Bell’s Theorem’s experiment resolved

Nature of an antiparticle

A positron can be interpreted as an electron travelling backwards in time.

Feynman and earlier Stueckelberg, proposed an interpretation of the positron as an electron moving backward in time, reinterpreting the negative-energy solutions of the Dirac equation. Electrons moving backward in time would have a positive electric charge. (

If the positron is an electron moving backwards in time, its positive charge is positive only in relation to normal matter moving forwards in time.  But if the positron is an electron travelling backwards in time, its reverse direction in time should not be disregarded and its reversed attributes viewed only as legitimate from an observer moving forwards in time.  A positron will of necessity have its spin measured according to how the positron approaches the measuring apparatus from our future and its new spin will carry on into our past.  This one concept completely invalidates the application of Bell’s Inequalities to the physical interpretation of a traditional Bell experiment.  Bell’s Theorem is wholly valid and the inequalities are unbreakable but they are irrelevant to the physics actually occurring when an antiparticle moving backwards in time is involved.  The Bell Inequalities are only valid for particle/antiparticle pairs both moving forwards in time.


Malus’s Law: the true determiner of the Bell correlation

 The mathematical equivalence of Malus’s Law results and a Bell experiment result is not usually relevant as Malus’s Law acts on polarised inputted beams whereas Bell acts on inputted unpolarised beams.  But this lack of equivalence is only true for particle/antiparticle pairs travelling forwards in time.  When the antiparticle travels backwards in time, Malus’s Law becomes the sole determiner of the Bell correlation of   – cos θ.

My paper: Malus’s Law and Bell’s Theorem with Local Hidden Variables at explains in detail the importance of Malus’s Law in deriving the Bell correlation in a Bell’s Theorem experiment.


Realism, locality, hidden variables and counterfactual determinism

 Realism and locality are features relevant to Bell’s Theorem but are superfluous in an explanation of the Bell correlation when antiparticles are travelling backwards in time.  It may be difficult, nevertheless, to accept the reality of this interpretation of antiparticles.  The particles and antiparticles can have hidden variables which could be their spin vector directions.  It is not possible to keep track of a particle’s hidden variable even in a simulation of the particle passing through a measurement (in a Stern Gerlach apparatus).  There is a statistical element in the outcomes and this chance element means that counterfactual determinism cannot apply.  So a table of simulated results cannot be constructed using counterfactual determinism to fill in blank spaces in a 2×2 table of results of paired measurements.  Say a pair of particles has identical hidden variables to another pair of particles.  The two pairs can have different outcomes to one another because of an element of chance in the measurement.  This chance is straightforwardly derived from Malus’s Law which is a probabilistic law and has been known for two hundred years.  So it is true that the Quantum Randi challenge cannot be met.  However, the challenge is irrelevant to issues of locality and realism as the physics of a Bell experiment with backwards-in-time antiparticles is classically solved using a very old statistical law.


The physics of a Bell Experiment

 In the conventional or forwards-in-time explanation of the physics of a Bell experiment a particle / antiparticle pair are emitted together from a source and travel to Alice and Bob who measure their spins with Stern Gerlach apparatuses.  The two spins are entangled which means, at the least, that they have coordinated spins, with net angular momentum of zero.  Entanglement of spins is the focus of the interpretation of the results.  Although there are Bell deniers, it is completely clear to me that Bell’s Theorem is correct and that in a classical sense the Bell correlation cannot be as great as  – cos θ.  To see this, one could simulate a Bell correlation just using one setting of Alice and Bob devices set at an angle of 45o and using a large number of pairs in the calculation.  It is impossible to exceed, in absolute magnitude, a simulated correlation of -0.5.  But the Bell correlation is -0.707 which is greater than can possibly be simulated using local hidden variables such as particle spin vector directions.

In a backwards-in-time antiparticle solution, the antiparticles arrive from outside the experiment and head towards the source.  Alice and Bob make measurements on them on their way to the source.  The antiparticles are unpolarised before measurement (This is ‘before’ from the perspective of the antiparticles whereas Alice and Bob of course see this as ‘afterwards’!) and polarised after measurement, either in Alice’s or in Bob’s setting direction.  One cannot pre-determine, even in a simulation, the track of a particle through a measurement because of the statistical chance involved in the measurement outcome.  But using Malus’s Law one can derive a distribution of spin vector directions immediately after measurement and follow the beam through the rest of the experiment.  After reaching the source, the beam of positrons is replaced by a beam of electrons travelling forwards through time.  Their spins are entangled with the spins of their partner positrons, so entanglement does play a role, but not the dominant role, which in fact belongs to Malus’s Law.

The electrons travelling to be measured by Alice are pre-polarised in the direction of Bob’s setting and those to be measured by Bob are pre-polarised in the direction of Alice’s setting.  So Alice and Bob are both measuring beams pre-polarised at 45o to the new measurement.  Even if a range of settings is used with random and late choices and even if randomised using distant astronomical data, the usual settings in a Bell experiment all involve angles related to 45o, and that is the only key value in a Malus’s Law outcome.


Duality of Malus’s Law results and Bell’s Experiment table of results

Table 1 shows the generalised table of results of a Bell experiment where A and B are Alice’s and Bob’s measurements which can take the values of +1 or -1.  Alice sets her apparatus at a vector setting of a while Bob uses a vector setting of b.  The difference in angles between a and b is θ.

