lkcl

ok so i worked out the answer, http://vixra.org/abs/1702.0131 and it's that it's possible to superimpose any two out of only eight unit-vectors around a clock separated by thirty degrees, if you phase-offset one of them by 180 first. this results in the elliptical axis being phase-shifted by 90 degrees, and it results in the EM field being orthogonal (at right angles) at all points. the waves must obviously be of the same frequency. triple superposition is also possible, but amazingly there are only 32 possible permutations (out of a possible 3^12) that will work. i do not know what the actual end-result looks like (what the actual sum is, nor the elliptical axis angle following the superposition) because i am not a mathematician. this is however an extremely important mathematical result that hasn't been published before. castillo in his 2008 paper notes the conditions under which superposition will occur but does not identify the possible candidates, also he assumes that there is no phase delay. the phase delay of 180 degrees is the key to allowing more candidates than the ones that castillo found. it would also be a signlficant advance for mathematics to find out what the superposition result is.

wtf: i don't know if you're completely aware of quite how hurtful and denigrating your comments really are. i've reported your comment to the moderators of the site, on the basis that it brings the forum into disrepute, doesn't answer the question, and harms my reputation as well as that of the forum. your comment has also unfortunately destroyed any opportunity for receiving an answer from anyone on this forum, when i went to a lot of trouble to write up an explanation of the problem's scope, as well as provide potential people considering answering it with some background about myself and my ability to understand their answer. i trust that you will be a little more careful in future before posting comments that deeply offend people and prevent them from working with others to improve their knowledge and understanding of science.

the 15 pages turned out to be necessary for the last job that i obtained. the skillset was exactly what they required, and they went carefully through every single page asking relevant questions to check that i was in fact competent in the areas that i'd stated that i was. likewise when applying for the H1-B1 visa for Internet Security Systems, demonstrating unique skillsets was an absolute requirement. i simply don't do "employment" any more. i'll do contracting, but the "lying" that is required (by omission) is not something i can tolerate. cutting down pages people demand "so what did you do during the missing years". when i give them the details and explain the comprehensive nature of what i am capable of, they become either scared that i will take THEIR job, or they go "you'll get bored. we can't hire you". then there is the sheer fundamental pathological dishonesty behind "articles of incorporation" - if you are not familiar with this watch the first few minutes of the documentary "The Corporation". and then there is also the fact that in my line of work it is DEMANDED that i sign over all rights to every thought, idea, concept and design, usually these are blanket 24/7 demands. in effect, employment for someone at my skillset is nothing short of outright slavery. don't tell me that a "wage" is sufficient compensation for an organisation that could make 90% of its profits from a concept that you develop, make billions, and not compensate you proportionately to those profits. anyway. what does this have to do with the question, wtf? i don't see the relevance on a maths forum, where i've asked a specific question about maths. if i wanted job advice i would have asked for... job advice, and i would not have asked for job advice on... a maths forum.

