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 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 = 45^{o }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 = 45^{o} 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. See https://arxiv.org/abs/1508.05949 ^{ } |
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 See https://www.youtube.com/watch?v=XlLsTaJn9AQ&p=A27CEA1B8B27EB67 AND http://www.lecture-notes.co.uk/susskind/quantum-entanglements/lecture-5/violation-of-bells-theorem/ |
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 real, local, 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!
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 (http://vixra.org/abs/1511.0115) 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.
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 http://vixra.org/abs/1510.0338). 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.
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: http://vixra.org/abs/1505.0076
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).
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 = Red^{1} | -1/3 |
Red up | (R’G’B’)(RG’B’) | R’G’B’RG’B’ = RR’ (G’B’) (G’B’) = RR = Red^{2} | +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 http://vixra.org/abs/1505.0076
*There are 24 preons per preon unit.
Revised on 25 October 2014
ABSTRACT
Pseudo-random data are used to illustrate the relationship between errors in raw data being comparatively judged and the resulting Rasch pairs location parameters, first for data which are relatively homogeneous and second for data which have various amounts of heterogeneity. For each data type, various error sizes are used. Rasch pairs location parameters are demonstrated to be plotted on a contracted scale when the objects appear to be homogeneous. As space is contracted near concentrations of mass, so is the Rasch scale also contracted when the objects in it are determined to be located very close to one another.
INTRODUCTION
There are two interesting feature of Rasch analysis.
The Guttman structure is not a fault with the Rasch model. The Guttman effect would also cause problems with constructing any physical scale.
The Rasch scale is investigated using pseudo random data sets generated for this paper. Different data sets have been generated to have different amounts of true error in their locations and the Rasch output parameters were computed for each such data set to find the corresponding ranges in parameter values.
The question of what determines the range of parameters, i.e. the scale of separation of objects.
METHODS AND RESULTS
In this part, sets of data were generated and the DOS BIGSTEPS Rasch pairs analysis was run on each set of data. (Ref.: http://www.winsteps.com/a/bigsteps.pdf, Example 13. Bigsteps is a free DOS version of Winsteps.)
Two types of data were generated using an MS Excel spreadsheet. In both types of data, twelve objects were compared, pair at a time, thus involving 12C2= 66 comparisons. There had to be an element of randomness in order for the program to run and a random adjustment to the true value of zero was added to each object for each pseudo-judge in each paired comparison. Therefore 66×2= 132 quasi-random numbers were generated for each set of data.
In the truly homogenous set of data, each of the twelve objects was set to have a true value of zero. Four sets of data were generated with different limits to the sizes of random numbers: within -2 to +2, within -1 to +1, within -1/2 to +1/2 and within -1/8 to +1/8 added to the true value of zero. The winner in each paired comparison was deemed to be the larger of the pair of random numbers.
Table 1: Rasch pairs results for truly homogeneous objects
Data set | +/- 2 | Data set | +/- 1 | Data set | +/- 1/2 | Data set | +/- 1/8 | |||
Object no. | Location parameter | Object no. | Location parameter | Object no. | Location parameter | Object no. | Location parameter | |||
3 | 0.91 | 7 | 0.97 | 1 | 0.56 | 2 | 0.56 | |||
4 | 0.52 | 11 | 0.97 | 5 | 0.56 | 4 | 0.56 | |||
8 | 0.52 | 1 | 0.57 | 7 | 0.56 | 5 | 0.56 | |||
2 | 0.17 | 10 | 0.57 | 11 | 0.56 | 10 | 0.56 | |||
6 | 0.17 | 3 | 0.19 | 6 | 0.20 | 8 | 0.20 | |||
9 | -0.18 | 9 | 0.19 | 8 | 0.20 | 9 | 0.20 | |||
10 | -0.18 | 2 | -0.18 | 10 | 0.20 | 11 | 0.20 | |||
11 | -0.18 | 5 | -0.18 | 2 | -0.16 | 1 | -0.16 | |||
12 | -0.18 | 4 | -0.55 | 3 | -0.16 | 7 | -0.16 | |||
1 | -0.53 | 6 | -0.55 | 4 | -0.16 | 12 | -0.16 | |||
5 | -0.53 | 12 | -0.55 | 9 | -0.94 | 3 | -0.94 | |||
7 | -0.53 | 8 | -1.45 | 12 | -1.42 | 6 | -1.42 | |||
Range of Location parameters | 1.44 | 2.42 | 1.98 | 1.98 | ||||||
Ave. error per object | 0.45 | 0.47 | 0.46 | 0.46 | ||||||
S.D. of object errors | 0.01 | 0.03 | 0.03 | 0.03 | ||||||
Table 2: Intercorrelations between order of merit of location parameters for truly homogeneous objects
Data set | +/ -2 | +/ -1 | +/ -1/2 | |
+/- 1 | -0.490 | |||
+/- 1/2 | -0.049 | 0.224 | ||
+/- 1/8 | -0.154 | -0.196 | 0.420 | |
The correlation coefficients for the orders of merit of objects in the four Rasch analyses vary from -0.49 to +0.42, with median value -0.05. These low values indicate that a lack of association can be expected when the objects are truly equal but with some random element added at every place in the 66 paired comparisons.
The four ranges of Rasch parameter location values are: 1.44, 2.42, 1.98 and 1.98 with median value 1.98. (Where, for example, 1.98 = 0.56 – -1.42 .)
This pattern of Rasch analysis results is what is desirable in a test of comparability of twelve scripts chosen say from two different tests intended to be equivalent or interchangeable. If replications were undertaken, one would hope for different results each time as a sign of homogeneity of objects.
The second type of data is for truly heterogeneous objects. True location values of objects were allocated as 1, 2, …, 12, for the twelve objects. Adjustments were made to the true values as for the homogeneous data. Random values were added of six different size limits: within +/-2, within +/-4, within +/-6, within +/-8, within +/-10 and within +/-12. As the size limit of the random adjustment decreases, the data should look more heterogeneous, i.e. should look less and less like the first data set in Tables 1 and 2. Five replications of data were made for each size of adjustment (except +/-2). There are too many results to show in as much detail as in Tables 1 and 2, instead summaries of results are shown in Table 3.
Table 3 Summary of results for truly heterogeneous objects.
