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Makiko Sato: on 12/12/10 at 2:53am UTC, wrote Dear Dr. Grgin, I am sorry that I don't understand the difficult physics...

Peter van Gaalen: on 11/21/09 at 16:15pm UTC, wrote Dear Dr Grgin, Thanks for answering. I also think that the gm-system and...

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Peter van Gaalen: on 11/21/09 at 9:52am UTC, wrote Dear Dr. Grgin, Grgin@: "The same physical system cannot be 'governed'...

Emile Grgin: on 11/21/09 at 8:34am UTC, wrote Dear Peter, I remember your discussions with Florin. Since you ask my...

Peter van Gaalen: on 11/20/09 at 18:40pm UTC, wrote Dear Dr. Grgin, Thinking about the fine structure constant I thougth that...

Emile Grgin: on 11/6/09 at 14:54pm UTC, wrote Dear Eckard, Our discussions are at cross-purpose. The only reason I got...

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FQXi FORUM
September 25, 2021

CATEGORY: What's Ultimately Possible in Physics? Essay Contest (2009) [back]
TOPIC: A Historical Approach to Research in Fundamental Physics by Emile Grgin [refresh]

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Author Emile - Grgin wrote on Sep. 25, 2009 @ 11:42 GMT
Essay Abstract

Research that aims at identifying new fundamental ideas in physics can greatly profit from a historical approach. The present essay develops this idea by conceptually analyzing the major physical theories created since antiquity and by distilling from them the research trends that have been unmistakably successful. The author's approach to research is based on extrapolating these trends into the future. It is a method that led to a unification of quantum mechanics and relativity based on a new number system structurally located between the complex numbers and the quaternions. Following a brief description of the concrete results obtained so far, the question of what's ultimately possible in physics is addressed by speculatively generalizing the results in question.

Author Bio

Emile Grgin studied mathematics and theoretical physics at the University of Zagreb and in Peter Bergmann's General Relativity Group at Syracuse University. He worked mostly as independent consultant in applications of physics. He is now an independent researcher in the field of structural unification of relativity and quantum mechanics.

this post has been edited by the forum administrator

Uncle Al wrote on Sep. 25, 2009 @ 19:33 GMT
One can exquisitely model one cycle of a sine curve with an odd-power polynomial to achieve an algebraic value arbitrarily close to the trigonometric value. Said model is worse than useless beyond that single cycle, for it will perfectly go in the wrong direction. One need not resort to abstractions. Economics is an arbitrarily perfect interpolation that disgorges Scientific Socialism, the Boys...

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Florin Moldoveanu wrote on Sep. 25, 2009 @ 20:02 GMT
Dear Dr. Grgin,

I am very happy you decided to enter this contest and make the case for the marvelous unification of quantum mechanics and relativity.

As I have said in my essay, your profound ideas have inspired me a great deal and it is my true belief you are trully deserving the Nobel prize for them.

Good luck!!!

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Author Emile - Grgin wrote on Sep. 25, 2009 @ 21:27 GMT
Dear Florin

Except for the over-overexaggeration at the end (you seem to be shoving under the rug the fact that that my work is "work in progress", not a finished product) I am very pleased with your having understood my approach and objectives. I am also delighted to see that it has helped you formulate your own approach. You have my best wishes.

Emile.

Ray Munroe wrote on Sep. 26, 2009 @ 13:26 GMT
Dear Dr. Grgin,

Florin has a great deal of respect for you, and I respect Florin. I skimmed over your paper, but will read it more thoroughly next week.

You define a quantion as a quadruple of complex numbers. If I understand this properly, your quantions would be a two-dimensional isomorphism with the Pauli sigma spin matrices or the two-dimensional real components of a four-dimensional Quaternion.

I understand that you are trying to avoid the Clifford divisor algebras, but these are the best understood algebras. Quaternions are very important to spacetime, Maxwell's equations, and the Dirac gamma matrices. It seems reasonable that if we can build twistors (the 4-D equivalent of Dirac 4-spinors) out of pairs of Pauli sigma spinors, then we should be able to represent Spacetime with pairs of quantions.

A personal bias of mine is that I think that 8-dimensional Octonions must be relevant because Einstein's Field Equations of General Relativity are ten coupled tensor equations. These ten tensors seem to reflect Octonion symmetries. Now we need quadruples of quantions to represent an Octonion. However, in their "Gravitation" book, Misner, Thorne and Wheeler tried to reduce the number of needed tensor equations down to six (reducing the number of necessary equations because we have 4 spacetime dimensions). We could represent six tensor equations with a Quaternion, and may thus be able to reduce down to a pair of quantions.

Now I need to read your paper more thoroughly and see if I understand your ideas!

Good luck in the contest!

Sincerely,

Ray Munroe - author of a Geometrical Approach Towards A TOE

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Juan Enrique Ramos Beraud wrote on Sep. 26, 2009 @ 13:42 GMT
Dr. Grgin:

I am mathematician by formation but been doing computer science for living for way too long (25 years) so I am out of shape on the formula manipulation and algebra side. Never the less I find your essay very clear. Although my essay to this contest propouses there is no such a thing as a final physical theory, I think your aproach does lead to a great step forward towards better physics.

Like Florin says: you might well deserve the Novel prize. Now speaking for my self, if for an unexplainable reazon I get a better prize on this contest than you I would gladly give it to you.

Best...

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Lev Goldfarb wrote on Sep. 27, 2009 @ 02:00 GMT
Dear Emile,

I noticed that in your essay you mention ‘structure’ or ‘structural’ about thirty times. I agree with your view on the continuously increasing role of ‘structure’ in mathematics (and hence in physics):

Author Emile Grgin wrote on Sep. 25, 2009 @ 11:42 GMT

“The ‘structural’ view of mathematics—according to which mathematical objects are not defined ontologically but only by their mutual relations—was introduced for two special cases in the 1830’s (Galois and Hamilton) and had become standard by the 1940’s (Bourbaki). This is ‘the mathematics of mathematicians’. It answers the question ‘What?’—as in ‘What is possible?’ or ‘What exists?’. The key word is ‘structure’. In this conception of mathematics, equations not anchored in mathematical structures are meaningless.

Just as mathematics was becoming more and more structural, its role in physics was becoming more structural as well.”

However, I want to draw your attention to the fact that, *so far*, all structures in mathematics (including those introduced by Galois, Hamilton, and you) are of completely numeric origin. And this is not surprising at all, since all of the present day mathematics stands on the foundation of numbers. Obviously, this constrains us in many ways: in the case of a finite-dimensional vector space, for example, there exists essentially only one metric (Euclidean) consistent with the underlying algebraic structure (see, for example, section 3 in our paper.

As implied by my post of Sept. 20 (under my essay), practically all concepts of ‘structure’ within the current mathematics have emerged in the *continuous setting*, even algebraic ones, since the final/formal separation of algebraic from topological concepts where accomplished by Bourbaki relatively late. In other words, within the conventional mathematical setting, we don’t really have *sufficiently general* concepts of structure—especially as it relates to the representation of processes/objects—completely independent of the ‘continuous’ setting. This situation, in part, motivated the development of the ETS formalism (outlined in my essay), which introduces a quite general concept of ‘discrete’, or ‘relational’, representational structure.

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Author Emile - Grgin wrote on Sep. 27, 2009 @ 03:03 GMT
Dear Ray,

Thank you very much for your comments.

I suspect that other readers will have views similar to those you expressed in the first two paragraphs. Since mine have a diferent slant (for being more complete), I hope you won't mind it if I take this opportunity to clarify my views and objectives by discussing several points taken from those two paragraphs. After reading them,...

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Author Emile - Grgin wrote on Sep. 27, 2009 @ 03:45 GMT
Dear Juan,

Thank you very much for your good wishes. Of course, I am particularly pleased to hear that my essay was clear. I am always concerned about being misunderstood -- and not without reason.

Incidentally, you might like to read my comments on Ray's post. They expand my essay.

Now, your second paragraph is a bit too strong. Please keep in mind that Florin is more enthusiastic than myself about quantions. Not that I have any particular reason to doubt them, but I am aware of too many examples in the history of physics when some idea remained promising for a long time, but then had to be dropped for not delivering the last chapter. I am not even near the last chapter on quantions.

Bast regards, Emile.

Author Emile - Grgin wrote on Sep. 27, 2009 @ 05:04 GMT
Dear Lev,

I am eager to read your essay very carefully. I just put it on my reading list for Monday evening.

Yes, I know that I sound like a broken record stuck in a groove with "structure" in it. This is due in part to my having had some rather frustrating discussions about my work with colleagues whose research falls in the category of Kuhn's "normal science". From that point of view, my goal seems ridiculous. I could never convincingly explain that I am working on a problem whose solution is neither a number nor a mathematical expression, but a structure that has no standard name because it has not yet been introduced by mathematicians.

I'll come back after having studied your essay.

Thanks for your observations on structures. I will better understand them in a couple of days.

Emile.

Ray Munroe wrote on Sep. 27, 2009 @ 13:02 GMT
Dear Emile,

Thank you for the explanation. I understand that this contest had restrictive length limitations and it was difficult to include everything in these papers that we wanted to. I am not entirely sold on the Clifford divisor algebras. As you pointed out, someone would have already unified QM and GR if the Clifford algebras had allowed it. I'm simply trying to understand quantions and their possible applications relative to what I understand (and to your point, Nature or the Creator did not choose an algebraic system based on what I understand). I will read your paper thoroughly next week.

Good luck in the contest!

Ray Munroe

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Steve Dufourny wrote on Sep. 27, 2009 @ 13:16 GMT
Hi Dear Dr. Grgin,

It's avery beautiful essay .Full of pragamatism and rationality about the structures and the rules of math and physics where the unification appears .

Good luck .

Best Regards

Steve

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Lev Goldfarb wrote on Sep. 27, 2009 @ 13:26 GMT
Dear Emile,

Please note that I was not implying that you overemphasized the concept of structure in mathematics.

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Author Emile - Grgin wrote on Sep. 27, 2009 @ 13:51 GMT
Dear Lev,

I was under the impression you were, and that puzzled me a little. Thank you for correcting my misinterpretation.

Author Emile - Grgin wrote on Sep. 27, 2009 @ 13:54 GMT
Thank you, Steve, for your good wishes.

I am glad you enjoyed the essay.

Emile.

Author Emile - Grgin wrote on Sep. 27, 2009 @ 14:30 GMT
Dear Ray,

No, none of us should be easily sold on anyone else's ideas. But we usually speak of our own views with such conviction (which is natural) that it may sound like campaigning (which is unfortunate).