Hi, I am looking for a very special and unique mathematical solution which, from another direction of investigation not related to maths, I have reason to believe exists, which is to work out those phases of a "mobius light" configuration that will superimpose properly. For references about the recent experimental work in which "mobius light" was successfully demonstrated, see arxiv:1601.06072, and for the theoretical work dating back to 2009, see Isaac Freund's paper arxiv:0910.1663 Please bear in mind: I am a software engineer, I have a CV 15 pages long, I am not a n00b but my mathematical ability is that of an O'Level / A'Level student, whereas my knowledge-derivation, inference, logical reasoning and reverse-engineering skills - and persistence - are extremely high. In looking up the wikipedia page on Jones Calculus https://en.wikipedia.org/wiki/Jones_calculus#The_Jones_vector i noted that there are two parts to a Jones Vector: the elliptical polarisation axis that is rotated (E0x), and an exponent part that performs the adjustment of that axis. Asking last week on maths.stackexchange someone kindly confirmed that if the exponent part of two elliptically-polarised light fields were IDENTICAL, then of course the vectors E0x would simply be superimposed (added) as... well... vectors The more challenging part to answer is: are there any *other* circumstances under which two Jones vectors will superimpose? More specifically: if two fields are arranged in a Mobius-strip configuration, under what circumstances (what phase shifts etc.) would the Jones Vectors of two such *ALWAYS* superimpose, other than in the trivial cases? To do that, first it's necessary to define an MS in terms of Jones Vectors, then it's possible to define the relationship between one MS and another. Also: I read up about euler's theorem, the bit where exp (-i x + -i y) = exp( -i x ) exp( -i y ) and that allowed me to re-express the equation for a Jones Vector that you can clearly see on the wikipedia page, as follows: [math]E_{\hat{x}} = E_{n\hat{x}} e^{-i \left( kz / 2 \right) } e^{-i \left( - \omega t / 2 \right) } e^{-i \left( \theta/2 \right) }[/math] and the relationship between each of the MS's elliptical polarization axes is: [math] E_{n\hat{x}} = E_{0\hat{x}} e^{-i \left( \theta \right) }, \theta = n\tau/12 [/math] And tau is of course 2pi Now, here's the bit where I kinda know the answer, but not enough "math" to fill in the gaps, so to speak. The situation which I suspect the Jones Vectors will superimpose is if: (1) The phases are a multiple of 1/12th tau (2) MS1 is rotated by tau / 4 (3) MS2 is rotated by tau / 2 (4) The starting phase of MS1 is *HALF* that of MS2. Under these circumstances, if you express MS2 theta in terms of MS1, you can, through Euler's theorem, find that the common factor is the exponential part of MS1 with the rotation of tau/4 doubled to match the rotation tau/2 of MS2, and it's sorted. so there are therefore situations at MS1 n=0 and MS2 n=6, likewise there is one at n=1,2 and another at n=1,8 another at n=2,7 and another at n=3,9 and so on. There's quite a few in fact, all of which fits *precisely* with what I've been working on... ... but I'm missing the interim steps, as you can see, but also I could use some help verifying that what I've come up with is in fact correct. I'm not a mathematician, I'm a software engineer.

the list shown at the right (browser tabs) is what will fit on a screen with only 1200 pixels depth. there are another two to three pages worth of tabs open, which won't fit on-screen. i think, ajb, that, regrettably, i'm not going to be responding further to anything you might have to say. i'm looking for advice on whether what i've written has any fundamental flaws, so that i may make an informed decision on whether to continue to pursue it or not. one person has very kindly found a mistake, which i'm really grateful for, and i've corrected it.

ok. the way that i view this, from the perspective of radio-waves, wave-forms, sine-waves, whatever it is, is that there is no "force", but that there is only "constructive and destructive recombination of wave-fronts". so imagine a wave at a point: it's a sine-wave. imagine another wave, at another point. it's also a sine-wave, and it is oscillating at the exact same frequency as the other sine wave. now imagine that those two sine-waves radiate outwards at the speed of light. the effect of their wave-fronts will reduce with distance according to a square law. when the wave-front of the first reaches the point at which the second is radiating (and vice-versa), they combine. what happens? well, that depends on the phase of the two waves, but you basically sum the two sine waves (one obviously being weaker than the other) and you get a new wave that's ever-so-slightly shifted off from the position it was previously "waving" from. the net result is that depending on the sign of the two "waves", the relative positions of where the two waves emanate from will either move towards each other (quotes attract quotes) or they will move away from each other (quotes repulse quotes), and it will also so happen that the amount of movement will be proportional to the inverse of the distance squared between them. this we call quotes forces quotes. so i don't think in terms of "forces", either, but it is the most convenient moniker. now, the next step i'll be taking is to endeavour to work out what the hell the relationships are between T and V particles in terms of wave-fronts-combining-to-create-the-illusion-of-forces-which-are-frowned-upon-but-are-the-best-word-to-use-unless-anyone-has-any-better-ideas.

ahh ok. right i get it: i apologise, i didn't understand the point you were trying to make. yes, strong force replaced with an effect which is still a force. nature of the replacement: i'm *guessing* it's inverse-square-law. i'm looking to understand what fits the evidence. the reverse-engineer in me demands that *grin*. to be honest i've kinda hit a brick wall, now: inference and analysis has only taken me so far. i'm still trying to get a handle on how these particles would interact. the bit that's completely missing is how T and V interact. T (electric charge), obviously that operates (duh) how electrical charge works. V cannot entirely be assumed to operate the same (V with V that is) but maybe it does. T with V? absolutely no idea. only when i have that can i start to write the simulations. i have some guesses, but... yeah. ok it's late here i'll take this up tomorrow, sleep on it. thank you studiot. ajb i'll reply tomorrow. thank you both for your time. l.