Data set+/- 12
Replication |
Range of parameters | location | Ave. error per object | S.D. of object errors | Correlation with true location(12 objects) | |
1 | 1.45 | (0.54 to -0.91) | 0.45 | 0.02 | 0.594 | |
2 | 2.56 | (1.53 to -1.03) | 0.50 | 0.03 | 0.730 | |
3 | 4.09 | (1.67 to -2.42) | 0.54 | 0.08 | 0.767 | |
4 | 2.39 | (1.43 to -0.96) | 0.47 | 0.03 | 0.589 | |
5 | 3.24 | (2.21 to -1.03) | 0.50 | 0.08 | 0.791 | |
Median | 2.56 | 0.50 | 0.03 | 0.730 | ||
Data set+/- 10
Replication |
Range of parameters | location | Ave. error per object | S.D. of object errors | Correlation with true location | |
1 | 2.56 | (1.03 to -1.53) | 0.50 | 0.03 | 0.812 (12) | |
2 | 3.00 | (1.50 to -1.50) | 0.49 | 0.04 | 0.756 (12) | |
3 | 2.94 | (1.47 to -1.47) | 0.48 | 0.04 | 0.653 (12) | |
4 | 2.74 | (1.11 to -1.63) | 0.52 | 0.04 | 0.699 (12) | |
5 | 2.98 | (0.89 to -2.09) | 0.52 | 0.07 | 0.709 (11) | |
Median | 2.94 | 0.50 | 0.04 | 0.709 (12) | ||
Data set+/- 8
Replication |
Range of parameters | location | Ave. error per object | S.D. of object errors | Correlation with true location | |
1 | 8.09 | (4.67 to -3.42) | 0.72 | 0.17 | 0.832 (11) | |
2 | 3.14 | (1.57 to -1.57) | 0.51 | 0.04 | 0.905 (12) | |
3 | 4.09 | (1.67 to -2.42) | 0.55 | 0.08 | 0.737 (12) | |
4 | 3.70 | (2.21 to -1.49) | 0.55 | 0.07 | 0.703 (11) | |
5 | 2.53 | (1.51 to -1.02) | 0.49 | 0.04 | 0.777 (12) | |
Median | 3.70 | 0.55 | 0.07 | 0.777 (12) | ||
Data set+/- 6
Replication |
Range of parameters | location | Ave. error per object | S.D. of object errors | Correlation with true location | |
1 | 4.32 | (2.16 to -2.16) | 0.61 | 0.09 | 0.756 (10) | |
2 | 4.72 | (1.93 to -2.79) | 0.66 | 0.09 | 0.828 (11) | |
3 | 3.71 | (1.86 to -1.85) | 0.58 | 0.03 | 0.884 (12) | |
4 | 5.14 | (2.58 to -2.56) | 0.58 | 0.09 | 0.835 (12) | |
5 | 3.51 | (1.75 to -1.76) | 0.56 | 0.04 | 0.870 (12) | |
Median | 4.32 | 0.58 | 0.09 | 0.835 (12) | ||
Data set+/- 4
Replication |
Range of parameters | location | Ave. error per object | S.D. of object errors | Correlation with true location | |
1 | 5.34 | (2.60 to -2.74) | 0.66 | 0.11 | 0.913 (11) | |
2 | 7.24 | (3.65 to -3.59) | 0.75 | 0.09 | 0.958 (12) | |
3 | 5.46 | (2.73 to -2.73) | 0.54 | 0.08 | 0.798( 9) | |
4 | 5.50 | (2.75 to -2.75) | 0.68 | 0.12 | 0.893 (11) | |
5 | 5.79 | (2.89 to -2.88) | 0.64 | 0.11 | 0.873 (12) | |
Median | 5.50 | 0.66 | 0.11 | 0.873 (11) | ||
Data set+/- 2
Replication |
Range of parameters * | location | Ave. error per object | S.D. of object errors | Correlation with true location | |
1 | 1.10 | (0.55 to -0.55) | 0.45 | 0.02 | n.a. (4) | |
*Based on only four objects as results for eight objects failed to converge due to a Guttman pattern of data.
Replications were thought to be unnecessary.
Heterogeneous objects with an inbuilt randomness of +/- 12 are those, in this second type of data, which are most like homogenous objects. As the size of random adjustment decreases to +/- 2 the data act more like the heterogeneous data that their true unadjusted values are. By the time the adjustment is only +/- 2, the Rasch pairs analysis cannot cope with eight of the objects and only four objects have converged location parameters. The best sign of heterogeneous data is a failure of the program to produce results. This is because much of the data are in a Guttman pattern and a Guttman pattern indicates non-locality of objects.
As the random element gradually decreases, the correlation of location parameters with the true locations tends to increase: 0.730 –> 0.709 –> 0.777 –> 0.835 –> 0.873 (median values in Table 3). At the same time, the range of location parameters also markedly increases: 2.56 –> 2.94 –> 3.70 –> 4.32 –> 5.50 (median values in Table 3). Thus, an indicator of the homogeneity of objects is the compressed range of location parameters. The Rasch analysis assesses that objects are relatively homogeneous and compresses the mark scale for them. Thus the Rasch analysis is maybe acting rather like the metric of physical space near a concentration of mass. The average error in the location parameter is calculated by BIGSTEPS and this value gradually rises from 0.50 to 0.66 as the data become more heterogeneous in nature and the location parameter sizes increase. The standard deviation of the location parameters also rises from 0.03 to 0.11, at the same time.
CONCLUSION
This paper shows that a Rasch analysis compresses its location parameter space according to the level of uncertainty in making judgements within that space. The more uncertain the judgements, the more compressed are the points on the scale.
References
Andrich, D. Relationships Between the Thurstone and Rasch Approaches to Item Scaling, Applied Psychological Measurement,Vol. 2, No. 3, Summer 1978, pp419-460.
Pollitt, A. and Crisp, V. Could Comparative Judgements of Script Quality Replace Traditional Marking and Improve the Validity of Examination Questions? Paper presented at the British Educational Research Association Annual Conference, 2004.
20 May 2011
(Version 2.0, 20 May 2011)
(Version 3.0, 30 August 2014)
(Version 3.1, 20 September 2014)
Preons
Preon model #5 is described in detail in Preon model 5: the building blocks of elementary particles. Preons can be grouped into neutral-coloured units and coloured sub-units, and only these units/sub-units need to be considered in interactions, as a preon in a unit/sub-unit is forever in that unit/sub-unit.
Elementary particles can have the following properties: (electric charge, [chiral] spin, weak isospin, colour charge). Particles also have a specific number of units/sub-units. The total properties of a particle can be obtained by summing properties across all of its unit/sub-units.
Preon Units and Sub-Units
To assist in calculating the properties of particles by summing across units/sub-units, the following table shows the properties of the individual units/sub-units.
Table of properties of preon units and sub-units
Unit/sub-unit | Number of preons | Electric charge | Spin | Weak isospin | Colour |
A | 24 | -1/2 | -1/2 | -1/2 | neutral |
B | 24 | -1/2 | +1/2 | 0 | neutral |
C | 24 | -1/2 | 0 | 0 | neutral |
A’ | 24 | +1/2 | +1/2 | +1/2 | neutral |
B’ | 24 | +1/2 | -1/2 | 0 | neutral |
C’ | 24 | +1/2 | 0 | 0 | neutral |
Cr | 8 | -1/6 | 0 | 0 | red |
Cg | 8 | -1/6 | 0 | 0 | green |
Cb | 8 | -1/6 | 0 | 0 | blue |
C’r’ | 8 | +1/6 | 0 | 0 | antired |
C’g’ | 8 | +1/6 | 0 | 0 | antigreen |
C’b’ | 8 | +1/6 | 0 | 0 | antiblue |
‘ denotes antimatter
To check that the properties of the units are correct, one needs to refer to Preon model 5: the building blocks of elementary particles where the properties of the individual preons are listed together with tables showing which preons are contained in which unit/sub-units.
Summary of interactions considered
Interactions
1. e- –> e- + γ
Parentheses are: (electric charge, spin, weak isospin)
(-1, -0.5, -0.5) –> (-1, 0.5, 0) + (0, -1, 0)
LH electron –> RH electron + γ-
However, 4 preon units –> 4 units + 4 units is unbalanced in preon numbers, and also the weak isospins do not balance, so a complete interaction is:
(0, 0, 0.5) + (-1, -0.5, -0.5) –> (-1, 0.5, 0) + (0, -1, 0)
¼ Higgs+ + LH electron –> RH electron + γ-
Where ¼Higgs+ has the same properties as the Higgs+ {i.e. no electric charge and no spin and weak isospin of +0.5} but with only ¼ of its preons.