Concerning my own long-standing fear of being biased by what I know better, I put the antidote, under the heading "Symmetry", in the preface of my book referenced in the essay. Here is the first page of that preface:

Preface

In the title of this book, "structural unification" refers to a merging of two physical theories into a single mathematical structure. We impose the following conditions on such a merging:

Symmetry: The component theories must enter unification on the same footing. This is to eliminate approaches to unification that treat as more fundamental the theory which happens to be better known.

Completeness: Within its domain of applicability, the unification must yield no unphysical theorems. This is to eliminate unifications that require ad hoc adjustments when faced with the real world.

Irreducibility: The unification must yield more physics than can be derived from the given theories taken independently. This is to eliminate from consideration physically empty unifications.

Maxwell's electromagnetic theory is an example of structural unification: In covariant form, this theory is symmetric because the electromagnetic tensor subsumes the electric and magnetic fields with equal weights; it is complete because none of its theorems has to be rejected as unphysical for clashing with observations; it is irreducible because it yields at least electromagnetic radiation as new physics.

In contrast, quantum field theory is not a structural unification of quantum mechanics and relativity for not being a "single mathematical structure". It is not symmetric either: Canonical quantization grafts quantum properties on relativistic fields, thus treating these properties as after-thoughts. This cannot possibly be the way of nature.

Steve Dufourny wrote on Sep. 27, 2009 @ 14:37 GMT
Dear Emile ,

You are welcome ,

Sincerely

Steve

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Lawrence B Crowell wrote on Sep. 27, 2009 @ 21:39 GMT
I read your paper with considerable interest. I am always looking for connections between what I am thinking with others, or between what others are thinking. I posted this on Ray's blog site. Mine essay is at

http://www.fqxi.org/community/forum/topic/494

where I indicate aspects of how exception algebras may work with respect to the cosmological constant.

I have been...

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Author Emile - Grgin wrote on Sep. 27, 2009 @ 22:24 GMT
Dear Lawrence,

These few words are only to thank you for your comments. Unfortunately, it's probably not until tomorrow night that I will be able to read your essay carefully, and then your post. You will then hear again from me. I just hope I will have something useful to say.

Regards, Emile.

Lawrence B Crowell wrote on Sep. 27, 2009 @ 23:14 GMT
I should have mentioned that the homotopy principles here are codified by Stasheff polytopes. I have had the thought that operators in quantum gravity may have an underlying geometry or topology which differs from standard QM. The distinction between complex norms and distance norms wiht quantions might be an element of how this happens.

Cheers LC

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Lawrence B. Crowell wrote on Sep. 28, 2009 @ 01:07 GMT
To follow up with the historical aspect of your essay, I think that in the ancient world the concepts of the universe beyond the Earth mirrored the type of building activity of the time. Hellenic and Roman construction was static for the most part. People built large structures which were long lasting. Of course if one goes back further in time this is even more the case, such as the Egyptian pyramids --- which will last in some part for up to 100,000 years. Ancient cosmology, such as Ptolenmy's world was geometrically fixed for eternity. In later times the tendency was more process oriented. Before Kepler watch making, optics, and other machines were a growing industry. Which mirrors the emergent physics of the time which was more process modelling.

The later physics of the mid-19th century to the current time is motivated by the need to unify distinct categories. In many ways this was accompanied by Charles Darwin, who demonstrated how distinct species of life were related to each other. Maxwell with his displacement current, Einstein with his unification of time and space, and then gravity with spacetime ilustrate the trajectory of field theory. Quantum mechanics might be seen as a generalization of the least action principle, where the variation in a path is replaced by a wave mechanics and interference principles.

Cheers LC

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Narendra Nath wrote on Sep. 28, 2009 @ 03:09 GMT
Emile,

your essay needed to be exhaustive since you chose the historic path. History often does not repeat and one only can learn the right lessons from the mistakes made. Innovation and excellence usually comes with unbiased attitude and freedom of approach. Physics has hardly been in the limelight as one finds Nobel awards going for lifetime achiements, etc. May i suggest that freshness of ideas is what is required. My guess is these may well come from Cosmological ideas, as several unexplained facts are hanging around there that have connection with fundamental aspects of Phyiscs. Particle Physics approach is escalating in costs while the early universe study contains all that knowledge that we now require. i am sorry if i have presented these ideas, in contrast to your emphasis on the historic approach. In fact that is a normal or usual approach and that is why we are producing so called new research that is merely like corollaries to what is already known, no path breaking ideas are emerging!

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Author Emile - Grgin wrote on Sep. 28, 2009 @ 05:39 GMT
Dear Narendra Nath,

I wholeheartedly agree with three of your mutually related statements, so much so that that I see them as a theorem:

(1) History does not repeat itself.

(2) We can learn lessons from past mistakes.

(3) We need fresh ideas.

Proof:

Any good idea that has already generated a paradigm shift has been squeezed dry of fresh juice. On the other hand, a barren idea could not have been exploited to the hilt because there there was nothing in it to begin with. It remains youthful forever -- and keeps coming back. Only a fresh idea has a remote chance of being fruitful.

Quod erat demonstrandum.

This is why I look at history to make sure I would waste no time on either good ideas or bad ideas. It follows that I have no choice but to follow fresh ideas. Eventually, others will decide whether my work belongs to the good heap or the bad heap, but that's not my concern. The main thing is that the interim be mine: I thoroughly enjoy what I am doing.

Thanks for your post. Emile

PS. Freshness is a necessary condition, not a sufficient one.

Author Emile - Grgin wrote on Sep. 28, 2009 @ 16:15 GMT
Dear Ray,

In preparation for reading your essay, I was just going over the posts related to it when I noticed your note to Florin:

{

Emile's ideas are interesting. It will take time for me to process these ideas. Off the top of my head, I expect to need pairs of quantions to rewrite the Dirac Equation in terms of quantions instead of gamma matrices. Still, a pair of quantions...

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Narendra nath wrote on Sep. 28, 2009 @ 17:21 GMT
Emile response to my comments appear to surprise me as to what he means by freshness in a historic approach. May be he has some hidden freshness that i have missed in his detailed presentation. i am definitly getting old for freshness and so Emile may well be correct as i miss the freshness of ideas he has presented!

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Author Emile - Grgin wrote on Sep. 28, 2009 @ 19:56 GMT
Narendra,

Quoting you:

" May i suggest that freshness of ideas is what is required."

Yes, you may suggest it, and you did suggest it, and I said I wholeheartedly agreed.

Moreover, I thought we both meant freshness of a physical or mathematical idea that yields theoretical results not obtained by less fresh ideas already investigared. If you meant something else and I did not correctly guess what it is, then (1) I apologize for wasting your time, and (2) bow out of the discussion because, whatever it is, it would be outside my very narrow area of expertise.

Best regards, Emile.

Lawrence B. Crowell wrote on Sep. 29, 2009 @ 03:25 GMT
Dear Emile,

I wrote the post below to Florin Moldoveanu. I have only been introduced to this concept at this point. There seem to be deep connections with Jordan algebras and I think this might be some aspect of how to work with E_8 physics. I don't have your book, and at this time I am just introduced to these ideas So I don't know if you might agree or disagree with what I write...

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Narendra Nath wrote on Sep. 29, 2009 @ 03:33 GMT
Dear Emile, i appreciate your attempt, no doubt about it. In your comment, may i say that ideas are mainly conceptual and not mathemetical or phsical. The tools we use in Physics may be mathematical or observational.You have no need at all to bow out of discussions. It is the way we all learn irrespective of our age. Stopping from participation shows some avoidance on your part to accept an alternate view or suggestion. Let us keep our options always open and enjoy the life with its usual ups and downs. best wishes and all possible encouragement from my side. May be you try going through my essay on this website and i will appreciate your critical comments/analysis of the same very much.

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Author Emile - Grgin wrote on Sep. 29, 2009 @ 13:03 GMT
Dear Narendra Nath,

I apologize for not having stated why I cannot get involved in discussions outside my narrow field of interest. The reason is very prosaic: I am currently pressed for time.

I read your essay, as well as many other ones, but taking a little time for reading is not the same as taking a lot of time for actively participating in discussions on different subjects -- which I would do with pleasure in some less hectic time of my life. What you say about keeping our options open is certainly true. This is not where my problem is.

With my best regards, Emile.

Peter Jackson wrote on Sep. 29, 2009 @ 14:45 GMT
Dear Emile

Wonderful Essay, ..and essential conditions of structural unification regarding Symmetry, Completeness, and Irreducibility.

I'm also impressed by our support of learning lessons from past mistakes, and of the need for new ideas.

One area I wonder if you could consider is that of reviewing abandoned theories. A postulate may be rejected on evidence which later proves mistaken. In historical research on a fundamental model I've been developing I came across the matter of stellar aberration, cited by Lorentz and others as disproving an important postulate originating from Fresnel (author of the original STR equation), but later proved wrongly so. By then physics had moved on and the case for the prosecution not reopened.

My rather too light hearted essay495 touches on this, but, if you are interested in it's genuine potential for unification in line with and support of your own philosophy, please go to; http://vixra.org/abs/0909.0047

I'd be most honoured of your view on compliance with your postulates.

Peter Jackson

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Author Emile - Grgin wrote on Sep. 29, 2009 @ 15:29 GMT
Dear Lawrence,

This is response to your post of Sept. 29, 03:25 GTM.

Let me begin with a piece of reverse advertisment concering my book. If you are now working on something else and intend to get to quantions later, I would suggest you wait and then contact me before looking for the book. I might have an update by then. The book is not 'wrong', it's just 'old fashioned'. For an...

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Anonymous wrote on Sep. 29, 2009 @ 16:13 GMT
Dear Peter,

I am very happy to hear (I mean read) that you like the three conditions of structural unification.

I put your paper on my reading list for tomorrow, bu I'll probably get to it tonight. I just hope I will have something useful to say about it. I know I will learn something, at least from the reference you mention.

As for reviving old ideas discarded for the wrong reason, this is exactly what quantions do. It was not my idea to extend the field of complex numbers at the foundation of quantum mechanics to a structurally riched number system. I saw in Adler's monograph on the subject that the idea of substituting quaternions for complex numbers is almost as old as quantum mechanics itself. It just happens (for a good structural reason) that quaternions do not support a unification with relativity. By itself, the idea of generalizing the number system of quantum mechanics does not tell us how to do it. One could only try the systems already known in mathematics -- and the field of quaternions was the only one that did not complain. While quaternions did not work, I was sufficiently familiar with the attempt to recognize, very early in the game, that quantions ought to be viewed as a number system. This worked out -- so far at least, but there is still much to be done before we can be sure that the approach will not hit a very thick brick wall.

Regards, Emile.

