Classical Spheres, Division Algebras, and the Illusion of Quantum Non-locality:

Joy Christian

You do have quite a knack of reading everything I write in a completely wrong way.

Bell made a stupid mistake in his argument. Get over it!

Thomas Ray

Quaternions and octonions describe how to calculate real measurement values; they do not describe the shape of space, which is what determines the measurement outcomes in Joy's framework.

As Richard correctly notes in the sci.physics.foundations forum, "Two copies of quaternions give you bi-quaternions, not octonions. The former is a torus but the latter is a sphere. Hence the difference in the multiplication tables."

The torus is mutltiply connected. The sphere is simply connected. One can get quantum correlations assuming a toroidal space; however, one must also bring essential assumptions of randomness and nonlocality -- along with collapse of the wave function for the observed quantum mechanical unitarity. In the simply connected space, just as Joy has exhaustively explained, the "4 sphere's worth of 3 spheres" or complete S^7 space which has the Lebesgue measure limit S^2 X S^2 on the S^3 manifold, is the natural physical space for quantum correlations, with minimal assumptions. S^7 is the space in which octonions live, not the space that octonions created. The physical generalization of the simply connected Euclidean S^n space is only possible, because the division algebras (admitting parallelizability) are limited to S^1, S^3, S^7, i.e., the even numbered dimensions > 0 and < 8. We live, therefore, in 7 1 dimensions of spacetime with manifestly discrete real measures in 3 1 dimensions; all of this space is demonstrably local and independent of scale, because topological torsion is nonvanishing at every scale.

In my opinion, until one understands the completeness of Joy's measurement domain, it is distracting to get down in the weeds over mathematical models and calculating techniques. I think that's been the problem all along.

Tom

Richard Gill

Sorry! 0.002, not 0.02.

Simulation accuracy: in the simulation you have published with Chantal Roth,

http://rpubs.com/chenopodium/joychristian

the sample size is 1 million so the accuracy is about 1 / sqrt (10^6) = 0.001.

So one may indeed ask, is a deviation equal to approx two times a standard error meaningful or not?

To determine that, we should just take a bigger sample!

I did the same simulation at sample size 10 million, see

http://rpubs.com/gill1109/ChaoticUnsharpBall

The accuracy is about three times (square root of 10) larger.

The discrepancy persists.

I've also run the same code with different random seeds several times. The discrepancy persists.

At sample size 100 million, the accuracy is 0.0001. I can run this on my computer too, I just have to be patient. Discrepancy persists.

For yet larger sample sizes I would have to adapt the program a bit, because at present everything - all 100 million samples - are all in the computer's memory at the same time. 1000 million real numbers is a Gigabyte. I have 16Gb memory.

Richard Gill

Joy wrote "You do have quite a knack of reading everything I write in a completely wrong way. Bell made a stupid mistake in his argument".

Since John Bell is dead one can accuse him of making a *stupid* mistake. As you know, I still think that Joy Christian made a mistake, and that John Bell didn't.

So yes, anyone who reads what I write, should bear in mind that I am pretty sure that it was not Bell who made the mistake. This difference of opinion between Joy and myself is obviously a motivation for my activity here. But I sincerely hope that my mathematical and computational contributions to the analysis and implementation of various simulation models are "value free".

Richard Gill

PS as Rutherford famously said, anyone who needs statistics did the wrong experiment. A bigger experiment and/or an experiment with better control of various errors can make statistical analysis of the outcome pretty irrelevant ... provided one knows for sure that this is the case. And for that purpose one might still need the advice of a statistician.

Joy Christian

John S. Bell was, and is, one of my heroes. But he did make at least one stupid and fatal mistake in his argument, if not several. This is not a matter of opinion. Anyone can see his stupid mistake by simply reading about it on my blog. The mistake is right there in the very first equation of his famous paper, as I explain on this page of my blog.

Robert McEachern

"Rutherford famously said, anyone who needs statistics did the wrong experiment."

One does not need statistics to determine that a pair of entangled coins does not behave like a pair of Bertlemann's socks, gloves, or anything else.

Regardless or whether or not either Bell or Christian did or did not make a math error, the one and only premise that links the math to the physics, is obviously false. There is nothing non-classical about the correlation statistics of so-called qu-bits. The experiments comparing quantum and classical entangled pairs, have simply been performed with the wrong type of classical entities.

Rob McEachern

pjackson

Richard,

(and all). As promised, the DFM Classroom Experiment Protocol, condensed enough to post here. (It's also on 'Linked in') extended from my 2013 essay. The full analysis is in the paper not yet published. The observer does affect the observation, more than QM and Bell assumed and locally, so SR and QM converge.