So we have:
A’B’CC + ACBB’ –> BCAA’ + B’B’CC
I.e. ¼ Higgs+ + LH electron –> RH electron + γ-
2. e- + γ –> e-
Parentheses are: (electric charge, spin, weak isospin)
(-1, -0.5, -0.5) + (0, 1, 0) –> (-1, 0.5, 0)
LH electron + γ+ –> RH electron
However, 4 preon units + 4 units –> 4 units is unbalanced, and also the weak isospins do not balance, so a complete interaction is:
(-1, -0.5, -0.5) + (0, 1, 0) –> (-1, 0.5, 0) + (0, 0, -0.5)
LH electron + γ+ –> RH electron + ¼ Higgs-
ACAA’ + BBC’C’ –> BCAA’ + ABC’C’
Note that a LH electron can be any one of three forms:
ACAA’, ACBB’ or ACCC’. The forms AA’, BB’ and CC’ are neutral in properties and act like neutral ‘bulk filler’ content.
3. e- + e+ –> γ
Parentheses are: (electric charge, spin, weak isospin)
(-1, -0.5, -0.5) +(1, -0.5, 0) –> (0, -1, 0) + (0, 0, -0.5)
LH electron + LH positron –> γ- + ¼ Higgs-
For example, ACBB’ + B’C’CC’ –> B’B’CC + ABC’C’
4. e- + e+ –> vacuum
Parentheses are: (electric charge, spin, weak isospin)
(-1, -0.5, -0.5) +(1, 0.5, 0.5) –> (0, 0, 0)
4 preon units + 4 preon units –> 8 preon units
LH electron + RH positron –> vacuum (second generation axion boson)
For example, ACBB’ + A’C’CC’ –> AA’BB’CC’CC’
where AA’ BB’ CC’ CC’ is a completely neutral axion and returns to the vacuum.
5. ν_{e} –> Z + ν_{e}
Parentheses are: (electric charge, spin, weak isospin)
(0, 0.5, 0.5) + (0, 0, -0.5) –> (0, 1, 0) + (0, -0.5, 0)
RH ν_{e} + ½Higgs- –> Z+ + LH ν_{e}
For example, A’CAA’ + ABC’C’BB’AA’ –> BBC’C’AA’AA’ + B’CAA’
4 units + 8 units –> 8 units + 4 units
6. down –> down + gluon
Parentheses are: (electric charge, spin, weak isospin, colour)
(-0.33, -0.5, -0.5, red) + (0, 0, 0.5) –> (-0.33, 0.5, 0, red) + (0, -1, 0)
red L.H. d + Higgs+ –> red R.H. d + g-
For example, AC’g’CrC’b’ BB’ + A’B’CC AA’ BB’ CC’ AA’ BB’ CC’ –>
BC’g’CrC’b’ AA’ + B’B’CC AA’ BB’ CC’ AA’ BB’ CC’
4 units + 16 units –> 4 units + 16 units
7. down –> W- + up
Parentheses are: (electric charge, spin, weak isospin, [colour if applicable])
(0, 0, 0) + (-0.33, -0.5, -0.5, red) –> (-1, -1, -1) + (0.67, 0.5, 0.5, red)
vacuum + red L.H. down –> W- + red RH up
8 preon units + 4 units –> 8 units + 4 units
For example, AA’ BB’ CC’ AA’ + AC’g’CrC’b’ AA’ –> AA AA’ BB’ CC’ + A’C’g’CrC’b’ AA’
8. W- –> e- + ν’_{e}
Parentheses are: (electric charge, spin, weak isospin)
(-1, -1, -1) –> (-1, -0.5, -0.5) + (0, -0.5, -0.5)
W- –> LH e- + LH ν’_{e}
8 units –> 4 units + 4 units
For example, AA AA’ BB’ CC’ –> ACBB’ + AC’ AA’
9. Z –> e- + e+
Parentheses are: (electric charge, spin, weak isospin)
Z- + ¼H- –> LH e- + LH e+ + vacuum (or first generation axion boson)
(0, -1, 0) +(0, 0, -0.5) –> (-1, -0.5, -0.5) + (1, -0.5, 0) + (0, 0, 0)
8 units + 4 units –> 4 units + 4 units + 4 units
For example, B’B’CC AA’ BB’ + ABC’C’ –> AC CC’ + B’C’ BB’ + AA’ BB’
10. top –> W+ + bottom
Parentheses are: (electric charge, spin, weak isospin, [colour if applicable])
(0, 0, 0) + (0.67, 0.5, 0.5, red) –> (1, 1, 1) + (-0.33, -0.5, -0.5, red)
vacuum + red R.H. top –> W+ + red LH bottom
8 preon units + 20 units –> 8 units + 20 units
For example, AA’ BB’ CC’ AA’ + A’C’g’CrC’b’ AA’ BB’CC’AA’BB’CC’AA’BB’CC’ –> A’A’ AA’ BB’ CC’ + AC’g’CrC’b’ AA’BB’CC’AA’BB’CC’AA’BB’CC’
11. top –> W+ + strange
Parentheses are: (electric charge, spin, weak isospin, [colour if applicable])
0.67, 0.5, 0.5, red) –> (1, 1, 1) + (-0.33, -0.5, -0.5, red)
red R.H. top –> W+ + red LH strange
20 units –> 8 units + 12 units
For example, A’C’g’CrC’b’ AA’ BB’CC’AA’BB’CC’AA’BB’CC’ –> A’A’ AA’ BB’ CC’ +
AC’g’CrC’b’ BB’CC’AA’BB’CC’
12. top –> W+ + down
Parentheses are: (electric charge, spin, weak isospin, [colour if applicable])
(0.67, 0.5, 0.5, red) –> (1, 1, 1) + (-0.33, -0.5, -0.5, red) +(0, 0, 0)
red R.H. top –> W+ + red LH down + vacuum (or second generation axion boson)
20 units –> 8 units + 4 units + 8 units
For example, A’C’g’CrC’b’ AA’ BB’CC’AA’BB’CC’AA’BB’CC’ –> A’A’ AA’ BB’ CC’ +
AC’g’CrC’b’ BB’ + CC’AA’BB’CC’
13. Z –> ν_{e }+ ν’_{e}
Parentheses are: (electric charge, spin, weak isospin)
Z- + ¼H- –> LH ν’_{e} + LH ν_{e} + vacuum (or first generation axion boson)
(0, -1, 0) +(0, 0, -0.5) –> (0, -0.5, -0.5) + (0, -0.5, 0) +(0, 0, 0)
8 units + 4 units –> 4 units + 4 units + 4 units
For example, B’B’CC AA’ BB’ + ABC’C’ –> AC’ CC’ + B’C BB’ + AA’ BB’
14. Z –> d + d’
Parentheses are: (electric charge, spin, weak isospin, [colour if applicable])
Z- + ¼H- –> red LH d + antired LH d’ + vacuum (or first generation axion boson)
(0, -1, 0) +(0, 0, -0.5) –> (-0.33, -0.5, -0.5, red) + (0.33, -0.5, 0, antired) +(0, 0, 0)
8 units + 4 units –> 4 units + 4 units + 4 units
For example, B’B’CC AA’ BB’ + ABC’C’ –> AC’g’CrC’b’ X + B’CgCbC’r’ X + AA’ BB’
{Note that C’g’CrC’b’ + CgCbC’r’ = CrCgCb C’r’C’g’C’b’ = CC’}
So, B’B’CC AA’ BB’ + ABC’C’ –> AB’CC’ BB’CC’ ^{ } + AA’ BB’
15. Higgs –> Z + Z
Parentheses are: (electric charge, spin, weak isospin)
H- + ¼H+ –> Z- + Z+ + vacuum (or first generation axion boson)
(0, 0, -0.5) + (0, 0, 0.5) –> (0, -1, 0) + (0, 1, 0) + (0, 0, 0)
16 units + 4 units –> 8 units + 8 units + 4 units