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Eckard blumschein wrote on Sep. 29, 2009 @ 16:44 GMT
Dear Emile, dear Lev,

Perhaps I am the only lonely one who tries to revive a mathematics beyond numbers in my essay. Be not misled by the matter of inner ear.

Regards, Eckard

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Ray Munroe wrote on Sep. 29, 2009 @ 19:38 GMT
Dear Emile,

On page 7 of your paper, you say "The algebra of quantions admits a derivation operator. Such an operator, D, is needed in equations of motion. Its two main properties are linearity and the Leibnitz identity D (FG) = (DF) G + F (DG); where F and G are quantionic fields. Formally, D must be a quantion, but since the product of quantions is not commutative, the Leibnitz identity cannot be satisfied if F and D belong to the same algebra. This problem does not arise, however, because the algebra L is pared with a dual algebra, R; which commutes with it. Fields belong to L while D belongs to R: This is a theorem, not a matter of choice. It is analogous to the geometric duality of contravariant vectors and the covariant derivation operator." In my own work, the initial state fermion seems to be an 8-dimensional subset of a 12-dimensional framework, the interaction boson can have dimensionality up to 11, and therefore the final state fermion must be a different 8-dimensional subset of the 12-dimensional framework. Furthermore, bosons exist in a reciprocal space (compare the "Charges" in my Table 4 vs. Table 7) to fermions. Perhaps your geometry, my geometry, and the contravariant/ covariant geometries are related (although different dimensional sizes).

On page 8, you say "It follows that the Minkowski space generated by the algebra of quantions is more structured than the Minkowski space of relativity: It has an intrinsically distinguished arrow of time." It is good to have an arrow of time. Does the arrow of time look different for initial state fermions versus final state fermions?

I enjoyed your paper, but would have enjoyed more quantions. Now I need to look up these other references, such as arXiv:0901.0332v2 and your book.

Have Fun!

Ray Munroe

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Author Emile - Grgin wrote on Sep. 29, 2009 @ 21:48 GMT
Dear Ray,

Of course, the first thing I noticed was a typo in the section you quoted. It sould be "...the algebra L is paired with a dual algebra, R;..", not "pared". I hope this will be obvious to everyone.

Well, it is certainly possible that the three geometries you mention are related. Now, if your geometry is related to Dirac's spinors, then it is related to quantions because 4-spinors and quantions are mutually related.

Concerning the arrow of time, the answer is easy: There is only one arrow of time. It come from the algebra of quantions, not from fermionic fields.

The quantionic approach is not sufficiently advanced to encompas interactions. Therefore, we cannoyt yet speak of initiaal and final states.

Concerning my book, what I said to Lawrence in my last post is true for all: Don't hurry to order it if you are not going to read it soon.

Regards, Emile.

Lawrence B Crowell wrote on Sep. 30, 2009 @ 02:35 GMT
Thanks for the references. I am interested in the connection with twistors since both quantions and twistors involve SO(4,2) ~ SU(2,2). I have found that the E_6 group is involved with twistor-like equations formed from the Hermitian and anit-Hermiain Jordan J^3(O), which are intertwined with the G_2 group. This appears to be some sort of generalizaiton of the rule

= (2ħ)^{-1}(G(ψ, φ.) + iΩ(ψ, φ)

for G(ψ, φ.) + iΩ(ψ, Jφ), J^2 = -1, J = G^{-1}Ω. The two terms correspond on the algebra level the hermitian and antiHermitian J^3(O), With the G_2 holonomy this defines teh E_6 realizatio of the Jordan algebra J^3(HxO), and the space of physical states are projective twistor spaces. I will try to write this up in more detail in the forth coming days.

Cheers LC

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Lawrence B. Crowell wrote on Sep. 30, 2009 @ 02:37 GMT
I keep forgetting this editor has fits and starts over carrot signs so this is meant to read

(ψ, φ)= (2ħ)^{-1}(G(ψ, φ) + iΩ(ψ, φ)

LC

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Author Emile - Grgin wrote on Sep. 30, 2009 @ 02:49 GMT
Hi Lawrence,

I don't know if it's a slip on your part or if I've been misunderstood. In case it's the latter, I'd like to fix it here. You say:

" since both quantions and twistors involve SO(4,2) ~ SU(2,2)."

Correction:

both quantions and twistors involve SO(4,2).

but only twistors involve the isomorphism SO(4,2) ~ SU(2,2.

Bye, Emile.

Lawrence B. Crowell wrote on Sep. 30, 2009 @ 12:18 GMT
The covering rule I included as a matter of fact. While it might not be explicitely used in quantions, it might still play some sort of role.

Cheers LC

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Ray Munroe wrote on Sep. 30, 2009 @ 12:33 GMT
Dear Emile,

I understand about your book - this is continuing research, which is why I chose to post my book with a free partial preview. In my mind, my book's research is never finished, and the wording is never perfect. Nonetheless, your book is reasonably priced and might help my research.

Did my analogies help you to understand SU(3)? My references 3 (posted on my site) and 11 might be more helpful than my book. Ironically, I had trouble with "Hyperflavor" SO(2,4) (Section 7.2 of my book is wrong on the particular Lie algebra).

Good luck in the contest!

Ray Munroe

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Narendra nath wrote on Sep. 30, 2009 @ 12:49 GMT
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!

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Author Emile - Grgin wrote on Sep. 30, 2009 @ 14:18 GMT
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.

Author Emile - Grgin wrote on Sep. 30, 2009 @ 15:17 GMT
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.

Ray Munroe wrote on Sep. 30, 2009 @ 17:15 GMT
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

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Steve Dufourny wrote on Oct. 1, 2009 @ 12:24 GMT
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...

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Author Emile - Grgin wrote on Oct. 1, 2009 @ 14:53 GMT
Thank you Steve,

Your points are well taken.

Best regards,

Emile.

Author Emile - Grgin wrote on Oct. 1, 2009 @ 15:32 GMT
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.

Steve Dufourny wrote on Oct. 2, 2009 @ 10:08 GMT
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

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Steve Dufourny wrote on Oct. 2, 2009 @ 10:37 GMT
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 ...…………………………… ……………………………………………………
…………………………………………………GLU
CID 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

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Cristinel Stoica wrote on Oct. 3, 2009 @ 14:53 GMT
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,

Cristi Stoica

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Author Emile - Grgin wrote on Oct. 4, 2009 @ 04:03 GMT
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...

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Cristinel Stoica wrote on Oct. 4, 2009 @ 06:29 GMT
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

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Author Emile - Grgin wrote on Oct. 4, 2009 @ 11:10 GMT
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.

Cristinel Stoica wrote on Oct. 4, 2009 @ 12:37 GMT
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

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Cristinel Stoica wrote on Oct. 4, 2009 @ 13:14 GMT
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

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Ray Munroe wrote on Oct. 4, 2009 @ 15:14 GMT
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

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Author Emile - Grgin wrote on Oct. 4, 2009 @ 15:22 GMT
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

Cristinel Stoica wrote on Oct. 4, 2009 @ 16:42 GMT
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

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Florin Moldoveanu wrote on Oct. 5, 2009 @ 02:51 GMT
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.

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Anonymous wrote on Oct. 5, 2009 @ 17:03 GMT
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.

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Florin Moldoveanu wrote on Oct. 5, 2009 @ 17:52 GMT
Emile,

Thanks for clarifying my position, I meant it like this: "Why then in this case two real numbers cannot achieve what a complex number can".

I struggled also a bit in the beginning with the very point Ray and Cristi raised, and with another issue I want to clarify: are quantions new physics? Superficially it looks that they are not, but this is deceiving. Let me explain.

Quantions are not just like useless rearranging the chairs on the deck of Titanic. Quantions do not have their motivation in clever reinterpretation of Pauli matrices, but in a systematic approach for discovering non-unitary realizations of QM. This led to quantions which turned out to be intimately linked with spinnors. It would have been very unfortunate if there was no link with Pauli matrices and Dirac equation. (If Dirac equation were not discovered by now, quantions would have led uniquely to it.) But do they lead to additional physics? The hope is that they will. The standard nonrelativistic QM is unsatisfactory from several points of view and let's present 2 of them: (1) space and time are outside concepts, (2) the measurement problem or the emergence of classical physics from QM.

The first issue is naturally solved by quantions, and there is hope for the second one. Relativistic QM should be the correct framework of nature. Instead of the standard Hilbert space, one deals with the non-commutative geometry framework, and this holds big promises as quantions make intuitive the non-commutative geometry approach.

Florin

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Cristinel Stoica wrote on Oct. 5, 2009 @ 18:35 GMT
Dear Florin, dear Dr. Grgin,

I agree with the affirmation that it is important the structure, not the underlying vector space. For example, in Hestenes' version of Dirac's equation, the usual Dirac spinors (elements of a complex vector space) are replaced by even elements of the Dirac algebra (identifiable with elements of the Pauli algebra).

Dirac spinors, as vectors, have no richer algebraic structure (the product of two spinors is not a spinor) while spinors regarded as even elements of the Dirac algebra not only form an algebra, they are very similar to the complex numbers they generalize.

Of course I agree that a new structure may provide at least fresh insight and, in some cases, more compact notations and calculations. After reading some of your papers, wanting to understand more, I took the liberty to ask you some questions, to see if the quantions' potentiality corresponds with my own exigencies. I like to do my homework. I hope I did not ask too many or inappropriate questions, please take it as a proof of interest. You both collaborated admirably in trying to answer mine and Ray's questions.

Best regards,

Cristi

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Author Emile - Grgin wrote on Oct. 5, 2009 @ 23:09 GMT
Florian, your clarifications are very good. Thank you for helping out. Concerning your point number (2), I doubt very much that quantions will help with the measurement problem, but then, we are both guessing.

I like your meraphor about the rearrangement of chairs because I've heard too many times that quantions are just that.

Emile

Florin Moldoveanu wrote on Oct. 6, 2009 @ 01:43 GMT
Emile,

I have a hunch of how to approach the measurement problem in relativistic (quantionic) QM. From 10,000 feet, the non-unitary evolution during measurement should occur naturally in a non-unitary representation of QM, but the actual mechanism I expect to be subtler.

Decoherence is only half the solution. My hunch is that Gleason’s theorem breaks down in general in relativistic QM, and its failure will generate superselection rules which will solve the remaining mystery of the measurement problem. But this means we have to look past the Zovko interpretation in the divergent case.

Florin

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Author Emile - Grgin wrote on Oct. 6, 2009 @ 01:50 GMT
Dear Cristi,

In your post of Oct. 4, 13:14 GMT, you are not asking a question but making a statement. You say that it it is owing to familiarity that I believe in quantions more than others do, not because they are more powerful.