 Table 1            Bell results for electrons with a – b = θ  

Results as proportions B = 1 B = -1 Total
A = 1 {P++ = }  0.5*sin2 θ/2 0.5*cos2 θ/2 0.5
A = -1 0.5*cos2 θ/2 0.5*sin2 θ/2 0.5
Total 0.5 0.5 1.0


It is easy to show that p++ = (1 + correlation coefficient)/4         and, conversely,

the correlation coefficient = 4 * p++  – 1

So, the correlation coefficient between A and B measurements = 4 * 0.5* sin2 θ/2  – 1

=  2* sin2 θ/2  – 1 =  (sin2 θ/2  – 1) + sin2 θ/2  =  sin2 θ/2  – cos2 θ/2  = – cos θ.


Malus’s Law shows that the intensity of the beam measured by Bob is cos2 (θ/2) for electrons where θ = angle a – b.  This value is needed for the cell of Table 1 where A = +1 and B = -1.   Alice’s measurements of A = +1 on her antiparticles form one quarter of the total measurements so she contributes 0.25*cos2 θ/2 to this cell of Table 2.  Similarly Bob’s measurement of B = -1 on his antiparticles contributes another 0.25*cos2 θ/2 to this cell making a total of 0.5*cos2 θ/2 for the final cell value.  Table 1 only has one degree of freedom as the marginal values are fixed, so the other three cells of results are filled in automatically once one cell value is known.


Photons versus electrons in Malus’s Law

Malus’s Law for photons is:

Intensity of a beam passing through a filter at an angle θ to an incoming polarised beam =  cos2 θ * original intensity of the beam.

Malus’s Law for electrons is:

Intensity of a beam passing through a filter at an angle θ to an incoming polarised beam =  cos2 (θ/2) * original intensity of the beam.


3 September 2020



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A comparison of Bell’s Theorem and Malus’s Law: action-at-a-distance is not required in order to explain results of Bell’s Theorem experiments

Full paper (10 pages, pdf file):


This paper shows that, using counterfactual definiteness, there is an enforceable duality between results of Malus Law experiments and the results from Bell experiments.   The results are shown here to be equivalent in the two experiments subject to extending the Malus experiment by doubling it to match the structure of the results table of a Bell experiment.  The Malus intensities also need to be converted into counterfactual correlations in order to enable results in both experiments to be compared using a common statistic.   It is therefore possible to use the duality to explain the more esoteric Bell results via the simpler Malus results.  As Malus results involve singleton particles rather than matched pairs of particles then there is no requirement for action at a distance nor entanglement to feature in an explanation of Malus results and therefore, using the duality, neither in Bell results.  The ‘magic’ in Bell’s Theorem results is not eliminated as it still exists contained within Malus results, and that ‘magic’ [of somehow exceeding the Bell Inequalities] remains unexplained by this paper, except it is shown that the ‘magic’ does not involve action-at-a-distance nor entanglement.


Malus’s Law and Bell’s Theorem


Bell’s Theorem in a nutshell points to the impossibility of finding the -cos θ curve for the correlation between Alice and Bob’s integer measurements when using local hidden variables to describe the states of the entangled pair of particles.  See Figure A for the graph of this curve.  Instead, simulating the Bell experiment using local hidden variables yields only the smaller (absolute magnitude) correlation on the sawtooth line given by correlation = 2*θ/π -1 (i.e. a sawtooth, where θ is in radians, and the sawtooth is merely a straight line for θ in this range).  There is a kind of magic in this result which is sometimes attributed to action-at-a-distance which in turn is said to be caused by the entanglement of the pair of particles.  For example, measuring particle 1 in a detector set at an angle corresponding to North, is somehow thought to instantly set particle 2, wherever it might be, no matter how far away, to an angle corresponding to South.  That is because the first particle is set to point North by the detector, and entanglement enforces the second particle to take the opposite state.

The way in which real experiments exceed the straight line relationships in practice is very much a certain kind of magic. My paper, however, shows that this magic has nothing to do with entanglement.  This is shown by finding that the much simpler Malus experiment (play with  two polaroid sunglasses and see how the intensity of the light varies passing through both of the pair depending on the relative angles at which you hold the sunglasses) also has the same magic as does Bell’s experiment.  Yet there is no entanglement involved in a Malus experiment.

Just as real experiments give = – cos θ for the Bell correlation, real Malus experiments give cos2θ for the intensity or amount of light passing through the filters.  However, a different amount of light is predicted in local hidden variable simulations corresponding to the straight line Intensity = 1 – 2*θ/π (= the classical intensity using local hidden variables, with θ in radians).

The situation in Malus experiment is just as magical as that in the Bell experiment yet the Malus experiment has no entanglement.  So using duality and Occam’s Razor one can look to the simpler Malus experiment to look for a solution to the magic.

Throw away any thoughts of spooky entanglement causing action at a distance.

Figure B gives the dual to Figure A.  They both have the same magic, but Figure B has no entanglement.

