May i suggest that narrow specialised research with little interest in other problems, can only result in routine research. Path breaking studies require widening one's horizon of study, intuitive thinking by the mind and a kind of love and friebdship with the cosmos. There is no shortage of time when one works out one's priorities and cut on non-essentials. The choice is your , Emile. i apologize for any impertinence here!
Dear Narendra,
In my opinion, honestly expressing one's belief's is not impertinence. Besides, I don't see how anyone could disagree in principle with your statements. But there is one exception. I would think twice before saying that there is no shortage of time to someone whose life situation is not known to me. It is true, however, that prioritizing helps. I do it systematically. For example, my priority on this forum is to discuss exclusively technical issues, and only when I have something useful to say.
Dear Ray,
Yes, it has to do with SU(3). In the quantionic approach, the root vectors of this group ALMOST come out of states defined as idempotents (no talk here of any group). But something is missing. I still did not find it in the quantions, but I continue searching because it is against the principles of the structural approach to keep introducing new axiomx ad hoc. Question: Is the missing premise concealed somewhere in the already developed mathematics of quantions? If yes, I must find it. If not, I'll have to go back to the first principles and see what I missed there.
I notices that you have an analogous situation in your representation of particle multiplets by simplices. Quote from the top of your page 3:
"We want to construct a simplex with the following properties: 1) the sum of all charges within a particle multiplet equals zero, and 2) all particles have the same distance from each other. As a consequence of these two requirements, we realize that all particles must also have thesame radius about the origin."
If I take your second premise, I get SU(3). Of course, I knew this, but what is interesting to me is that you also had to assume it.
I still believe in the existence of a deeper reason from which your second premise follows as a theorem. It is much too technical a premise to be acceptable as is. It is perfectly acceptable, however, in an intermediate theory (before "structuralization").
Emile.
Dear Emile,
I think of my work as being in the explanatory stage, and not the finalization stage. Perhaps there is an underlying theorem to these lattices. With my book, I realized that tetrahedral symmetries might provide a useful explanation of the Standard Model. I immediately extended it into a Face Centered Cubic (FCC) close-packing lattice of hypothetical Hyperflavor quarks and leptons.
Then I was reinspired by Garrett Lisi's application of the Gosset lattice.
A Simplex is a natural n-dimensional extension of the 3-D FCC close-packing lattice. If we build our Simplices following my requirements, then they reflect anticipated GUT requirements (such as the sum of a charge within a particle multiplet equalling zero).
I suspect that it is a theorem, and presented it as such in Ref.[3] (posted as "A Case Study 3.3.pdf" near the top of my site).
I hope my Simplices help...
Have Fun!
Ray Munroe
Dear Emile ,
Very interesting the anthropic point of vue and the link with SU(5) like an universal link towards the complexification .Like a beautiful ocean of creations ,these biological lifes and their intelligences towards harmony .
These steps thus is our Universe ,well thought this extrapolated vue with complexs.
The time ,I think ,must be inserted with a quantification too for the mass correlated with the evolution point of vue since the begining of these polarisations .
Our history ,the story of our Spherical Universe is specific in its dynamic.
An other point is what too the thermodynamics laws correlated with the evolution of complexification must be considered .
Without that it's an imaginaries extrapolations .The mass and the motion I think must be considered .
If the very weak plarisations is correlated with this evolution point ???Probably the results shall be relevant about the complexification .
A specific serie exists and the physicality have many parameters to optimize imaginaries .The mass ,the gravity ,the forces must be considered I think .
In all case ,very creative your essay .Good luck for the contest
And for you too Dr Cosùic Ray and all in fact hihihi but really all ,the complemenatrity and the fundamentals could optimize your datas .
Best Regards
Steve
Thank you Steve,
Your points are well taken.
Best regards,
Emile.
Dear Ray,
When I referred to your second premise, I meant equidistance. I have no problem in my work with the vanishing of the total charge.
I am going to redo my proof in a different formalism -- in the hope I overlooked something in the first pass. If I deed, it's at some deeper level, because I verify my results with interactive numerical simulation (in C++) whenever something is outside my expectations. It is encouraging that, coming from very different directions, we both have tetrahedra and cubes. I will study your papers and we'll compare notes in the future.