For example, ABC’C’ AA’ BB’ CC’ AA’ BB’ CC’ + A’B’CC –> B’B’CC AA’ BB’ + BBC’C’ CC’ AA’ + AA’ CC’
16. Higgs –> W- + W+
Parentheses are: (electric charge, spin, weak isospin)
H- + ¼H+ –> W- + W+ + vacuum (or first generation axion boson)
(0, 0, -0.5) + (0, 0, 0.5) –> (-1, -1, -1) + (1, 1, 1) + (0, 0, 0)
16 units + 4 units –> 8 units + 8 units + 4 units
For example, ABC’C’ AA’ BB’ CC’ AA’ BB’ CC’ + A’B’CC –> AACC’ AA’ BB’ + A’A’ CC’ CC’ BB’ + BB’ CC’
17. Electron antineutrino –> sterile muon antineutrino
Higgs+ + LH electron antineutrino –> sterile muon RH antineutrino + Z-
(0, 0, 0.5) + (0, -0.5, -0.5) –> (0, 0.5, 0) + (0, -1, 0)
16 units + 4 units –> 12 units + 8 units
A’B’CC BB’AA’BB’CC’AA’BB’ + AC’ CC’ –> BC’ CC’ AA’AA’BB’CC’ + B’B’CC AA’BB’
18. Muon antineutrino –> sterile tau antineutrino
Parentheses are: (electric charge, spin, weak isospin)
Higgs + LH muon antineutrino –> sterile tau RH antineutrino + Z-
(0, 0, 0.5) + (0, -0.5, -0.5) –> (0, 0.5, 0) + (0, -1, 0)
16 units + 12 units –> 20 units + 8 units
A’B’CC BB’AA’BB’CC’AA’BB’ + AC’ CC’AA’BB’CC’AA’ –>
BC’ CC’ AA’AA’BB’CC’AA’BB’CC’AA’ + B’B’CC AA’BB’
19. Sterile electron antineutrino –> muon antineutrino
Parentheses are: (electric charge, spin, weak isospin)
Higgs- + RH sterile electron antineutrino –> muon LH antineutrino + Z+
(0, 0, -0.5) + (0, 0.5, 0) –> (0, -0.5, -0.5) + (0, 1, 0)
16 units + 4 units –> 12 units + 8 units
ABC’C’ BB’AA’BB’CC’AA’BB’ + BC’ CC’ –> AC’ CC’ AA’AA’BB’CC’ + BBC’C’ BB’BB’
20. Sterile muon antineutrino –> tau antineutrino
Parentheses are: (electric charge, spin, weak isospin)
Higgs- + RH sterile muon antineutrino –> tau LH antineutrino + Z+
(0, 0, -0.5) + (0, 0.5, 0) –> (0, -0.5, -0.5) + (0, 1, 0)
16 units + 12 units –> 20 units + 8 units
ABC’C’ BB’AA’BB’CC’AA’BB’ + BC’ CC’AA’BB’CC’AA’ –>
AC’ CC’ AA’AA’BB’CC’AA’BB’CC’AA’ + BBC’C’ BB’BB’
21. Gluon interactions
Parentheses are: (electric charge, spin, weak isospin).
In preon model #5, three forms of the gluon: rr’-gg’, rr’-bb’ and gg’-bb’ are three different faces of one complex structure. This arises because a red quark in my model is not purely red, but is dominantly red. And an rr’ pair is completely neutral in colour which could be reassembled into a gg’ pair or a gg’ pair of quarks.
For example B’B’CC gives the basic structure for a photon or gluon with (0, -1, 0) and BBC’C’ gives the photon or gluon with the opposite spin: (0, 1, 0). But the gluon needs to be bulked out with another 6 pairs of neutral preon units, e.g. B’B’CC plus AA’ BB’ CC’ AA’ BB’ CC’.
Gluon (1) could be say B’B’CC & CC’ & CC’ & AA’ & AA’ & BB’ & BB’
Gluon (2) could be say B’B’CC & CC’ & AA’ & AA’ & AA’ & BB’ & BB’
A gluon contains enough preons to form a quark within its contents, where:
ACgCbC’r’ & AA’ is an antired antiup antiquark {where AA’ is just one possibility from AA’, BB’ or CC’}
A’C’g’C’b’Cr & AA’ is a red up quark
B’CgC’r’C’b’ & BB’ is a green up quark
BC’g’CrCb & BB’ is an antigreen antiup antiquark
The total of the colour sub-units, alone, for these four quarks is:
Cg Cb C’r’ & C’g’ C’b’ Cr’ & Cg C’r’ C’b’ & Cg’ Cr Cb
which is equivalent to CC’ & CC’.
These four quarks together make AAA’ A’AA’ B’BB’ BBB’ plus the CC’ & CC’,
i.e. makes AA’ AA’ AA’ BB’ BB’ BB’ CC’ CC’ which is eight pairs of neutral units. This has as many preons as the gluon or the higgs, but is neither: it is a neutral vacuum particle or field.
For a gluon- to be able simultaneously to play the roles of rr’ and gg’ (i.e. rr’+gg’), it would need CC’ & CC’ in its composition. Any gluon- must always have CC in its basic composition so an extra C’C’ is needed in its scalar unit pairs, ie it needs CC’ & CC’ as two of its scalar pairs. So Gluon (1) could do this job.
Gluon (2) only contains the following C units: CC & CC’, so Gluon(2) only has one pair of CC’ units and cannot make a gluon of the form rr’+gg’. However, Gluon(2) can use the one CC’ pair to make either a rr’ or a gg’ (or a bb’). So Gluon(2) can make a gluon of the form rr’-gg’.
Pros and Cons – dark matter, lightweight higgs forms and neutral blocks units forming vacuum fields
My earlier preon models were very simple and I took it as axiomatic that: electron + positron = photon+ + photon-. But in these earlier models, first the electric charge was modelled, then gradually the spin was modelled better, and finally the weak isospin was modelled well. But then the modelling of spin for the bosons had to be corrected. At that stage the axiomatic assumption that the preons in an e- and e+ could simply be rearranged into the preons of two photons was lost. That loss of simplicity still seems like a negative feature. However, it is possibly a positive feature as it requires the use of a ¼higgs to allow an electron to emit a photon [see interaction 1]. That could be a ½higgs or a full higgs depending on what energy is put into the interaction but I have assumed that the ¼ higgs is a possibility in lower energy interactions as the preon model allows a ¼ higgs+ to be made from four units: A’B’CC; the full higgs needing 16 units.