Figure A          BELL: Plots of 2*θ/π -1 (i.e. sawtooth, where θ is in radians) and -cos θ: for θ between 0o and 90o    

figure A

Figure B           MALUS: Plots of cos2 θ (= the Malus Intensity) and 1 – 2*θ/π (= the classical intensity using local hidden variables, with θ in radians) for θ between 0o and 90o    

figure B



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Leptoquarks and possibly some new physics

The CERN Courier of 2 May 2019 carries an article The flavour of new physics

My post here explores that suspicion of a faint possibility (less than 5 sigma significance) of new physics using the details in my Preon Model#6  given at .

The CERN article shows at the far right of its Figure 1 one path for the decay of

b –> c τ ν’  that is

bottom quark  –>  charm quark   &   tau   &   tau-antineutrino

An intermediary in the decay is the LQ or Leptoquark, which is a relative newcomer and appears to be acting as if it were a force carrier and would be a particle beyond the Standard Model, were it to exist.  My aim here is to try to specify the exact structure of the Leptoquark in Figure 1 in terms of my Preon Model #6.

First, according to my preon model, each Standard Model particle is composed of a number of preons.  Also, the left- and right-handed forms of particles are structurally different from one another; at least, in my model, they are different.  The structure in terms of actual named preons will be shown later but for the moment it is only necessary to know the total number of preons in each particle and the summary qualities in each particle.  Below is a list of these qualities for the particles used in this post.  The higgs is also shown in this list as I believe the higgs has a role in this bottom decay.

Parentheses indicate (electric charge, spin, weak isospin, colour charge).

LH = left-handed form of the particle;  RH = etc…

bottom LH = (-1/3, -0.5, -0.5, red)     20 preons    (where red could alternatively be green, or blue, as desired)

bottom RH = (-1/3, 0.5, 0, red)          20 preons

charm LH = (2/3, -0.5, +0.5, red)  12 preons

charm RH = (2/3, 0.5, 0, red)         12 preons

tau LH = (-1, -0.5, -0.5, 0)             20 preons

tau RH = (-1, 0.5, 0, 0)                  20 preons

tau-antineutrino LH = (0, -0.5, 0, 0)       20 preons      which does not occur in the Standard Model as it is the antiparticle of the sterile or RH neutrino

tau-antineutrino RH = (0, 0.5, -0.5, 0)    20 preons

higgs LH = (0, 0, -0.5, 0)    16 preons

higgs RH = (0, 0, 0.5, 0)    16 preons

Some liberties are taken with the definition of handedness here.  Normally LH refers to negative spin.  This has been extended here to have LH referring to negative weak isospin, but only when spin is zero. This only applies to the higgs and the leptoquark and is for my convenience only and also is not strictly correct as weak isospin has connection with electric charge or hypercharge rather than spin.

A simple totaling of the numbers of particles before and after decay shows that there are more preons outputted into c τ ν’ (52) than are inputted by b (20).  This discrepancy is due to extra preons inputted from the vacuum.  In other decays described by my preon model it is normally a higgs boson which is taken from or given up to the vacuum.  Also, spontaneous random decay is anathema to my model and the interactions in my model are exactly balanced before and after the interaction,  as with a chemical reaction.  To do this the model has two particles inputted and two outputted for each interaction vertex.  So the b –> c τ ν’ decay is re-modeled, by me, here as two separate interactions:

bottom + higgs   –>   tau + leptoquark

20 +16 –> 20+ 16 preons

followed by the interaction

leptoquark + higgs –>  charm + tau-antineutrino

16 + 16 –> 12 + 20 preons

Both of these interactions balance in numbers of preons in and out, which means that the leptoquark has 16 preons as does the higgs.  In my model the gluon also has sixteen preons so the leptoquark is in this way in step with force carriers.  In my model, the force carriers have 4 or 8 or 16 preons and are allocated to (my) three generations of forces while the fermions have 4 or 12 or 20 preons as in the Standard Model’s three generations.

Taking the first interaction: bottom + higgs   –>   tau + leptoquark ,

each of these four particles comes in LH and RH forms. It is not shown here but all of the permutations of these variants have been checked for elegibility and consistency and the outcome is that the Leptoquark has 16 preons and has the qualities:

LH Leptoquark  (electric charge = 2/3,   spin = 0,   weak isospin  = -1/2,    colour  [= R or G or B])

RH Leptoquark  (electric charge = 2/3,   spin = 0,   weak isospin  =  1/2,    colour  [= R or G or B])

These properties appear in the interactions as follows:

LH bottom + RH Higgs –>  LH tau + RH leptoquark

(-1/3, -1/2, -1/2, Red) + (0, 0, 1/2, 0)  –>  (-1, -1/2, -1/2, 0) + (2/3, 0, 1/2, Red)

followed by

RH leptoquark  +  LH higgs   –>    LH charm   +   RH tau-antineutrino

(2/3, 0, 1/2, Red)   +   (0, 0, -1/2, 0)    –>    (2/3, -1/2, 1/2, Red)   +  (0, 1/2, -1/2, 0)

Where the numbers of preons balance into and out of the interactions and the particle qualities of charge, spin, weak isospin and colour balance into and out of the interactions.