Take four identical packs of 19 blank coloured cards. Each card a different hue from a spectral distribution between Red (R) and Yellow (Y). The 9th and 10th cards are then almost indistinguishably orange.

A number 0-18 to represent "setting angles" >Y and Y->>R) into bins of numbers nearest to; 0,.... 6,.. 9,.. 12,....18. but uncertainties emerge; Is 0 a number? And where do 3 and 15 belong?]

Two rooms (A and B) of students, some distance apart are each given one R0 and one Y0 pack. A random 'coin toss' by a third party, (which may be in advance) tells each tutor from which pack to select a single card each 'round'. We will designate pack R0 as 'heads', and pack Y0; 'tails'. Each card choice then gives a unique colour and a number. The card number ('angle') may be chosen or picked blind from a shuffled pack.

The students have two 'tick boxes', R.... for Red, and Y.... for Yellow. Beside them is another box to enter the 'angle' (0 - 18) of that card. [The 'simple' version may have further 'bin' tick boxes for 'angles'; 0,... 6,... 9,... 12,... 18,...]. The number of rounds is unlimited.

Each student then decides if the card colour shown at each round is MORE RED or MORE YELLOW. He then ticks the appropriate box (R or Y) then also records the angle [or bin number] of the card. Each student finds that the difficulty of R/Y colour choice increases the closer the card colour is to orange (9/10 = 90 degrees). As colour changes towards R or Y the choice quickly becomes easier. Closest to red or yellow has highest probability of a correct choice. For each class the results R/Y should then give a non-linear probability distribution with changing setting at each detector.

It worked well for me. Do give it a test run. When the tosser correlates the results he assumes he's doing H/T but he really using R/Y. But the proof also derives higher order cosine distributions to the cosine distribution, so '50:50 coin toss' precision would show it to be false! The simple (dipole) particle case is also set out, and the '45 degree filter inserted between 2 orthogonal ones' anomaly consequentially resolved.

Do ask any questions.

Best wishes, and Thanks.

Peter

Richard Gill

I cannot make head or tails of this, sorry.

Akinbo Ojo

Peter,

You need to simplify this as Richard says, although I am not inclined towards the conversation here since it is not foundational in my opinion as I have pointed out here in the past.

Akinbo

[deleted]

Richard, Akinbo,

If you run it, it works. The 'weird' QM 45^o filter effect resolves too; When inserted between 2, 90^o, filters the 'blocked' light is 'released'! It's all in the helical 3D path.

So first bear in mind that polarising filters don't just 'block some of the light', they CHANGE it's state! (equiv. to; 'observer as part of the system'). So in this model, at 90^o setting a torus is 'flipped', whereon it's 'detected' with the OPPOSITE spin!

A simplified test; Bob and Alice have just 2 sets of 5 card each, each card from the part of the spectrum from Red through Orange to Yellow, but one set numbered 1-5 on the back, from Red=1 we call 'HEADS', the other from Yellow=1 we call 'TAILS' (so Orange is always No 3). Visualise the 5 different cards in each set.

Bob always uses the opposite SET to Alice for each card selection, the tosser says Heads or Tails. Each card is then selected freely or at random; No. 1-5 ('setting').

Students are shown one card at a time and must decide if each is MORE Red, or MORE yellow. They MUST tick one box each time, then put the ('setting angle') number 1-5 against the tick. Repeat interminably. That is all!

Clearly ~all Red and Yellow cards (1 & 5) will be properly identified, and the ORANGE card may have a near 50% distribution (Orange's number; 3, represents 90^o, half way from 0 to 180^o). Cards 2 and 3 colour identification may be significantly more correct than wrong.

Statistical correlation of R/Y/Number data by the tosser finds;

1. A high non-linear probability distribution ('violation') of answers from 1-5 (representing 0-180^o angle settings) with 50:50 at mid point.

2. Zero correlation with Bob on 'heads' and either 1 or 5 (0 or 180^o) (R/Y, Y/R).

3. Full correlation if Alice is 'heads' and either 1 or 5. (R/R, Y/Y).

(And also reciprocally) This is because the initial 'head/tails' state does NOT translate to the correlated R/Y state, which the silly coin tosser assumed it did. This is because 'discrete field' (DFM) dynamics and toroid particle model says that the spin direction 'detected' is RELATIVE TO DETECTOR ANGLE and reverses 90^0. (The phase modulation mechanism and effects are not entirely unknown in parts of the optical sciences).

