Ghostly activeness at a distance: a non-technical explanation of the Bell inequality (arXiv, June 2015, null citations)The newspaper claims that locality is violated inward the EPR experiments. (Alford has emitted lots of extra fog almost hidden variables etc. inward the give-and-take thread at Hsu's spider web log but I don't desire to inundation this spider web log post service past times all the mist. I desire to focus on the locality.)
Alford uses the term "strong locality" or "local causality" – together with you lot suspect that it could go i of the ill-advised conflations of "locality" together with "realism". But if you lot seem at his paper, you lot volition run across that the "strong locality" or "local causality" are defined to go goose egg else than the ordinary locality or relativistic causality – it's plenty to know the information inward the past times lite cone of the share R to calculate probabilities inward the share R (see the 2nd paragraph of the paper).
He says that this regulation fails inward quantum land theory but already inward the foremost 5 or so quantum land theory lectures, students larn that together with why this regulation is obeyed inward whatsoever relativistic quantum land theory. What's going on? Why is this guy writing so completely wrong things almost locality?
Here, I won't pretend that I am a lonely warrior for the truth inward the body of body of water of stupidity together with dishonesty, something that you lot know from hundreds of other situations. I am a warrior but in that location are many others. Even Backreation emphasized that no superluminal influence occurs inward the EPR experiments (principle #4) together with she wrote similar things when she was correcting Bill Nye's nonsense.
Cristi Stoica, a guy calling himself a quantum foundation person, agreed. There can't go whatsoever faster-than-light-signalling.
Of course, in that location have got been much to a greater extent than of import people who have got stressed this of import indicate – so oft confused inward the debates almost the "interpretations of quantum mechanics". (Much of the confusion was spread past times John Bell himself. The theorem he proved was sold every bit a mixed packet of a rudimentary termination almost a degree of wrong theories of physics; together with lots of wrong would-be philosophical claims added to the mix.) In his Caltech lectures, Feynman exploited the illustration of a decaying positronium to demo why quantum mechanics predicts the high correlations inward many measurements of polarizations – together with doesn't demand to violate the relativistic restrictions on the speed of influences.
In the 1990s, Murray Gell-Mann wrote almost the Quark together with the Jaguar. Chapter 12 was dedicated to "Quantum Mechanics together with Flapdoodle". Gell-Mann argued that the #1 wrong thought underlying all the nonsense inward low-brow pop books together with periodical articles (they had to explode already inward the early on 1990s if non earlier) was the thought that the EPR-style experiments handle to ship some information faster than light, inward a voodoo style. It's completely wrong and, every bit Gell-Mann argued, this misinformation was the ground why people began to advocate telekinesis together with other paranormal phenomena every bit consequences of quantum mechanics.
Well, Alford's newspaper is goose egg else than the 3,854th re-create of this flawed pop thought that some "faster than lite influences" are the right explanation of the EPR correlations. And to brand certain that he's a textbook illustration of the paranormal apologists criticized past times Gell-Mann, Alford invented i novel phrase. The "spooky activeness at a distance" was no longer spooky plenty so inward his title, Alford called it a "ghostly action". To brand things fifty-fifty worse, the word "telepathy" or "telepathic" appears 8 times inward the paper.
Well, every bit you lot know, I am i of the ghostbusters. Hahaha. Sorry, in that location are no actions at a distance together with in that location are no ghosts. His newspaper is completely wrong.
The foremost paragraph of his newspaper promotes diverse other wrong papers together with misinterpretations of Bell's theorem. His ain (not so) master copy current of wrong statements begins alongside the 2d paragraph of the paper:
Strong locality, also known every bit “local causality”, states that the probability of an lawsuit depends alone on things inward the event’s past times lite cone. Once those have got been taken into business organisation human relationship the event’s probability is non affected past times additional information almost things that happened exterior its past times lite cone.He defined the ordinary locality nosotros hash out inward quantum land theory rather carefully. I may utilization this Definition basically without whatsoever disclaimers (I would likely supersede "on things" past times "on measurements"). The alone occupation is that Alford states that this regulation fails inward our cutting-edge quantum mechanical theories. The reality is that it is perfectly obeyed! It has to go because it follows from the special theory of relativity.
