## Quantum Cheshire Cat

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### Re: Quantum Cheshire Cat

Ben6993 wrote:You know that I do not disagree with your model, and was not querying it. I was just trying to see where my preon model matched GA. But while you mention it, the GA calculation within a single run, and therefore a single say εijk, makes one pair of observables A and B for one pair of particles. The next step is the overall calculation across pairs of particles*. Does this next step need to be done using GA or R3? I assume that you want it calculated using GA. The trouble is that once you have observables A and B written down in a notebook, do you have enough information to process them using GA? I thought that GA information was lost as soon as you have an observable, as you have lost track of which of the two possible laps of the Moibus circuit the particle was on when it was measured/or/had its interaction? Isn't the same true for the macro laboratory experiment? The macro experiment won't need the first stage GA calculations but will it need the second stage GA calculation ... and without enough information to do that GA calculation?

Hi Ben,

The beauty of GA is that scalars, vectors, bivectors, and trivectors are all part of the same algebra. For the EPRB setup (or the 3-sphere) we only need scalars and bivectors to do the calculation. We can of course write down bivectors in terms of vectors and trivectors using the duality relation, but that is not essential. More important is the fact that---since scalars are a part of GA---we can define the basis of the embedding space R^4 of S^3 by graded basis, composed of both scalars and bivectors. The scalar results, +1 and -1, then come out as limit points of a quaternion made up of a scalar and a bivector. Thus the entire calculation---both step one and step two---can be consistently done within GA. In other words, what is written down in a notebook, i.e. the results +1 and -1, is as much a part of GA as the spin variables I.a and I.b. This is quite clear already in my one-page paper, and it is clarified further in this paper. See, especially, eqs. (9.21) and (9.75). I hope this helps.

Best,
Joy

### Re: Quantum Cheshire Cat

Hi Joy,

You know that I do not disagree with your model, and was not querying it. I was just trying to see where my preon model matched GA. But while you mention it, the GA calculation within a single run, and therefore a single say εijk, makes one pair of observables A and B for one pair of particles. The next step is the overall calculation across pairs of particles*. Does this next step need to be done using GA or R3? I assume that you want it calculated using GA. The trouble is that once you have observables A and B written down in a notebook, do you have enough information to process them using GA? I thought that GA information was lost as soon as you have an observable, as you have lost track of which of the two possible laps of the Moibus circuit the particle was on when it was measured/or/had its interaction? Isn't the same true for the macro laboratory experiment? The macro experiment won't need the first stage GA calculations but will it need the second stage GA calculation ... and without enough information to do that GA calculation?

As I said, I was not querying your model but was trying to see where the observer 'stands' during a GA calculation. I am still working on that. On a large-scale, one would not know which lap of the universe a particluar particle was inhabiting, it could be particle or antiparticle (wrt spin at least) depending on which lap of the universe it was on. And a human observer's viewpoint would be frozen because he could not make a round trip of the universe to see it from a different lap (in which all his particles' spins would have flipped over).

But on a small scale for compactified dimensions, with a detector electron acting as the observer of the experimentally generated electron, the detector electron could be looking from either lap of the compactified spin dimension(s). And it would not take the electron long to change lap. It would however need an interaction. I suppose all (many?) of the detector electron (fields) are lined up in harmony wrt spin in the magnetic field, though we never know which lap they are on. Presumably, this is what the εijk is doing, i.e. setting the handedness of the notional observer of the GA calculations.

* Ideally you would do all the calculations in GA and only come out of GA to display the final -cos answer.

Best wishes

### Re: Quantum Cheshire Cat

Ben6993 wrote:Switching from describing a chiral particle in a (flat and infinitesimal) R3 box to describing a chiral volume, or trivector. Presumably a trivector cannot exist without its own enclosing volume. Infinitesimally, that would be a flat R3, [can you have an infinitesimal enclosure of a finite volume?] but on a bigger scale it would be another trivector. In GA the only handednesses of 3D volumes are εijk and εjik [= -εijk]. One can only use a flat R3 as an enclosing volume if it is infinitesimal. I assume that this corresponds to the dispute about your using both εijk and εjik in the same calculation in your model.