The revision of the boson structure in the model also prevented the original axiomatic assumption for a second reason. The two photons are: B’B’CC and BBC’C’ which do not contain an A or A’. The left-hand electron and right-hand positron contain the A and A’ respectively and so cannot be formed from preons of photons alone. Interaction 9 shows how the same feature requires the use of vacuum particles/fields. The Z particle in model #5 is simply the photon with two extra pairs of neutral preon units, e.g. photon+AA’BB’ . Likewise, the gluon is a photon plus six extra pairs of neutral preons, e.g. photon+AA’BB’CC’AA’BB’CC’. In interaction 9, a ¼higgs- {i.e. ABC’C’} is one of the particles going into the interaction and a vacuum particle/field (or axion boson) is emitted {AA’BB’}. The ¼higgs and ½higgs are candidates for dark matter. The full higgs was only detected by its decay paths whereas the ¼higgs cannot decay and it is already participating {according to model #5} in ordinary, well known interactions as a silent partner.
24 May 2014
(Revised 29 September 2014 to include the term axion for the scalar boson or vacuum)
Manchester, UK
GAME NO LONGER WORKS BECAUSE THE EXCEL FILE TYPE IS NOT ALLOWED ON WORDPRESS.
Attached is an Excel 2007 (.xlsm) file which uses Virtual Basic software
to allow virtual dice to be rolled. Different combinations of rolled dice
generate different elementary particles, according to my Preon Model 5.
Dice game for Model 5 elementary particles
Just download the file and click on appropriate buttons to roll the dice.
4 big dice give electrons, photons and neutrinos.
8 big dice give the Z and W.
12 big dice give the muon and muon neutrino.
16 big dice give the higgs and gluon.
20 big dice give the tauon and tauon neutrino.
3 small dice and three big dice give the up and down quarks
3 small dice and eleven big dice give the charm and strange quarks
3 small dice and nineteen big dice give the top and bottom quarks.
Have fun!
Ben6993
Manchester
England
1 January 2014
(Revised and renamed 14 January 2014)
(Revised 27 January 2014)
Introduction
In this paper, 48 types of preon are listed. Preons of various types are arranged in six autonomous blocks or neutral-colour units with 24 preons per unit in Units A, B, C, A’, B’ and C’. Two of the neutral-colour units (C and C’) can each be divided into three single-colour sub-units with eight preons per sub-unit (Cr, Cg, Cb, C’r’, C’g’ and C’b’). Elementary particles are formed when multiples of four units combine, ranging from the left-handed electron (four units: AAA’C) to a right-handed top quark (nineteen units plus three sub-units, for example: A’C’g’CrC’b’AA’BB’CC’AA’BB’CC’AA’BB’CC’).
The 48 Preons
The first property of a preon is electrical charge, either + or – charge. This can be associated with a chiral structure for the preon. Say the negative charge is connected to a left-handed preon, L. The right-handed preon, R, will have a positive charge. There are also three colour charges (red [r], green [g] and blue [b]) and three anticolour charges (antired [r’], antigreen [g’] and antiblue [b’]). Colour charges are connected to the L preon while anticolour charges are connected to the R preon. Every preon has either spin + or spin – and has weak isospin + or -. The 24 matter preons can have 24 antimatter preons (denoted L’ and R’) making 48 different preons in total.
Preons can be labelled as : Preon (electric charge) ( spin) (weak isospin) (colour charge) e.g. R ’ – + – r.
The 48 preons are:
24 preons
L- – -r | L–+r | L-+-r | L-++r | |
L- – -g | L–+g | L-+-g | L-++g | |
L- – -b | L–+b | L-+-b | L-++b | |
R+–r’ | R+-+r’ | R++-r’ | R+++r’ | |
R+–g’ | R+-+g’ | R++-g’ | R+++g’ | |
R+–b’ | R+-+b’ | R++-b’ | R+++b’ |
24 antipreons
L’+–r’ | L’+-+r’ | L’++-r’ | L’+++r’ | |
L’+–g’ | L’+-+g’ | L’++-g’ | L’+++g’ | |
L’+–b’ | L’+-+b’ | L’++-b’ | L’+++b’ | |
R’- – -r | R’–+r | R’-+-r | R’-++r | |
R’- – -g | R’–+g | R’-+-g | R’-++g | |
R’- – -b | R’–+b | R’-+-b | R’-++b |
(A preon’s electric charge is + or – 1/48; A preon’s spin is + or – 1/48; A preon’s weak isospin is + or – 1/48.)
The six neutral-colour units: A, B, C , A’, B’ and C’
Preon Unit A : 24 preons with equal numbers of types L- – -a, L- – -g, L- – -b, R’- – -r, R’- – -g and R’- – -b.
Total electric charge -1/2; total spin -1/2; and total weak isospin -1/2
L- – -r | L- – -r | L- – -r | L- – -r | |
L- – -g | L- – -g | L- – -g | L- – -g | |
L- – -b | L- – -b | L- – -b | L- – -b | |
R’- – -r | R’- – -r | R’- – -r | R’- – -r | |
R’- – -g | R’- – -g | R’- – -g | R’- – -g | |
R’- – -b | R’- – -b | R’- – -b | R’- – -b |
Preon Unit B : 48 preons with equal numbers of types L-+-a, L-+-g, L-+-b, R’-+-r, R’-+-g, R’-+-b and
L-++a, L-++g, L-++b, R’-++r, R’-++g, R’-++b
Total electric charge -1/2; total spin +1/2; and total weak isospin is zero
L-+-r | L-++r | L-+-r | L-++r | |
L-+-g | L-++g | L-+-g | L-++g | |
L-+-b | L-++b | L-+-b | L-++b | |
R’-+-r | R’-++r | R’-+-r | R’-++r | |
R’-+-g | R’-++g | R’-+-g | R’-++g | |
R’-+-b | R’-++b | R’-+-b | R’-++b |
Preon Unit C : 48 preons with equal numbers of all types of L and R’ preons
Total electric charge -1/2; total spin is zero; and total weak isospin is zero
L- – -r | L–+r | L-+-r | L-++r | |
L- – -g | L–+g | L-+-g | L-++g | |
L- – -b | L–+b | L-+-b | L-++b | |
R’- – -r | R’–+r | R’-+-r | R’-++r | |
R’- – -g | R’–+g | R’-+-g | R’-++g | |
R’- – -b | R’–+b | R’-+-b | R’-++b |
Preon Unit A’ : 48 preons with equal numbers of types L’+++r’, L’+++g’, L’+++b’, L’+++r’, L’+++g’, L’+++b’ .