Off-topic: David Cameron has made some turn a profit from his daddy's Panama fund. But it was alone plenty to purchase a Škoda Octavia, Škoda's most best-selling model, every bit a furious Tory MP calculated. If Cameron is forced to demo his taxation return, the MP volition innovate a nib to ban curtains at homes so that everyone may verify what sort of coitus you lot prefer. The Nasty Russian Girl was added to the package. She's cute, explains the novel features of the 2016 Octavia, every bit good every bit the history of the 1959-1971 Octavia, together with Cameron should go forgiven this profit, I believe, unless some self-evident serious offense is uncovered. BTW just 75 years ago, on Apr 9th, 1941, trolleybuses were introduced to Pilsen (trams have got been installed past times Czech Edison Mr Křižík inward 1899, 8 years later Prague; the lines are almost the same every bit today together with later 1914, most of the drivers were female; buses appeared inward 1922). The state of war was terrible together with the business was shockingly humiliating but the relaxed feeling inward which "everything works" is an impression from the video i can't avoid, tin he?
It's remarkable that a homo similar Mark Alford who has over 8,000 citations from 112 papers, including 4 papers inward a higher identify 500 citations together with thirty other papers inward a higher identify 50 citations, is capable of writing something so fundamentally wrong, something that fifty-fifty ordinary students know to go wrong later several lectures of quantum land theory. But it's true.
If you lot seem at Alford's 34 most cited papers, you lot volition run across i troubling sign: alongside i exception (and it's just a review), all of them have got at to the lowest degree two, together with usually more, authors – inward many of import cases, it's Frank Wilczek. You may cash inward one's chips suspicious that "something would cash inward one's chips wrong" if you lot allowed to produce him inquiry every bit an "independently thinking entity". And the newspaper argument against locality would go an illustration showing that your suspicion was justified.
By now, I believe that most people are aware of the basic explanation why the faster-than-light influences aren't allowed inward relativity. If the spacetime indicate Influenza A virus subtype H5N1 influenced the indicate B where \(\Delta t = t_B-t_A\gt 0\) together with \(\Delta x = x_B-x_A\) which tin go connected past times a line alongside \(|\Delta x |/ \Delta t = v \gt c\), so the points Influenza A virus subtype H5N1 together with B are spacelike-separated. For 2 spacelike-separated point, you lot may switch to a dissimilar inertial organisation – perform a Lorentz transformation – so that inward the novel coordinates, you lot volition have got \(t'_B-t'_A\lt 0\). So for this observer, the effect precedes the cause. Such acausal influences (backwards inward time) clearly Pb to contradictions.
So inward classical relativistic mechanics, objects may displace at most past times the speed of light, \(v \leq c\). All massive objects must really have got \(v\lt c\). In classical land theory, i may demo that the grouping velocity of the waves – or the speed past times which the moving ridge forepart moves – never exceeds the speed of lite inward the vacuum \(c\), either. In classical physics, the important of the restriction on the speed is straightforward.
Well, it's straightforward inward quantum mechanics, too, but the formalism describing locality inward quantum land theory requires the same "advanced physics tools" that quantum land theory requires inward general. As students of quantum land theory courses remove heed during the foremost 2 lectures, if you lot desire to reconcile quantum mechanics alongside relativity, you're forced to switch to quantum fields, or second-quantize, or produce something that is basically equivalent. Quantum land theory is the "minimal" sort of a theory that is compatible both alongside the principles of special relativity together with the postulates of quantum mechanics (string theory is the alone known consistent extension or deformation – together with it's a affair of advanced subtleties whether string theory is a "totally different" framework than quantum land theory).
So quantum land theory is the simplest framework respecting the laws of quantum mechanics inward which nosotros may hash out what it agency for physics to go local. Related questions are covered sometime inward the fourth or fifth lecture of a quantum land theory course. Instead of allowing you lot to pick your favorite i or a favorite quantum land theory textbook, let's seem at Peskin-Schroeder. Not because I am confident that it's silent the best textbook on the market. But because it has been a novel touchstone – a modern-era replacement of Bjorken-Drell – but it's been some for decades so a whole generation of particle physicists who are some was milk-fed past times Peskin-Schroeder. In this sense, Peskin-Schroeder may silent go considered the "least controversial" or "most mainstream" textbook of QFT (no i has ever screamed that they had covered causality incorrectly) together with that's what is desirable inward a text trying to solve or cut controversies.