ajb: whilst you have every right to make such a statement, i feel obligated to point out that it may be viewed - and this is purely an observation from my perspective in reading those few words - as not constructively contributing to the goal which i asked for contributions to. now please consider this from my perspective, of having a certain amount of time available, you have certain skills and knowledge that i entirely lack, and i have others which have, i believe, allowed me to come up with things that other people - with similar skills to that which you have - simply could not think of. so we are at a bit of a paradoxical position where the knowledge and skills that have brought current scientific theories to its current limited perspective (missing things like an explanation for the nuclear force, for example) are way beyond the average intelligent person, and we have another perspective which *is* capable of explaining things like the nuclear force but, by nature of that explanation having had to come from a completely different perspective it comes with a completely different set of paradigms, i.e. it needed to be discovered by someone who is *not* encumbered by the intensely-complex maths used by the current scientific community. the problem is, then, that in order to *think* of this theory i had to *not* have the very mathematical skills that you believe i *should* have! in short: if you can accept that, then we'll get along fine. if you cannot, then i deeply apologise but any questions that you may put here which include mathematical or theoretical concepts beyond my abilities to answer, i will reluctantly have no choice but to leave them for other people to answer, in the hope that someone here (perhaps later) may be able to act as a bridge between the two theoretical worlds, and provide the answers which we both seek. ok? l. ok, let me try and clarify. what you believe is that i have defined the strong force as being the strong force, is that correct? what you're saying is that i've said "the strong force is defined in terms of the strong force". because i most definitely am *not* saying that! in the second sentence, you repeat the currently-accepted theory that the strong force is "fundamental". in the third, you come much closer to understanding what i've said, but... unfortunately may be missing parts of the explanation so. first thing: "strong nuclear force is a fundamental force". this is... and i'm taking a risk here... ok, how do i word this in a way that you wouldn't reject outright.... ok i think i have it: I INVITE YOU TO CONSIDER (useful words those).... i INVITE you to CONSIDER that that statement, "nuclear force is fundamental" is wrong. i INVITE you to CONSIDER that the reason *why* it has been logically inferred that the strong force is "fundamental" is because people don't understand its mechanism: they don't have a handle on how it operates. therefore it's been put into a "black box" for the time being. would you be happy to do that? suspend belief for a moment in accepting the current inferred scientific conclusion that the "nuclear force" is "fundamental"? let me assume that you're happy to do that, and carry on... so, forget "nuclear force". let me do some drawings.... achh! me daughter's nicked the pen ok, done - i'll cut/paste the associated text and provide a URL to the diagram: http://lkcl.net/reports/rishon_model/strong_force_illustrated.png here's the text i've added to the paper: In this illustration there is a proton with an up quark at A and D, and a down quark at C. There is also a neutron with a down quark at B. The top diagram has the neutron and proton close together; the bottom diagram has them further apart. Here it is clear that in the top diagram, the sum of the inverse-square-law forces (A-B, C-D and D-B) when the neutron's down quark is close to the proton's down quark, results in a net total \textit(repulsion), and yet at distances slightly further away, as shown in the bottom diagram, the sum of those exact same forces is a net total \textit(attraction). if that's still unclear, then think of it in these terms - and i do actually recommend that you try this out! Thinking of this purely in mechanical terms that would allow an actual physical and practical demonstration: Take 12 small permanent magnets of equal strength. Tape or glue 6 of them back-to-back with North-to-North Mark the North-North magnets with the letter "u" Tape or glue 6 of them back-to-back with South-to-South Mark the South-South magnets with the letter "d" Take 2 rigid sticks of equal length. On stick 1, tape or glue a "u" double-magnet at each end On stick 1, tape or glue a "d" double-magnet at its centre On stick 2, repeat this but with "d" at ends and "u" in centre Take some string, wrap it round the centre of each stick Suspend the two sticks at right-angles and see what happens. you might have to orientate the permanent magnets such that the ones at the ends have their magnets facing outwards (parallel to the line of the stick) whilst the ones in the centre face outwards PERPENDICULAR to the stick. the idea is to create two sticks where the centres of each repel the ends of the other stick. i'm sure you get the idea. now. does that help make things clearer? FORGET "strong force equals fundamental force". think in terms of magnets. attraction and repulsion. think in terms of "sum of attraction and repulsion at different distances".

