## Quantum Cheshire Cat

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

### Quantum Cheshire Cat

Here we go again; an experiment that claims to have detected spatial separation of a neutron and its magnetic moment (spin).

http://www.nature.com/ncomms/2014/14072 ... s5492.html
"Observation of a quantum Cheshire Cat in a matter-wave interferometer experiment"
From the abstract, "The experimental results suggest that the system behaves as if the neutrons go through one beam path, while their magnetic moment travels along the other."

What the heck are we to call a neutron that has no spin? It certainly can't be a fermion.
FrediFizzx
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### Re: Quantum Cheshire Cat

FrediFizzx wrote:Here we go again; an experiment that claims to have detected spatial separation of a neutron and its magnetic moment (spin).

http://www.nature.com/ncomms/2014/14072 ... s5492.html
"Observation of a quantum Cheshire Cat in a matter-wave interferometer experiment"
From the abstract, "The experimental results suggest that the system behaves as if the neutrons go through one beam path, while their magnetic moment travels along the other."

What the heck are we to call a neutron that has no spin? It certainly can't be a fermion.

Fred,

Wow! Just the type of thing you and I were talking about to maintain locality in the double slit experiment. Keep in mind, the proton spin crisis (which applies as well to neutrons) says that the spin 1/2 is distributed mostly into the gluon plasma, and that only about 30% of the overall spin sticks with the quarks. So the spin is already somewhat "transportable."

If this experiment proves to be accurate (and that is an if), then it will either compound the proton spin crisis, or provide a clue to resolve that problem.

I would make a side bet that the electron or the photon cannot be separated from its spin in this way, but who knows: they all (electron, photons, protons, neutrons, and more) create the same probability density patterns when they strike a detector far afield from the slits. That fact is an underlying unity which cuts across spin type and particle type and interaction type and even whether a particle is elementary or composite, and is on the road to something very deep about nature.

Jay
Yablon
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### Re: Quantum Cheshire Cat

Jay wrote:
I would make a side bet that the electron or the photon cannot be separated from its spin in this way, but who knows: they all (electron, photons, protons, neutrons, and more) create the same probability density patterns when they strike a detector far afield from the slits. That fact is an underlying unity which cuts across spin type and particle type and interaction type and even whether a particle is elementary or composite, and is on the road to something very deep about nature.

EXTRACT from:
http://en.wikipedia.org/wiki/Spin%E2%80 ... separation:

In condensed matter physics, spin–charge separation is an unusual behavior of electrons in some materials in which they 'split' into three independent particles, the spinon, orbiton and the chargon (or its antiparticle, the holon). The electron can always be theoretically considered as a bound state of the three, with the spinon carrying the spin of the electron, the orbiton carrying the orbital degree of freedom and the chargon carrying the charge, but in certain conditions they can become deconfined and behave as independent particles.

In my preon model (based on the Rishon model), every individual preon has either a + or - loading on every property, but blocks of preons can be neutral in an overall quality. My preon block C is neutral wrt spin and weak isospin. My preon blocks A and B have both charge and spin. The electron has blocks A and C plus some more neutral blocks eg A plus anti-A. A virtual electron could become separated wrt spin in my model into a 1) chargeon&spinon [A] composite and 2) a chargon [C] and 3) a neutral of bulk filler with no properties [A+antiA].
Ben6993

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### Re: Quantum Cheshire Cat

Ben6993 wrote:EXTRACT from:
http://en.wikipedia.org/wiki/Spin%E2%80 ... separation:

In condensed matter physics, spin–charge separation is an unusual behavior of electrons in some materials in which they 'split' into three independent particles, the spinon, orbiton and the chargon (or its antiparticle, the holon). The electron can always be theoretically considered as a bound state of the three, with the spinon carrying the spin of the electron, the orbiton carrying the orbital degree of freedom and the chargon carrying the charge, but in certain conditions they can become deconfined and behave as independent particles.

Ben,

This is great stuff, real food for thought. Some of my earliest forays into new theory back in the 1980s were based on preon models, and there is a lot of merit to thinking about the "aspects" of the particles we observe, such as spin and orbital and charge and isospin, as aspects which do not necessarily have to come bundled together.