Well, the relativistic causality – which is the same thing nosotros called locality hither – is already discussed on pages 27-31, using the foremost illustration of the gratis Klein-Gordon (scalar) land together with its propagator. You volition hopefully concord that it's a rather early on topic inward the textbook because it has something similar 850 pages.
Alternatively, you lot may seem e.g. at the Wikipedia page almost a propagator.
Well, if you lot desire to calculate the land \(\Phi(x)\) at some spacetime indicate \(x\) out of the values \(\Phi(y)\) of the land inward the past, you lot may utilization the Green's role \(G(x,y)\) or the propagator every bit the "kernel". The Green's role alone depends on \(x-y\) due to the translation invariance. So this role \(G(x-y)\) may go Fourier-transformed together with this 4D Fourier transform is something similar the park momentum-space propagator\[
G(p) = \frac{1}{p^2 - m^2}
\] where \(p\) is the four-momentum dual to the coordinate \(x-y\). When you lot calculate the Fourier transform of \(G(p)\), you lot volition run across that the integral has 2 singularities every bit a role of e.g. \(p_0\) – because the denominator becomes null twice. You must bargain alongside these singularities inward some way. The most natural choices are that your integration left-to-right contour along the existent axis should either cash inward one's chips "above" them or "below" them inward the complex plane. If you lot cash inward one's chips twice "above" them, you lot obtain the "retarded" propagator\[
G_\text{ret}(x,y) = i \langle 0| \left[ \Phi(x), \Phi(y) \right] |0\rangle \Theta(x^0 - y^0)
\] This is cool because it vanishes for spacelike-separated \(x,y\) but it also vanishes if \(x\) precedes \(y\). Similarly, if you lot cash inward one's chips twice "beneath" the poles, you lot obtain the advanced propagator where the fourth dimension ordering of \(x,y\) has to go the reverse one. The vanishing of the retarded or advanced propagator is the ground why the gratis land \(\Phi(x)\) may go fully calculated from its values inward the past times lite cone of \(x\). Note that the quantum fields obey the "same" Heisenberg equations of displace every bit the classical equations (it is plenty to add together hats if you lot demand them) so this locality is just copied from locality of classical land theory. Interactions don't really interruption the locality, either. At to the lowest degree when the interaction price are non-derivative ones, they alone add together "point-wise" changes of the quantum fields but they don't "enhance" the abilities of the quantum fields to propagate quickly.
However, the right propagator to utilization inward quantum land theory is the Feynman propagator where your contour goes "below" the left singularity but "above" the right one. This selection may go made unambiguous past times writing the momentum-space propagator to a greater extent than carefully as\[
G_F(p) = \frac{1}{p^2 - m^2+i\varepsilon}
\] together with it's this selection that guarantees that the quantum land "converges" to "mostly the vacuum" at \(t\to \pm\infty\) which is why the Feynman propagator gives to a greater extent than right results than you lot could have got alongside the advanced/retarded propagators (I could give you lot a improve lecture of these things but this materials isn't the focus here; what's to a greater extent than of import is that it's a rather touchstone materials that everyone learns inward the foremost semester of goodness quantum land theory courses).
Funnily enough, however, the seat representation of the Feynman propagator does not vanish at the spacelike separation:\[
\begin{align}
G_F(x-y) & = -i \langle 0|T(\Phi(x) \Phi(y))|0 \rangle \\
& = -i \left \langle 0| \left [\Theta(x^0 - y^0) \Phi(x)\Phi(y) +\right.\right.\\
&+\left.\left. \Theta(y^0 - x^0) \Phi(y)\Phi(x) \right] |0 \right \rangle.
\end{align}
\] The position-representation version of the Feynman propagator has the "time ordering" inward it (this fourth dimension ordering, together with thence the superiority of the Feynman propagator for the calculations, tin also go derived through Dyson's derivation where the development operator \(S\) is the time-ordered exponential of the integrated Hamiltonian \(iH\)) but it cannot go reduced to commutators. So it's a provoking result. As Peskin-Schroeder together with other teachers of quantum land theory instantly indicate out, you lot could go worried that this nonvanishing value of \(G_F(x-y)\) for spacelike-separated but nearby points \(x,y\) (the value of the propagator drops apace if the spacelike interval \(x-y\) becomes long) could hateful some violation of locality.