Next, the exact preon structures of the leptoquarks are sought.  If the interaction

LH bottom + RH Higgs –>  LH tau + RH leptoquark

is written out as exact preons, we get

AC’g’ Cr C’b’ x^9    +  A’B’CC x^6    –>  AC x^9  + RH leptoquark

Cancelling on both sides of the interaction by the 20 preons in AC x^9 gives

RH leptoquark =  A’B’C C’g’ Cr C’b’ x^6  which has 16 preons

where C’g’ Cr C’b’ is equivalent to one preon as C’g’ is a sub-preon which is a coloured  (antigreen) one-third slice of preon C and so three such sub-preons make up the equivalent of a whole preon, at least in quantity of matter contained.  This aggregate of three coloured sub-preons causes the net colour Red.  The twelve preons in x^6 are completely neutral in properties as each x is a pair comprising a preon and an antipreon, for example, AA’ where A’ is the antipreon of preon A.

Next the interaction for the RH bottom quark is investigated.

RH bottom + LH higgs  –>  RH tau + LH leptoquark

(-1/3, 1/2, 0, Red) + (0, 0, -1/2, 0)  –>  (-1, 1/2, 0, 0)  +  (2/3, 0, -1/2, Red)

followed by the interaction

LH leptoquark + RH higgs  –>  RH charm  +  LH tau-antineutrino

(2/3, 0, -1/2, Red) + (0, 0, 1/2, 0)    –>  (2/3, 1/2, 0, Red)  +  (0, -1/2, 0, 0)  {NB this is the sterile antineutrino which could mean that the RH charm is not produced, or at least not detected, in this interaction}

Next, the exact preon composition of the LH leptoquark is sought.  If the interaction

RH bottom + LH higgs  –>  RH tau + LH leptoquark  is written down as exact preons we get

B C’g’ Cr C’b’ x^9 + ABC’C’ x^6  –>  BC x^9 + LH leptoquark

Cancelling on both sides of the interaction by the 20 preons in BC x^9 gives

LH leptoquark =  ABC’C’C’ C’g’ Cr C’b’ x5  which contains 16 preons.

x refers to a preon-antipreon pair so that one of the x pairs on the input side of the interaction equation needs to be CC’ and is therefore usable in the cancellation step to supply the C preon, on the input side of the interaction, to be cancelled.


8 May 2019







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Negative mass as the cause of dark energy and dark matter

I have recently loaded a paper Negative mass as the cause of dark energy and dark matter onto vixra at


If this paper is correct, the impact on our world view is cataclysmic.

It is easy to find in wikipaedia that:

“Positive mass attracts both other positive masses and negative masses. Negative mass repels both other negative masses and positive masses. For two positive masses, nothing changes and there is a gravitational pull on each other causing an attraction. Two negative masses would repel because of their negative inertial masses. For different signs however, there is a push that repels the positive mass from the negative mass, and a pull that attracts the negative mass towards the positive one at the same time. Hence Bondi pointed out that two objects of equal and opposite mass would produce a constant acceleration of the system towards the positive-mass object, an effect called “runaway motion” …”.

There are four circumstances to consider, assuming that all the masses are initially at rest.

A positive mass accelerates towards a positive mass

A negative mass accelerates towards a positive mass

A positive mass accelerates away from a negative mass

A negative mass accelerates away from a negative mass.


A positive mass accelerates towards a positive mass

This is simply normal matter in motion.  Normal matter is positive mass and is on the right hand vertical lines in Figures A to D of the vixra paper.  The two vertical lines should be a single line as this simulation only uses one dimension of space but the line is separated to more clearly show the positions of  the negative and positive masses.

A negative mass accelerates towards a positive mass

This is the main cause of dark matter.  Some of the negative mass in the dark energy is attracted to the normal matter, in say galaxies, and surrounds the galaxies. See the red circles on the left hand vertical line in Figure B from the vixra paper also copied here. The red circles identify negative mass clumps as dark matter.  The right hand vertical line of positive mass in Figure B shows two blue circles representing two galaxies corresponding to the two clumps of dark matter in red.  Again, there is really only one line so the left and right lines should be viewed as coincident.

A positive mass accelerates away from a negative mass

This is a contributory factor to dark matter.  The negative mass surrounding a galaxy repels the mass in the galaxy away from edges of the galaxy and towards the galactic centre.  In the absence of the concept of negative mass, it has been assumed that dark mass is a positive mass in the galaxy attracting the galaxy towards the galactic centre.  The negative mass is a mass surrounding the galaxy and repelling the galaxy from expanding.  Thus the mass in the galaxy itself does not take part in the expansion of the space between galaxies.  That is the dark energy effect is not apparent within a galaxy because of the dark matter effect within the galaxy.

A negative mass accelerates away from a negative mass.

This is the main component of dark energy as dark mass repels itself throughout the universal space available to it.  The normal mass is carried along with the dark mass and galaxies accelerate away from each other.

Negative masses within the galaxy repel other negative masses so that the dark matter is a shell around a galaxy rather than mainly residing in the galaxy.

(There may also be a central cloud of negative mass surrounding a black hole at the galactic centre?)

In Figure B, the two galaxies were 18 units apart.  In Figure A they had only been three units apart while in Figure C they became 40 units apart and this demonstrates a dark energy effect. (See Table 1 of the vixra paper.)