OK, I'll give you the opportunity to prove that quantions do not add anything to our present understanding of physics.

Let's hit the reset button...

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Author Emile - Grgin wrote on Oct. 6, 2009 @ 01:59 GMT
Florin,

If you have a hunch, that something else. I hope it works out.

I don't understand what's happening: I think I am doing things right, and then my posts end up under "anonymous", like the one above to Cristi. Let's see what will happen to this one.

Emile

Cristinel Stoica wrote on Oct. 6, 2009 @ 08:35 GMT
Dear Dr. Grgin,

I did not say "stop using quantions, because spinors and Clifford algebras can do the same job, factually". But it seemed to me that you misrepresented the state of art in physics, when compared it with quantions. I tried to show this in some examples (please correct me if I am wrong):

You compare quantions with complex numbers and quaternions, and say that only...

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Author Emile - Grgin wrote on Oct. 6, 2009 @ 11:35 GMT
Dear Cristi,

I think I have to admit defeat and accept the unpleasant fact that I am unable to make myself understood by some (probably very many) physicists, including you. After having tried hard to explain that my work in foundations ended up in extending the number system of quantum mechanics (just as QM extended the number system of classical mechanics), you tell me that you like quantions but (I quote) "I just wanted to be fair about other structures and results too." Since fairness is an argument I've never seen before (I've seen it in labor arbitrarions, but not yet in physics or mathematics), I don't understand some of your reasoning. This also applies to the first sentence of your essay: "I propose a gentle (requiring minimal changes to both theories) reconciliation of Quantum Theory and General Relativity." Since the theories in questions are the most rigid in all of physics, I suspect I will never understand how they could be minimally modified. Reading the essay did not help.

My suggestion: Let's broadmindedly accept the not very terrible fact that the probability of our understanding each other's objectives in physics in the very near future is not high enough to justify the effort. This does not prevent me from wishing you success in your approach to the problem we are both working on.

Best regards,

Emile.

Florin Moldoveanu wrote on Oct. 6, 2009 @ 16:22 GMT
Dear Emile and Cristi,

I think Cristi does have a valid point. It may not have anything to do with fairness, but great claims deserve great scrutiny and this should include positioning the claim into the state of the art knowledge. Positioning the work in the proper context does not reduce the value of the conceptual breakthrough. Special relativity for example is not diminished by the fact Lorenz already discovered his transformation earlier.

Quantions are (for now) a conceptual breakthrough. Any such endeavor takes time to fully appreciate because: (1) it is always an uphill battle to push a new paradigm, and (2) you have to invest some time to study it and understand it. However, ultimately it will have to produce new results. I am a firm believer quantions would explain new things in the near future. This is not blind fate, it is based on the intuition I am building about them.

There is more to quantions than as an even dimensional subalgebra. If this is all that was to it, it is no wonder why Hestenes did not made additional progress since he discovered the U(1)XSU(2) symmetry in 1966. [This is not meant to diminish Hestenes’ results after the electroweak symmetry discovery because he certainly achieved his research goals resulting in the intuitive geometrical algebra approach leading to the recent gauge theory of gravity. I am only pointing out that the link between his “space-time algebra” and Connes’ non-commutative geometry was not investigated and this is where I think the true future value of quantions resides.]

The value of quantions does not reside at all in the ability to derive Dirac’s equation. Deriving Dirac from quantions is only a sanity/reality check along their development.

Their main strength is in their uniqueness proof as the only mathematical structure which is compatible with quantum mechanics and relativity. To fully understand that you have to first understand what is quantum mechanics. I am not talking about the textbook Hilbert space formulation. QM is a vast domain: Jordan algebra approach, operator algebras, geometric quantization, lattice approach, Hilbert space, GNS construction, Tomitza-Takesaki, Gleason - K-S - Bell theorems, non-commutative geometry. Composability leads to an intuitive coherent axiomatization of QM. On one hand you have complex numbers for the non-relativistic case; on the other you have quantions at the center of the relativistic case.

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Owen Cunningham wrote on Oct. 6, 2009 @ 17:19 GMT
A copy of this message is being left in each thread of the essay contest forum.

Submitters: Tired of constantly checking the FQXI site to see how your paper's doing in the rankings? I've written a simple program that periodically checks the FQXI site and sends you an email if the status of your paper has changed in any way. Here is a sample email:

The following changes were detected in the status of your paper:

* Number of posts in discussion forum went from 0 to 20.

* Community rating went from 0 to 3.4.

* Community vote count went from 0 to 10.

* Public rating went from 0 to 4.3.

* Public vote count went from 0 to 6.

* Community ranking went from being in 0th place to being tied for 16th out of 112.

* Public ranking went from being in 0th place to being tied for 19th out of 112.

You just run the program once, in a command prompt window, and then minimize that window and let it do its thing in the background.

If you're interested in a copy (with source for those who care) drop me a note at ramblinplan@yahoo.com.

Thanks,

Owen Cunningham

P.S. This program requires Windows and the .NET Framework. It has been tested only on Windows XP Service Pack 3 running .NET Framework 3.5, but has a good chance of working with earlier versions.

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Terry Padden wrote on Oct. 7, 2009 @ 04:03 GMT
Emile

Good essay. I have a number of points I want to discuss here. The first one is this:

Your first part shows by historical (vertical) analysis why for you it is mathematics holding up progress in physics. My essay arrives at the same conclusion by a horizontal analysis emphasisng current issues facing mathematical science. In your second part you propose a resolution to the problem through the new Quantion structures you have developed. Your approach is what I call "progressive" in my essay. You accept the maths we have today as being correct as far as it goes - it just needs extending. Which you have done.

It seems to me the progressive approach is open-ended. New mathematical structures can always be extended - ad infinitum over time as the need arises. So the progressive approach only addresses current problems facing physics; in your case the current need to unify QM and GR - just as historically Maxwell united Electricity and Magnetism. Such unifications - although magnificent achievements in themselves - do not address ultimate questions, which is what we are asked to do. I include issues like "emergence" as being ones we should be able ultimately to address.

Are you asserting that Qantions are an ultimate mathematical structure ?

For me, science including maths and physics will always be open ended. Progress will always be possible - but only if the foundations are sound. I am sure in mathematics they are not. They are incomplete.

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Author Emile - Grgin wrote on Oct. 7, 2009 @ 06:32 GMT
Terry,

I will definitely read your essay, but I can comment on your post immediately.

I have the impression you understood my essay pretty much the way I like it to be understood. Thus, there being no 'corrections' to be made, let me answer your question

"Are you asserting that Qantions are an ultimate mathematical structure ?"

No, I am not. In general, I am never asserting anything beyond what I can prove. What's more, I am not even interested in unprovable assertions. For example, You say:

"For me, science including maths and physics will always be open ended."

To comment on this statement, I have to break it up into three:

For science I agree with you because emergent phenomena give rise to new science, and I can't see how the superstructure of such phenomena could ever hit a ceiling.

For mathematics I also agree with you because Goedel proved it.

For fundamental physics I neither agree nor disagree with you. I plead total ignorance. And I have no need to fill this ignorance with beliefs.

Next quote:

"Progress will always be possible - but only if the foundations are sound. I am sure in mathematics they are not. They are incomplete."

I fully agree with this statement taken in isolation, but to the extent that it refers the preceeding one about physics, I have no opinion. I take it that the incompleteness you mean is Goedel's. Now, Is Goedel's theorem applicable in fundamental physics? Maybe it is, but I don't see by what mechanism. A necessary condition for that is the presence of a set of relevant objects whose cardinality is aleph zero. Yet, there are only 10^180 Planck cells in the entire visible universe. This is humongous on the human scale, but not even worth mentioning in comparison with infinity. Even if every cell could communicate directly with every other cell, the whole thing would have the complexity of tic-tac-toe (from the standpoint of aleph zero, of course). So, the question is: Does the mathematical set of natural numbers have a concrete realization in ultimate physics? My final answer is I DON'T KNOW, but if I were forced by some nasty deity to bet my life on it, I would probably hit the NO button (and that might well be the end of me, but I would never know it).

You might have gotten the impression that I view quantions as the ultimate mathematical structure in physics because I said something to the effect that quantions seem to be the last number system (relevant to physics). They indeed seem to be that because they leave no wiggle room for deformation, and offer no opening into which one could add some structure --- which is not the case with complex numbers (otherwise they would not generalize to quantions). Now, "ultimate number system" is not the same as "ultimate structure". And for the latter, I don't have anything to say.

Regards,

Emile.

Steve Dufourny wrote on Oct. 7, 2009 @ 08:56 GMT
Hi all ,

It's super your discussions to all ,with Mr Christi Stoica ,the dream team increases thus the extrapolations dance with the ideas of all ,a beautiful synchronization arrives ....Florin ,Ray ,Mr Grgin,Lawrence ,Mr Stoica ,Mr Crane ,some I forget...the sing of primes ,naturals ,reals ,complexs imaginaries...arrives and goes towards a beautiful physical synchronisation ,the complemenatrity ,focus on fundamenatls, increases many things .

Dear Mr Grgin,

Does the mathematical set of natural numbers have a concrete realization in ultimate physics?

Here is a suggestion .

The multiplication of prime numbers gives naturals ,and complexification.

The physical serie is limited with prime numbers .The infinity is in the imaginaries thus a limit is necessary inside the closed system with 3D and a constant of building .Inside the complexification with naturals can be inserted but the imaginaries aren't considered due to the non physicality of course .

There the Goedel Theorem must be adapted in its axiomatisation of course with rationality and pragmatism .

In one word the unknew is the unknew and our rule ,our pure rule is to understand these 3D more a constant .

Sincerely

Steve

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Author Emile - Grgin wrote on Oct. 7, 2009 @ 10:34 GMT
Steve,

"Does the mathematical set of natural numbers have a concrete realization in ultimate physics?"

The answer is absolutely not!

At least I don't think so.

If I am not mistaken.

I hope this will help, more or less.

Sincerely, Emile.

Steve Dufourny wrote on Oct. 7, 2009 @ 17:21 GMT
Dear Emile ,

Yes I understand better your works and researchs.I reread your essay too .

that helps .Indeed I see more clear .

Best Regards

Steve

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Steven Oostdijk wrote on Oct. 9, 2009 @ 19:53 GMT
Dear Emile,

Like your fellow contributor Florin you seem to suggest that the Ultimate Possible in Physics is pure mathematics. Does'nt that sound odd? Where are your connections to reality then?

We know for instance that the physical zero dimensional point is a non-existent one, since the smallest point we currently could observe would be the size of a photon. That would mean that all physical limits (as in calculus) should resolve into an whole multiple of photon constants. Since this is currently only partially reflected in physics, I cannot imagine how a more complex math is going to help.