If the new DFM dynamics were dead simple to first assimilate they would have been found long before now. It takes a little effort. Many glimpsed them in my essay but it takes much learning and rehearsal to hold them in mind.

Best of luck.

Peter

pjackson

Akinbo,

I think converging SR and QM to unity is quite foundational. Not quite as each stands of course, but taking both from the 1927 Solvay state further up each's own apparently divergent road leads to the convergence.

In a discrete field model (DFM) nutshell; the detector as part of the system (QM) influences the findings, which creates a universal set of LOCALLY REAL inertial systems (SR), where time is absolute (QM) but the SR postulates re-emerge. All the rubbish that's surrounded both since inception falls away.

What I DON'T blame you for doing is avoiding these parts as it 'does your head in'. Now that's fair enough! But if you follow my experiment you'll find the simple classical alternative to weird nonsense. (and no 'chaotic spinning spheres'!)

Best wishes

Peter

Richard Gill

I don't even see anything like quantum correlations yet. And it is still not clear what is the bare bones experiment. Why do we need a classroom of students? Isn't one student in each room enough?

When I understand the experiment I will think about it. But I still don't know what it is.

pjackson

Richard,

Crossed with the post below. The QM correlations are twofold. I'll walk you through them as they're hard to first spot;

1) I think you saw the uncertainty distribution and it's 'non-linearity' between 90 and 0 (180) degrees, where a modest change near 0 has ~0 effect, but the same change near 90 (orange) has a bigger effect. The Bell inequality is clearly violated. But do tell me if you don't see (it like) that.

2) We now also need to show that a change of Alice's setting will appear to instantly effect Bob's setting. So if Alice 0^o correlates with Bob 180^o, (RED/RED) then if she changes to 180^o she should then ANTI-correlate. So (see the first line in the simplified '3 card pack' list below; H1 at T3 = 100%);

Alice (H) 0^o finds (1) RED, and Bob (T) 180^o finds (3) RED = 100% correlation.

Now Alice switches to 180^o so if she now still finds RED (1), Bob should classically then find YELLOW (3). ok? But the bizarre 'Quantum effect' is that he too now finds RED! So let's see what our experiment produces;

Alice (T) 180^o now finds (3) RED, and Bob (H) also still finds (3) RED! (bottom line of list below T3 at H3 = 100%) so Alice must have sent an FTL signal to change his setting!!

That quantum prediction permeates the data. It simply and classically emerges from the Chirality of the packs and random change of packs for each card tuple.

Peter

Richard Gill

I still don't have a brief precise description of the experiment in front of me. So I still can't comment on what it might or might not tell us. I asked a few times, but got no answer: is there one student in each classroom or a whole classfull?

But anyway, this is not a proper Bell type experiment since the setting (the number on the card) is not independently determined outside of the classrooms, but is part of the measurement outcome.

Obviously the whole set-up is classical.

So my present opinion is that it is not relevant. And if we made it relevant, so that it was a local-realistic and classical Bell-type experiment, and such that it did not violate the standard experimental requirements, it obviously would not violate any bounds set by classicality, so it would not be interesting and would exhibit the features you are hoping for.

Richard Gill

Sorry, responses in different threads crossed. OK I get the set-up. I don't find see that it has any interest.

[deleted]

Just been checking some classic references from

http://freespace.virgin.net/ch.thompson1/Papers/The%20Record/TheRecord.htm

Apparently Caroline Thompson didn't realise it herself, but her "unsharp" chaotic rotating ball had at least two precursors:

Pearle, P, "Hidden-Variable Example Based upon Data Rejection", Phys. Rev. D 2, 1418-25 (1970).

T. W. Marshall, E. Santos and F. Selleri: "Local Realism has not been Refuted by Atomic-Cascade Experiments", Phys. Lett. A 98, 5-9 (1983).

Using the isomorphism between the generalized 3-D Minkwe simulation model (generalized to allow an arbitrary probability distribution of S = sin(f(theta_0)) and the generalized chaotic ball models (the radius R of the circular caps becomes random, R = arc cos(S)), one can use Pearle (1970) to deduce the *unique* probability distribution of S = sin(f(theta_0)) = cos(R) which will reproduce *exactly* the cosine. So here is mathematical proof that all choices dreamt up to date are actually off target, since they are clearly not quite identical to Pearle's solution.

Marshall et al. essentially give us a numerical procedure to determine the probability distribution of f(theta_0) to any desired degree of accuracy, using Fourier theory, but apparently they did not realise that Pearle had got an exact analytical solution. For many years his paper was considered too difficult for anyone to read. So his result got re-discovered time and time again.

pjackson

Dammit, that was me, a program flaw masquerading as quantum weirdness!