However, every bit Peskin-Schroeder together with everyone else apace show, this worry isn't justified. The nonzero value of the Feynman propagator for spacelike separations really agency that the vacuum solid pose down is "entangled". There are quantum fluctuations of \(\Phi(x)\) everywhere but if the value of \(\Phi(x)\) at some indicate \(x\) is randomly "elevated to to a greater extent than positive values", it's real probable that \(\Phi(y)\) at nearby points \(y\) volition also go "positively elevated" together with closed to \(\Phi(x)\). It's this correlation of the quantum fields at nearby points – which results from the continuity of the fields i.e. from the spatial derivative price inward the Hamiltonian – that is responsible for the nonzero value of the propagator.
In spite of that nonzero value, you lot can't utilization it to influence spacelike-separated points. There may go diverse ways to justify this assertion but most authors including Peskin-Schroeder utilization i of import insight: Whether an activeness at indicate \(x\) influences predictions for the indicate \(y\) is e'er encoded inward commutators, non generic products of fields, together with the commutators are null for spacelike-separated \(x,y\).
The commutator really tin go written inward price of the Feynman propagator every bit well:\[
[\Phi(x),\Phi(y)] = \dots = G(x-y) - G(y-x)
\] The effect of events at \(x\) on the measurements at \(y\) is given past times the commutators only. And the commutators are equivalent to the divergence of the Feynman propagator from \(x\) to \(y\) together with the Feynman propagator from \(y\) to \(x\). These 2 price may go understood every bit the contribution from "particles" together with "antiparticles". Each of those may inward some sense "propagate faster than light" but all physically observable quantities e'er have contributions both from "particles" together with "antiparticles" together with i time you lot amount these 2 values of the propagator, the termination is already vanishing at spacelike separations. The antiparticles' together with particles' "superluminal" effects just cancel.
Now, this indicate is oft left unexplained. Why is the effect of the mensuration at \(x\) on the measurements at \(y\) null if the commutators of fields at those points are zero? The advanced together with retarded propagators inward a higher identify are plenty to fence that the "normal unitary" development of the physical organisation respects locality. But there's also the other "part" of the development of the moving ridge functions, the reduction of it associated alongside the measurement.
In fact, all "willful interventions" that tin go done at/around indicate \(x\) may go considered to go measurements. If you lot interruption something, you lot also seem whether you lot broke it together with have got some fun – that's why you lot did it. If you lot don't seem together with don't have got fun, you're just a dead component of the physical organisation whose harmlessness for locality was already proven.
OK, if you're an observer who observes some quantity \(L\) some the indicate \(x\), you lot disclose an eigenvalue \(\lambda\) of \(L\) together with the moving ridge role instantly collapses to\[
\ket\psi \to P_\lambda \ket\psi.
\] Similarly, if you lot utilization a density matrix, it changes every bit \(\rho\to P_\lambda \rho P_\lambda\). After the collapse, you lot may renormalize \(\ket\psi\) or \(\rho\) for its norm or line to go i again. But now, the projection operator \(P_\lambda\) may go considered to go a role of \(L\), together with inward quantum land theory, \(L\) is a functional of quantum fields nigh the indicate \(x\). So \(P_\lambda\) is a functional of fields \(\Phi(x\pm \epsilon)\), too.
We desire to know if it affects predictions for fields closed to \(\Phi(y)\) together with their functional \(M\) whether the collapse took identify due to the mensuration of \(L\) nigh \(x\). The probability that \(M\) volition have got the eigenvalue \(\mu\) is given past times \({\rm Tr}(\rho P_\mu)\) where \(P_\mu\) is the projection operator for the eigenvalue \(M=\mu\).