Your reflections in this would be appreciated.

Good luck with the contest!

Steven Oostdijk

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Author Emile - Grgin wrote on Oct. 10, 2009 @ 01:31 GMT
Dear Steven,

You are reading much too much into my essay. I am definitely not suggesting that "the Ultimate Possible in Physics is pure mathematics."

I am not suggesting anything about Ultimate Anything because I don't know the future. If I did, I would not be suggesting it but telling it for a fee.

While I don't know the future, I know enough of the past to extract trends from the history of physics and mathematics. Since these trends happen to admit extrapolation into the near future, they suggest an approach that is likely to lead us to the next paradigm in fundamental physics. And this is plenty for me. The ultimate paradigm is none of my business.

Another point: Your linking Florin's objectives and mine is unfair to both him and me. I noticed that Florin has a very wide range of interests in physics and the knowledge to go with it. One of these is my work, which pleases me very much. My interests, on the other hand, are limited to a single question: What is the NEXT paradigm. Florin will speak for himself if you ask him.

I am sorry to disappoint you by not having any reflections concerning your question. But, more to the point, why should that question be addressed to me? It has absolutely nothing to do with anything I ever wrote (or even thought).

Good luck with the contest!

Emile.

Peter Morgan wrote on Oct. 10, 2009 @ 01:37 GMT
Hi Emil,

I find your mathematical presentation of quantions difficult to follow. I've read through the comments here as well, but couldn't find anything that clarified the distinctions between quantions, Clifford algebras, even subalgebras of the Clifford algebra (e.g. as Hestenes), ideals of Clifford algebras (spinors, but I see you explicitly say that quantions are algebraic objects, in contrast), or the various bundles over space-time that can be constructed starting from such algebraic objects. Are there any (anti-)commutation relations that are satisfied by the quantion algebra, or, if not, I don't see some other kind of presentation of the algebra anywhere? Is the quantion algebra freely generated, for example?

I've not read your paper thoroughly, and I've not followed any links, but it's not even clear to me whether a quantion algebra is defined at a point or requires a bundle structure (or something like it) for its definition. You seem to have a fair degree of mathematical sophistication, but I don't see clear relationships to conventional mathematics being made in conventional ways. Then I would feel more able to see how your algebra is unconventional. I worry, for example, that the Clifford algebras are universal for the algebraic anticommutation relation u.v+v.u=2(u,v), which leads naturally to spinors as ideals of Clifford algebras (and slightly less naturally to Hestenes approach in terms of constructing an action of the Clifford algebra on its even-graded subalgebra).

The other aspect of assessing a theory that I find difficult in your case is the extent to which your constructions make contact with quantum field theory, say. It's not clear to me that you satisfy a modern correspondence principle, that your theory must make contact with at least quantum mechanics in a clear way, at least in the sense of approximation.

I'm sorry this is not more helpful, and that it's somewhat late to the party. I couldn't bear to look at the rush of late entries to the competition until now. If I could understand what is different about quantions, it seems as if your paper might be interesting.

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Terry Padden wrote on Oct. 10, 2009 @ 11:02 GMT
Emile

Thanks for a prompt, detailed, and perceptive response. You write as your "Ultimate Postulate"

"It thus appears that what is ultimately possible in observable physics ( ...) coincides with how deep one can go in mathematics and still find a fundamental structure which is both very rich (to support all of physics) and very specific (to guarantee finality)."

Agree

Then you write "In the quantionic approach the fundamental structure is a number system. I cannot think of something deeper that would not be too general (like set theory)."

I don't think the different number systems are important in themselves. What is important is the interpretation of what the progression from one number system to another implies - physically. These number systems are not fundamental. Abstractly they are all multiples of the Reals which derive from the Naturals. I am looking closely at the physics of the Naturals.

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Author Emile - Grgin wrote on Oct. 10, 2009 @ 13:31 GMT
Hi Peter,

(Note: I was forced by the server to split this post in two. Please view them as one.)

Your first sentence -- to the effect that the mathematical presentation of quantions in my essay is difficult to follow -- is an understatement. I think it is impossible to follow for anyone not already familiar with it (Florian Moldoveanu being probably the only one who is on this forum). It is much too condensed to serve as a primer. Since you may be wondering why I even put it there, the following explanation is meant to anticipate your question.

It is by seeking trends in the sequence of major paradigms in the histories of physics and mathematics (though I wrote only about physics) that I arrived at the approach to research which led to quantions. Having outined this trend analysis, I had to emphasize that my essay is not meant to tell others what to do while not doing it myself (there are more than enough of those essays), but to show that the approach in question does yield physically meaninful results. A book being needed to do this cogently, a few pages cannot do it justice. Yet, without these few pages, the essay would not even belong to the contest.

You say that you don't see clear relationships to conventional mathematics being made in conventional ways.

Very true. This is because I did not work along conventional lines (I did not take it for granted that the structures mathematicians have investigated so far are the only ones relevant to physics at its foundations). Thousands of physicists and mathematicians actively engaged in research have been very familiar with the conventional math you mention for as long as quantum mechanics exists. So was I, in my graduate student days (and you may add twistors to that). When I realized that the conventional approach was over-crowded, I decided not to delude myself into believing that I could make a dent where others didn't in the only subject of interest to me: A true unification of quantum mechanics and relativity. I thus had to strike out on my own (though an initial part of the journey was made in collaboration with Aage Petersen, whose memory I cherish). Not surprisingly, the outcome (i.e., the number system that brings about the unification in question) is NOT a conventional mathematical structure. It looks like four different structures when viewed from four different 'angles', and each one has a different physical interpretation -- and this is what supporst the unification of two very different theories. I wish I could write a short tutorial on the subject, but it is impossible. Maybe later when some more dust settles. There is just too much deductive work that relates the conceptual view of mechanics developed in first abstract algebraic paper on the subject (2001) and the second book, whose last chapter is about the complementary roles played by Dirac's spinors and quantions (2007).

Author Emile - Grgin wrote on Oct. 10, 2009 @ 13:36 GMT
Let me now answer your specific questions:

1. The algebra of quantions is generated, but not freely (the generators satisfy some identities). It is a unique and rigid structure, like the algebras of complex numbers, quaternions, or octonions. It is useful to view it as a number system because it replaces the complex numbers in quantum mechanical states.

2. The algebra of quantions...

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Author Emile - Grgin wrote on Oct. 10, 2009 @ 14:30 GMT
Terry,

You write:

"I don't think the different number systems are important in themselves. What is important is the interpretation of what the progression from one number system to another implies - physically. These number systems are not fundamental. Abstractly they are all multiples of the Reals which derive from the Naturals."

I agree that the interpretation of what the progression from one number system to another implies - physically - is important. This is even the 'raison d'etre' for any new number system.

But I have a different view of number systems in general - both mathematically and physically.

Mathematically, saying that a particular structure, S, is the number system of some theory is a powerful statement. It tells us to forget about any simpler underlying number system and accept as syntactically valid only those statements (postulates and theorems) that can be formulated exclusively in the number system S. This does not apply to the ephemeral statements within proofs of theorems, but theorems that can be proved within S alone are invariably more impressive - at least aesthetically. Consider, for example, a complex projective space. It is equivalent to two real projective spaces only in information capacity related to geometric objects. But is not equivalent structurally: Division by complex numbers is not automatically contained in a pair of real projective spaces.

Physically, what I said above still applies, but there is more. The Catesian and polar representations of complex numbers are mathematically equivalent (we use what suits us better), but the polar representation is distinguished in quantum mechanics: The unobservable phase factor gives rise to the gauge group U(1) while the norm is subject to Born's interpretation. The same is true for quantions, which also amit a polar representation: The unobservable phase factor gives rise to the gauge group U(1)xSU(2) while the norm is subject to Zovko's interpretation and gives rise to the equations of motion.

Eckard Blumschein wrote on Oct. 10, 2009 @ 14:54 GMT
Dear Emile,

You ignored my hint on Sept. 29. Do you object?

I consider my view justified. It claims to resolve some enigma not by means of tortuous definitions and interpretations but with some tangible consequences.

Isn't it better to correctly re-transform originally measurable quantities from their arbitrarily chosen mathematical representation back into the original realistic domain as do engineers like me?

Regards,

Eckard

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Author Emile - Grgin wrote on Oct. 10, 2009 @ 16:36 GMT
Dear Eckard,

What was your hint?

If it's that I read your essay, I did. I read it then and I reread it now.

If it's that I comment on your essay, I can't because I always keep quiet when I have nothing useful to say.

I can tell you, though, that I enjoyed very much the part where you talk about the things you know. I will even reread it more carefully. Thank you for sharing those insights.

Regards,

Emile.

Author Emile - Grgin wrote on Oct. 10, 2009 @ 17:24 GMT
Daryl,

I see only one connection between our essays: We both speak of the arrow of time.

I have the impression that this concept can be interpreted in more than one way.

The standard interpretation has to do with the time parameter that appears in the equations of motion. If the entropy is preserved, the motion is reversible. If the entropy increases, it is not -- which means that a direction of time is distinguished. We call it the future. This is clear. What is not clear to me, even after having read much on the subject, is why many physicists are uncomfortable with the problem 1) in your essay. If you have solved this problem, I would like to understand the solution, but for that I would have to go to your articles and study them carefully -- a project that will have to wait.

In my work, an arrow ot time appears at the microscopic level. I don't see how it could propagate to the macroscopic level. My impression is that the existence of this arrow is related to the failure of the P and T symmetries in the electroweak theory. Time will tell.

Regards, Emile.

Darryl Jay Leiter wrote on Oct. 12, 2009 @ 02:08 GMT
Hi Emile,

You commented that:

"If you have solved connection between macroscopic and the microscopic arrow of time, I would like to understand the solution....

In my work, an arrow ot time appears at the microscopic level. I don't see how it could propagate to the macroscopic level. My impression is that the existence of this arrow is related to the failure of the P and T symmetries

in the electroweak theory. Time will tell.

-------------------------------------------------------
---------

I actually think the existence of the arrow of time in the universe is caused by related to the spontaneous breaking of the CPT symmetry in the nonlocal, relativistic, observer-participant Measurement Color Quantum Electrodynamic (MC-QED) formalism. This occurs because the photon operator carries the arrow of time in MC-QED and causes the physical requirement of the existence of a stable vacuum state to spontaneously break the T and the CPT symmetry of the MC-QED formalism, by dynamically selecting the operator solution which contains a causal, retarded, quantum electrodynamic arrow of time.

The Measurement Color Electrodynamic formalism represents a new observer-participant quantum field theoretic language in which both microscopic and macroscopic forms of quantum de-coherence and dissipation effects may be studied in a relativistically unitary, time reversal violating quantum electrodynamic manner.