I have two earlier blog posts that you might like. First is at http://jayryablon.wordpress.com/2008/02 ... -fermions/, and it references my first published paper from 1988, at http://jayryablon.files.wordpress.com/2 ... tiplet.pdf. This 1988 paper summarized a very large set of materials I had pulled together in 1986, discussed and available at http://jayryablon.wordpress.com/2012/04 ... ification/. It was by writing these 200 or so pages, that I taught myself Dirac theory and particle theory and the basics of Yang-Mills and Lie Groups, but of course, assimilated this all in my own particular way and saw a preon model in the middle of it all.

These earlier pursuits are never far beneath the surface in my thinking as I tackle other issues. Thank you guys for helping me get them back to the surface.

Jay
Yablon
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### Re: Quantum Cheshire Cat

Yablon wrote:Fred,

Wow! Just the type of thing you and I were talking about to maintain locality in the double slit experiment. Keep in mind, the proton spin crisis (which applies as well to neutrons) says that the spin 1/2 is distributed mostly into the gluon plasma, and that only about 30% of the overall spin sticks with the quarks. So the spin is already somewhat "transportable."

If this experiment proves to be accurate (and that is an if), then it will either compound the proton spin crisis, or provide a clue to resolve that problem.

I would make a side bet that the electron or the photon cannot be separated from its spin in this way, but who knows: they all (electron, photons, protons, neutrons, and more) create the same probability density patterns when they strike a detector far afield from the slits. That fact is an underlying unity which cuts across spin type and particle type and interaction type and even whether a particle is elementary or composite, and is on the road to something very deep about nature.

Hmm... I never heard of the proton "spin crisis". I thought is was proton momentum that was 1/2 from gluon plasma. Anyways, I figure this is a related trick that Nature is doing similar to "entanglement". Well... actually we are just tricking ourselves; not Nature really tricking us. Just a matter of figuring out the "trick" if the experiment is correct.
FrediFizzx
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### Re: Quantum Cheshire Cat

FrediFizzx wrote:Here we go again; an experiment that claims to have detected spatial separation of a neutron and its magnetic moment (spin).

http://www.nature.com/ncomms/2014/14072 ... s5492.html
"Observation of a quantum Cheshire Cat in a matter-wave interferometer experiment"
From the abstract, "The experimental results suggest that the system behaves as if the neutrons go through one beam path, while their magnetic moment travels along the other."

What the heck are we to call a neutron that has no spin? It certainly can't be a fermion.

The claim by the authors is based on a fundamental misconception of what is meant by "spin." Contrary to the indoctrination we are subjected to in our quantum mechanical textbooks, "spin" is not a "property" of a particle, but a reflection of its relationship with the rest of the universe (see Ref.[3] of this paper). Thus a fermion, for example, is an "anchored" particle (anchored to the rest of the universe), and a boson is a "free" particle (unanchored to the rest of the universe).

Compound the lack of appreciation of this basic fact with the defective recipe of quantum mechanics (evolution of a superposed state + ad hoc measurement process = a probability of the observed result), and you can make anything look like magic. The deceitful magician here is the recipe of quantum mechanics, not Nature.

http://libertesphilosophica.info/blog/
Joy Christian
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### Re: Quantum Cheshire Cat

FrediFizzx wrote:
Yablon wrote:Fred,
Hmm... I never heard of the proton "spin crisis". I thought is was proton momentum that was 1/2 from gluon plasma. Anyways, I figure this is a related trick that Nature is doing similar to "entanglement". Well... actually we are just tricking ourselves; not Nature really tricking us. Just a matter of figuring out the "trick" if the experiment is correct.

Oh yes, Fred, see http://en.wikipedia.org/wiki/Proton_spin_crisis. And this is a big deal in the nuclear physics community. As I discovered when I attended the APS Nuclear Physics Division conference last October, the nuclear people regard this is the #1 problem in nuclear physics.

Jay
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### Re: Quantum Cheshire Cat

Joy Christian wrote:The claim by the authors is based on a fundamental misconception of what is meant by "spin." Contrary to the indoctrination we are subjected to in our quantum mechanical textbooks, "spin" is not a "property" of a particle, but a reflection of its relationship with the rest of the universe (see Ref.[3] of this paper). Thus a fermion, for example, is an "anchored" particle (anchored to the rest of the universe), and a boson is a "free" particle (unanchored to the rest of the universe).

This is great discussion. There are a lot of things here which I intuitively feel are connected.