For those preferring numbers to words; The simple full sample space 'circuit' of possible results; All ladies (A) first and Bob 2nd. 1=0 degree detector setting, 3=180 degree setting.

H1 at T3 = 100%

H3 at T1 = 100%

T1 at H3 = 0%

T3 at H1 = 0%

H1 at T3 = 0%

H3 at T3 = 0%

T1 at H1 = 100%

T3 at H3 = 100%

The related non-linearity is then also visible at intermediate settings. Is it making heads & tails now Richard?

Best wishes

Peter

Richard Gill

Please: no numbers, no words. Just a plain description of the experiment. Who does what, when. Let's get that straight first. Afterwards we can talk about what comes before (some kind of connection to physics) and what comes after (deduction of the expected results of the experiment, and conclusions for physics).

My best friend once said to me "cut the crap, Richard".

Describe the experiment. Not its motivation. Not the results. Not the conclusions.

pjackson

Richard,

Great. That's how I like it.

1. The tosser sends random H/T coin results to lecture hall A, (+inverse to hall B).

2. The tutors there use the H or T set of coloured cards (numbered inversely 0-180)

3. The tutor shows any one card to the students who each decide; RED, or YELLOW.

4. The students note the NUMBER of that card (0-180) next to the R/Y decision.

5. Repeat ad nauseum. Toss, Send pack info, Pick card, Decide R/Y, Note, with No.

6. The data; A/B, and R/Y for each number (0-180) are collected and returned to the tosser afterwards for statistical correlation.

Owzat? Peter

Richard Gill

Getting better.

Isn't it enough to have just one student in each of the two lecture rooms? So one coin toss goes to Alice, the opposite goes to Bob. Depending on heads/tails, one card is selected from one of the two packs.

The number is written down. The student says whether the card is red or yellow.

And if I understand correctly, all four packs have the same 180 different colours, in a spectrum from red to yellow with orange in the middle. Both packs have the same numberings 1 - 180, but the "H" packs have the opposite numbering to the "T" packs.

Repeat ad nauseam and look at the statistics of the collected quadruples: number A, colour A, number B, colour B.

As I understand it, with the middle two cards (cards 90, 91) the student is more or less just guessing 50-50 (they're both basically orange) but on either side the probability of guessing "correct" increases to 1.

pjackson

Richard,

Good thinking, one student is fine but allows bias. Safest with a few, averaged (90th percentile?). I've allowed that one student may be colour blind (and one'll almost certainly be a bit 'slow'!)

Yes, you've got the rest. We also really only need a few card colours for 'proof of concept' representing a few key setting angles.

The cards should really also 'fade' on passing through orange to better represent the real particle hypothesis which the experiment models. No chaotic spheres are needed, just simple dipoles or even a monopole, and a process which well fits optical science.

Let me know of any QM predictions you can't see how it derives. Once you're happy with the basics I'll pass you the rest.

Richard Gill

One randomly student in the class does not create bias. A proper Bell type experiment has repeatedly one pair of settings in each wing of the experiment and one binary outcome in each wing of the experiment.

pjackson

Richard,

I agree no exact copy of a 'Bell type' experiment could find differently. (I'm replying to the string above, but let's now stay on this one!).

However the proposed set up DOES circumvent Bells actual Theorem as it identifies the false assumption made by Bell (and thus QM) of 'no structure' except 0,1.

The discovery of such a 'starting assumption' has been identified as a key to overcoming the theorem, and as I recall you've said yourself that it only needs a classical experiment to produce the same QM predictions to crack the nut.

If something isn't what's 'expected' then it normally isn't first recognised. I suggest that's what's happened here. But what were we 'expecting'!?

The real point for me is that the experiment derives from a real particle hypothesis that's entirely consistent with the latest quantum optics findings, (and still consistent with Maxwell's first conception of an orbiting entity also itself spinning). In QO we now know this also produces a non circular orbiting 'wave' path. The interaction and Fourier superposition with detector electrons can then produce the exact 'switch' set-up from the phase shift that the classroom experiment models.

The Bell assumption about spin and detection were then over simplistic. If Bohr were around now he's certainly agree we could "say" far more now than he could 90 years ago!

And can any other experiment predict the 'rotational invariance' found by Aspect and discarded? I suggest you'll find not. It just needs another good single photon experiment to falsify. (Weigh et al's 15,000 counts/sec and 20ns interval resolution didn't have the resolution as their focus was elsewhere). It'd probably need some interest from a recognised authority to encourage an experiment so I'm very disappointed by your lack of interest. Simon at Kalifa hasn't yet even 'seen' that it produces the 'A1/B1' correlation.