I don't really see how you can use anything but both handednesses when using GA applied to particles. IF GA bars you then GA needs to be amended. The universe is made up of both handednesses and there has to be some way of using both. The bar presumably relates to horizons making it impossible for communication between particles permanently beyond each others' horizon. Or, the particle, once formed, always stays in the same handedness of volume that encloses it, ie until it next interacts. The last few words are key to my puzzlement, how can two particles interact under GA if GA never allows the interaction on mathematical grounds?

Hi Ben,

The trivector in my model defines the orientation (or handedness) of the physical 3-space (or the 3-sphere) itself. Contrary to the claims made by some, I have never used both εijk and εjik in the same calculation in my model. εijk and εjik correspond to two entirely different experimental runs in my model. GA does not bar me to use two different orientations of the 3-sphere in two different runs of the EPR-Bohm experiment. Moreover, orientation or handedness of a vector space is a relative concept, as I have explained in this paper: http://arxiv.org/abs/1211.0784. The calculations in my model are thus perfectly consistent with the usual rules of GA.

### Re: Quantum Cheshire Cat

Hi Joy,

Thanks. Yes, I know and appreciate the Moibus toy example.

I have already shifted stance and agreed with you that the chiral handedness of a particle needs to be considered as part of its R3 box, but I would like to add that that box needs a time dimension. Again, I get a feeling of tautology or overkill by adding the time dimension, as one can't think of an R3 space without its time dimension. But I had that same feeling when adding the R3 box too, and I now agree it is essential.

One can put a left-handed electron in one R3 box, and one can use the same box for the RH positron if the time dimension is added to the R3.
One can make a different R3 box plus time to make one environment for the RH electron and the LH positron.
Can one next use the same box for all four particles? I think the answer from GA for the electron is that we can use the one box if we add an extra or fifth dimension. I can't see that in a commonsense way, but I don't disagree with it.

Switching from describing a chiral particle in a (flat and infinitesimal) R3 box to describing a chiral volume, or trivector. Presumably a trivector cannot exist without its own enclosing volume. Infinitesimally, that would be a flat R3, [can you have an infinitesimal enclosure of a finite volume?] but on a bigger scale it would be another trivector. In GA the only handednesses of 3D volumes are εijk and εjik [= -εijk]. One can only use a flat R3 as an enclosing volume if it is infinitesimal. I assume that this corresponds to the dispute about your using both εijk and εjik in the same calculation in your model.

I don't really see how you can use anything but both handednesses when using GA applied to particles. IF GA bars you then GA needs to be amended. The universe is made up of both handednesses and there has to be some way of using both. The bar presumably relates to horizons making it impossible for communication between particles permanently beyond each others' horizon. Or, the particle, once formed, always stays in the same handedness of volume that encloses it, ie until it next interacts. The last few words are key to my puzzlement, how can two particles interact under GA if GA never allows the interaction on mathematical grounds?

QM uses R3 in the laboratory (aka flatland). But using GA, flatland only exists infinitesimally. That may be OK for particle interactions because a particle is at a point in space when at an interaction, and a point can be enclosed by an infinitesimal R3.

In my preon model, I definitely agree with space being made of trivector volumes and not R3 volumes. Your previous post made me review my own perception of my model, though my model is unchanged. I believe in emergent space but despite that I have it in my model as a property. One of my preon properties is a value chosen from L, R, L' and R'. [' represents antimatter.] If one assumes a volume around the preon then the preon has a choice of one trivector handedness [L and L'] or the other trivector handedness [R and R'].
An electron is set in space and for me that is being set inside another particle [or, inside a field, which for me is just another particle when it is not at the instant of an interaction]. So a particle is set inside another particle and the latter also has to be one trivector handedness or the other, and not an R3 volume. I built preons with chirality for every property because to have a field you seem to need activity which I identify with chirality. All these spaces need to have other outer spaces, else they cannot be chiral [a chiral entity needs an enclosing space]. I am afraid this is turtle territory, all the way... [unless having a closed algebra exempts one from this] Anyway, I feel convinced that my preon model fits GA rather than R3.

### Re: Quantum Cheshire Cat

Hi Michel,

Sorry for the delay in replying but Joy's post has delayed me by setting me to think harder about my preon model...