This "anchoring" notion that Joy introduces immediately feels like entanglement, but it also seems to drag the Fermion Exclusion Principle into the mix. We take it for granted that no two fermions in a given "system" (whatever defines a system) can occupy the same state. And we may envision this as if the seats in a theater can only hold one person each and no two seats are exactly alike. But we often end the discourse right there, and do not inquire how it is that electron B knows, simply because there is already an election A, that it cannot also be an electron A. And isn't entanglement really based on the fact that we are deeming Alice and Bob's particles to be part of a "system," thus subjecting them to exclusion, thus finding that they must be in exclusive states?

So either either exclusion is at the root of all of this entanglement stuff, or all this entanglement stuff is at the root of exclusion.

Jay
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### Re: Quantum Cheshire Cat

Yablon wrote:
Joy Christian wrote:The claim by the authors is based on a fundamental misconception of what is meant by "spin." Contrary to the indoctrination we are subjected to in our quantum mechanical textbooks, "spin" is not a "property" of a particle, but a reflection of its relationship with the rest of the universe (see Ref.[3] of this paper). Thus a fermion, for example, is an "anchored" particle (anchored to the rest of the universe), and a boson is a "free" particle (unanchored to the rest of the universe).

This is great discussion. There are a lot of things here which I intuitively feel are connected.

This "anchoring" notion that Joy introduces immediately feels like entanglement, but it also seems to drag the Fermion Exclusion Principle into the mix. We take it for granted that no two fermions in a given "system" (whatever defines a system) can occupy the same state. And we may envision this as if the seats in a theater can only hold one person each and no two seats are exactly alike. But we often end the discourse right there, and do not inquire how it is that electron B knows, simply because there is already an election A, that it cannot also be an electron A. And isn't entanglement really based on the fact that we are deeming Alice and Bob's particles to be part of a "system," thus subjecting them to exclusion, thus finding that they must be in exclusive states?

So either either exclusion is at the root of all of this entanglement stuff, or all this entanglement stuff is at the root of exclusion.

Jay,

Conceptually it is very important to distinguish between the "orientation entanglement" and "quantum entanglement." Orientation entanglement is a straightforward classical notion, whereas quantum entanglement is riddled with magic and mystery. What I am referring to above with "anchoring" is what is known as orientation entanglement (see, for example, the discussion on the pages 1148 to 1150 of Gravitation by Misner, Thorne, and Wheeler). On the face of it, quantum entanglement is a very different concept. The fundamental property of quantum entanglement is non-factorizability, which translates into non-locality in Bell's framework.

Now a parallelized 3-sphere---which happens to be diffeomorphic to the spinor or fermionic group SU(2)---is a quintessential mathematical expression of the orientation entanglement. But the 3-sphere is also one of the well known solutions of Einstein's field equations of GR, which is a purely classical (and local) field theory (cf. the discussion in this paper). What is more, in my work I have shown that the quantum correlation predicted by the emblematic (or simplest) quantum entanglement (i.e., the EPRB or singlet state) is exactly that between the points of a parallelized 3-sphere: E(a, b) = -a.b (cf. the discussion on this page).

Thus, at the root of all is the orientation entanglement, not quantum entanglement. In my view, the so-called quantum entanglement is simply an illusion.
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### Re: Quantum Cheshire Cat

Joy Christian wrote:Jay,

Conceptually it is very important to distinguish between the "orientation entanglement" and "quantum entanglement." Orientation entanglement is a straightforward classical notion, whereas quantum entanglement is riddled with magic and mystery. What I am referring to above with "anchoring" is what is known as orientation entanglement (see, for example, the discussion on the pages 1148 to 1150 of Gravitation by Misner, Thorne, and Wheeler). On the face of it, quantum entanglement is a very different concept. The fundamental property of quantum entanglement is non-factorizability, which translates into non-locality in Bell's framework.

Now a parallelized 3-sphere---which happens to be diffeomorphic to the spinor or fermionic group SU(2)---is a quintessential mathematical expression of the orientation entanglement. But the 3-sphere is also one of the well known solutions of Einstein's field equations of GR, which is a purely classical (and local) field theory (cf. the discussion in this paper). What is more, in my work I have shown that the quantum correlation predicted by the emblematic (or simplest) quantum entanglement (i.e., the EPRB or singlet state) is exactly that between the points of a parallelized 3-sphere: E(a, b) = -a.b (cf. the discussion on this page).

