The short answer is that the rishon model doesn't have anything to do with the paper quoted.  First of all, it is possible to write the Standard Model and, in general, any field theory, in the Hamiltonian formalism, i.e. in phase space-so the premise, already, isn't appropriate. Next, in the non-relativistic approximation studied in the paper, there *isn't* any relation between a particle and its putative antiparticle: the CPT theorem, that does establish the relations between particles and antiparticles and proved by Pauli, Lüders and Zumino (cf. also Burgoyne's work later), relies on locality, Lorentz invariance and a positive definite Hilbert space. 

Models that unify quark and lepton representations are relativistic quantum field theories, that attempt to generalize the Standard Model. They, too, can be written in the Hamiltonian formalism. Insofar as the ``rishon model'' is a Grand Unified Theory, the issue is proton decay. But its validity doesn't have anything to do with the paper quoted.

Thank you, Stam, for your answer. Best wishes

I've been playing with the central problem of the rishon model which I think is "what happens to that darned spin angular momentum? Cause 2x2x2 doesn't give 2." My claim is that the spin of the Ts and Vs becomes the generations of the standard model. The paper is "Spin Path Integrals" at Foundations of Physics: http://arxiv.org/abs/1006.3114

That paper promotes Koide's coincidence in the lepton generation masses to a double coincidence and proposes a corresponding formula for the neutrino masses. The extension of these to the quarks was published (PRD) by the same Piotr Zenczykowski whose paper you reference, see: http://arxiv.org/abs/1301.4143v2 and http://arxiv.org/abs/1210.4125v2

A way to get to Koide formula without having the Spin Path integral idea is to note that these coincidences arise by taking the discrete Fourier transform of the square roots of the masses (idea due to Marni Sheppeard for example see http://vixra.org/pdf/0711.0001v1.pdf ). This makes sense in that in making simplifications in particle physics, Fourier transforms are your buddy, so why shouldn't they work on the generations. But I think the simplicity of the rishon model is a good argument that it's related to the generation problem.

@Carl: thank you for your answer, i will read the paper you cited. Best wishes

carl: fascinating to see that you are also pursuing the rishon model, i will definitely read up on what you wrote, i haven't kept up-to-date for 18 months since writing the "extended rishon model".

victor: i first explored the original rishon model back in 1986, and discovered (as i rediscovered in 2012) that there are discrepancies in the sign of the V particles as designated by professor harari.  once i inverted the sign of the V particles everything fell into place and, unlike the time in 1986, when the particles discovered were far fewer, this time i was able to make a significant number of logical deductions and even make some predictions about possible particles and research for particle physicists.

but the thing you have to remember is that the rishon model is unnnnnbelievably low-level, yet really quite crude at the same time.  it's sort-of a topological model, so doesn't give you any "maths" to work with, as such - just logic.

if you can accept that the rishon model's "T" and "V" are like "machine code bits" rather than "Full-Blown Pentium Processor With Floating Point" then it is possible to get along with it.

to give you some idea, i managed to work out the strange quark-anti-quark interaction, in terms of rishons.  there were over 90 rishons in the diagram (including in the intermediary bosons), every single one of those rishons needed to find a "home" - an arrow - to the intermediary particle and from there to the end result.  in other words FANTASTICALLY tedious (like executing machine code *BITS* -  not even BYTES - by hand!!) and it often would take me THREE hours just to work out a single phase transform (the name i eventually gave to "particle decay").

what the rishon model that haim harari came up with does *NOT* include any kind of lepton-style rules for particle "decay".  i had to work those rules out, and go a lot further than anyone else has - so i called it the "extended rishon model" because that's what it is.

if you're interested, an HTML version of the paper i wrote is at http://lkcl.net/reports/rishon_model/

btw, stam: yes i managed to solve the issue of proton (and neutron) "decay"  (aka "phase transform" in extended rishon terminology).  it's... complicated, and unfortunately for the standard model indicates that there is a gluon unaccounted for (i.e. has been overlooked) in the particle "decay" of the proton (and the neutron).   let me just double-check that, it's been a while since i was working on this stuff... yes, look up the section "the puzzle of the neutron and its decay".

basically, for phase transforms (aka "decays") to work, the total number of rishon-anti-rishons in each of the T and V types *must* come *exactly* to zero (and the intermediate particles comprising T and V rishons must also obey the rules i.e. must be stable particles themselves).

what that means is that the standard model's rules are... wonky.  but unless you take "V" into account, it is *impossible* to determine that!  in other words, taking only the available electrical charge into account, it is *perfectly reasonable* to empirically derive the "Lepton Number" rules and so on... but when you add in "V" particles the standard model rules just do not add up.