Regards, Emile.
Hi Dear Emile ,
An Universal taxonomy can be created with all its fundamenatl paramaters where the mass is inserted in the line and space line .
The rotations of quantum spheres and its quantification is essential for all polarised system .
Our biological system for exemple is a specific polarisation and furthermore continues to polarise by weak interactions and electromagnetism .About the gravitation it's the same the sense of rotation thus is essential to become a strong interactions and a gravity system too .....Our quantum spheres polarise ....and increase in its numbers due to this complexifictation of system......the intelligence which is too a result of the physical sphere evolution is there to optimize too the polarisations of systems ,minerals ,biological ,planetars ,stellars,galactical.....thus the time and the mass ,the gravity and the evolution must be inserted it seems to me .Thus te rotating spheres ,quantum and cosmological.
Regards
Steve
In fact all must be considered ,it's what I do with my classments,I class all with the mass and thus rotations too ,centrip and orbital .
In this kind of universal taxonomy where all must be considered .There the mass must be quantified .Thus a direct correlation with the entanglement of quantum spheres .
Here is a little rersume of the universal taxonomy where we insert all constants and laws,fundamenatls .
BIG BANG THEORY ??? since about 13.7 to 15 billions years .............multiplication of entangled quantum spheres........the fact to ratote implies all in the physicality thus possible spheres without rotations thus dark matter ???hypothesis..............space time energy mathematic code.................polarization +-...3.5billlions years......hydrospheroid.......................................................................................... SPHERISATION ..............H......Helium Deuterium Hydrogen and others .....C.........N.........O......++++++++CODED ENERGY ........H2O .... NH3... CH4 H2C2.... HCN....... K... Fe Mg Mn Al ...... S ...PYROXENS AMPHIBOLS ........SiO SILICATES...............proteins/enzyms INE ASE........AMINO-ACID......BUILDINGS .ADN ......SPHERISATION.......... SILICATES ...............................all systems are a polarised quantified mass,evolved and adapted .................................... .....................................................................................................................GLUCID LIPIP PROTID PROTIST UNICELL PROTOZ phytoflagellates zooflagellates .....animal vegetal SPHERISATION dedifferenciation.....PLURICELL EVOLUTION harmonisation ,optimisation ,improvement by very weak interaction of complexification................................. SPHERISATION ............................................................... ....LOCOMOTION NUTRITION REPRODUCTION...............evolution ..................ANNELIDS .......... SPONGES ........... .. MEDUSAS................. CHORDS ........... VERTEB....................SPHERISATION............HOMINIDS ..........LUCY TOUMAI.........erectus......habilis ...............HOMO SAPIENS SAPIENS NOT REALLY SAPIENS...IN FACT... ...intelligence ...SPHERISATION HOMO REALLY SAPIENS FOR ................ • LOGIC...PHILOSOPHIC... SPHERISATION .......RESOLVE PROBLEMS AND LEARN ..................UNIVERSAL SPHERE
It's what i d like to do in a big 3D ,a evolutive system of our Universl sphere in optimisation with all its mass .
I say me sometimes what the time permits too the strong interactions ,the evolution is essential and the time constant too .Without these fundamntals all quantifications are not correlated .
What do you think Lawrence .
Regards
Steve
Dear Dr. Grgin,
I enjoyed your historical trip, which explains well the paradigm shifts introduced by each major discovery. It also emphasized various unifications occurred in Physics. The stages you propose, as well as your observations related to them, contain the essence of the evolution of theories in physics.
I had to complete the part where you introduce quantions with additional readings, which I enjoyed too. I have several questions.
- In terms of spinors calculus, Infeld and van der Waerden showed how we can obtain the Dirac equation (L. Infeld and B.L. van der Waerden, Die Wellengleichung des Elektrons in der allgemeinen Relativitatstheorie, Sitzungsber. Preuss. Akad. Wiss. (1933), no. IX, 380-401.). Also Wigner's idea of particles as representations of the Lorentz group leads to the Dirac equation. Anyway, the spinor calculus and Wigner's theorem shows the very straight relation between relativity, based on Lorentz metric, and quantum mechanics, based on Lorentz' group double-cover SL(2,C).