Darryl

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Anonymous wrote on Oct. 12, 2009 @ 02:37 GMT
Darryl,

We seem to be turning in circles.

You asked me two days ago to read your essay. I told you I read it, but that I would have to read your articles to understand it.

Today you come back and tell me again to read your essay. All I can do is tell you again that I've read it, but that I would have to read your articles to understand it.

The first three are not readily accessible to me, so I went to the fourth on ArXiv:0902.4667 but got the message that Windows cannot find it.

Then I reread your essay in the hope of doing better in the second pass. No luck! I don't understand it.

I do believe that you see a connection between your work and mine, but this is normal since our final objectives coincide. The differences between all posted essays are not in the final objectives but in the initial premises. As far as I could tell so far, they are all different.

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Author Emile - Grgin wrote on Oct. 12, 2009 @ 02:40 GMT
Darryl,

We seem to be turning in circles.

You asked me two days ago to read your essay. I told you I read it, but that I would have to read your articles to understand it.

Today you come back and tell me again to read your essay. All I can do is tell you again that I've read it, but that I would have to read your articles to understand it.

The first three are not readily accessible to me, so I went to the fourth on ArXiv:0902.4667 but got the message that Windows cannot find it.

Then I reread your essay in the hope of doing better in the second pass. No luck! I don't understand it.

I do believe that you see a connection between your work and mine, but this is normal since our final objectives coincide. The differences between all posted essays are not in the final objectives but in the initial premises. As far as I could tell so far, they are all different.

Emile

Author Emile - Grgin wrote on Oct. 13, 2009 @ 12:52 GMT
Dear Eckard,

In my 16:36 GMT answer to your post of Oct 10,14:54 GMT I overlooked your question, namely:

"Isn't it better to correctly re-transform originally measurable quantities from their arbitrarily chosen mathematical representation back into the original realistic domain as do engineers like me?"

Sorry. I did not ignore this question intentionally. I 'got stuck' trying to figure out what your hint was, and then I forgot.

Concerning the beginning "Isn't it better to correctly re-transform ...?", I dont see why you would even ask this question. We are all completely free to make any transformations we find useful in our work. If the transformation is reversible, nothing is either lost or arbitrarily inserted -- so no one will ever object. And if the transformation is very important (but please, not in the author's opinion alone, but in that of the world), the author's name ends up attached to it -- as in "Fourier transform", "Laplace transform", etc.. That's the way things are.

Being thus puzzled by the motivation behind your question, I consider the two possible interpretations.

If the question was rhetorical, but actually meant to enjoin physicists to think like engineers, I have no comment. Not even my parents could tell me how to think.

If the question was genuine, and you actually want to know, I will answer it in a broader setting:

A child asks why the grass is green. The botanist answers in terms of plant physiology.

The child goes on to study physiology, and then asks about its underlying mechanisms. The biologist answers in terms of ... etc... etc.... until, after five or six steps, he reaches atomic physics.

The student asks why the constituents of atoms behave as they do. The fundamental physicist answers in terms of quarks, gluons, vector bosons, etc., (which, by the way, are not "arbitrarily chosen mathematical representation"; they are the only surviving representations after countless other ones that did not numerically relate to measurable quantities had to be mercilessly discarded).

The graduate student asks Why quarks? Why intermediate vector bosons? Why ...? But there are no definitive answers yet. For the time being, the buck stops here.

You want to know why fundamental physicists do not take over engineers' way of thinking. The reason is that they've already been there and thoroughly exploited that approach in Archimedes's time, some 2000 years ago. At that time, the buck stopped at engineering. It no longer does. Sorry, but that's the way it is! Returning in our days to engineering-level thinking would close the circle, and we all know that circular arguments are for the birds -- but even that is questionable, considering they can't even tell us what came first, the chicken or the egg (or is it the other way around?).

I hope this answers your question. And, of course, good luck with your essay.

Regards, Emile.

Chris Packham wrote on Oct. 23, 2009 @ 11:25 GMT
Wonderful essay and postulate Emile.

I've also just come across the proof that you're correct, check out Peter Jackson's 'Perfect Symmetry' essay, but look below the dressing.

I've given you the score you deserve but afraid it's only 'public'.

Best of luck.

Chris

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Author Emile - Grgin wrote on Oct. 23, 2009 @ 15:31 GMT
Hi Chris,

I am very pleased about your having enjoyed my essay, and thanks for your brownie points and good wishes.

I had already read Peter Jackson's essay, and I must admit that the "dressing" you mention was very much an obstacle to understanding. But then, prodded by your suggestion, I just read his longer article, "Doppler Assisted Quantum Unification allowing Relativistic Invariance". It is much better, but not in my style of work -- which implies that I have no intelligent comments about it. Peter's views are very broad (which is a valid style in my opinion) while I focus on details (valid or not, I made it my style because I enjoy it most).

Sorry you did not submit an essay, for I would wish you good luck too.

Regards, Emile.

Jayakar Johnson Joseph wrote on Oct. 23, 2009 @ 16:17 GMT
Dear Emile Grgin,

Formulations on metric norm of geometric origin may unify the algebraic norms of the roots of gauge group. As there is problem in coalesce of the norms of geometric origin with the norms of algebraic origin, I think their combined application with wave function is not possible due to its inconsistency on physical reality, whereas it is applicable with U(1), SU(2), SU(3) gauge groups. For this we may need further geometric representational model on gauge groups that are relatively transformable and the products of metric norms may be positive integers.

This mathematical constrain on wave function, that is on geometric origin and causal for the inconsistency of Newton's mechanics with Maxwell's electromagnetism; is arising from the transition of Rutherford planetary model of atom to the Bohr model of atom on quantum mechanics.

In a Coherent-cyclic cluster-matter universe model, the combination of Plum pudding and Rutherford models with appropriate cyclic structured representation of matters is expressed as the atomic analogy for this model. Transformation of circle from ellipse in a cone may be descriptive on the adaptability of Kepler's laws with this model; that describes the coherency of motion in elliptical orbits with their super-structures of celestial objects that are the coherent super-cluster-matters of this model and the Kepler conjecture is applicable on this.

I think if the '0' point of the quaternions number system is combined with a metric norm of Pythagorean geometric origin, the expandability of this system may be complete and may resolve many of the inconsistencies of physical realities, including that are in this model; it's really an article of the core, thanking you ..

With best wishes,

Jayakar

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Author Emile - Grgin wrote on Oct. 23, 2009 @ 17:30 GMT
Dear Jayakar,

Thank you very much for your thoughts and wishes.

Maybe I did not understand exactly what you meant in the first paragraph, but there is no problem with deriving the wave function and the Schroedinger equation from quantions. The two norms are not in the way because only one is relevant in this derivation. It is the algebraic norm. Of course, you might have meant something else. But it is very true that the two norms throw a new light on the gauge groups you mention, in particular on the root systems. This has not been published yet because these results must agree with everything else, and it takes a lot of time to double check everything.

For the other ideas you have, you are probably right, but I don't know because I look at things from a somewhat different angle -- at least for the time being.

Best regards, Emile.

Jayakar Johnson Joseph wrote on Oct. 24, 2009 @ 10:02 GMT
Dear Emile,

Thank you very much for your kind replay.

As I need further guidance on the model of universe in that I am working on, in particularly for the mathematical aspects it requires; I would like to discuss with you and your article is much elegant and more informative for me. To analyse the experimental and observational probabilities for this model, I have published an article, http://www.fqxi.org/community/forum/topic/493 and I may continue my discussions with you from the middle of November on this year onwards and that will provide me much valuable guidance to assign experimentation projects on this; thanking you ..

Yours jayakar

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Terry Padden wrote on Oct. 25, 2009 @ 22:06 GMT
Emile

Thanks for your response of Oct 10th. I have been busy responding to posts re my essay.

I agree completely with your response that more complicated & subtle Number Systems enable effective theories of more complex & subtle physics - but

Your response is another endorsement of the "progressive" approach - which I think we agreed is open-ended. My view is that - Ultimately - we need a change at the foundational level, the Naturals. This should be done without disturbing the Naturals or any developments of them, such as the Complex, Hypercomplex, or Quantions.

I think Lev Goldfarb has even suggested replacing all Number Systems at the foundational level. That is too revolutionary for me.

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Author Emile - Grgin wrote on Oct. 26, 2009 @ 01:20 GMT
Terry,

If by "progressive approach" you mean the march Naturals --> Rationals --> Reals --> etc., then I may or may not agree that it is mathematically open ended. That would depend on what we minimally expect of number systems.

Physically, however, I don't expect the sequence to be open ended. I expect it to end at quantions. This may sound self-serving, but it is not meant to be. The argument has to do with the idea of rigidity. Complex numbers still contain some soft spots. This is what makes it possible to generalize them to quantions, which are much more structured. But quations appear to be absolutely rigid. Without soft spots, the only possible generalizations are structure-reducing, but that's not interesting. My objective is to have as much physics as possible encoded in the number system.

I am curious about your view that we need a change at the fundamental level without disturbing the Naturals.

(1) Why would we need such a change? Not that I have any objection, but not having an objection is not equivalent to agreeing. To agree, I would have to see a reasonably convincing heuristic argument, or an example, or something.

(2) Something more fundamental (= structurally more primitive) than the Naturals might be Wolfram's cellular automata. Lev woud say it's his linguistic constructions, but, unlike you, he wants to get rid of numerics. This is OK with me, but I happen to be interested in an intellectual game in which outcomes are numerical. In other words, Lev and I work in different professions. If he thinks otherwise, it is his responsibility to derive interesting physical consequences that have experimental interpretations -- and I mean numerical one, as opposed to hand-waving contributions.

Mark Stuckey wrote on Oct. 27, 2009 @ 22:03 GMT
Emile,

I enjoyed your essay. I'm wondering why you see physics going from complex numbers (U(1)) straight to a non-division algebra, skipping over the other normed division algebras, i.e., the quaternions (SU(2)), which have a well-established connection to physics, as well as octonions (SU(3) via G2, indirectly since octonions are not a group being non-associative), which also has connections to physics including string theory Baez post. Are octonions a subalgebra of quantions? Pardon my ignorance, this is not my area of expertise :-)

Mark

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Author Emile - Grgin wrote on Oct. 28, 2009 @ 03:24 GMT
Mark,

Last question first, to get it out of the way:

No, octonions are not a subalgebra of quantions, nor are the two in any way related. It is true that both quantions and octonions are defined by eight real numbers, but this is a coincidence without deeper meaning. On the other hand, Dirac spinors, which are also defined by eight real nubers, are physically equivalent to...

