows up in the general ...
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  • 42.5k
6 votes

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

This is the first time I write an answer here. Tell me if it's bad or if I did something wrong. I think I can contribute something here: My mental image is the following: A simple derivative is $$ f'(...
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  • 61
6 votes
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Why would classical correlation in Bell's experiment be a linear function of angle?

I think you misunderstood the significance of could for a classical theory. The text below the picture you took from Wikipedia says: "Many other possibilities exist for the classical correlation ...
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  • 108k
6 votes
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How exactly does the proof of Bell's theorem fail if you remove the locality assumption?

In my derivation, I make my error at equation $(2)$, attempting to extend the logic employed by Bell in arriving at equation $(1)$. Bell's local derivation uses the assumption that the system being ...
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  • 412
6 votes

Decoherence: faster than light?

For the record I do not necessarily want to claim that decoherence solves all the subtle interpretational issues that go under the "measurement problem", at least not without some extra ingredient(s) ...
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  • 1,972
6 votes
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Can a single photon behave in a non-local way?

Demonstration of single-photon non-local behavior Can a single photon behave in a non-local way? Yes. This has been demonstrated in many experiments and is now done routinely. Here's a ...
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6 votes
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What is a local operator in quantum mechanics?

A local operator is one whose action only depends on the value of the wave function (and its derivatives) at a single point. Almost all the ordinary operators one encounters are local in this sense, ...
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  • 12.7k
6 votes
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Is QFT "more" non-local than QM, at least mathematically?

Entanglement doesn't break locality. Entanglement must be generated locally. Wavefunction collapse a la Copenhagen interpretation breaks locality. QM and QFT are equivalent with respect to to locality....
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  • 9,458
5 votes
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Are Forces Involved Non-Local?

We must be careful with what we mean by "locality." There are two relevant related, but distinct, concepts: Einsteinian non-locality: superluminal communication/transfer of information is possible. ...
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  • 14.7k
5 votes
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Why infinite order derivative in Lagrangian density implies non-local?

$\exp(a\partial)~f(x)=f(x+a)$ gives $f$ translated by a, as it summarizes its Taylor expansion in a around a=0. f then actually depends on its value at a shifted point.
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5 votes

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

Despite this, both ∫ρ(A(a,c,λ)A(c,a,λ)A(a,b,λ)A(b,a,λ))dλ and P(b,c) are restricted to the range −1≤x≤1, so both inequalities should lead to the same experimental conclusions regarding local realism. ...
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5 votes
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Non-local potential

In your nonlocal potential, the potential that your partical feels at each point in space depends not on the value of some single function, but the sum (Integral) of all the values of a function ...
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5 votes
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Is there a deep reason why action comes from a local lagrangian?

Lagrangian theories are indeed obiquitous because those are the ones we can understand better and ultimately those with which we can do computations. However, sadly, they only make sense when the ...
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  • 6,187
4 votes
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Legendre transform for non-local Lagrangians, or Hamiltonian of non-local Lagrangian and their properties

Let here consider point mechanics (as opposed to field theory) for simplicity, i.e. the generalization to field theory is left as an exercise. I) Bad news. If the Lagrangian action functional $S[q]$ ...
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  • 172k
4 votes

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

Just for info: there is a so called shift operator $\text{e}^{h\frac{d}{dx}}$ that shifts a function argument to another point, for example: $\phi(x+h)=\text{e}^{h\frac{d}{dx}}\phi(x)$. It is obvious ...
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4 votes
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Natural entanglement system

The answer is definitely yes. The ground states (and low-lying eigenstates) of many-body systems are generically entangled. Examples include the ground states of local quantum field theories (which ...
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4 votes

What is the speed of Newtonian gravity?

In the Newtonian theory, gravity is instantaneous. This is because the force law says that whenever you have two objects a distance $r$ apart, there will be a force between them inversely proportional ...
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  • 26k
4 votes

Non-locality vs. non-realism: Arbitrary choice?

The answer to the linked question is misleading (and I've left a comment there). You don't get to choose between nonlocal and non-real. While experiments violating Bell's inequalities do imply that ...
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