- It is not yet clear to me why we should use quantions and not complex quaternions or the Pauli algebra, which seems to contain both the Lorentz metric and the electroweak group. Probably because you emphasized on them some properties which are not directly obvious in the Pauli algebra. Considering the relation between the quantions and the Pauli algebra, I wonder whether is not more natural to use the real Dirac algebra itself, directly associated with the Lorentz metric. Taking the quantions as fundamental seems to involve a special time-like direction; is this approach Lorentz-invariant?
I see that you reached the quantions starting from the quantal algebras, but something is not clear to me yet. In order to complete my understanding of your work, I need to ask you why should we use quantions, instead of the spinor and Clifford fields naturally associated with the spacetime endowed with a Lorentz metric? If the answer is that the quantions have a special derivation property, then I ask why using the quantion derivative, and not the Dirac operator, naturally associated with semiriemannian manifolds?
My essay contains an approach to the unification of quantum and general relativistic theories, which is complementary to yours. I would be honored if you would like to read it, since I think that it is complementary and compatible with your ideas. I am using the usual spinor fields and Dirac operator, but it would be easy to replace them with quantions, if this would be the case. It is also possible to replace the Standard Model group with a GUT group, again, if this would be the case.
Congratulations for your essay, and success with this contest,
Dear Cristi,
Thank you for making the effort to understand my approach to physics, but I conclude from your questions and remarks that I have not been successful at conveying the the essence of the approach. I will try to be more explicit. Three historical examples will help illustrate what I mean.
(1) General relativity. Before 1911 (let's say) probably no physicist ever heard of Riemannian geometry, and even fewer (which means zero) suspected it might be of any use in physics. Mathematicians themselves, Riemann excluded, thought of it as nothing more than interesting for its own sake, something like number theory (at that time, of course). This is why historians of physics cannot even suggest when general relativity would have been discovered had it not been for Einstein. Maybe not to this very day. It is with deep admiration that I look at Eistein's contribution, but I cannot say the same thing for what followed -- especially since I wasted a lot of time in it myself. Once it had been established that space is not the rigid thing Kant believed it to be, ideas for generalization were not hard to come by. Examples: Increase the numbers of dimensions and then fall back to 3 plus 1 by some imaginative procedure; add structure by considering torsion in addition to curvature; remove structure by falling back to conformal geometry. There is enough here to sustain searching for possibilities for almost a century so far, and probably for a long time to come.
(2) Dirac's equation. The unification of Pauli's spin with relativity was a burning question around 1927. Dirac had a brilliant idea that solved the problem, but since the solution rested on a stroke of genius, rather than on a conceptually justified derivation from some deeper principle, it was not intellectually satisfactory. This bothered Pauli (who referred to it as acrobatics), and even more Dirac himself (who was apparently hoping all his life that something more conceptual will be found). Now, once you have Dirac's matrices and you understand their relationship to the Minkowski metric, it is evident that they belong to the branch of mathematics known as Clifford algebras. An then, unavoidably, this algebra becomes the foundation of a new branch of research with aspirations in physics.
(3) Quarks. I'll start again with a rhetorical question: How many physicists were familiar with the root systems of simple Lie algebras before Gell-Mann put them on the map? My guess hovers around zero (on the positive side, though). But this number jumped up following Gell-Mann's impressive discovery. We now have a lively branch of research aimed at discovering one-to-one mappings between the elementary particles of multiplets and the roots of simple Lie algebras.
Let's now look at these three examples from some distance: Einstein, Dirac and Gell-Mann discovered some profound new paradigms, and their results motivated (and still motivate) a small percentage physicists to search for new paradigms in their wake. If I am not mistaken, this approach cannot boast much success so far (the success I mean has nothing to do with publication counts).
You say "It is not yet clear to me why we should use quantions and not complex quaternions or the Pauli algebra, which seems to contain both the Lorentz metric and the electroweak group.". I' give you two answers.