Peter

Richard Gill

In your experiment, Peter, the "settings" (numbers between 0 and 180) are part of the measurement outcome. Not pre-set, independently, by experimenters. Hence it does not prove anything. We Bell-admirers can say that you are using the conspiracy loophole.

pjackson

Richard,

If a classical mechanism reproduces QM's predictions it none the less circumvents Bells theorem! The 'loopholes' are not 'irrelevant', they're exactly the opposite!

I too am a John Bell admirer. His maths was right but what the model shows, finally, is how correct he also was in his motivation and belief, as he expressed in 1981;

"...nobody knows just where the boundary between the classical and the quantum domain is situated. (...) More plausible to me is that we will find that there is no boundary."

I agree the 'settings' arise from the measurement, which IS quantum theory; the electron wave CHANGES on detection' and indeed the detector is part of the system'. John von Neumann's insistence on this (Quantum 'meter') effect for consistent QM is then ALSO now proved true in this model.

The reason the measurement helps produce the 'switch' result becomes clear by studying the latest most precise model of an electron, which 'turns' bodily with 'screen' field setting, changing the phase, so 'spin direction' of the signal passed through to the multiplier. Here is just the latest of many showing the complex fractal OAM structure that QM presently still 'denies';

Max Plack Inst, Precision Electron Model Nature Feb.2014.

Making QM entirely consistent by bringing it up to date then also allows it to converge with SR, because the interaction implements the 'Continuous Spontaneous Localisation' required to implement true a Local Reality of discrete local 'rest frame' fields.

I'd suggest it may again be time to; "cut the bullshit Richard!" and stop trying to run off with the goalposts you helped set so well yourself! Let me quote you;

"we are still waiting for a really conclusive experiment to be done, despite Aspect's (1982) splendid contribution and later refinements; however, since real physicists are no longer saying that it is a waste of time to perform that definitive experiment, we may conclude they think they can almost do it, and that it is now". Now re-read exactly what Bell wrote; "NO classical....etc!!" not just 'some but not others'!

A the view you proffered will then do is further suppress truth and understanding.

pjackson

Richard,

Mapping the 'real' and 'classroom' cases a small change overcomes your objection about the tossers influence.

In the 'particle' case we invoke the additional dynamic structure. In that case we can save money and use just ONE handed set of cards, held by the tosser and sent to each student (or group) subject to each toss.

Of course he may also hold an infinite number of packs of three (just Red/ Orange/ Yellow), or send the full 0-180 (180-0) signal electronically to a VDU.

I prefer the latter as a closer model to the optics findings, of effectively a simple 'wavefunction exchange'. Technically this can then be represented by; psi(x) and φ(y), then psi(x)φ(y) = -φ(y)psi(x) but related as a parity violation recognising the lack of mirror symmetry switching sign; psi(x) = -psi(-x). 3-momentum reversal does not then necessarily leave 'spin direction' unchanged. I prefer the wave interference description, which includes OAM as the 'spin' of the next gauge each time (and vice versa).

Frankly I think I'll mainly stick with just the conceptual model; 'Flipping the donut'. As space is 3D everything is relative including orientation, so what is 'up' to one man is 'down under' to another.

pjackson

Richard

I'll try posting that Max Planck Inst. electron link again, sorry;

Max Plack Inst, Precision Electron Model Nature Feb.2014.

Peter

pjackson

Richard,

Dammit, praps just google the below; It's worth it.

http://scitechdaily.com/high-precision-measurement-electron-precise-factor-13/

pjackson

Richard,

(Feb.28.pt2). "Bell's theorem shows that this selection *must* be measurement-setting dependent."

I agree, and not just the theorem itself. But you suggested above;

"In your experiment, Peter, the "settings" (numbers between 0 and 180) are part of the measurement outcome. Not pre-set, independently, by experimenters."

Not necessarily; The ideal set up (as Weihs) allows Alice to decide her setting BETWEEN the toss and the arrival. My protocol does so. Alice chooses a number instantly BEFORE arrival and only the corresponding card colour is shown.

The tosser can send the H or T pack each time (physically or electronically) to ensure no possible problem with the "no-conspiracy" condition. Each detector behaves consistently and symmetrically, (exactly as is anyway required for the Bell set up), but the outcome IS setting dependent.

I have a particle analogue not dependent on incomprehensible maths. We can have a Bohr 'sphere' if we want, but critically it's EM field is toroidal, as all are. We then invoke a torus spinning on it's axis.