(edited to remove smileys because unlike in straight text, the happy-little-images really are quite objectionable and in-yer-face. please therefore imagine that this is all said with a happy and carefree perspective, thank you....) oo, that's really appreciated! i did realise (only yesterday) that i really need to start using latex, so began converting it (from raw HTML) to this - if you prefer: http://lkcl.net/reports/rishon_model/deriving_quarks.tex let me look at the rest and get back to you. you may have highlighted an error in the equations: i'll be honest, it's pretty close to thinking in binary (machine code!) so it does my head in, a bit. i'll refer to the charts i've got written on paper and make sure they're correctly transcribed to latex. imatfaal, i appear to have made lots of mistakes, one of them is getting the pion+ decay-equation wrong! http://en.wikipedia.org/wiki/Pion#Charged-pion_decays corrections underway... right done! so yes, thank you imatfaal, you spotted some inconsistencies in the text versions of the equations. the drawings *are* correct, it was just everything else that was wrong! firstly, i'd got the pion+ decay equation wrong. it's pion+ -> positron and neutrino. second, i'd been confused by "e+" being "positron" not "electron". so that really is: pi+ -> e+ + ve ud -> e+ + ve TVT:VTV -> TTT + VVV which now makes sense when you compare that against the drawing. (wow, latex2html really does a poor job converting from tex to html, doesn't it? overlines become underscores, and the page numbers keep changing. if you're familiar with latex - i keep having to refer to internet searches every couple of minutes, apologies - feel free to use http://lkcl.net/reports/rishon_model/deriving_quarks.tex instead ok?) thanks for spotting the error and bringing it to my attention, imatfaal. hmm, let me try and add something here, experiment with scienceforums.net latex capability start from [latex] TVT + VTV[/latex] add an anti-TVT plus another TVT (to balance out) [latex] TVT + VTV+\bar{TVT}+TVT[/latex] apply a [latex]V\bar{T}0[/latex] transform [latex]VTV + \bar{TVT} -> \bar{VTV} + VVV[/latex] [latex] TVT + \bar{VTV} + VVV + TVT[/latex] apply a [latex]\bar{V}T0[/latex] transform [latex]TVT + \bar{VTV} -> TTT + \bar{TVT}[/latex] [latex] TTT + \bar{TVT} + VVV + TVT[/latex] now "balance out" the TVT and anti-TVT which we added in purely for step-by-step convenience here [latex] TTT + VVV [/latex] ta-daaaa so those are the steps. i had to add an anti-TVT and a TVT as a way to break that down into something approaching a mathematical equation that can step-by-step be solved, but in reality what i believe is happening is that the two transforms are occurring simultaneously. this matches up with observations that gluons are instantaneous. my understanding is that gluons are just pions that are *literally* destroyed at the exact same time they are created. in other words, they're used as a phase-transition mechanism. does that make any sense? l.

ajb, you see: you've lost me already with the word "Lagrangian". i'd need to spend several hours looking that up and understanding it, then several days or possibly weeks working out how to rewrite the paper in terms of that mathematical notation. right now, i'm writing this up in terms of simple diagrams, rules, logic and algorithms: exactly as a software engineer would tackle this, basically. now, because i seem to have an ability to "recognise" correct formal maths when i see it (rather than an ability to write it), what i *might* be able to do is, if someone *else* were to write this out in "Lagrangians", i would be able to go "yeah that looks right". in the meantime - i.e. without the assistance of formal mathematicians - i'm much more likely to be able to demonstrate this by using discrete computer simulations than i am by any other means. i say that with the qualifier "much more likely this century"

