# Tagged Questions

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### 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 ...
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### Local Effective actions

While studying partition functions in general, i came across a statement which says that "the partition function of a theory without gapless excitations must be a local functional of the background ...
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### 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 ...
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### Hamiltonian lattice gauge theory with physically observable local degrees of freedom

In my answer at What, in simplest terms, is gauge invariance?, I mentioned that in certain contexts there can be a "gauge theory" with a local symmetry that leave the Lagrangian/Hamiltonian invariant ...
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### Lagrangian gauge theory with physically observable local degrees of freedom

In my answer at What, in simplest terms, is gauge invariance?, I mentioned that in certain contexts there can be a "gauge theory" with a local symmetry that leave the Lagrangian/Hamiltonian invariant ...
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### 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 ...
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### 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 ...
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### 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 ...
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### Near Energy In the Null of a Hertzian Dipole

Since $\mathbf E = -∇Φ - ∂\mathbf A/∂t$ one expects an oscillating $\mathbf E$ field even in the null of a Hertzian Dipole unless the two right hand side terms cancel -- which they do in the far field ...
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### 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 ...
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### How is no-conspiracy theory compatible with determinism? [closed]

Bell's theorem states that any physical theory that incorporates local realism and the no-conspiracy assumption cannot reproduce all the predictions of quantum mechanical theory. Hence, we cannot ...
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### 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 ...
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### Is viscosity excluded by Lorentz symmetry in spatio-temporal discreteness?

"In the case of spatio-temporal discreteness, viscosity is excluded by Lorentz symmetry". This statement is from here. Can anyone explain why this is the case? I'm looking for an intuitive way to ...
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### Shouldn't local realism imply the superdeterminism?

I see that Bell has ruled out Einstein's local realism but not supredeterminism. I see that Bell has confessed that superdeterminism kills his inequality. You cannot apply Bell's inequality if ...
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### 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. ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### Newton's third law at the quantum level? [closed]

let's look at force at the atomic level to understand the newtons third law of motion. I'll use Helium atoms as an example. Now imagine we start with one atom HE2 stationary, and throw another atom ...
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### 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, ...
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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^...
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### 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 ...
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### 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 ...
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### can extra dimensions explain the non locality of entanglement? [closed]

This is the question of layman fascinated by quantum theory. Entanglement of particles far apart from each other (relative to the speed of light) has been addressed in some other questions where the ...
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### Vector Potential Oscillating E Field of the “Null” Field of a Hertzian Dipole?

The vector potential of a Hertzian dipole falls off spherically as $1/r$. The polar axis of the dipole is a "Null" field -- meaning no electric and magnetic field. The absence of magnetic field is ...
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### Why is locality an important requirement in physics?

Why is locality insisted upon in physics? Is it simple because empirical evidence suggests it, and also taking relativity into account, required due to the upper limit of propagation limited by the ...
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### 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 ...
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### Is microcausality a statement about locality?

As far as I understand it locality is the rejection of action-at-a-distance. By this I mean that in a given frame of reference at a given instant of time (in that reference frame), two physical ...
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### 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 ...
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### Coincidence of spacetime events & Lorentz invariance

Am I correct in thinking that if two spacetime events are coincident in one frame of reference, then they are coincident in all frames of reference, i.e. coincidence of spacetime events is a Lorentz ...
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### Lagrangians densities & interactions in field theory

To avoid ambiguity, this question pertains to the construction of Lagrangian densities (including interaction terms) in terms of their values at single points in spacetime. In classical mechanics in ...
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### 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 ...
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### Locality, unitarity & vacuum energy

I've read in a set of lecture notes that the requirement of locality and unitarity in QFT imply that the vacuum must have a non-zero energy associated with it (http://arxiv.org/abs/1502.05296 , top of ...
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### Why do we consider Lagrangian densities in QFT?

My question is: Why do we consider Lagrangian densities in QFT (as opposed to Lagrangians as in classical mechanics)? Is it simply because of the following? We wish the theories to be Lorentz ...
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### Exact meaning of locality and its implications on the formulation of a QFT

As far as I understand it, locality in physics is the statement that interactions can only occur between physical objects if the spacetime interval separating them is null or time-like. Thus, if the ...
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### 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? ...
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### Entanglement and Special Relativity [closed]

There are 2 particles entangled and move far apart to 2 measuring devices . The first measurement of either particle will collapse the wave function and set spin up and spin down on the particles. 2 ...
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### Why does a violation of locality not imply a violation of relativity?

This question is closely related to: What counts as information? Taking the specific example, again, of the EPR experiment. I think everyone agrees on the following: The act of measuring the ...
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### Does the many worlds interpretation eliminate the spooky action at a distance paradox? [closed]

I'm sorry if this is a stupid question. I'm a novice at physics. I have read the article about entanglement and EPR paradox. The spin of two particles is measured when they are very far apart, and ...
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### Does quantum theory obey locality?

Bell's inequality together with the Aspect experiment shows that that we cannot have local realism. But does quantum theory obey locality? and if not how can locality be violated but not special ...
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### 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 ...
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### 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 ...
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### How come the concept of an instant of time is such a controversial topic with relativity, but with entanglement it's completely acceptable?

When talking about relativity most people say that a universal instant of time doesn't exist, but when talking about entanglement most will say that the particles are both measured instantaneously. ...
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### Why don't we have logarithms or exponentials of the fields in the Lagrangians?

All tbe Lagrangian densities I have seen have always been polynomials of the fields. Is this a coincidence or is there a reason forbid, say, Lagrangians with logarithms or exponentials of the fields?
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### What does Bell's theorem rule out?

What exactly did Bell's theorem rule out? Did it rule out "locality", so we must give up and think of Copenhagen or maybe some realism theories (Bohmian for example)? ... That's how I understand Bell'...
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### Does Bell's theorem sort out local field theories?

For example the Maxwell's equations is a local theory. It's a set of differential equations that describe how should the state at a point change based on its neighbourhood. Counter example: Newtonian ...
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### Is gravity instantaneous? [duplicate]

I want to know if (hypothetically) a star appears out of nowhere at a certain distance (say 20 light seconds) away from me, how long will it take for me to get the feel of it's gravity? Will I know it ...