Thus, at the root of all is the orientation entanglement, not quantum entanglement. In my view, the so-called quantum entanglement is simply an illusion.

Joy,

This is all very interesting to me. I went back to pages 1148 to 1150 of Gravitation by Misner, Thorne, and Wheeler, dealing with the "orientation-entanglement," or "version," or spinors. I studied that thirty years ago and so have known about this ever since. This what so-called "double covering" as all about: a vector has a twofold ambiguity that a spinor does not. What I did not realize until now, is that you are making use of this in your explanations of EPR correlations between the Alice and Bob observations. Am I correct? If so, I want to get my head around exactly how you are doing this.

But even beyond Alice and Bob, this suggests some generalizations to think about which may tie some seemingly disparate things together, specifically, as regards your statement that "On the face of it, quantum entanglement is a very different concept," and what I said above about Exclusion.

If one takes the view spacetime and internal symmetry space are the two operative geometric spaces of the observed universe, then spacetime of course has an underlying Dirac spinor structure in which the states are particle and antiparticle (orientation in time) and spins up and down (orientation in space). As to space orientation, the spinor has an entanglement to its surroundings, per 1148 to 1150 of MTW, and what you refer to as anchoring. But these two spins are also "up" and "down" and they establish eigenstates for Exclusion as well. So I can get two electrons into the 1S shell of helium, because the spins up and down do represent different exclusionary states. The third electron has to go into a new 1P shell, because up and down spin are used up in 1S.

Now let's go over to internal symmetry, which I believe you would say crosses over from orientation entanglement to quantum entanglement. But what is internal symmetry? Taking the simplest SU(2) internal symmetry of weak isospin, we use a three-dimensional SO(3) space which we analogize to ordinary physical space, and we deconstruct this into spinors which have isospin up and isospin down as their two states. These states are also exclusionary, which is to say, isospin up and and isospin down also define quantum numbers that are meaningful for exclusion. This is how an up quark differs form a down quark, and at the composite level, how a proton differs from a neutron. Thus, for example, a helium nucleus a.k.a. alpha particle, which is exceedingly stable, gets to contain a spin up and spin down proton plus a spin up and spin down neutron. So in the alpha particle, we have both spin and isospin providing exclusionary freedom, which means both physical space and internal symmetry space are the operative spaces.

But the isospin spinors also have an entanglement; this is just an entanglement to the internal symmetry space. And it is totally analogous to the orientation - entanglement discussion by MTW. It is just an abstract SO(3) space rather than the real one into which you can put a box tied to the space with strings. Is this in fact the basis for what you call "quantum entanglement"? Are we just talking about an entanglement in an internal symmetry space? Or this there more to it than that?

If quantum entanglement is just orientation entanglement generalized to internal symmetry spaces, and if you have found a local explanation for orientation entanglement, might you not be able to generalize that to take all the mystery out of quantum entanglement as well? We just need to bring the locality versus non-locality discussion into the internal symmetry space.

Then, you get to questions such as what is a meaning of "distance" and "separation" in the internal symmetry space, and what in that space, corresponds to the material limit of the speed of light? And since internal symmetry only generalizes space but does not generalize time which bears a Minkowskian relationship to space, there is that wrinkle too.

Jay
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### Re: Quantum Cheshire Cat

Joy Christian wrote:. . . What I am referring to above with "anchoring" is what is known as orientation entanglement (see, for example, the discussion on the pages 1148 to 1150 of Gravitation by Misner, Thorne, and Wheeler). . .

So, before we even get to the parallelized 3-sphere -- which I may ask about next -- are you saying that the crux of your argument based on 1148 to 1150 of MTW, is this?

From a singlet state, prepare a pair of electrons in the same place at the same time, one with spin up and one with spin down. So these two electrons have entanglements with the physical space which differ from one another by 2pi. But via their entanglements with the same space, these are necessarily entangled with one another. That is, A anchored to space, and B anchored to the same space, means A is anchored to B. Then, it is just a question of evolving these anchors as time passes and the particles are separated, which is to say, we are simply studying the time evolution of 1148 to 1150 of MTW for two particles which start out together in opposite versions.

Is this on the fairway?

Jay
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### Re: Quantum Cheshire Cat

Yablon wrote:
Joy Christian wrote:. . . What I am referring to above with "anchoring" is what is known as orientation entanglement (see, for example, the discussion on the pages 1148 to 1150 of Gravitation by Misner, Thorne, and Wheeler). . .