sure - i'll try! (i'll do a maths summary separately as well). that would help me as well. begin with 4 particles - T and V - add two signs (+,-) and three phases (RGB). RGB represents 120 degree sine-waves exactly like 3-phase electricity. *exactly* like 3-phase electricity. allow 3 particles (3 phases) to spin in a line, about a central one. call these "triplets" there are 8 combinations that "work", these give the basic particles (electron, neutrino, quarks). triplets have *TWO* charge values: T-Charge and V-Charge that's basic Rishon theory (ok, basic Rishon theory with a couple of corrections). what is really *really* new is this: allow "triplets" to spin about each other in the form of the letter "I" or "H". these give neutron, proton, strange, charm, top and bottom as well as muon and muon neutrino. call the triple-triplet sub-structure an "I-Frame". I-Frames rotate around the central triplet, with their own "spin" characteristic that is *independent* of the end triplet's spin. in a further extension to the "I-Frame" as a 5-triplet body, allow two *extra* quarks to attach themselves to the top and bottom of the letter "I" (or the vertical sides of the letter "H"). this gives you the tau and two previously undiscovered quarks, which i've named ultra-up and ultra-down allow 2-particle bodies to spin about each other as long as they're quarks (1/3 or 2/3 charges). doesn't matter how "heavy" they are. different combinations of 2-particle bodies give the pions, kaons *and*, if you use the ultra-quarks, the W and Z Bosons if you allow *another* application of the I-Frame Hierarchy then you get the Higg's Bosons. note Bosons *plural*. when you look more closely, you see that the Higgs is an "ultra-heavy proton" because it is made up of the ultra-heavy variants of the up down and up quarks.... ... which allows us to predict the existence of an "ultra-heavy neutron" made up of the ultra-heavy down up and down quarks. taking the mass-ratio of the neutron and the proton and comparing it to the mass-ratio of the two experimentally observed Higgs Bosons (125.3 GeV and 126.0 GeV), the two mass ratios are EXACTLY the same to within 4 decimal places. so i *believe* that the Higgs+ and Higgs-0 have already been experimentally observed... just not yet recognised. particle "decay" is not *actually* "decay", it's phase-transitions. as the individual Rishons can be considered to be just "sine waves" (one of each type of matter), if you allow the interchange of two particles (each way) between two sets of two triplets, that covers the majority of particle "decay" patterns.... but they're not *actually* "decay". these are called "VT0 phase-shifts". there's a couple of exceptions to that (which really _do_ result in "decay" - one of them's gamma radiation). one of the exceptions i've called "VT*" (V T star). so that covers the particles, but the implications go on from there, to include the following tentative areas of investigation: with a proper structure to the neutron and the proton, the spinning orbits can "interlock" at 90 degrees, allowing the repulsion and attraction of the up and down quarks to "balance", neatly giving the "Nuclear Force". no other particle physics theory even _remotely_ has a handle on the Nuclear Force. if the neutrino has a +1 V charge and the neutron has a -1 V charge then there is no reason why the neutrino should not be in orbit about the neutron. this has *huge* implications for science as a whole, especially chemistry. i am TENTATIVELY exploring the hypothesis that "V charge" is "Magnetic Flux". this is extraordinarily difficult to prove... or disprove. i've made some recommendations on practical experiments to do which include separating out isotopes of materials, on the basis that they would have different numbers of neutrons, therefore different neutrino orbital shells, therefore potentially different magnetic properties. there's a number of other implications, including quite reasonable explanation such as "why the Higgs has zero spin despite being 3 particles" and so on. it's a huge and comprehensive rationalisation of particle physics, basically. i've had some... errr.. fun with the neutron decay. it took me about 2 weeks to work it out. the fact that it *didn't* work - the phase-shift diagrams simply don't balance - meant i had to look closer (i.e. read more of the wikipedia page ) and i noted that there's something called "decay energy". that was it: *click* - that's why the phase transition diagrams didn't balance. so - apologies for the length, but that really really _is_ a summary. there is actually a full summary of the observations and findings at the end of the paper, i'll try reorganising it so that it has hyperlinks on the titles, that would make life a bit easier, neh? sure. it's actually quite simple, not least because i don't have the time to go into complex maths. as a software engineer with rusty A-Level maths i've simply not been able to go into that much depth, but actually what _is_ there is more set theory, group theory, logic etc. than it is "heavy-duty quantum mechanics". *actual* maths - has already been done. Piotr Zenczykowski wrote a consistent and published mathematical paper using O(6) Clifford Algebra (reference can be found via http://en.wikipedia.org/wiki/Rishon_model) explaining how the basic Rishon Model can "fit" into Standard Models. so. these are the areas: simple logic, rules and sets. this covers the structure, phase transforms and the particle structure. but, bear in mind: these "rules" and "sets" are simply "summaries" of the underlying structure, which is actually in terms of "sine waves with phase" in a 6-dimensional universe (my money's on that being complex numbers in a 3 dimensional one, but that's yet to be determined). an understanding of sine waves and phases and how waves propagate (radio waves, gamma waves etc. etc.) and combine, and cancel (diffraction patterns), and have polarity, and are expressed as complex numbers (I and Q) etc. etc. etc. etc. etc. etc. mass ratio analysis. i take a simple formula: "(mass of particle 1 divided by mass ratio 2) to the power of 0.5, 1/3 or 2/3" then look for the closest fractional number. the source code of a program which does all that is here: http://lkcl.net/reports/rishon_model/energy_levels.py in the explanation of "Nuclear Force" i had to throw out a bit of maths that involved sine and cosine (gosh! ) which is basically 1/math.sqrt(2 * math.sin(angle)) - 1/math.sqrt(math.cos(angle)) - that's 2 "attractive" forces counter-balancing against 1 "repulsive" force. where those equal out is around 26.56 degrees. the source code of a program which hunts for this angle is here: http://lkcl.net/reports/rishon_model/angle_search.py so... uhh..... that's it! that's all. there's actually no need for quantum mechanics if the fundamental basis of matter is considered to be just sine-waves operating at exactly the same frequency as every single other fundamental particle in the universe. reason: no statistics or probabilities required if you *know* what phase the wave-form of every particle has! ok, assume you know, not "know" know. so simple mechanics (albeit probably in 6 dimensions not 3) is, i believe, all that's required to simulate this. my money's on taking some standard 3 dimensional square-law attraction equations, written in python, then shoving *complex* numbers into it and see if it all falls in a heap or not. the nice thing about python is that you can do that: code written for floating-point numbers will work seamlessly with complex numbers (he said.... ) thrown at it. l.