now the thing about the gluon that has to be there alongside its matching W-Boson is that the gluon is, by definition, an instantaneous creation-and-disappearance act.  given that the W-Boson is 90MEv or thereabouts and longer-lived, it's hardly surprising that, if the extended rishon model is correct, the associated and necessary gluon would have been completely overlooked!

now, with all that as background.... :)

... in the *mainstream* theoretical physics community, i get the feeling that anyone exploring anything *other* than the standard model is taking a huge risk with their career.  i do not *have* a career in particle physics to be threatened by publishing in this field, so may be honest and up-front.  and anyone that *does* publish anything different is forced to link it somehow - mathematically - to the standard model, otherwise it cannot be accepted.

that having been said, the rishon model (or the extended rishon model) is.... how can i put this... it's like it's the "equals zero" or "equals one" at the end of a huge set of mathematical equations.  it's like... it's a "summary position".  i found that i *didn't need* all the complicated equations from the standard model in order to be able to make perfectly rational and logically-consistent (albeit incredibly tedious and long-winded) conclusions, rules and deductions.

and i believe that's what piotr managed to do, as well: he came up with some equations, the end summary of which (the eigenvalues or whatever) turned out to be "The Rishon Model".

summary: in my view, the approach is valid... but you won't find many theoretical physicists doing it.

[edit to carl: in equation [56] of http://arxiv.org/pdf/1006.3114v1.pdf if you are taking g from values 0 to 2 and considering them to be entries in a matrix, summing them somehow later, the fact that the equation says 2/3 pi times g... *THAT* is what i would consider to be "Rishons", mathematically.  in other words you simply cannot have "separate rishons" because i believe they are three "pickup points" - the peaks if you will - of a single continuous wave that goes on a 3/2 cycle.  you cannot EVER separate Rishons but you can at least create some rules based on their inferred existence.  the other clue: T = +1 / -1, whilst V = j / -j] - ok that should be 1/3 not 1 :)

@Luke: thank you for your answer. Yours

hi victor it turns out that i had written a much abridged version (and forgotten about it!) http://vixra.org/pdf/1403.0016v2.pdf

1) Stam 's answer is based on a philosophical assumption which - roughly speaking -  identifies theoretical description with physical reality. It does not allow for the possibility that there may be different (perhaps mutually inconsistent) descriptions of reality, which  - starting from somewhat different assumptions - may also be successful. Historical examples for that possibility are not hard to show. The fact that a given theory successfully describes certain aspects of reality does not permit treating this theory as an established *truth*. It may be treated only as a temporary and/or limited truth. Therefore, attempts at different descriptions should be made. My paper involves elements of such an attempt. 

2)  The word "anything" in the statement "The short answer is that the rishon model doesn't have anything to do with the paper quoted." is not appropriate. Indeed, anybody can see that there are certain similarities. Yet, it is true that one should distinguish the original rishon model from its successful 'preonless' part. This is stressed in my recent paper "The Harari-Shupe observation without preons - a glimpse into physics to come?", arXiv:1503.07773 [physics.gen-ph] to appear in  April 2016 issue of Acta Phys. Pol. B.    

3) Relativity is not a necessary assumption needed to infer the existence of antiparticles, Nonrelativistic Schrodinger equation when linearized a la Dirac also leads to solutions that may be interpreted as antiparticles. As an intuitive argument against the crucial role of relativity consider Feynman's picture of antiparticles as particles 'moving backward in time' which does not depend on the velocity of particle's motion. The fact that CPT theorem is proved in field-theoretical framework does not exclude the possibility that CPT may be built also into a different scheme.  It is built in into my approach.

4) Going beyond the Standard Model description may require questioning several pieces of the standard field-theoretical framework. The questionable pieces include the concept of mass, and the concept of point. Explanation of the details would take too much here. The proper place are the papers themselves, eg. 'Elementary particles, the concept of mass, and emergent spacetime' - J.Phys.Conf.Ser. 626 (2015) 1, 012022. (open access)

piotr, nice to see that someone is still publishing papers about rishons, especially someone with the mathematical knowledge to understand the standard model as well.

since posting on this topic last, my thoughts began to coalesce around the idea that particles are pure light (photons), and that the rishon model is merely showing the "peaks" and "troughs" of the phased-array of photons that happen to be so curled that they actually meet back where they started, and thus continue in a consistent and self-sustaining endless cycle.

finding particle physics papers that support this concept were... basically... zero.

so i began to explore optics physics (both theoretical and practical) because there, at least, the "stigmatism" against the idea of light bending in circles or other shapes is something that is considered normal and even observable.