So, before we even get to the parallelized 3-sphere -- which I may ask about next -- are you saying that the crux of your argument based on 1148 to 1150 of MTW, is this?

From a singlet state, prepare a pair of electrons in the same place at the same time, one with spin up and one with spin down. So these two electrons have entanglements with the physical space which differ from one another by 2pi. But via their entanglements with the same space, these are necessarily entangled with one another. That is, A anchored to space, and B anchored to the same space, means A is anchored to B. Then, it is just a question of evolving these anchors as time passes and the particles are separated, which is to say, we are simply studying the time evolution of 1148 to 1150 of MTW for two particles which start out together in opposite versions.

Is this on the fairway?

Sort of on the fairway. But you can you scan those pages of MTW and email them to me? Thanks.
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### Re: Quantum Cheshire Cat

Hi Jay

Jay wrote:
I have two earlier blog posts that you might like. First is at http://jayryablon.wordpress.com/2008/02 ... -fermions/, and it references my first published paper from 1988, at http://jayryablon.files.wordpress.com/2 ... tiplet.pdf. This 1988 paper summarized a very large set of materials I had pulled together in 1986, discussed and available at
http://jayryablon.wordpress.com/2012/04 ... ification/. It was by writing these 200 or so pages, that I taught myself Dirac theory and particle theory and the basics of
Yang-Mills and Lie Groups, but of course, assimilated this all in my own particular way and saw a preon model in the middle of it all.

I have seen your preon blog several times before but never commented. I have written endlessly on preons on s.p.f, as you know, but will summarise here. If I understand your "isospin redundancy" then I agree with it. The left-hand electron, lh neutrino and lh quark all share the same preon (in my model they share a block of preons: Block A which has electric charge - 1/2 and spin -1/2).

In commenting on Volovik's 2003 work you seem averse to having a holon which is fundamental yet lacks chirality. I agree. I started out in my Preon Model 1 with an electron having 2 preons whereas in my latest model (#5) it requires 96 preons to make an electron. So I have a terminology problem as my preons are a further layer down from the blocks of preons corresponding to holons or to the Rishon model preons. The latter are like my preon blocks A, B and C rather than like my version of preons. So I have a holon (my preon block C) with zero net spin. The word "net" is important as the preons themselves always have chirality for every attribute one can give them. I liked the famous Lisi Garret article and based my preons on the Lie algebra. Which sounds grand but just means that I took a generalised preon pro forma and gave it a + or - attribute on each fundamental quality. My Model #5 seems complete now as I cannot find an interaction which it does not cope with. A further reason for using the Lie structure is that all preons have an attitude on all qualities which will be true for all time. So that as symmetry breaking over time has evolved, the same preons are always at work, but in different blocks of preons or combinations of blocks of preons. And at the BB one could have a collection of all preons of all possible types, with chirality on all qualities, in one particle in one bosonic state.

I am not sure about your fifth dimension (called matter?). For me, the preon overall is matter, whatever that is. Dimensions seem to me to be associated with chirality. Matter points one way and antimatter points back in time in that dimension. So a preon can be both matter and antimatter at the same time but wrt different fundamental attributes or qualities. The idea of antimatter seems more complicated (or is it more simple?) for preons than for particles.
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### Re: Quantum Cheshire Cat

Hi Jay,

I am indeed making use of orientation entanglement in my explanation of the EPR correlation. Orientation entanglement is also responsible for the exclusion principle. So we are indeed talking about "double covering", SU(2), and all that. So we are on the same page as far as the orientation entanglement is concerned. I often use the phrase "parallelized 3-sphere" which may not be too familiar, but that is just a matter of language. Ultimately this is all about the significance of the SU(2) symmetry.