Your comment about 'chicken or beef' is IMO related to the current most active post on sci.physics.research. The original poster there admits to knowing almost zero maths. I was party to the discussion on sci.physics about three years ago where the poster artful/aka/inertial persuaded me, by a few lines of logic, that changing from a quantum state 0 to a quantum state 1 had to occur instantly. The original poster referred to above did not accept that and is still arguing about it. In other words the state changes from 0 to 1 like this: 01 which in a longer time period could be like this: 00000000000000111111111111.

One can introduce virtual particles (assuming the 0s and 1s refer to particle states) into this pattern like this: 0000000000010010011001101011111111111111111
One can think of this as a particle testing the environment and changing state from 0 to 1. Then instantly reverting back as the new state was not viable. After more probing, eventually the environment is such that a more permanent change of state to 1 is possible.

These virtual particles seem to be identical to the real particles, ie a 0 is a 0 and a 1 is a 1. But that is because the whole particle, in this scenario, has no structure.

In my preon model, the particle does have structure and dissociates at an interaction so during the interaction there can be a not-quite-fully formed particle which has an off-shell mass ie the virtual particle. The virtual particle can instantly revert back to a state 0, then keeps trying and eventually move to a more stable state 1. But a string of 0000000100100110011011111111111111 does not do justice to the interactions of particle with structure.

In my model the spin 0 particle is a different particle than the spin 1 particle. Than is an added element which imposes quantum-ness on the interaction. In string theory, quantum-ness or compactification from continuous to binary is cause by speed c effects.

In my preon model, the structure of an electron is a triple helix where the three strands are the three colour branes. The ends of the helix may join together, and in that view, it does seem like a fibration, at least in a common sense view rather than mathematical.

### Re: Quantum Cheshire Cat

Hi Joy

Thank you again. It took me a while but I have to agree definitely with your version of the wording. However it does feel like something of a truism/tautology to say that the electron chirality needs a host R3 infinitesimal space. It reminds me that everything is relative to something.

Moreover, it is a lesson I had already drawn for myself in May 2013 concerning my preon model, and promptly forgot it or at least put it to the back of my mind. Quote from my website of May 2013:
Further, the model was designed using preons alone but, when trying to see the shapes of structures, it seemed that coloured branes were also required. It seems that the branes are the extra dimensions that come with the preons and one cannot have a preon or string without its habitat of higher dimensionality.

I wrote that because I had designed elementary particles using preons then found, when making a lego-like model of an electron, I had designed colour branes too without realising it earlier. In fact, 15 dimensions excluding five time dimensions. When I mentioned truism/tautology, I mean that I had concentrated on designing the preon chiralities and found that the dimensions had slipped in uninvited. You can't have one without the other. Still despite accusing the parenthetical "in an infinitesimal R3 space" of being a truism, in May 2013 I though it was very interesting bonus that the necessary dimension came along for a free ride.

Hi Michel: I will respond to you asap.

### Re: Quantum Cheshire Cat

Ben6993 wrote:I can imagine a demon travelling in the infinitesimal box with the electron. Though I prefer to use a guardian angel, and to personify the electron. The angel keeps telling the electron, yes you are still LH. Although the infinitesimal R3 boxes keep changing during the flight, the angel keeps reassuring the electron that it is still LH. In my view the electron is worried unnecessarily as its chiral LH-ness is in its structure, despite what any distant observers might imagine.

Yes, I almost like this picture. But I would rewrite it as follows:

Joy Christian wrote:I can imagine a demon travelling in the infinitesimal box with the electron. Though I prefer to use a guardian angel, and to personify the electron. The angel keeps telling the electron, yes you are still LH. Although the infinitesimal R3 boxes keep changing during the flight, the angel keeps reassuring the electron that it is still LH, with respect to its infinitesimal R3 box. In my view the electron is worried unnecessarily as its chiral LH-ness is fixed with respect to its R3 box, despite what any distant observers might end up inferring.

So, once again, the chiral handedness of an electron is meaningful only with respect to its local R3 box, since globally, to an observer in S3, it may not be the same.

An instructive analogy here (and I am sure you know this) is the toy example of the Mobius world I have described in the first appendix of this paper.