Total electric charge +1/2; total spin +1/2; and total weak isospin +1/2
L’+++r’ | L’+++r’ | L’+++r’ | L’+++r’ | |
L’+++g’ | L’+++g’ | L’+++g’ | L’+++g’ | |
L’+++b’ | L’+++b’ | L’+++b’ | L’+++b’ | |
R+++r’ | R+++r’ | R+++r’ | R+++r’ | |
R+++g’ | R+++g’ | R+++g’ | R+++g’ | |
R+++b’ | R+++b’ | R+++b’ | R+++b’ |
Preon Unit B’ : 48 preons with equal numbers of types L’+–r’, L’+–g’, L’+–b’, R+–r’, R+–g’, R+–b’ and
L’+-+r’, L’+-+g’, L’+-+b’, R+-+r’, R+-+g’, R+-+b’
Total electric charge +1/2; total spin -1/2; and total weak isospin is zero
L’+–r’ | L’+-+r’ | L’+–r’ | L’+-+r’ | |
L’+–g’ | L’+-+g’ | L’+–g’ | L’+-+g’ | |
L’+–b’ | L’+-+b’ | L’+–b’ | L’+-+b’ | |
R+–r’ | R+-+r’ | R+–r’ | R+-+r’ | |
R+–g’ | R+-+g’ | R+–g’ | R+-+g’ | |
R+–b’ | R+-+b’ | R+–b’ | R+-+b’ |
Preon Unit C’ : 48 preons with equal numbers of all types of L’ and R preons
Total electric charge +1/2; total spin is zero; and total weak isospin is zero
L’+–r’ | L’+-+r’ | L’++-r’ | L’+++r’ | |
L’+–g’ | L’+-+g’ | L’++-g’ | L’+++g’ | |
L’+–b’ | L’+-+b’ | L’++-b’ | L’+++b’ | |
R+–r’ | R+-+r’ | R++-r’ | R+++r’ | |
R+–g’ | R+-+g’ | R++-g’ | R+++g’ | |
R+–b’ | R+-+b’ | R++-b’ | R+++b’ |
The six colour sub-units: Cr, Cg, Cb, C’r’, C’g’ and C’b’
Preon Unit Cr : 16 red preons with equal numbers of all types of L and R’ preons
Total electric charge -1/6; total spin is zero; and total weak isospin is zero
L- – -r | L–+r | L-+-r | L-++r | |
R’- – -r | R’–+r | R’-+-r | R’-++r |
Preon Unit Cg : 16 green preons with equal numbers of all types of L and R’ preons
Total electric charge -1/6; total spin is zero; and total weak isospin is zero
L- – -g | L–+g | L-+-g | L-++g | |
R’- – -g | R’–+g | R’-+-g | R’-++g |
Preon Unit Cb : 16 blue preons with equal numbers of all types of L and R’ preons
Total electric charge -1/6; total spin is zero; and total weak isospin is zero
L- – -b | L–+b | L-+-b | L-++b | |
R’- – -b | R’–+b | R’-+-b | R’-++b |
Preon Unit C’r’ : 16 antired preons with equal numbers of all types of L’ and R preons
Total electric charge +1/6; total spin is zero; and total weak isospin is zero
L’+–r’ | L’+-+r’ | L’++-r’ | L’+++r’ | |
R+–r’ | R+-+r’ | R++-r’ | R+++r’ |
Preon Unit C’g’ : 16 antigreen preons with equal numbers of all types of L’ and R preons
Total electric charge +1/6; total spin is zero; and total weak isospin is zero
L’+–g’ | L’+-+g’ | L’++-g’ | L’+++g’ | |
R+–g’ | R+-+g’ | R++-g’ | R+++g’ |
Preon Unit C’b’ : 16 antiblue preons with equal numbers of all types of L’ and R preons
Total electric charge +1/6; total spin is zero; and total weak isospin is zero
L’+–b’ | L’+-+b’ | L’++-b’ | L’+++b’ | |
R+–b’ | R+-+b’ | R++-b’ | R+++b’ |
Summary of preon unit and sub-unit properties
Unit/sub-unit | Number of preons | Electric charge | Spin | Weak isospin | Colour |
A | 24 | -1/2 | -1/2 | -1/2 | neutral |
B | 24 | -1/2 | +1/2 | 0 | neutral |
C | 24 | -1/2 | 0 | 0 | neutral |
A’ | 24 | +1/2 | +1/2 | +1/2 | neutral |
B’ | 24 | +1/2 | -1/2 | 0 | neutral |
C’ | 24 | +1/2 | 0 | 0 | neutral |
Cr | 8 | -1/6 | 0 | 0 | red |
Cg | 8 | -1/6 | 0 | 0 | green |
Cb | 8 | -1/6 | 0 | 0 | blue |
C’r’ | 8 | +1/6 | 0 | 0 | antired |
C’g’ | 8 | +1/6 | 0 | 0 | antigreen |
C’b’ | 8 | +1/6 | 0 | 0 | antiblue |
Unit properties of electric charge, spin and weak isospin are simple sums of the values of those properties of the preons in those units . Every unit and sub-unit contains an equal number of matter and anti-matter preons.
Calculating particle colour from preon sub-unit colour
Firstpreon color sub-unit | Secondpreon color sub-unit | Thirdpreon color sub-unit | Particle colour | |
r | g | b | neutral | |
r | g | b’ | antiblue | |
r | g’ | b | antigreen | |
r | g’ | b’ | red | |
r’ | g | b | antired | |
r’ | g | b’ | green | |
r’ | g’ | b | blue | |
r’ | g’ | b’ | neutral |
Index of tables of particles
Particles are made from combinations of :
four preon units (electron, photon, neutrino) | |
eight preon units (Z, W) | |
twelve preon units (muon, muon neutrino) | |
sixteen preon units (Higgs, gluon) | |
twenty preon units (tauon, tauon neutrino) | |
32 preon units (2-Higgs, gluon) | |
three colour sub-units plus three unit (up, down) | |
three colour sub-units plus eleven units (charm, strange) | |
three colour sub-units plus nineteen units (top,bottom) |
Two preon units
Combinations of only two units, in Model 5, are not elementary particles but show the essential constuents which give the required charge, spin and weak isospin properties of electrons, neutrinos and W particles. The scalar combinations are important to the model as they form neutral building blocks to add to the two-unit combinations to generate 4-unit or more particles.
21 combinations of two units:
Preon units | Electric charge | Spin | Weak isospin | Combination type | |
AC | -1 | -0.5 | -0.5 | l.h. electron | |
BC | -1 | 0.5 | 0 | r.h. electron | |
AC’ | 0 | -0.5 | -0.5 | l.h. antineutrino | |
B’C | 0 | -0.5 | 0 | l.h. sterile neutrino | |
A’C | 0 | 0.5 | 0.5 | r.h neutrino | |
BC’ | 0 | 0.5 | 0 | sterile antineutrino | |
AA | -1 | -1 | -1 | W- | |
A’A’ | 1 | 1 | 1 | W+ | |
B’C’ | 1 | -0.5 | 0 | l.h. positron | |
A’C’ | 1 | 0.5 | 0.5 | r.h. positron | |
non-standard model: | |||||
AB | -1 | 0 | -0.5 | quasi-electron? | |
A’B’ | 1 | 0 | 0.5 | quasi-positron? | |
B’B’ | 1 | -1 | 0 | l.h. W+ ? | |
BB | -1 | 1 | 0 | r.h. W- ? | |
AA’ | 0 | 0 | 0 | scalar particle | |
BB’ | 0 | 0 | 0 | scalar particle | |
CC’ | 0 | 0 | 0 | scalar particle | |
CC | -1 | 0 | 0 | spinless electron | |
C’C’ | 1 | 0 | 0 | spinless positron | |
AB’ | 0 | -1 | -0.5 | quasi-photon? | |
A’B | 0 | 1 | 0.5 | quasi-photon? |
Four preon units (electron, photon, neutrino)
The four-unit combinations are the smallest combinations for the photon and higgs particles and the four-unit block is taken here as the smallest form of any elementary particle. For example a left-handed electron could be ACAA’ or ACBB’ or ACCC’.