But the relationship between the orientation entanglement and quantum entanglement is not so straightforward. To begin with, quantum entanglement is a quantum concept, involving superposition principle and non-factorizability. Thus it is dramatically different from the classical concept like the orientation entanglement. Let me elaborate on this a little because it is important to appreciate just how profoundly different the concept of quantum entanglement is. Consider the simplest entangled state---i.e., the singlet state:

$|\Psi\rangle = \frac{1}{\sqrt{2}}\left\{ |{\bf n}, +\rangle_1\otimes|{\bf n}, -\rangle_2 -|{\bf n}, -\rangle_1\otimes|{\bf n}, +\rangle_2\right\}.$

This state cannot be factorized into a product of a state representing the first spin alone and a state representing the second spin alone, such as (for example)

$|\Phi\rangle=\left\{|{\bf n}, \pm\rangle_1\otimes|{\bf n},\mp\rangle_2\right\}.$

Because of this non-factorizability the singlet state is said to be entangled. And this entanglement is responsible for the so-called non-locality of quantum theory. Note that this entanglement is a purely quantum mechanical concept. It has nothing whatsoever to do with the classical concept of orientation entanglement. In particular, it has nothing to do with internal symmetry or spacetime. Quantum entanglement can be between energy and momentum of a particle, for example.

Why do I then claim that at the root of it all is orientation entanglement and not quantum entanglement? Was Schrodinger wrong to call quantum entanglement the characteristic trait of quantum mechanics? No, he wasn't wrong. Quantum entanglement is indeed a powerful, succinct, and phenomenally successful concept. But unlike orientation entanglement, one cannot observe either quantum superposition or quantum entanglement directly. In this respect quantum entanglement is no different from the idea of a phlogiston in a combustible body. Recall that phlogiston theory was a very successful and powerful theory which remained popular in accounting for the actually observed phenomena, such as burning wood producing ash lighter than wood. But phlogiston itself was merely a hypothetical substance which could not be observed directly. Conceptually quantum entanglement is no different. It can never be observed directly (although time and again some people falsely claim that they have "observed" quantum entanglement itself ). If we could observe quantum entanglement directly, then all controversies over the interpretation of quantum mechanics would end instantly. Then Einstein and the followers of Einstein like you and me would have no choice but to concede defeat.

What we can observe directly are probabilities, expectation values, and correlations among observed results. Those are the "realities", not quantum entanglement. This is markedly different from orientation entanglement, which is itself a "reality" (cf. Dirac's belt trick). Given a self-adjoint operator, say $\cal{\widehat O}$, representing some observable quantity, the expectation value of this operator in an entangled state, $\langle\Psi|{\cal{\widehat O}}| \Psi \rangle$, provides the predictions of what we observe in any physical scenario. What I have found in my work is that this expectation value, which is closely related to correlation among the observed results like +1 or -1, can be understood local-realistically as correlation among the points of the mathematical space, namely the 3-sphere, representing all possible orientation entanglement in three dimensions.

This immediately raises the question of generalization you have raised: "...might you not be able to generalize that to take all the mystery out of quantum entanglement as well?". Well, I think I have indeed taken all the mystery out of quantum entanglement. But to understand how, one has to understand the octonionic spinors and the corresponding parallelized 7-sphere. I have already given the general argument in another thread, but let me repeat it here for completeness:

Suppose we consider an arbitrary quantum state $|\Psi\rangle$ and the corresponding self-adjoint operator $\cal{\widehat O}({\bf a},\,{\bf b},\,{\bf c},\,{\bf d},\,\dots\,)$ in some Hilbert space $\cal H$, parameterized by an arbitrary number of local parameters ${{\bf a},\,{\bf b},\,{\bf c},\,{\bf d},}$ etc. Note that I am imposing no restrictions on the state $|\Psi\rangle$, or on the size of the Hilbert space ${\cal H}$. In particular, $|\Psi\rangle$ can be as entangled or un-entangled as one may like, and ${\cal H}$ can be as large or small as one may like (in the case of the double slit there is no entanglement, for example). The quantum mechanical expectation value of the operator ${\cal\widehat O}({\bf a},\,{\bf b},\,{\bf c},\,{\bf d},\,\dots\,)$ in the state $|\Psi\rangle$ would then be

${\cal E}_{{\!}_{Q.M.}}({\bf a},\,{\bf b},\,{\bf c},\,{\bf d},\,\dots\,)\, =\,\text{Tr}\left\{{W}\,{\cal\widehat O}({\bf a},\,{\bf b},\,{\bf c},\,{\bf d},\,\dots\,)\right\}$,

where ${W}$ is a statistical operator of unit trace representing the state. Now I have shown that the quantum correlation predicted by this expectation value can always be reproduced as local and realistic correlation among a set of points of a parallelized 7-sphere, by following a procedure very similar to the one discussed above for the 3-sphere, which is simply one of the Hopf fibers of the 7-sphere. In fact, I have proved the following theorem:

Every quantum mechanical correlation can be understood as a deterministic, local-realistic correlation among a set of points of a parallelized 7-sphere, specified by maps of the form

$\pm\,1\,=\,{\cal A} ({\bf a},\,\lambda): {\rm I\!R}^3\!\times\Lambda\longrightarrow {\rm I\!R}^7\!\times\Lambda\longrightarrow S^7 \hookrightarrow{\rm I\!R}^8$.