Figure B:  Scatterplot of 100 masses against position

(Time = 20 cycles; masses are -1 and +1; scaling factor = 0.01)

Figure B

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Unified model of forces using Preon Model #8

Assume an overriding aim that the four forces of physics are unifiable.  Therefore all the forces must have a lot in common as the original or ancestral unified force must be a coherent and fully-functioning composite of all other forces.

QCD is colour-based, with an SU(3) group structure while QED is colourless [or rather is a neutral mix of colours] with a group stucture embedded within an electroweak structure. The group structure of SU(3) allows QCD-colour to behave like light in that one colour contains others within it.  Specifically, adding Red + Green + Blue gives white.  Re-using this suggests QED white charge is an amalgam of QCD colour charges.

It is clear that a red up quark has a positive charge while a red down quark has a negative charge. This is a major stumbling block for accepting that, at my preon level, QCD colour (e.g. red) has QED electric negative charge while QCD anticolour has QED positive electrical charge. QED particles are colour neutral having either white (negative) or black (positive charge). In a preon model, some aggregates of preons can be net white or net black and adding those aggregates into the quark can change the overall sign of the electric charge at quark-level.

The Weak force is harder to cope with in detail as it is affected by the higgs field, but basically weak isospin is an electric vacuum field and fits into a total composite unified force.

A graviton, acting on a mass charge with spin 2, has two incorrect features which need to be corrected. The first is that mass, as a charge, is not present in QCD or QED or Weak. And mass does not feature in my model as either a charge or a fundamental quality of a preon. Spin 2 seems to me only to be required to cope with having a plus sign always associated with mass. A spin 1 boson would repel two masses, so spin 2 is required to attract two positive mass charges. Eschewing spin 2 goes along with eschewing the mass charge. Using a spin 1 graviton acting on colour charges unifies gravitation with the other forces and allows the four forces to be integrated into a single composite force.

Gravitational colour is weaker than QCD colour so imagine an optical cable with very many strands representing QCD. Gravitation is enforced through just a few strands which have spit off from the main bundle.  The force of QCD is approximately one thousand million million million million million million times (that is 10^39 times) stronger) than the gravitational force so there needs to be that many more fibres in the QCD ‘cable’ than in the gravity ‘cable’.

In my model the photon, Z and gluon are three family members. Gravity, in my model, can be enforced by these same three bosons, so long as all elementary particles contain gravitational colour/anticolour, similar in colour format to the QCD colour contained in the gluon, but a thousand million million million million million million times weaker.

The three bosons can provide the same suite of features as QED and QCD but on a very much larger scale of distance (10^39 times larger). The QCD-like feature providing the generally attractive quality of gravity up to 60 million light years. The QED-like aspect causing dark energy repulsion at an even greater distance.

For more, see my vixra paper at

Hexark and Preon Model #8 and the Unification of Forces: a Summary

This paper summarises a model for building all elementary particles of the Standard Model plus the higgs, dark matter, dark energy and gravitons, out of preons and sub-preons. The preons are themselves built from string-like hexarks each with chiral values for the fundamental properties of elementary particles. The four forces are shown to be unified by hexarks being string-like objects comprising a compactified multiverse-like structure of at least 10^39 strands of string-like 4D space and time blocks (septarks). Despite the individual forces seeming very different from each other, they all derive from the same colour strands, either as net colour braids (QCD and attractive gravity) or as net neutral-colour braids/strands (electric charge, weak isospin and dark energy, or repulsive gravity). Different strength forces have different numbers of braids in them but QCD-colour is qualitatively, but not quantitatively, the same as gravitational colour while electric charge, weak isospin and dark energy are all qualitatively the same neutral-colour mix, but not quantitatively the same.

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Breaking Bell’s Inequality using hidden variables?

I have posted a paper on the vixra website at

with the title:

Correlation of – Cos θ Between Measurements in a Bell’s Inequality Experiment Simulation Calculated Using Local Hidden Variables

and abstract:

This paper shows that the theoretical correlation between elementary particles’ hidden variable unit vector spin axes p, projected onto Alice’s and Bob’s respective detector angle unit vectors a and b, in a Bell’s Inequality experiment, is – cos θ. This equates with the quantum correlation value and exceeds the “Bell’s Inequality” attenuated correlation in absolute magnitude. Further, aggregates of elementary particles’ hidden variable unit vector spin axes p, when projected onto appropriate detector angle vectors, give values which break the Bell’s Inequalities in exact accordance with values given by Quantum Mechanics calculations. On the other hand, Bell’s attenuated correlations correspond to correlations calculated without fractionalising the raw integer measurements A and B made by Alice and Bob. Also, when aggregating the raw integer measurements, the Bell’s Inequalities are not broken.

To be clear, neither in the paper nor in this blog am I claiming to have broken Bell’s Inequality with a model based on hidden variables.     To make such a claim would at the least require the use of integer measurements, that is involve fuzzy vectors rather than exact vectors in my terminology below.

To summarise my findings. There is a 2 x 2 way of looking at my two computer simulations in this paper.

Exact vectors _ Fuzzy vectors on a hemisphere
My Simulation #1: correlations (a) The Quantum Mechanical correlation of 0.707 for theta = 45o cannot be directly calculated via QM but

(b) has been directly calculated in my Simulation#1, so there is nothing spooky going on here despite 0.707 breaking Bell’s Inequality.