Preon units | Electric charge | Spin | Weak isospin | Particle name |
ACx^{1} | -1 | -0.5 | -0.5 | l.h. electron |
BCx^{1} | -1 | 0.5 | 0 | r.h. electron |
A’C’x^{1} | 1 | 0.5 | 0.5 | r.h. positron |
B’C’x^{1} | 1 | 0.5 | 0.5 | l.h. positron |
AC’x^{1} | 0 | -0.5 | -0.5 | l.h. antineutrino |
BC’x^{1} | 0 | 0.5 | 0 | r.h.sterile antineutrino |
A’Cx^{1} | 0 | 0.5 | 0.5 | r.h. neutrino |
B’Cx^{1} | 0 | -0.5 | 0 | l.h. sterile neutrino |
B’B’CC | 0 | -1 | 0 | photon |
BBC’C’ | 0 | 1 | 0 | photon |
non-standard model: | ||||
x^{2} | 0 | 0 | 0 | scalar particle or axion |
ABC’C’ | 0 | 0 | -0.5 | Higgs-like particle |
A’B’CC | 0 | 0 | +0.5 | Higgs-like particle |
where x^{1}=any one of three pairs: AA’ or BB’or CC’
where x^{2}= any two pairs from AA’ or BB’or CC’, e.g. AA’AA’ or AA’BB’ or BB’CC’
Hence there are 3 forms reperented by an x^{1}, 9 forms represented by an x^{2} , and 3^{n} forms represented by x^{n}.
The higher generations of particles which follow use the above basic forms plus the addition of scalar pairs of preon units. Quarks are dealt with later in the paper.
Eight preon units (Z, W)
Preon units | Electric charge | Spin | Weak isospin | Particle name |
AAx^{3} | -1 | -1 | -1 | l.h. W- |
A’A’x^{3} | 1 | 1 | 1 | r.h. W+ |
B’B’CCx^{2} | 0 | -1 | 0 | Z |
BBC’C’x^{2} | 0 | 1 | 0 | Z |
non-standard model: | ||||
x^{4} | 0 | 0 | 0 | scalar particle or axion |
ABC’C’x^{2} | 0 | 0 | -0.5 | Higgs-like particle |
A’B’CCx^{2} | 0 | 0 | 0.5 | Higgs-like particle |
where x^{2}= any two pairs from AA’ or BB’or CC’, e.g. AA’AA’ or AA’BB’ or BB’CC’
where x^{3}= any three pairs from AA’ or BB’or CC’, e.g. AA’AA’BB’ or AA’BB’CC’
where x^{4}= any four pairs from AA’ or BB’or CC’, e.g. AA’AA’BB’CC’
Twelve preon units (muon, muon neutrino)
Preon units | Electric charge | Spin | Weak isospin | Particle name |
ACx^{5} | -1 | -0.5 | -0.5 | l.h. muon- |
BCx^{5} | -1 | 0.5 | 0 | r.h. muon- |
AC’x^{5} | 0 | -0.5 | -0.5 | l.h. muon antineutrino |
B’Cx^{5} | 0 | -0.5 | 0 | l.h. muon neutrino |
BC’x^{5} | 0 | 0.5 | 0 | r.h. muon antineutrino |
A’Cx^{5} | 0 | 0.5 | 0.5 | r.h. muon neutrino |
B’C’x^{5} | 1 | -0.5 | 0 | l.h. muon+ |
A’C’x^{5} | 1 | 0.5 | 0.5 | r.h. muon+ |
non-standard model: | ||||
x^{6} | 0 | 0 | 0 | scalar particle or axion |
ABC’C’ x^{4} | 0 | 0 | -0.5 | Higgs-like particle |
A’B’CC x^{4} | 0 | 0 | +0.5 | Higgs-like particle |
where x^{n}= any n pairs from AA’ or BB’or CC’
Sixteen preon units (gluon, Higgs)
Preon units | Electric charge | Spin | Weak isospin | Particle name |
B’B’CCx^{6} | 0 | -1 | 0 | gluon |
BBC’C’x^{6} | 0 | 1 | 0 | gluon |
ABC’C’x^{6} | 0 | 0 | -0.5 | Higgs |
A’B’CCx^{6} | 0 | 0 | 0.5 | Higgs |
x^{8} | 0 | 0 | 0 | scalar particle or axion |
where x^{6 }= any six pairs from AA’ or BB’or CC’, e.g. AA’AA’BB’BB’BB’CC’
where x^{8 }= any four pairs from AA’ or BB’or CC’, e.g. AA’AA’AA’BB’BB’CC’CC’CC’
Twenty preon units (tauon and tauon neutrino)
Preon units | Electric charge | Spin | Weak isospin | Particle name |
ACx^{9} | -1 | -0.5 | -0.5 | l.h. tauon- |
BCx^{9} | -1 | 0.5 | 0 | r.h. tauon- |
B’Cx^{9} | 0 | -0.5 | 0 | l.h. tauon neutrino |
BC’x^{9} | 0 | 0.5 | 0 | r.h. tauon antineutrino |
A’Cx^{9} | 0 | 0.5 | 0.5 | r.h. tauon neutrino |
AC’x^{9} | 0 | -0.5 | -0.5 | l.h. tauon antineutrino |
B’C’x^{9} | 1 | -0.5 | 0 | l.h. tauon+ |
A’C’x^{9} | 1 | 0.5 | 0.5 | r.h. tauon+ |
non-standard model: | ||||
x^{10} | 0 | 0 | 0 | scalar particle or axion |
ABC’C’ x^{8} | 0 | 0 | -0.5 | Higgs-like particle |
A’B’CC x^{8} | 0 | 0 | +0.5 | Higgs-like particle |
where x^{n}= any n pairs from AA’ or BB’or CC’
Three colour sub-units plus three units (up quark, down quark)
Preon unit andsub-units | Electric charge | Spin | Weak isospin | ParticleColour | Particle name |
ACgCbC’r’X^{1} | -0.7 | -0.5 | -0.5 | r’ | LH antiup |
AC’g’CbCrX^{1} | -0.7 | -0.5 | -0.5 | g’ | LH antiup |
ACgC’b’CrX^{1} | -0.7 | -0.5 | -0.5 | b’ | LH antiup |
BCgCbC’r’ X^{1} | -0.7 | 0.5 | 0 | r’ | RH antiup |
B C’g’CbCrX^{1} | -0.7 | 0.5 | 0 | g’ | RH antiup |
B CgC’b’CrX^{1} | -0.7 | 0.5 | 0 | b’ | RH antiup |
AC’g’CrC’b’ X^{1} | -0.3 | -0.5 | -0.5 | r | LH down |
ACgC’r’C’b’ X^{1} | -0.3 | -0.5 | -0.5 | g | LH down |
AC’g’C’r’Cb X^{1} | -0.3 | -0.5 | -0.5 | b | LH down |
BC’g’CrC’b’ X^{1} | -0.3 | 0.5 | 0 | r | RH down |
BCgC’r’C’b’ X^{1} | -0.3 | 0.5 | 0 | g | RH down |
BC’g’C’r’Cb X^{1} | -0.3 | 0.5 | 0 | b | RH down |
B’CgCbC’r’ X^{1} | 0.3 | -0.5 | 0 | r’ | LH antidown |
B’C’g’CbCr X^{1} | 0.3 | -0.5 | 0 | g’ | LH antidown |
B’CgC’b’Cr X^{1} | 0.3 | -0.5 | 0 | b’ | LH antidown |
A’CgCbC’r’ X^{1} | 0.3 | 0.5 | 0.5 | r’ | RH antidown |
A’C’g’CbCr X^{1} | 0.3 | 0.5 | 0.5 | g’ | RH antidown |
A’CgC’b’Cr X^{1} | 0.3 | 0.5 | 0.5 | b’ | RH antidown |
B’C’g’CrC’b’ X^{1} | 0.7 | -0.5 | 0 | r | LH up |
B’CgC’r’C’b’ X^{1} | 0.7 | -0.5 | 0 | g | LH up |
B’C’g’C’r’Cb X^{1} | 0.7 | -0.5 | 0 | b | LH up |
A’C’g’CrC’b’ X^{1} | 0.7 | 0.5 | 0.5 | r | RH up |
A’CgC’r’C’b’ X^{1} | 0.7 | 0.5 | 0.5 | g | RH up |
A’C’g’C’r’Cb X^{1} | 0.7 | 0.5 | 0.5 | b | RH up |
where x^{1}= any one pair from AA’ or BB’or CC’.