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Author Emile - Grgin wrote on Oct. 28, 2009 @ 12:52 GMT
Mark,

In answering your questions last night, I was already more asleep than awake. Afraid of having said something I wouldn't if it had been the other way around, I just reread your post and mine. Fortunately, there are no very great sins of comission and only two of omission, both easily fixed:

(1) I forgot to thank you for your questions. They are specific and, as it seems to me, representative of what others might also ask. Well, thank you, and don't hesitate to come back with questions in the same style.

(2) My saying that Dirac spinors and quantions are physically equivalent but mathematically very different may be more puzzling than useful. A well-known example ought to help: The Heisenberg and Schroedinger pictures are physically equivalent, but the Hilbert space and the Jordan algebra of self-adjoint operators are mathematically very different.

Nevertheless, equivalence, or equality, are rarely perfect -- an imperfection humoristically conveyed by the phrase "more equal". When referring to perfect equality, we use the word "identity". Coming back to quantions, let's make two observations related to equivalence: (a) Quantions and Dirac spinors are identical from the point of view of information contents (4 arbitrary complex quantionic components = 4 arbitrary complex spinor components) and the one-to-one correspondence is well defined. (b) In the big picture, quantions are "more equal" than spinors because we only have to add an interpretation (Zovko's, which generalizes Born's) to obtain the Schroedinger and Dirac equations with all possible potentials. And if the vector potentials are interpreted as differential connections, the corresponding gauge group is U(1) x SU(2).

Referring to your post, you see that my not postulating U(1) and SU(2) does not mean that these objects do not enter the picture.

Emile

Mark Stuckey wrote on Oct. 28, 2009 @ 18:19 GMT
Emile,

"Your other questions are not really applicable to my work because I am interested in a very specific research topic: Does a structural unification of quantum mechanics and relativity exist? Or, to put it in another way, Does a mathematical structure which encompasses both quantum mechanics and relativity exist?"

Again this is not my area of expertise, but Tony Smith claims "the Octonions naturally unify the Standard Model with General Relativistic Gravity in 4-dimensional SpaceTime." When I embed the link to that website, it doesn't work in the Preview Post Text, so let me simply type it here: http://www.valdostamuseum.org/hamsmith/QOphys.html. At the bottom of that page you'll find What if you extend from Quaternions to Octonions? with his claim.

"It is well known that quantm mechanics is rigid, which means that it has no soft spots that could be modified to admit relativity."

We know the spacetime of NRQM is not M4, but it can be considered to harbor relativity of simultaneity per Kaiser (J. Math. Phys. 22, 705-714 (1981)), Bohr & Ulfbeck (Rev. Mod. Phys. 67, 1-35 (1995)) and Anandan (Int. J. Theor. Phys. 42, 1943-1955 (2003)). RoS is certainly a key aspect of relativity, so I would say that QM does harbor a "soft spot" for relativity.

Mark

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Author Emile - Grgin wrote on Oct. 28, 2009 @ 20:50 GMT
Mark,

When you asked me questions about my own work I answered gladly and told you not to hesitate to ask other questions of the same type. Your new questions are not about my work but about other people's pronouncements. I have no comments.

Emile

Terry Padden wrote on Oct. 29, 2009 @ 06:31 GMT
Emile

Like you i think Lev goes too far - but he may be onto something. Some people have read my essay as being "against mathematics" it is not. We need all the maths we already have and more, including the Quantions I suppose. I am just setting the bar higher. We not only need more, we need better maths. Whether the Quantions are enough is something we probably disagree on.

My focus is on foundations. Hence on the Naturals when looking at number systems. At this stage I am content to rely on Godel "incompleteness" and "human fallibility over 2500 years" as the basis of my heuristic argument.

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Author Emile - Grgin wrote on Oct. 29, 2009 @ 10:31 GMT
Terry,

Lev goes too far for me to follow him at this point, but I remain open-minded. I will join him as soon as his linguistic approach starts yielding more elegantly the results we normally get using standard numerical math. I know that waiting means leaving to others the opportunity to harvest the low-hanging fruits, but that's the predicament of those of us who can't do everyting at the same time for not having access to our parallel selves in parallel universes.

Your essay is of a different nature. I experienced it primarily as philosophical, and enjoyed reading it as such. I also thoroughly agree with your statement in the post concerning math.

Emile.

Lev Goldfarb wrote on Oct. 29, 2009 @ 23:15 GMT
Emile & Terry,

My apology for jumping in, but I just wanted to note that what I'm suggesting is that information is about the new kinds of (i.e. relational) structures and not about numbers.

I came to this very gradually over a long period of time trying to understand what biological information is all about, and then realizing that it applies not just to biological information processing (how else could this mechanism have emerged?)

Numbers are the simplest form of this structural representation.

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Author Emile - Grgin wrote on Oct. 30, 2009 @ 03:07 GMT
Lev,

First, you are welcome to jump in.

An almost randomly selected quote from your essay:

"Certainly, very few of us are willing to take seriously the possibility of existence of another scientific road, fundamentally different from the numeric-based road.

The last paragraph in your post:

"Numbers are the simplest form of this structural representation."

I have no doubt that the two statements are mutually compatible in your own mind because you are thoroughly familiar with the subject, which means that you can see it from different angles at the same time. But your readers (including myself) do not have that advantage. For us, two statements like

"A is fundamentally different from B"

"B is the simplest form of A"

seem to contradict each other.

As for your essay, it runs on two tracks. One is very interesting (at least to me), the other turns me off.

The interesting part is you contrtibution (ETS, primacy of temporal over spatial representations, your definition of a class, etc.). These are ideas I will remember, and I thank you for them.

The part that bothers me is your relentless criticism of numerical physics.

Emile.

Lev Goldfarb wrote on Oct. 30, 2009 @ 04:07 GMT
Dear Emile,

I’m sorry but I can’t see any contradiction at all!

1. "Certainly, very few of us are willing to take seriously the possibility of existence of another scientific road, fundamentally different from the numeric-based road.

Here, I’m simply stating that the scientific emphasis of the proposed formalism is indeed radically different: the formulas are supposed to be ‘replaced’ with the generative/structural class representations, i.e. with the ‘structural formulas’.

2. "Numbers are the simplest form of this structural representation."

Here, I’m stating the obvious fact explained in my essay (section 2.3.2) that natural numbers are one of the simplest special cases of the proposed structural representation.

There is no contradiction: in this case, the generalization is of such nature that the main features of the scientific language itself are changing. So far in mathematics, the generalizations were arrived at in a different manner, by generalizing some underlying mathematical structure, but in this case, the generalization had to be obtained by going outside mathematics proper and generalizing the primordial intuition that led to the construction of numbers. Simultaneously, we also arrive at a more general understanding of temporality, since our current understanding of temporality is a consequence of the structure of natural numbers.

3. “The part that bothers me is your relentless criticism of numerical physics.”

Actually, I didn’t do so: to a sufficient extent it has already been done by the late Milič Čapek in his outstanding book “The Philosophical Impact of Contemporary Physics”.

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Author Emile - Grgin wrote on Oct. 30, 2009 @ 12:23 GMT
Lev,

As I said in my post, I have no doubt that there is no contradiction from your point of view. But if a well-intentioned reader like myself completely misunderstands you, only two (pure) reasons suggest themselves: (a) you did not succed in conveying your ideas, (b) I am unable to understand you.

Personally, I think it's (b) because I am fully aware of my limitations.

Let's leave it at what I said in my post to Terry:

"Lev goes too far for me to follow him at this point, but I remain open-minded. I will join him as soon as his linguistic approach starts yielding more elegantly the results we normally get using standard numerical math."

If you get there, let me know. In the interim I'll be working on my own ideas.

Emile.

Lev Goldfarb wrote on Oct. 30, 2009 @ 12:32 GMT
Emile,

Of course!

Your position is quite understandable.

Best wishes,

Lev

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Jeffrey Nicholls wrote on Nov. 2, 2009 @ 00:51 GMT
Dear Emile,

Thank you for your essay. I am in close agreement with you on the first part. I find the second part a bit obscure but I have sent away for your 2007 book. Here I submit a different possible outcome which also seems to fit your guidelines:

“(1) There is no return to more naive intuitions.” So let us abandon the notion that the universe is continuous, since we observe...

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Author Emile - Grgin wrote on Nov. 2, 2009 @ 14:07 GMT
Dear Jeffrey,

The half-a-dozen 'guidelines' I listed (and quite a few I did not, like "don't beat a dead horse") are not meant to tell other people what to do. This is why I also refer to them as observations. Yet, they have been effective guidelines to me since graduate school -- not in telling me what to do, but in telling me what to avoid doing. By reinterpreting them in a manner that suits yout thesis you distort their original purpose. Let me take your second paragraph to make my point:

"(1) There is no return to more naive intuitions." So let us abandon the notion that the universe is continuous, since we observe only discrete events at all scales from fundamental particles to the stars and beyond. Like Heisenberg, let us not talk about things we cannot see.

Sorry, but this is a non sequitur at best. How could my statement be interpteted as "Let us abandon the notion that the universe is continuous"? There is no relationship whatsoever. Besides, the idea of a continuous spacetime has been dropped long ago. But dropping an obsolete picture of the world does not, by itself, bring a new one into existence. Thousands of physicists (as opposed to outside commentators on physics) are actively searching for a new working picture, examples being string theory and Connes's geometric quantization. As for the injuction you attribute to Heisenberg, "let us not talk about things we cannot see" (even though Heisenberg did talk about neutrinos and wave functions), it has been a dead horse for a long time.

I've read your esssay and all related posts. I honestly don't understand what you are advocating, so I cannot comment. If your objective is condensed in the fragments

"... the mitigation of religious conflict"

"... bringing our species into harmony with the rest of the world"

then I am one hundred percent with you. I just don't see how these lofty ideals (which may well become reality in the future) gain anything by being diluted with speculations about physics.

Best regards,

Emile

Jeffrey Nicholls wrote on Nov. 3, 2009 @ 01:01 GMT
Dear Emile,

Thank you for your reply to my comment. I am an 'outside commentator on physics' searching for a way to base my primary interest, theology, on observable reality rather than ancient texts. So I am inclined to look at physics as a description of the 'physical layer' of all the networks that constitute our world. I would like find that the world is completely self sufficient and in no need of supposed outside powers and revelations from unobservable sources. So I would like to find a picture of the evolution of the world that does not rely on any initial conditions put in place by a 'creator'. This leads me to think in terms of digital logical and computational systems and 'logical' rather than 'geometric' continuity.