The magnitude of this correlation would be equivalent to a CHSH statistic S=2.828 except that the CHSH statistic only applies to fuzzy vectors, not to exact vectors.

The Bell correlation of 0.5 for theta = 45o is the mundane attenuated correlation associated with failure to break Bell’s Inequality. Equivalent to a CHSH statistic of S=2.

The most recent CHSH experiment finds S=2.4 based on 245 pairs of particles.



My Simulation #2: proportions (a)  There exist truly amazing QM calculations of proportions which are projections on exact vectors by Susskind which are accurately matched by

(b) my Simulation#2 calculations, so there is nothing spooky going on here despite them breaking Bell’s Inequality



Bell proportions, mundane values which do not break Bell’s Inequality

The fuzzy vector column results are straightforward, and my simulations show these as failures to break the Bell’s Inequality. They both use fuzzy vectors on a hemisphere.  Fuzzy vectors on a hemisphere correspond to raw measurements by Alice and Bob at their detectors.  They have unit magnitude but the vector is only known to be pointing at either one hemisphere or the other.  Hence a fuzzy vector.  Proportions and correlations both use simple counts and sums of 1s and -1s to obtain the mundane results.  The exact particle vector direction is irrelevant to these ‘fuzzy’ calculations.

Next on to Column 1: exact vectors. Amazingly, QM allows calculations of proportions which break the Bell Inequality.  I used Susskind’s online example of a Bell Inequality in my Simulation 2 for this.

Even more amazingly, I obtained the QM values for these proportions very accurately using my hidden variable Simulation 2!!!

What my simulation 2 does is start with the hidden particle unit vectors and use the standard dot product calculation of projections or loadings onto the detectors’ exact vectors.  These projections are not integer values in general and so fractional values are being added along exact vectors.  As this agrees accurately with QM calculations and I conclude that QM calculations are measuring the same thing.  No real surprise as these QM calculations use Projection Operators!  Bell’s Inequalities however are designed to be applied only to integer measurements.

So far so good.

It is the correlations using exact vectors which causes all the problems of misunderstanding in this field.

I have found in my Simulation 1 correlation = 0.707 for theta = 45 degrees.

My simulation 1 starts with the exact particle unit vectors and again uses the standard dot product calculation of non-integer projections onto the detectors’ exact vectors.  So again fractional projection values are being added along exact vectors.

AFAIK, no QM calculation can go directly to correlation= 0.707 because it requires the knowledge of the hidden variables i.e. the particles’ exact directions, for individual particles, and these are never, ever known in a real experiment.  So calculating a correlation for an exact vector needs a lot more information than does calculating an overall proportion along an exact vector. Too much information for a real experiment.

However, my Simulation 1 gives 0.707 because I can generate artificial particles with known (to my computer) hidden variables.  So I and everyone else knows that the quantum correlation really exists for theta = 45 degrees and is 0.707.  After all, I have obtained it in Simulation 1 based on exact vectors.

So on to the misunderstanding. QM has no access to the hidden variables for calculating the quantum correlation, so it cannot do it.  But it is known with certainty that the quantum correlation actually exists.  So somewhere along the line over the years someone must have decided that the quantum correlation must be able to arise from the fuzzy vector data.  But this is a complete misunderstanding of the situation.  The situation is that the quantum correlation corresponds to a correlation on exact vectors whereas the CHSH statistic using real experiments is derived using correlation between fuzzy vectors.

This mis-match of what the correlations are measuring underlies all the supposed mystery of the quantum correlation.  There is no spookiness attached to these quantum correlations as I have simulated them non-spookily for exact vectors.  The only spookiness is why anyone should chase the supposedly spooky correlation in the wrong cell above, searching in the top right hand cell of correlations between fuzzy vectors, for which my Simulation 1 gives the mundane and attenuated value of correlation = 0.5.  It is no surprise that the correlation is attenuated as the vectors are fuzzy, and fuzziness indicates lack of reliability of measurement which is well-known in reliability theory to attenuate a correlation.

Of course there could be something going on in nature which is very very spooky and much more spooky than anything above, and that I have not covered in my local, real simulations.  My own preon model ( subdivides the electron into many components which does allow a glimmer of scope for non-local effects.  Also my preon model has 24 dimensions as the preons contain strings, and it is also possible that what looks like a local effect in multi-dimensions could look like a non-local effect when viewed in three dimensions.

The really strange outcome for me is that using exact vectors, for theta = 45 degrees, and non-integer measurements by Alice and Bob in a particle-at-a-time simulation (which is impossible in practice) one can obtain a correlation of 0.707 between Alice and Bob’s measurements. This same correlation is obtained via Quantum Mechanics in a summary way using integer measurements from Alice and Bob as starting points though the subsequent calculations involve Projection Operators and abstract mathematical space.

So there is a kind of parallel here between these two approaches.

But in a particle-at-a-time simulation using fuzzy vector measurements, that is integer measurements, by Alice and Bob, the correlation is reduced to 0.5.  However in real-life experiments, of necessity using integer measurements by Alice and Bob, the higher correlation of 0.707 is obtained. (To be more exact, the correlation of 0.5 is exceeded at a statistically significant level.)