What is the probability if a mensuration of \(L\) took identify before? It's \[
{\rm Tr} ( P_\lambda \rho P_\lambda P_\mu )
\] This human face depends on both eigenvalues \(\lambda,\mu\) together with knows almost all the correlations. But the experimenter who measures \(M\) doesn't know the termination of the mensuration of \(L\). We desire to know whether the act of the mensuration has affected him. So he must amount the probabilities over all possible outcomes of the mensuration of \(L\).\[
\sum_\lambda {\rm Tr} ( P_\lambda \rho P_\lambda P_\mu ) = \dots
\] In general, in that location would go no way to genuinely simplify this sum. In particular, nosotros can't utilization the fact that \(\sum_\lambda P_\lambda = 1\) to simplify the amount of products\[
\sum_\lambda P_\lambda P_\mu P_\lambda
\] However, because all the fields some \(x\) together with \(y\) commute due to their spacelike separation, their functionals \(P_\lambda\) together with \(P_\mu\) commute alongside i another, too. So nosotros may telephone commutation their social club above:\[
\dots = \sum_\lambda {\rm Tr} ( P_\lambda \rho P_\mu P_\lambda ) = \dots
\] But due to the cyclic belongings of the trace, the final \(P_\lambda\) may go moved to the start of the line where nosotros acquire \((P_\lambda)^2\) together with that's just \(P_\lambda\) because \(P_\lambda\) is a projection operator:\[
\dots = \sum_\lambda {\rm Tr} ( P_\lambda \rho P_\mu ) = \dots
\] But at nowadays it's easy. We just have got the amount of \(P_\lambda\) over all eigenvalues. But the amount of all the possible projection operators is just \(1\), so the termination is\[
\dots = {\rm Tr} (\rho P_\mu).
\] The probability that \(M=\mu\) is the same every bit if the mensuration every bit if the mensuration of \(L\) didn't have got place. The vanishing commutators of the fields some the points where the observables \(L,M\) alive was needed to attempt this result.
There are likely to a greater extent than elegant proofs (one may also focus on the fact that the probabilities of measurements \(L=\lambda,M=\mu\) factorize to the production of probabilities – every bit expected for independent, uncorrelated, properties, assuming that the mensuration events of \(L,M\) weren't affected past times a mutual campaign inward the intersection of their past times lite cone – because the initial solid pose down is a tensor production inward that case, together with "everything" probability-like factorizes) but the decision is to a greater extent than of import than the peradventure messy ways that convince you lot that it's true: The vanishing of the commutators at spacelike separations is what guarantees that the measurements – together with thence all willful acts – done inward i share don't influence the predicted probabilities inward the other region.
This was the final thing needed to flora the fact that the "strong locality" or "local causality", every bit Alford calls it, holds inward whatsoever salubrious relativistic quantum land theory. Why did Alford skip his fourth or fifth lecture of the introductory quantum land theory course?
Strong locality or whatever Alford calls it holds because the fields (graded) commute at spacelike separations. And they do. One may flora this termination inward many dissimilar ways. For example, at equal times, the commutators are null for spacelike separations due to the "canonical quantization" together with the identification of the canonical momenta. The commutator remains null for non-equal times (but spacelike separation) because the development is generated past times the Hamiltonian which is an integral of the Hamiltonian density, so it alone modifies \(\Phi(x)\) past times fields some \(x\) that also commuted alongside \(\Phi(y)\), together with vice versa. The commutators stay null if \(x-y\) is spacelike.
You may run across that his serious papers, e.g. this most cited paper co-authored past times Alford, Rajagopal, together with Wilczek inward 1997, e'er incorporate some formalism of quantum land theory, some integrals that are familiar to students inward quantum land theory courses. His newspaper almost the "ghostly action" doesn't incorporate anything of the sort. It alone contains rather childish pictures together with claims that straight contradict the basic fabric that the students of the quantum land theory courses usually learn. It's really 12 pages of garbage that is every bit offensive every bit this tertiary paragraph of the paper:
Given some reasonable-sounding assumptions almost causation (see Sec. III), the violation of potent locality inward EPR experiments implies that in that location are causal influences that go faster than light. The primary destination of this newspaper is to give an extremely elementary non-technical explanation of how EPR experiments Pb to this striking conclusion.No, in that location is no superluminal activeness together with no violation of "strong locality" inward Nature.
One must conclude that the "ghostly action" materials is really some hobby that is completely disconnected from the normal, professional person life of Mark Alford. Like Superman, he seems to alive 2 lives. It looks similar when Alford was writing almost the "ghostly action", he must have got been completely unaware of the fact that he has co-authored many papers that really utilization quantum land theory – together with non just the materials from the foremost 5 lectures. Has Mark Alford forgotten all of his QFT expertise? Did he ever know it? Or doesn't he realize that when he's writing papers almost the "violations of potent locality" inward Nature, he discusses questions that should properly go discussed past times the same formalism – that of QFT – that was used inward his serious papers? And that the decision is clearly the reverse i than the decision of his "ghostly" paper?
I e'er have got so many questions almost the people's irrational conduct but I almost never acquire clear answers. People's irrationality likely cannot go rationally explained.