A torus has a very unusual quality. This needs some fundamental 'outside all invisible boxes' non-homocentric thinking as the common assumption that spin can't be found as 'changed' when electron 3-momentum is flipped at 90^o is shown to be wrong;

Let me jet you out into deep space and ask you two questions;

1. Which way is 'up'?

2. Two donuts approach you face-on (within plastic spheres if you wish), each spinning on it's axis in opposite directions. Now thinking in 'absolute' terms, Are they identical entities, or different? (if different, then how?)

In the discrete field dynamic they are identical - but still observer frame dependent. i.e. Only their *direction of propagation* wrt a particular observer defines if each is spin 'up' or 'down'.

Richard Gill

Peter, the ideal experiment allows Alice and Bob to *set* their settings just how they like while the photons are in flight from source to measurement station. In particular, they are allowed to choose a setting by performing a coin toss. In your experiment the setting is co-determined by the coin toss and packs of cards, which all came from the source. There is no freedom to choose whichever setting they like.

pjackson

Richard,

Understood, but Alice HAS random OR free choice angle 'in flight', as has Bob.

As Weihs (referred above), Alice can select a setting BETWEEN the toss and the arrival. NOTHING STOPS all selections being entirely random! The no-conspiracy' rule specification used in the QM case applies exactly; Absolute consistency and symmetry from the detector.

What I model is toroidal not 'spherical' particles. Toroids are ubiquitous in EM and have a unique property (thus my question above) which is non-mirror symmetry. the 'handed' heads/tails card sets the exactly model that dynamic. Do consider the questions again.

Peter

A fundamentally different assumption is then revealed, a closer fit to optical science. Bell's inequalities are entirely conserved, but the full 'sample space' domain of reality is broadened.

In any case, the experiment is completely classical and reproduces the exact results found experimentally (and 'predicted' by QM), but now INCLUDING the 'anomalous' results found by Aspect!

Did you find the beautiful Planck institute electron model, which helps define and clarify the 'spin/OAM' relation?

Peter

Richard Gill

"NOTHING STOPS all selections being entirely random! ". No nothing stops that. But letting the selection be made inside the measurement apparatus makes the exercise totally devoid of any sense. There's no way we can do your experiment with the selection being made independently, whether by free will of Alice and Bob or by Alice and Bob tossing coins or using other pseudo random generators ... not linked in any way to the measurement process.

You have fallen into the conspiracy loophole.

pjackson

Richard,

In the Bell set up the selection and measurement is made precisely the same way. Who is to say what 'information' is contained within the particle state? You are assuming none, which we already know is wrong!

You didn't say if you saw the new Plank Institute electron morphology finding. That non-mirror symmetric toroidal OAM is the exact information contained in the particles which the opposing numbering system models. I'll post it again if you can't find it, but just Google the link above.

My hypothesis is that there was a far more fundamental false assumption about particles in early QM that John Bell inherited. His mathematics and inequalities are not in question, just shown to part of a greater understanding.

All present evidence about particles supports my case, and as you've clearly seen, the simple experiment perfectly reproduces the QM prediction (and does so however hard want to try removing and running off with the goalposts!!) All spookyness and FTL is kicked into touch along with our infinite stupidity.

The understanding that toroidal OAM is recursively interchangable with 'spin', and OAM direction entirely dependent on axial translation for 'orientation' (there is NO 'up' in space!) allows a 'duality' not recognised in the old assumption of what 'singlet states' really means.

There may well be 'entanglement', but it's in the topology of ALL particles, and it seems the only 'conspiracy' is in their identicality and 'duality'.

Peter

pjackson

Richard,

My 'IQbit' essay showed nature is 3D. Ternary data decodes it but binary data cannot. My classical DFM experiment employs a simple dipole (torus = twin helix in axial motion) and OAM, not spheres and binary 'spin', so has the 3rd dimension that non-mirror symmetry brings. Bell's result is conserved but it's domain is shown not to model all of nature, so is constrained.

The experiment classically reproduces the predictions of QM Locally. It can violate no Bell rules as it circumvents them all by building from new, deeper, rock foundations. Please show me where this is 'wrong';

There are 2 identical sets of 7 cards, each with a HEADS and TAILS side. One side has sequential spectrum colours; Green, Lime, Yellow, Sand, Buff, Orange, Red, the other side has the same sequence but in the reverse order.