I can write off any mystery in the 0.707 correlation in QM calculations as being a side effect of using higher mathematics in the calculations, and moreover QM does not produce the raw data of the individual integer measurements by Alice and Bob.  But in real experiments we do have both the raw data of integer measurements by Alice and Bob and we also have the correlation greater in absolute magnitude than 0.5.  It is in the real experiments where the mystery lies as one has the cake (integer measurements) and eats it (disattenuated correlation greater than 0.5 using an ordinary statistical calculation)!

(Revised 14 March 2019)


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Quantum Gravity and a new table of elementary particles

This week I have used Preon Model #7 to make a model for gravitation based on the exchange of graviton bosons.  See for Models for Quantum Gravity, Dark Matter and Dark Energy Using the Hexark and Preon Model #7 and for Hexark and Preon Model #6: etc.  A full report on Preon Model #7 is in draft.

First, how does the graviton fit into a table of elementary particles?  It does not easily fit into such a table without modifying the table structure.  The first change is that the photon, Z and gluon are three members of the same family.  Note that they all have zero electric charge, spin +1 or – 1 and zero weak isospin.  In my model that makes them one family.  The photon deals mainly with uncoloured particles.  The Z is designed to interact, albeit neutrally, with coloured quarks, while the gluon can alter quark colour in interactions.  That means that the photon is first generation, the Z is second generation and more complex in structure while the gluon is third generation and even more complex in colour, containing enough preons to exhibit colour and anticolour properties simultaneously.

The table of elementary particles in my model has a very simple structure of row by column, where the columns are for the generations and the rows are different families.  The graviton is a single family of bosons with zero electric charge, spin + or – 2 and weak isospin + or – 0.5.  There are at least three generations of graviton the third generation is as complex as the gluon and has colour-anticolour properties.  Just as the electron has two forms: left handed and right handed, so the graviton has two forms, one where the spin and weak isospin have the same sign or handedness as each other and another form where the signs are different.

The higgs family also has at least three generations and the third generation higgs is complex enough to have colour-anticolour.  The higgs has no electric charge, no spin and weak isospin of +0.5 or -0.5.

The dark boson family has at least a third generation member with zero properties except colour-anticolour, and that colour-anticolour property is just like that for the gluon, graviton, higgs and dark boson.  It also may be possible that the top and bottom quarks share this colour-anticolour property.  They could have colour plus colour-anticolour.  A fourth generation gluon could have colour-anticolour plus colour-anticolour.

So why is gravity always attractive?  In my model, it is not always attractive!  It is no more so than are the photon, Z and gluon taken in combination, and the types of gravitons combined are as numerous as types of QED photons, weak and strong QCD gauge bosons.  So why does gravity appear to be always attractive?  The answer lies in its weakness.  In my model, an electron repels an electron using the first generation graviton, just as an electron repels an electron via QED.  But that repulsion is too weak to be presently detectable.    The third generation colour-anticolor graviton is the most important as it attracts quarks (and gluons and higgs and dark) together gravitationally.  But why do we never see quarks repelling quarks gravitationally?  There is a parallel question: why do quarks attract quarks, as a net effect, within the atomic nucleus?   The answer to that answers the question about gravitational attraction.  the strong force is very approximately 10 to the power 40 greater than gravity.  That means that where the sphere of influence of the strong force is on the order of the diameter of the nucleus, the sphere of net attractive gravitational influence of the third generation graviton is of the order 10 to the power 40 times as big as the nucleus.  That is a sphere of attractive-only influence on a universal scale, or at least intergalactic scale.  But far enough away, the first generation gravitational influence between quarks, which is repulsive, can assume dominance. And that repulsion at a remote distance is seen as dark energy.

The dark boson of the third generation can interact gravitationally only with the third generation gravitons.  The first and second generation dark bosons (if they exist … as they have no properties we know of) cannot interact repulsively through the first generation graviton and so cannot take part in dark energy.  In my guestimation, the higgs is also a candidate for dark matter and it could take part in both attractive gravitation via the third generation graviton and also in dark energy.

I am possibly more pleased at finding a neat structure for the table of elementary particles than at finding the graviton structure.  I have always been disconcerted by three things about the Standard Model table:  (1) the higgs stuck out on its own, (2) the non-recognition that the photon, Z and gluon are three generations of one family and (3) the W lumped with the Z because tof their weak force connection.  The W in my table is a second generation boson in a separate family row.

A further modification in my model is for the way interactions are represented.  I have made it a rule in interactions that weak isospin is conserved.  This means that an electron cannot simply radiate a photon because it is accelerating.  This is basically as issue of field interaction effects versus particle interaction effects.  In my model, there is an incoming catalyst boson (the 1/4 higgs+ ) which interacts with the left-handed electron and, as a result, the electron changes handedness and emits a photon-  (Figure S in    For a left-handed red down quark, say the incoming calalyst boson is a Z- (see Figure C), the quark changes handedness and a 1/2 graviton- is emitted.   (Where a 1/2 graviton is a second generation graviton.)  The QED-like repulsion in this second generation gravitational interaction will be swamped by the third generation attractive QCD colour forces taking place in in other interactions.