The proof of this theorem can be found in this paper. I think you will not find this satisfactory because you would like to have intuitive, physical understating of what is going on. But that could be a dangerous undertaking. Without understanding the intricacies of the octonionic 7-sphere, it could lead to serious misconceptions.

Joy
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### Re: Quantum Cheshire Cat

FrediFizzx wrote:Here we go again; an experiment that claims to have detected spatial separation of a neutron and its magnetic moment (spin).
http://www.nature.com/ncomms/2014/14072 ... s5492.html

First thing, I checked if it was an April-fool's joke but unfortunately it is not. The authors are severely confused. They do not understand the difference between properties of single system, and properties of an ensemble of similar systems. For example, they say:
Denkmayr et al wrote:A surprising effect originating from pre- and post-selection of a system is the ability to 'separate' the location of a system from one of it's properties'

How do you pre- or post-select a system. Don't you have to select from a set of more than one system? I'll encourage everyone interested to read that paper again and everytime you see the cat, or the neutron, put a big question sign and check if you are convinced they are measuring a single neutron, as opposed to an ensemble of similar neutrons. For example, they say on page two:
In our experiment, the? neutron plays the role of the cat, and the cat's grin is represented by the? neutron's spin component along the z-direction. The? system is initially prepared so that after entering the beam splitter its quantum state is given by ...
In order to observe the quantum Cheshire Cat, after we preselect the ensemble, we will next perform weak measurements of the neutrons’ population in a given path on the one hand and of the value of the spin in a given path on the other.... Whenever the postselection succeeds, that is, when a Cheshire Cat is created, a minimally disturbing measurement will find the Cat in the upper beam path, while its grin will be found in the lower one.

If anyone knows what "the neutron's population" means, they should help me understand it. It seems, what they did was measure the position of one set of neutrons in one arm, the spin of a similar but different set of neutrons in another arm, and then after confusingly mixing up "ensemble", "the", "a", "its", claim that they separated "the neutron's" spin from it's position. Sad indeed.
minkwe

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### Re: Quantum Cheshire Cat

minkwe wrote:If anyone knows what "the neutron's population" means, they should help me understand it. It seems, what they did was measure the position of one set of neutrons in one arm, the spin of a similar but different set of neutrons in another arm, and then after confusingly mixing up "ensemble", "the", "a", "its", claim that they separated "the neutron's" spin from it's position. Sad indeed.

And they never show what effect the absorber has for the H detector. Yep, sad indeed.
FrediFizzx
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### Re: Quantum Cheshire Cat

FrediFizzx wrote:
minkwe wrote:If anyone knows what "the neutron's population" means, they should help me understand it. It seems, what they did was measure the position of one set of neutrons in one arm, the spin of a similar but different set of neutrons in another arm, and then after confusingly mixing up "ensemble", "the", "a", "its", claim that they separated "the neutron's" spin from it's position. Sad indeed.

And they never show what effect the absorber has for the H detector. Yep, sad indeed.

What is even sadder is that the paper has been published in Nature Communications simply because their conclusion adds to the prevalent quantum mysticism.

Had they concluded that they could not really "separate" the cat from its grin, the paper would not have been accepted by Nature Communications.

I remember the rejection letter I received from Nature for this paper. They rejected the paper without sending it for a review simply because, in their opinion, what I conclude in it is not what their readers wanted to read. And Nature is by no means the only prominent "science" journal with such a blatantly anti-science policy.
Joy Christian
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### Re: Quantum Cheshire Cat

Joy Christian wrote on Thu Aug 14, 2014 1:02 am:
Contrary to the indoctrination we are subjected to in our quantum mechanical textbooks, "spin" is not a "property" of a particle, but a reflection of its relationship with the rest of the universe (see Ref.[3] of this paper). Thus a fermion, for example, is an "anchored" particle (anchored to the rest of the universe), and a boson is a "free" particle (unanchored to the rest of the universe).