A general answer: Taking the lessons of history seriously, I could not possible search for the paradigm I am interested in (I mean the idea that will eventually lead to a satisactory merging of relativity and quantum mechanics) in the wake of far-reaching discoveries made by others in the past. I don't think the paradigm in question will be found there, but I do think that the field is crowded enough without me.
A specific answer: First, I am not saying or implying that you should use quantions and that you should not use complex quaternions. By all means, use the latter if you think you'll make a breakthough where many others have not (reminder: breakthrough = unification; if you mean anything else, I'll have nothing to say because, like kiltmaking or fly-fishing, it would be outside my sphere of interests). But there is more: Your question is stated upside down. My objective was not to re-derive Dirac's equation or bust -- and then quantions just happened to do the job. The quantions came from elsewhere as a new number system that seems to be just right to support the unification I am after. But then, my friend Nikola Zovko correctly pointed out that I should take a break from further developing the mathematics of quantions and verify as soon as possible that they are not spuriously relativistic and that they are consistent with quantum mechanics. For the latter, he suggested the verification of Schroedinger's equation, as well as the approach I call "Zovko's interpretation". This worked out beautifully. Both Schroedinger's and Dirac's equations, together with potentials, follow as theorems from the quantionic number system augmented only with Zovko's interpretation.
You mention in your post other things I would enjoy discussing, but not util (if you feel like it) you reformulate them in the spirit of my work, which I just described. I need this to be sure we are on the same wavelength.
But if you need additional clarifications, please ask.
Best regards,
Emile.
Dear Dr. Grgin,
Thanks for the reply, I totally agree with your historical examples. I agree with your point that Dirac's derivation of his equation is unnatural, and that's why I referred to very straight and natural ones: in the Infeld-van der Waerden spinor formalism, and as representations of the Poincare group, following Wigner and Bargmann. And this provides the desired breakthrough relating quantum mechanics and relativity (and not kiltmaking, as you humorously say): particles' wavefunctions are spinors (i.e. the natural objects of relativity) which naturally obey Bargmann-Wigner's equation (in particular Dirac's equation, for spin=1/2). I sincerely wanted to know if quantions provide more than this.
Best regards,
Cristi
Dear Cristi,
Your last sentence, "I sincerely wanted to know if quantions provide more than this" makes all the difference. I thought you meant "Why bother with quantions since several natural-looking derivations of Dirac's equation already exist?" Sorry for the misunderstanding.
This settled, the answer is easy.
Referring to observation (5) on page 6 of my essay ( "The unification of theories takes place automatically once the correct mathematical structure has been identified"), the first objective is to find the structure in question -- assuming there is one. All indications so far speak in favor of the algebra of quantions viewed as the new number system that is to supplant the field of complex numbers in the formulation of quantum mechanics. In the long run, this will either prove to be true, or it will hit a snag and be dropped. In the interim, it does yield Dirac's equation without any additional postulates. This answers your question to the fullest. Adding anything would only dilute the idea. Maybe you don't see it yet, but that's OK. It takes time to get accustomed to a new paradigm. The way I see it is that new neural paths have to be formed in our brains, and that, in my case at least, takes much more effort and meditation than merely reading a few sentences.
Coming back to the derivations you mentioned, they cannot possibly be the magic key that opens the door to unification. Setting aside the fact that they have been too thoroughly investigated to still conceal the key in question, they are overly specific to do the job. Think of how they compare in depth with the principle of special relativity (there is a maximal speed), or with the principle of general relativity (equivalence of two concepts of mass), or with my suggestion (the ultimate number system of physics is not the field of complex numbers but the algebra of quantions).
In conclusion, two-spinors presuppose the Lorentz group. In contrast, quantions imply it. Representations of the Poincare group presuppose the flatness of space, which blocks extension to general relativity. In contrast, quantions form an algebra, and an algebra is a linear animal that brooks no translations. It is thus a priori compatible with curvature in an underlying event manifold.
Best regards,
Emile.