The cards are also numbered, representing 'angle settings' Green (representing negative charge) = 0, Red (positive charge) = 180, with 30, 60, 90, 120, and 150 between. So we always have a HEAD and TAILS sides as follows;

HEADS starting; Green = .0...30.....60....90...120..150..180 = Red

TAILS starting; Red. = ...180.150..120...90....60....30.....0 = Green

90 is always then 'Sand'. Setting are selected at random 'in flight'. On arrival a colour is show to each corresponding to each setting, and for H or T. Alice and Bob have to decide if the colour is then 'MORE' Red or 'MORE' Green. (their friend's may join if if you'll let them, or a low res spectrometer may 'decide'). Each ticks a box; R..../ G.... and notes the setting alongside. The results give as simple a logical tautology as Bells own;

Identical settings, say 150/150 give perfect correlation = Orange/Orange. Opposite settings give perfect ANTI correlation, say 0/180 = Red/Green.

Intermediate relative settings give varying results which violate Bells Inequalities; i.e. 150/30 = 120 = Orange/Lime, = clearly no more than 25% correlation, and 60/90, = 30 = Yellow/Sand, = clearly no less that 75%!

All quantum predictions are produced, because there is NO BAR to two parts of a pair being found the same 'colour' ("spin") because the torus spin direct reverses when the setting crosses 90^o without the assumed 'angular momentum change' problem inherent in Bell's hidden starting assumptions. I identified in my essay that my results fit Aspects actual (discarded) data perfectly!

Joy's impenetrable maths may or may not be analogous (Joy suggested not but found my own model impenetrable) but I suspect they may reasonable well model the real physical process. For the purposes of falsifying the experiment however that's neither here nor there. If it needs new maths then it'll need help (Joy wasn't interested).

I hope you can 'step back' and give me a fresh overview of what the physical model achieves.

Best wishes

Peter

Richard Gill

Sorry Peter, it is impenetrable. Your experiment with the cards shows that you are completely missing the point of the whole Bell business, so I see no point in trying to penetrate.

Joy's mathematics on the other hand is crystal clear. Only, one has to read it as poetry, not mathematics. He knows what it is meant to mean, and he explains that, poetically, in the accompanying text. Unfortunately text and formulas are disconsonant. From time to time the math goes off track, no longer matches the ideas.

For a physicist, mathematics is merely a language used to describe reality. So if the maths and the physics don't match, it is the mathematics which is at fault. Stupid mathematicians are hampered by the rigidity of mathematical reality.

Fred Diether

That is total BS. Joy's math always relates exactly to the physics. If you don't understand it, ask a question about what you don't understand.

Richard Gill

Thanks Fred.

Well every time I had a question about something I didn't understand, I asked it and got an answer I didn't understand. So maybe this is all just completely above the head of a simple mathematical statistician like me? On the other hand, I don't know any mathematician or theoretical physicist who did understand it, either. But maybe I just don't know any good ones!

None of Joy's papers got published yet, and as far as I know, none of his results got cited either.

Of course that could just be an establishment conspiracy!

Joy Christian

OK, now we are well and truly done.

I have revised my simulation again: http://rpubs.com/chenopodium/joychristian.

The initial state of the system (e_o, theta_o) is derived in this one-page document, and the choice of the initial function f(theta_o) is

f(theta_o) = (1/2) sin^2(theta_o).

What is different in this version is the range of theta_o.

This time any remaining wrinkles in the correlation are indeed well within the accuracy of the simulation.

Joy Christian

To avoid any misconception, let me stress that the above simulation has nothing whatsoever to do with the detection loophole (or any other loophole for that matter).

As specified in my analytical model, the initial state of the physical system is a pair of hidden variables, (e, t), where e is a vector and t is a scalar. In other words, the complete state of the system is the pair (e, t), not just e, and every initial state (e, t) uniquely leads to a detection. Thus there is one-to-one correspondence between the states (e, t) and the outcomes (A, B). Clearly, one cannot detect that which is not there in the first place. If there are no clouds in the sky, then there can be no rain. It is as simple as that. To claim otherwise is to make a false claim and mislead the physics community.

It is also important to remember that the numerical simulations by themselves are not the actual model. They only provide confirmation of the exact analytical model, which has been summarized in eight elementary equations in the two pages liked above. After all, Bell's analytical claim was hardly about numerical simulations.

Richard Gill

The above simulation is mathematical isomorphic to a simulation of Caroline Thompson's chaotic rotating ball model, with random radius R of the circular caps in the Thompson model. The isomorphism is through identifying cos(R) from the Thompson model with sin(1/2 sin^2 theta_0) in the Christian-Roth simulation model. The latter was derived by further tweaks, found through numerical experimentation by Chantal Roth, to a simulation model of my own; and that was inspired by a simulation model of Michel Fodje.