hi, my name's luke leighton, i did the usual maths further maths physics and chemistry (A,B,D,D in that order, and an S-Level Distinction in single-maths), and in 1986 developed a fascination for particle physics. i developed a career in programming, moved into software libre, pursued all sorts of wonderful things but still kept at the back of my mind the pictures i'd seen in a book i'd bought back at school, and, critically, still remembered the theory i'd independently developed which i later learned was called the "Rishon Model", by Haim Harari. 27 years and a number of false starts later i've started to write it up again, but this time something happened: a runaway train of logical deduction which is beginning to unnerve me slightly at 18,000 words (and still increasing), with - at the time of this posting - over *seventeen* separate discoveries, predictions, avenues of exploration (theoretical and experimental) and explanations, all based on the theoretical basis of four simple and fundamental particles. these include a reasonable and rational explanation for the Nuclear Force (which no other particle physics theory has a handle on), a prediction of the existence of *two* separate Higgs Bosons (Higgs+ and Higgs-0), the discovery of two new quarks (ultra-up and ultra-down) - i simply can't list them all here. suffice to say i should point out the following: 1) i am an experienced internet user. i HAVE read the FAQ. all of it. it's hilarious. i even read the "how to spot quacks" link. that was funnier though. 2) despite reading the FAQ i'm still here. that should tell you what you need to know. if you don't know, allow me to make it clear: by posting here we *all* agree to honour the requests and advice given in the FAQ. 3) i have some basic maths: as a programmer i now substitute lack of maths knowledge with "write it as a program and get the same results, near as damnit". i grok quantum mechanics but haven't the time or capacity to learn it to the point where i can work with it. i grok set theory (programming), i can just about handle the concept of Clifford Algebra, if i think back hard enough to my A-Level Maths from 1987. but now, with experience in programming, i think in logic, inference, deduction and simple maths, like complex numbers. 4) i've removed several mistakes from this *DRAFT* paper already. which is still being written. 5) i really, *really* need some expert help in reviewing this material, which i am in the process of rapidly becoming slightly dazed and strangely disassociated from, on account of both the quantity of words written in under four weeks as well as the extraordinary implications of what is in effect little more than reverse-engineering and logical reasoning. 6) ultimately, i'd greatly appreciate some advice on where to go with this, as if it's inherently unsound i'd *really* like to stop writing, now, please, y'know what i mean? with that in mind, here is a link to the DRAFT paper, on which i would greatly appreciate useful comments. http://lkcl.net/reports/rishon_model/deriving_quarks.html apologies in advance for the length. l.