and i found something amazing: there are REAL experiments where people have managed to create phased-array coherent beams that can LITERALLY go round in circles (or parabolas).  and what's particularly fascinating is that as the phased coherent array bends, the phase also rotates... by half the amount of the angle that the beam turns.  these are PRECISELY the conditions required to generate the concept of "spin 1/2", if we imagine that the x-ray laser was sufficiently tuned so as to create a phased array where the diameter of the circle was of the order of a compton wavelength.

with this in mind, it is fascinating to note, piotr, that your papers talk about "phase space".  if we consider rishons to be the "peaks" and the "troughs" of a circularly-linked phased-array of photons, then it would make simple sense that an electron would be comprised of peaks and troughs - measurements at critical points on the photons - that are entirely within the "real" number space, that a neutrino would be 90 degrees out of phase with that, such that all three measurement points were in the *complex* number space, and that the up and down quarks are a corresponding mix of the real and imaginary phases inherent within simple Maxwell's Equations as applied to photons.

even the concept of mass is covered by an experimental optics paper that shows that there exists conservation of momentum within light (photons) that are successtully bent in a circle.  the bending actually results in a slow-down of the phased-array of photons (in a way that i cannot say that i fully comprehend).  the only way that a slow-down could possibly occur is if the photons had somehow taken on "mass".  in fact, this concept is covered in other papers which hint that mass *DIRECTLY CORRELATES* with the amount of curvature [of the photon(s)].

from this perspective, the concept of a superconducting electron may be considered to be simply a different harmonic of the wave-pattern - one with two "nodes".  this is borne out by j hirsch's analysis of superconducting electrons, which postulates that the radius of the superconducting electrons has increased.  it also explains "cooper pairs", where is is *believed* that there are two electrons somehow "bound together", but a much simpler explanation - in light of the hypothesis that particles are phase-coherent photons in an infinite-loop - is that a single electron's "inner photons" have jumped to a second-order harmonic.

in further support of this theory, looking closely at how superconductivity occurs, it is when there are rows of opposing-spin particles in a regular pattern (spin-up, spin-down, spin-up, spin-down...).  the hypothesis goes that the photon's normal desire to operate in the simplest (single-order-harmonic) oscillating spin-1/2 pattern is prevented and prohibited... so instead it "pops into second-order harmonic" mode.

i have yet to consider how superconducting electrons should be described in terms of rishons - honestly it is too much to contemplate!

anyway the point is that with rishons being merely a record of the behaviour of a photon (a way to describe its trajectory and phase), it becomes LITERALLY impossible to even contemplate the concept of "A Rishon Particle", because such "particles" - when they are merely a record of the phase at key strategic points - is literally and flat-out impossible.

thus, i believe that piotr is definitely onto something with his work, but also i believe that his work is made much more complex by having to "tie in" earlier work - the direction that the standard model has taken.  that's a much more challenging task, to understand both the old and the new, and i look forward to seeing more papers from you, piotr.

victor, hi: just a follow-up, here, because public discussions about the Rishon Model are so rare.  i am very excited to be able to announce the simple realisation that the Rishon "triplets" (up, down, neutrino, electron) fit equidistantly and logically around a circle - exp(-i 2pi theta) - 0

@Carl Brannen, after re-reading your paper in light of the recent insights on the ERM (elliptically-polarised gaussian mobius light) i can say that categorically equation 56 and the subsequent paragraph are HIGHLY significant.

the following paper gives a formal mathematical link between SU(2)xU(1) and the poincare sphere https://arxiv.org/abs/1303.4496 whereupon it becomes possible to transform between the standard model and the concept of mobius double-gaussians.

note that Jones Calculus the elliptical polarisation axis is AUTOMATICALLY divided by two, which is where that pi / 12 (not pi / 6) keeps cropping up that you and Marni noticed and worked on.

it's a hell of a long mathematical trail of breadcrumbs but i can say that you were definitely on to something.

ok so the exploration that i did last year paid off, as i am finally crystallising what the heck is going on here. the key is that the Rishon Model is a beautiful mathematical coincidence relating to the properties of an equilateral triangle (sin30 = 1/2 and sin^2(30) + cos^2(30) = 1).

by mapping rishons onto a circle (with a phase associated with each), so TTT = a unit vector straight up at phase 0, TVT = a unit vector at 30 degrees, VTV at 60, VVV at 90 and so on round the clock, we then find that compound particles can fulfil critical Jones Matrices on Poincare Sphere (Castillo 2008) non-destructive interference criteria that allow *multiple* base particles to co-exist simultaneously.

so it's not that the Rishon Model is valid (or invalid), it's that it's a single glimpse onto what's going on, where unfortunately a trick has been missed for over 30 years (by everyone including myself) which underscores the Model's true significance.