These simulation models were previously studied by Marshall et al (1983) and Pearle (1970). In fact the best result is the oldest: Pearle showed that there is exactly one probability distribution for theta_0 (equivalently, for S, equivalently, for R) which reproduces exactly the cosine correlation. It is different from the current solution of Christian-Roth (and also different from my current best solution, which is four times better than the Christian-Roth solution).

So in a sense we are well and fully done, and we were so already in 1970. Christan and Roth just need to incorporate Pearles exact analytic solution into their simulation model, and then they will be done too, as far as simulation is concerned. And Christian needs to *derive* the Pearle probability distribution of theta_0 from his own S^3 model. Presently, his simulation models are all just inspired guesses. They all turned out pretty well, but they weren't the right answer, exactly. And indeed he still did not supply us the theoretical bridge.

Joy Christian

My local models for the quantum correlations are based on a hypothesis---supported by a rigorous theorem---that ALL quantum correlations are local-realistic correlations among the points of a parallelized 7-sphere (which is simply a 4-sphere worth of 3-spheres, with a twist in the Hopf bundle). This hypothesis has experimental consequences. I have proposed an experiment to test one of the consequences. The proposed experiment is described on my blog.

As for the "theoretical bridge" between Chantal Roth's original simulation of my local model for the EPR-Bohm correlation and all of the versions of Michel Fodje's simulation, it can be found in this book-chapter. See, especially the Appendix.

Yes, it would indeed be very nice to be able to derive the Pearle probability distribution from within S^3. I will attempt to do so when time permits. It would certainly lend further support to my overall hypothesis about the origins of quantum correlations.

Richard Gill

Joy writes "Yes, it would indeed be very nice to be able to derive the Pearle probability distribution from within S^3. I will attempt to do so when time permits. It would certainly lend further support to my overall hypothesis about the origins of quantum correlations. "

I am really looking forward to this.

Joy Christian

I am reading Phil's paper first time. I kick myself for not having read it carefully before.

It is one of those classic papers one cites ad nauseam but never bothers to read.

Another such paper is the original EPR paper, but that one I have read ad nauseam.

Richard Gill

Pearle does show very clearly that his solution is not unique! I had not realised that, sorry for my mistake. He goes for a simple solution, and it is very very simple indeed, much more simple than appears from his paper (which I do find very difficult to read).

s := 2/sqrt(V) - 1 where V ~ Unif(1, 4)

Translated to Caroline Thompson's model, the random radius R of the circular caps is arc cosine s

As far as I know, nobody ever actually simulated the Pearle model in a computer simulation. Apparently a whole lot more people found it too difficult to figure out what was going on exactly (including Caroline herself).

Thomas Ray

Lest one confuse Joy's framework with the chaotic ball variety -- remember that the space of Pearle et al is the S^2 manifold of R^3 real measures and demonstrably incomplete for being multiply connected. Joy's measure space is the parallelized S^3 manifold of complete correlations between simply connected points of the Hopf fibration. One simple pole at infinity compactifies R^3 in the entire physical space of S^7 (a "4 sphere's worth of 3 spheres" in Joy's terms), with nonzero topological torsion at every scale, and includes all measure results.

It is very important to specify the measure space of a simulated function.

Rick Lockyer

Tom wrote:

"Here's what I'm talking about, Rick, from your own essay forum of 2012. Answering a post to Jonathan Dickau, you ended with the comment, "It all comes down to the structure constants p_ijk."

To which Joy made a short reply, "Or structure variables p_ijk(x) in my variable torsion picture, at every point x in S^7."

Your views topologically make the difference between passive diffeomorphism (yours) and active diffeomorphism (Joy's). "

The concept of "structure variables p_ijk(x) .... at every point in S^7" is nonsense. You will no longer have a connected space in which you can do anything useful. I have said this before, and I will say it again for surely it has not sunk in. You cannot combine algebraic elements from different algebras in a single mathematical expression, nor can you combine mathematical expressions that have algebraic elements from different algebras. This includes related algebras where the distinction is a chiral choice. This is Algebra 101.

Diffeomorphism?? You can't even define differentiation if the algebra changes within the coordinate neighborhood.

Rick

Joy Christian

Rick,

You wrote: "The concept of "structure variables p_ijk(x) .... at every point in S^7" is nonsense."

I am afraid you are grossly mistaken. Please check out references [21], [40], and [41] of this paper. You will find in these references that the concept of structure variables at every point of S^7 is neither new nor problematic. In fact it is quite enlightening and refreshing.

Joy

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