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Ben6993’s Hexark and Preon Model #6

I have finished a vixra paper (27pp),

Title: Hexark and Preon Model #6: the Building Blocks of Elementary Particles. Electric Charge is Determined by Hexatone and Gives a Common Link Between QED and QCD.

and it is now loaded onto the vixra website at:

Abstract: The paper shows a model for building elementary particles, including the higgs, dark matter and neutral vacuum particles, from preons and sub-preons. The preons are built from string-like hexarks each with chiral values for the fundamental properties of elementary particles. Elementary particles are unravelled and then reformed when preons disaggregate and reaggregate at particle interactions. Hexark colours are separately described by hue (hexacolour) and tone (hexatone). Hexacolour completely determines particle colour charge and hexatone completely determines particle electric charge. Hexacolour branes within the electron intertwine to form a continuously rotating triple helix structure. A higgs-like particle is implicated in fermions radiating bosons.

Warning:  Model#6 supersedes models #5 and earlier, and any of my write ups before May 2015 contain errors in the eigenvalues for weak isospin in the up quark and neutrino.  The W and Higgs have more forms in Model#6 than previously and my gluon model structure now conforms more closely to the standard model.

Amendments to Model#6 from earlier models:

My error prior to Model#6 was to assume the following incorrect eigenstates for the up quark and the neutrino:
where () = (electric charge, spin, weak isospin)
LH up = (2/3, -0.5, -0.5)
LH ν = (0, -0.5, -0.5)

whereas they should be:
LH up (2/3, -0.5, +0.5)
LH ν (0, -0.5, +0.5)

But I have now corrected this in the new Model#6. It required a fourth preon, preon D, with properties (-0.5, 0, +0.5) in order to be able to build the ν and up quark using only four preons to conform with the pattern for the first generation elementary particles.

There were two other structural effects: the higgs (0,0,-0.5) can now be built in two different ways: ABC’C’ X6 as before but also as D’C X7 (where Xn is n neutral pairs of preon + antipreon).

Also, there must be two different forms of W- : (-1,-1,-1) and (-1,+1,-1). This is because to send an LH up (2/3, -0.5, 0.5) to a RH down (-1/3, 0.5,0) requires an addition of (-1, +1, -0.5) while to send a RH up (2/3,0.5, 0) to a LH down (-1/3, -0.5, -0.5) requires an addition of (-1,-1,-0.5). That requires the two forms of W-. And the extra 0.5 weak isospin that is needed comes from a 1/4 higgs which complies with many interactions in my preon model which require the 1/4 higgs or 1/2 higgs or higgs as a participant.

I have also introduced a new term which correlates exactly with electric charge: hypertone. If the hypercolour of the preon is relabelled as white (=-1) for coloured preons and black (=1) for anticolour preons then blackness and whiteness represent tonal values for the preons. Aggregating the tonal values across preons in an elementary particle gives an exact match for electric charge in my model.

If you are drawing/painting you need to take into account both hue (colour) and tone (lightness to darkness).  Quarks and gluons already have the hue analogy (red, green, blue) incorporated as QCD, but a red up quark has + electric charge and a red down quark has – electric charge.  So there is no relationship between colour and electric charge for quarks.  At the more fundamental level of preons, the red preon is always -ve electric charge  while the antired preon has always +ve electric charge.  So the electric charge can be considered as preon tone with colour being lightness of tone and anticolour being darkness.  So the preons have both hue and tone and the hue determines QCD (colour charge) while the tone determines QED (electric charge).



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Electric charge and coloured socks

Socks can be red, green, blue, antired, antigreen or antiblue.  Every sock has a colour charge and an electric charge, as follows:

Sock name Colour charge Electric charge
Red Red (R) -1/6
Green Green (G) -1/6
Blue Blue (B) -1/6
Antired Antired (R’) +1/6
Antigreen Antigreen (G’) +1/6
Antiblue Antiblue (B’) +1/6

These socks have a clear correlation of colour charge with electric charge.  Unfortunately, unlike these socks, quarks do not have a clear dependence of negative electric charge on colour and positive electric charge on anticolour.  A red down quark has negative charge but a red up quark has positive electric charge.

But, can we build quark properties out of these socks?  Yes.  Say a red down quark and a red up quark contain the following socks:

Quark name Quark’s six socks Quark’s colour charge Quark’s electric charge
Red down (RGB)(RG’B’) RGBRG’B’ = RR(GG’)(BB’) = RR = Red1 -1/3
Red up (R’G’B’)(RG’B’) R’G’B’RG’B’ = RR’ (G’B’) (G’B’) = RR = Red2 +2/3

1 where GG’ and BB’ are both colour neutral.

2 where RR’ is colour neutral and (G’B’) is red {R’G’B’= neutral, so R’ (G’B’) is neutral, so G’B’=R}

See also

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Summary table of elementary particles in Ben6993’s Preon Model#5

No. of preon units* 4   12   20
quarks up charm top
down strange bottom
leptons Electron neutrino muon neutrino tau neutrino
electron muon tau
No. of preon units 4 8   16   32
bosons photon Z and W gluon 2-gluon
¼-higgs ½-higgs higgs 2-higgs
¼-axion ½-axion axion 2-axion

*There are 24 preons per preon unit.



Revised on 25 October 2014

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