Dear Dr. Grgin,
Thank you for the time and patience. I think I understand better now where you see the potential of quantions, and why you are investigating them.
Best regards,
Cristi
Dear Dr. Grgin,
On the other hand, I continue to have no doubt that the "old fashioned" spinors, and Pauli and Dirac algebras, are the natural objects in special and general relativity. I think that quantions, as an algebra equivalent to Pauli's, cannot do more than spinors and Clifford algebras, including the breakthrough you mentioned. Perhaps they are recommended for you more than the others, but only because you worked with them so much, and not because they are more powerful.
Best regards,
Cristi
Dear Emile and Christi,
I must admit that I have similar questions. Having read Emile's essay and most of Florin's arXiv paper, I see that quantions have some advantages, but do not understand why Pauli and Dirac spin matrices cannot accomplish the same thing - albeit in a possibly more awkward manner. Perhaps it is this awkwardness that has confounded our attempts to unify QM and GR.
I would love to see a completed quantion theory with interactions, so that we can compare it with our current theories, and see if anything new arises, or if it is just a more beautiful or succinct way to write our equations.
Have Fun!
Ray Munroe
Dear Cristi,
You wrote:
"I think that quantions, as an algebra equivalent to Pauli's, ..."
Where does this come from? Anyone reading it would conclude that I am selling the Pauli matrices in a new wrapping labeled "quantions". You need not believe that quantions hold any promise, but it is very unfair to misrepresent them in a public forum.
Best regards,
Emile
Dear Dr. Grgin,
Thank you for the correction, I also wouldn't want somebody to misunderstand that I say the two algebras are isomorphic, because certainly they are not.
Best regards,
Cristi
Ray and Cristi,
Let me give you a reason why quantions are not simply Pauli, Dirac spin matrices. (This explanation is in part in Emile's fist book). Let's consider a simpler case, the case of complex numbers. A complex number is just a pair of reals with a (simple) multiplication rule. Let's ask the similar question here. Why then in this case a complex number cannot achieve what real numbers can? In QM, this approach leads to the Bohmian approach which decomposes the wave function in the real and imaginary parts. Can Bohmian approach work in QM? If you ignore the spin, it does, but you certainly do not get the correct picture. Similarly the same thing happens with quantions. Quantions are the natural distinguished way of unifying QM with relativity. In this perspective they are the Goldilocks structure: not too hot, not too cold, with just the right mathematical properties. No extra features, no missing features.
Thanks, Florian, for the clarification, but I think your hand reversed your thought. Replace:
"Why then in this case a complex number cannot achieve what real numbers can?"
by:
"Why then in this case two real numbers cannot achieve what a complex number can?"
The difference is in the key word "structure". A pair of real numbers contains exatly the same amount of information as a complex number, but there is a world of difference between the two concepts. In practical applications, we have three possibilities:
1. The complex numbers may be deselected because whatever is being modeled has its own structure which is not isomorphic with the algebraic structure of the complex numbers. For example, making a complex number out of the voltage and current in some circuit element would be going against nature. The product of these compex numbers could not be used because it is physically meaningless.
2. The complex numbers and the phenomena being modeled have the same algebraic structure. In this case, complex numbers greatly simplify the calculations and, more importantly, make the entire phenomenon more intuitive. This is the case in radio-frequency circuits, where currents, voltages and impedances are routinely represented by complex numbers. In the absence of non-linear circuit elements, the entire circuit theory reduces to polynomial algebra.
3. In quantum mechanics it's the same as above to begin with, but interpretations make it very different: The phase of the complex number (wave function) is not directly observable.
So much for the example with complex numbers.
Concerning quantions, they contain the same amount of information as Dirac spinors (4 complex quantionic components = 4 complex spinorial components). Even better: A quantion uniquely defines a 4-spinor, and vice-versa. Even better: The unique general quantionic field equation contains Dirac's equation as a distinguished special case. Yet, quantions and 4-spinors are very different because they are differently structured. Spinors have no algebraic structure (the product of two spinors is not a spinor) while quantions not only form an algebra, they are very similar to the complex numbers they generalize.
Emile.