Hi Joy, I hope you can tell me if I am going wrong. I thought that the spin of an electron was a chiral property of the electron indicating that LH and RH electrons had different structures. The helicity can be different from the chirality. The -cosθ value indicates that the measured spin is not always equal to the chiral spin, else the value would always be -1. So, yes, I can see that the measured spin of the electron is not a property of the electron alone. But that does not mean that the chiral spin does not exist as a property of the electron alone, does it? I cannot see how a chiral spin can be anything but a spin of the electron alone.

One can put a hypothetical, infinitesimal R3 box around an electron and in that box the chiral spin would be evident, hypothetically.

One can put a hypothetical flat infinitesimal R3 box around the electron at various points in its flight so that all the R3 boxes record the same chiral spin, each relative to its own box. All the boxes are aligned alike in the wider R3 space, but in the S3 space, the alignement would be different. So, under S3, the electron spin is actually changing during flight to an observer outside all the infinitesimal boxes. That would fit in with the electron not having a fixed measurable spin property. I think, though, that if an electron in an infinitesimal R3 box has a chirality of either + or -, then that is a property of the electron alone. It is just that an observer not in that infinitesimal boxhas a hard time knowing its chiral spin if the spin is variable in S3. So in R3 the electron chiral spin is constant (plus the mystical random choice on detection) but in S3 the spin is changing according to formula with no need for any mysticism on detection. Yet I still like to think of the electron having its own chirality, or call it a self-observed constant spin state determined by its structure.

I am not sure about the relevance here of anchoring as both electron and photon have spin, but one is anchored and the other isn't.
Ben6993

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### Re: Quantum Cheshire Cat

Ben6993 wrote:The -cosθ value indicates that the measured spin is not always equal to the chiral spin, else the value would always be -1.

Hi Ben,
Just to clarify some issues. What do you mean by "measured spin"? I think sometimes we are misled by oversimplification of what is possible in experiments. Try to imagine how you would go about measuring the spin, and then let me know if the result you get out of your measurement is still what you called "spin" to begin with.
minkwe

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### Re: Quantum Cheshire Cat

Hi Ben,

I think Michel has raised a very good point and you need to address it:

minkwe wrote:What do you mean by "measured spin"? I think sometimes we are misled by oversimplification of what is possible in experiments. Try to imagine how you would go about measuring the spin, and then let me know if the result you get out of your measurement is still what you called "spin" to begin with.

Putting this point aside for now, let us indulge in a purely hypothetical scenario you have envisaged. In what follows I am picturing the spin as ordinary rotation:

Ben6993 wrote:One can put a hypothetical, infinitesimal R3 box around an electron and in that box the chiral spin would be evident, hypothetically.

One can put a hypothetical flat infinitesimal R3 box around the electron at various points in its flight so that all the R3 boxes record the same chiral spin, each relative to its own box. All the boxes are aligned alike in the wider R3 space, but in the S3 space, the alignement would be different. So, under S3, the electron spin is actually changing during flight to an observer outside all the infinitesimal boxes. That would fit in with the electron not having a fixed measurable spin property. I think, though, that if an electron in an infinitesimal R3 box has a chirality of either + or -, then that is a property of the electron alone. It is just that an observer not in that infinitesimal boxhas a hard time knowing its chiral spin if the spin is variable in S3. So in R3 the electron chiral spin is constant (plus the mystical random choice on detection) but in S3 the spin is changing according to formula with no need for any mysticism on detection.

So far so good, provided we understand that the "rotation" of the "electron" is meaningful only with respect to the R^3 box. Thus your following statement is not true:

Ben6993 wrote:Yet I still like to think of the electron having its own chirality, or call it a self-observed constant spin state determined by its structure.

How can you say anything about the rotation of the electron without any reference to the R^3 box you have put around it? You cannot. Therefore you should not think of an electron as having its own chirality. I think your picture of electron is corrupted by too much exposure to the quantum mechanical picture of the electron spin.

Ben6993 wrote:I am not sure about the relevance here of anchoring as both electron and photon have spin, but one is anchored and the other isn't.

The relevance of anchoring has to do with the periodicity (or value) of the spin---whether it comes back to the same value, + or - , after 2pi rotation or 4pi rotation.
Joy Christian
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