Quantum Cheshire Cat

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

Re: Quantum Cheshire Cat

Postby Ben6993 » Fri Sep 05, 2014 10:32 am

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!
However, I do not follow your logic for the other lines.

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.
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Re: Quantum Cheshire Cat

Postby minkwe » Fri Sep 05, 2014 5:16 pm

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 :D . 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
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Re: Quantum Cheshire Cat

Postby Joy Christian » Sat Sep 06, 2014 2:25 am

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.
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Re: Quantum Cheshire Cat

Postby Ben6993 » Sat Sep 06, 2014 11:13 am

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.
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Re: Quantum Cheshire Cat

Postby Ben6993 » Wed Sep 10, 2014 3:04 am

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.
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Re: Quantum Cheshire Cat

Postby Ben6993 » Fri Sep 12, 2014 8:14 am

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.
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Re: Quantum Cheshire Cat

Postby Joy Christian » Sat Sep 13, 2014 4:39 am

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.
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Re: Quantum Cheshire Cat

Postby Ben6993 » Tue Sep 16, 2014 5:51 am

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
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Re: Quantum Cheshire Cat

Postby Joy Christian » Tue Sep 16, 2014 10:52 am

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
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