Three colour sub-units plus eleven units (charm quark, strange quark)
Preon unit andsub-units | Electric charge | Spin | Weak isospin | ParticleColour | Particle name |
ACgCbC’r’X^{5} | -0.7 | -0.5 | -0.5 | r’ | LH anticharm |
AC’g’CbCrX^{5} | -0.7 | -0.5 | -0.5 | g’ | LH anticharm |
ACgC’b’CrX^{5} | -0.7 | -0.5 | -0.5 | b’ | LH anticharm |
BCgCbC’r’ X^{5} | -0.7 | 0.5 | 0 | r’ | RH anticharm |
B C’g’CbCrX^{5} | -0.7 | 0.5 | 0 | g’ | RH anticharm |
B CgC’b’CrX^{5} | -0.7 | 0.5 | 0 | b’ | RH anticharm |
AC’g’CrC’b’ X^{5} | -0.3 | -0.5 | -0.5 | r | LH strange |
ACgC’r’C’b’ X^{5} | -0.3 | -0.5 | -0.5 | g | LH strange |
AC’g’C’r’Cb X^{5} | -0.3 | -0.5 | -0.5 | b | LH strange |
BC’g’CrC’b’ X^{5} | -0.3 | 0.5 | 0 | r | RH strange |
BCgC’r’C’b’ X^{5} | -0.3 | 0.5 | 0 | g | RH strange |
BC’g’C’r’Cb X^{5} | -0.3 | 0.5 | 0 | b | RH strange |
B’CgCbC’r’ X^{5} | 0.3 | -0.5 | 0 | r’ | LH antistrange |
B’C’g’CbCr X^{5} | 0.3 | -0.5 | 0 | g’ | LH antistrange |
B’CgC’b’Cr X^{5} | 0.3 | -0.5 | 0 | b’ | LH antistrange |
A’CgCbC’r’ X^{5} | 0.3 | 0.5 | 0.5 | r’ | RH antistrange |
A’C’g’CbCr X^{5} | 0.3 | 0.5 | 0.5 | g’ | RH antistrange |
A’CgC’b’Cr X^{5} | 0.3 | 0.5 | 0.5 | b’ | RH antistrange |
B’C’g’CrC’b’ X^{5} | 0.7 | -0.5 | 0 | r | LH charm |
B’CgC’r’C’b’ X^{5} | 0.7 | -0.5 | 0 | g | LH charm |
B’C’g’C’r’Cb X^{5} | 0.7 | -0.5 | 0 | b | LH charm |
A’C’g’CrC’b’ X^{5} | 0.7 | 0.5 | 0.5 | r | RH charm |
A’CgC’r’C’b’ X^{5} | 0.7 | 0.5 | 0.5 | g | RH charm |
A’C’g’C’r’Cb X^{5} | 0.7 | 0.5 | 0.5 | b | RH charm |
where x^{5}= any five pairs from AA’ or BB’or CC’.
Three colour sub-units plus nineteen units (top quark, bottom quark)
Preon unit andsub-units | Electric charge | Spin | Weak isospin | ParticleColour | Particle name |
ACgCbC’r’X^{9} | -0.7 | -0.5 | -0.5 | r’ | LH antitop |
AC’g’CbCrX^{9} | -0.7 | -0.5 | -0.5 | g’ | LH antitop |
ACgC’b’CrX^{9} | -0.7 | -0.5 | -0.5 | b’ | LH antitop |
BCgCbC’r’ X^{9} | -0.7 | 0.5 | 0 | r’ | RH antitop |
B C’g’CbCrX^{9} | -0.7 | 0.5 | 0 | g’ | RH antitop |
B CgC’b’CrX^{9} | -0.7 | 0.5 | 0 | b’ | RH antitop |
AC’g’CrC’b’ X^{9} | -0.3 | -0.5 | -0.5 | r | LH bottom |
ACgC’r’C’b’ X^{9} | -0.3 | -0.5 | -0.5 | g | LH bottom |
AC’g’C’r’Cb X^{9} | -0.3 | -0.5 | -0.5 | b | LH bottom |
BC’g’CrC’b’ X^{9} | -0.3 | 0.5 | 0 | r | RH bottom |
BCgC’r’C’b’ X^{9} | -0.3 | 0.5 | 0 | g | RH bottom |
BC’g’C’r’Cb X^{9} | -0.3 | 0.5 | 0 | b | RH bottom |
B’CgCbC’r’ X^{9} | 0.3 | -0.5 | 0 | r’ | LH antibottom |
B’C’g’CbCr X^{9} | 0.3 | -0.5 | 0 | g’ | LH antibottom |
B’CgC’b’Cr X^{9} | 0.3 | -0.5 | 0 | b’ | LH antibottom |
A’CgCbC’r’ X^{9} | 0.3 | 0.5 | 0.5 | r’ | RH antibottom |
A’C’g’CbCr X^{9} | 0.3 | 0.5 | 0.5 | g’ | RH antibottom |
A’CgC’b’Cr X^{9} | 0.3 | 0.5 | 0.5 | b’ | RH antibottom |
B’C’g’CrC’b’ X^{9} | 0.7 | -0.5 | 0 | r | LH top |
B’CgC’r’C’b’ X^{9} | 0.7 | -0.5 | 0 | g | LH top |
B’C’g’C’r’Cb X^{9} | 0.7 | -0.5 | 0 | b | LH top |
A’C’g’CrC’b’ X^{9} | 0.7 | 0.5 | 0.5 | r | RH top |
A’CgC’r’C’b’ X^{9} | 0.7 | 0.5 | 0.5 | g | RH top |
A’C’g’C’r’Cb X^{9} | 0.7 | 0.5 | 0.5 | b | RH top |
where x^{9}= any nine pairs from AA’ or BB’or CC’.
Conclusion
The paper shows a model for building elementary particles from six neutral-colour units and six coloured sub-units of preons. The units are buit up from 48 different types of preon.
The sterile neutrino is in the list of particles, as is the Higgs and some completely scalar particles (or axion bosons). There are spinless bosons and spinless fermions in each generation of particles. In the higher generations, there are many combinations of spin with weak isospin, not listed in this paper, which are not found so frequently in the early generations, e.g. spin -3.5 with weak isospin -1.5. There are elementary particles found, but not listed here, listed with absolute values of electric charge greater than 1.
20 January 2014
Revised 22 May 2014 (Revised labelling of neutrinos and antineutrinos)
Revised 29 September 2014 (to include the term axion and to amend a typo in the forms of the RH d’, RH s’ and RH b’ antiquarks)
Manchester
England