### Re: Quantum Cheshire Cat

Ben6993 wrote:Michel:
As you will have noted, I admitted in my wording that I was hypothesising and referring to a self-measured electron spin. I know that these do not correspond to lab measurements. To me, a measurement is the recording of an event, and then that event can be used to infer some change in state. For example an electron gives off a photon. That photon is somehow recorded (ie the event) and an inference is made, such as an electron has emitted that photon. It adds detail to the inference if the photon is given off in controlled conditions such as in a controlled magnetic field. And that you have directed a beam of electrons at that magnetic field. For example it adds to the inference if the electron can be recorded as an up or a down depending on where it lands on a photographic plate or CCD or whatever. So I concede that the only known is the event (a photon is given off) and the rest is inference. And I also concede that none of that physical measurement can occur within an infinitesimal R3 box travelling with the electron.

Hi Ben,
I hear you . But that is not what I was after. I'm thinking about how the particle you described responds to the magnetic field. The process of deciding which direction to turn is probably a lot more complicated that simply picking "chicken" or "beef" based on what an angel tells you (I mean LH or RH). First the particle has to sense the presence of the field, and this will probably not be binary but will be a non-scalar periodic function of the relative orientation between the spin axis direction and the direction of the field. Then the particle has to respond to the field, and again this response will be another continuous function of the previous "sense" function (reminds me of fibration, though it may have no relation to it ). In my view the UP and DOWN results are cumulative effects of exposing a particle to a magnetic field for an extended time period. I don't know if this experiment has been done but I would predict that the spread of the spots in the UP or DOWN clusters will be dependent on the duration of the magnetic pulse.

The short of it is that

### Re: Quantum Cheshire Cat

Hi Joy and Michel. Thank you very much for your replies.

Michel:
As you will have noted, I admitted in my wording that I was hypothesising and referring to a self-measured electron spin. I know that these do not correspond to lab measurements. To me, a measurement is the recording of an event, and then that event can be used to infer some change in state. For example an electron gives off a photon. That photon is somehow recorded (ie the event) and an inference is made, such as an electron has emitted that photon. It adds detail to the inference if the photon is given off in controlled conditions such as in a controlled magnetic field. And that you have directed a beam of electrons at that magnetic field. For example it adds to the inference if the electron can be recorded as an up or a down depending on where it lands on a photographic plate or CCD or whatever. So I concede that the only known is the event (a photon is given off) and the rest is inference. And I also concede that none of that physical measurement can occur within an infinitesimal R3 box travelling with the electron.

Joy:

Joy wrote:
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.

"So far so good," .... that line is fine and encouraging!

I will have another try. This time with reference to your hidden variables, say -1 for the electron and +1 for its paired partner. Before I go further I should say that I have always thought of the LH or RH chirality belonging to the electron as its hidden variable. I think that Fred asked you if you had ideas about what the hdden variables were and you replied, if my memory is correct, that you were working on it.

If an electron has a hidden variable -1 rather than a +1, that is compatible with a chirality, say Left Handed rather than Right Handed. If the value stays constant during time of flight then that variable value is conserved during the time of flight, and stays a constant in your geometric algebra calculations. Ie if the electron is LH it stays LH and that is a property of that electron irrespective of its S3 environment.

In my terms, I envisage the LH electron as a different structure to the RH electron, so it has to be conserved during time of flight. It can only change structure at an interaction. I can imagine a demon travelling in the infinitesimal box with the electron. Though I prefer to use a guardian angel, and to personify the electron. The angel keeps telling the electron, yes you are still LH. Although the infinitesimal R3 boxes keep changing during the flight, the angel keeps reassuring the electron that it is still LH. In my view the electron is worried unnecessarily as its chiral LH-ness is in its structure, despite what any distant observers might imagine.

Now what one calls the hidden variable other than a hidden variable is not well founded. You are still working on it.

A complication is that of LH and RH helicity, which is not what I mean here. That does depend on the observer as well as the particle.

An additional point is that I liked your reply in a nearby thread about having optimism wrt mathematics. I agree entirely. Maths is essential for physics, however complicated the maths needs to be, and what you and Jay are doing is terrific. And that is irrespective of whether you are correct or incorrect.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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

### 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.

### 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.

### 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

### 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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