The beauty of this competition, for me, is the rich harvest of opinions (not least yours) about what physics might be and where it might go. I look forward to your book, though it might go over my head

All the best,

Jeffrey

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Eckard Blumschein wrote on Nov. 4, 2009 @ 22:53 GMT
Dear Emile,

I am not yet sure how to estimate your for my feeling somewhat lecturing reply to me of Oct. 13.

Meanwhile I decided to frankly address at topic 527 what I am suspecting and some consequences if I am correct.

Let me briefly summarize my basic and presumably irrefutable objection to t-symmetry in QM:

Claude Shannon: The past is known but cannot be changed. The future is unknown but we can influence it.

I would like to add: Future time, future events evade measurement. The ordinary time is an abstraction and extrapolation of measurable elapsed time.

Einsteinian physics ignores these fundamentally important levels of quality.

As a consequence, complex Fourier transform of a realistic (in the sense of measurable) function of time must be a unphysical complex function of positive and negative frequency or vice versa. The four mutually equivalent components in case of Hermitian symmetry must be interpreted as an inseparable entity.

Heisenberg, Schroedinger, and Dirac and the whole Bohrfestspiele in Copenhagen were not aware of this necessity. This obviously led necessarily to a misinterpretation of complex wavefunction: putative t-symmetry.

You suggests to solve problems by means of more complicated mathematics. Please do not ignore the possibility to avoid arbitrariness and redundancy instead.

I would appreciate your reaction before the end of voting.

Regards,

Eckard

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Author Emile - Grgin wrote on Nov. 5, 2009 @ 06:23 GMT
Dear Eckard,

I am awfully sorry, but after rereading several times your first paragraph, namely

"I am not yet sure how to estimate your for my feeling somewhat lecturing reply to me of Oct. 13."

I still don't know what it means. Possibly because English is not my native language.

My Oct. 13 post. was motivated by frustration: I wanted very much to respond to your post as well as possible, but I did not understand it. If you feel I was lecturing in a condescending sense, all I can do is assure you that I had no such intention. I was only trying to be clear. Obviously I failed. Mea culpa. To avoid making the same mistake this time, I'll be succinct in commenting each of your statements. If I don't understand something, I'll say so -- instead of trying to guess what you mean and miss the point.

(1) "Claude Shannon: The past is known but cannot be changed. The future is unknown but we can influence it."

I would agree completely with this statement even if it were not Shannon's.

(2) "I would like to add: Future time, future events evade measurement."

I also noticed that we cannot measure future events.

(3) "The ordinary time is an abstraction and extrapolation of measurable elapsed time."

Sorry, I don't understand.

(4) "Einsteinian physics ignores these fundamentally important levels of quality."

Sorry, I don't understand. But if pressed, I'd go with Einstein.

(5) "As a consequence, complex Fourier transform of a realistic (in the sense of measurable) function of time must be a unphysical complex function of positive and negative frequency or vice versa."

OK.

(6) "The four mutually equivalent components in case of Hermitian symmetry must be interpreted as an inseparable entity."

Sorry. I don't understand.

(7) "Heisenberg, Schroedinger, and Dirac and the whole Bohrfestspiele in Copenhagen were not aware of this necessity. This obviously led necessarily to a misinterpretation of complex wavefunction: putative t-symmetry."

Not obvious to me.

(8) "You suggests to solve problems by means of more complicated mathematics."

No I don't. Absolutely not! The more advanced mathematics of relevance to physics is conceptually simpler than the math it supplants, but it is very true that it appears more complicated to outsiders. Besides, I am not suggesting anything in my essay. I am only describing what I am doing, stating why I am doing it, and briefly presenting some of my results. I was very careful to use the word "guidelines" in describing ideas I found useful for myself, but I switched to "observations" when guidelines might have been interpreted as my telling other people how to think. It is against my personal religion to tell anyone how to think.

(9) "Please do not ignore the possibility to avoid arbitrariness and redundancy instead."

Sorry, you lost me again. What does this refer to?

Best regards, Emile.

Eckard Blumschein wrote on Nov. 6, 2009 @ 12:37 GMT
Dear Emile,

Unfortunately my reply got lost.

(1) Shannon's words were slightly different.

(2) Does not (3) follow from (2)?

(3) I argue that abstract quantities were abstracted from reality.

(4) Coward or lazy?

(5) Congratulation if you are honest

(6) http;//home.arcor.de/eckard.blumschein/M283.html version by Fritzius

(7) topic 527

(8) "a method that led to a unification of quantum mechanics and relativity based on a new number system structurally located between the complex numbers and the quaternions"

(9) see (6)

Regards,

Eckard

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Author Emile - Grgin wrote on Nov. 6, 2009 @ 14:24 GMT
Dear Jeffrey,

Thank you for your clarification of Nov.3. I had misunderstood your essay.

Since you are searching for a self-sufficient understanding of the world, an understanding free of revelations, physics is the place where (in my opinion) you will find the most correct answers discovered to date. These answers are far from complete, and it is not known whether they will ever be...

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Author Emile - Grgin wrote on Nov. 6, 2009 @ 14:54 GMT
Dear Eckard,

Our discussions are at cross-purpose. The only reason I got involved is that you wanted to have my opinion. It was a mistake. Sorry!

I concluded from your essay that you are an expert in a particular btanch of applied physics. In that branch, I would not open my mouth in front of you because you know the stuff while I don't. Now, if you believe that being an expert in a particular application of physics makes you an expert in the foundations of physics, that belief cannot possibly be affected by what others think.

Let me end the discussions by agreeing with you on one thing: Anyone who does not see things the way you do is a fool for missing important insights (this includes me, of course).

The best of luck in your research!

Emile.

Peter van Gaalen wrote on Nov. 20, 2009 @ 18:40 GMT
Dear Dr. Grgin,

Thinking about the fine structure constant I thougth that the fine structure constant is the ratio of two different planck constants. an electromagnetic and an gravitomagnetic planck constant
$\alpha = \dfrac{h_e}{h}$

But Florin Moldoveanu wrote to me that "..there is only one Planck constant and the root cause for it is the existence of the tensor product in QM. In physical terms it corresponds to the ability to compose 2 QM systems and the combined system is still a QM sytem. See: http://arxiv.org/abs/quant-ph/0301044"

I objected that the quantities of the electromagnetic system (em-flux and electric charge) are completely separated from the quantities of the gravitomagnetic system (time, energy, momentum and length).

But Florin went on: "The paper does contain the proof of the uniqueness in section 5, independent of the mixing of classical and quantum systems.

The story goes like this. In 1974 Grgin and Petersen wrote a seminal paper: “Duality of observables and generators in classical and quantum mechanics” J.Math.Phys. 15, 764....."

Florin mentioned Dr Grgin, so thats why I ask your opinion about my suggestion that the fine structure constant is the ratio of two different planck constants. I am very interested in what you think about it.

Cheers, Peter van Gaalen

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Author Emile - Grgin wrote on Nov. 21, 2009 @ 08:34 GMT
Dear Peter,

I remember your discussions with Florin.

Since you ask my opinion, my answer is simple: I agree with Florin. The same physical system cannot be 'governed' (for lack of a better word) by two different values of the Planck constant (or two values of the gravitational constant), and if two different systems exhibit two values of h, these systems cannot self-consistently interact to yield a new composite system. This is indeed the case for quantum and classical mechanics, where the Planck constants are different (to see this, QM has to be formulated in phase space). Thus, there is no mixing of the two theories, and measurement interaction are one-time affairs.

Incidentally, I don't quite understand why you are asking this question. If you have a formally developed theory with two Planck constants and have derived some results that agree with experiments better than the standard theories do, I will study your work very carefully. My current opinion on the subject will not matter, and I will modify it if I am convinced that you results are valid. But please, I am talking about formal results, not about verbal arguments alone.

Cheers, Emile.

Peter van Gaalen wrote on Nov. 21, 2009 @ 09:52 GMT
Dear Dr. Grgin,

Grgin@: "The same physical system cannot be 'governed' (for lack of a better word) by two different values of the Planck constant (or two values of the gravitational constant), and if two different systems exhibit two values of h, these systems cannot self-consistently interact to yield a new composite system."

The question is: Is the gravitomagnetic system different or not from the electromagnetic system? Are they the same physical system?

Isn't what you are saying a proove that the electromagnetic system is completely different from the gravitomagnetic system?

The fine structure constant can be written as the planck constant in the denominator. If the fine structure constant is dimensionless then the nominator has the same dimension as the denominator. if the finestructure constant is a constant and also the planck constant is a constant, then the nominator must also be a constant.

So what is the nominator if it is not a 'planck constant'?

Grgin@: If you have a formally developed theory with two Planck constants and have derived some results that agree with experiments better than the standard theories do, I will study your work very carefully. My current opinion on the subject will not matter, and I will modify it if I am convinced that you results are valid. But please, I am talking about formal results, not about verbal arguments alone.

No I don't have a formally developed theory with two planck constants. And I do think that you are right (I am not in the position to argue that). But I think that your results maybe proove that the electromagnetic system is completely separated from the gravitomagnetic system.

Regards, Peter van Gaalen

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Peter van Gaalen wrote on Nov. 21, 2009 @ 10:13 GMT
My octonion model of gravity governs all gravitomagnetic quantities including the planck constant. It is a closed system. It doesn't use any quantity from the electromagnetic system.

Regards, Peter van Gaalen

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Author Emile - Grgin wrote on Nov. 21, 2009 @ 15:17 GMT
Dear Peter,

Answer to your question "Is the gravitomagnetic system different or not from the electromagnetic system? Are they the same physical system?"

Based on what I know about gravitomagnetic systems (a strictly passive knowledge because I made no contribution to this subject), I would say that the two systems share some strong formal similarities, but that they are not the same system. But please ask an expert, not me. Better yet, do what all other physicists do: Study the original papers and you won't have to ask anyone.

Good luck with your octonionic model of gravity.

Regards, Emile.

Peter van Gaalen wrote on Nov. 21, 2009 @ 16:15 GMT
Dear Dr Grgin,

Thanks for answering. I also think that the gm-system and the em-system are not the same physical system. Maybe this could have big implications for unifying gravity with the other forces. Or at least we have to rethink what for example charges are with respect to gravity, eventhough we have theories that describe the number of different charges, like the dimensions of unitary groups. Somehow the different unitary groups represent different physical systems.

Interesting essay you wrote, it is very clear.

Friendly regards,

Peter van Gaalen

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Makiko Sato wrote on Dec. 12, 2010 @ 02:53 GMT
Dear Dr. Grgin,

I am sorry that I don't understand the difficult physics you work on and am using this site only to try to have a contact with you. Could you please send me e-mail at makiko.h.sato@gmail.com? Thank you very much in advance.

Best wishes,

Makiko Sato

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