A Historical Approach to Research in Fundamental Physics by Emile Grgin

Emile Grgin

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

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.

Emile Grgin

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.

[deleted]

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.

Emile Grgin

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.

[deleted]

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".

Emile Grgin

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.

[deleted]

Emile,

Of course!

Your position is quite understandable.

Best wishes,

Lev

[deleted]

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 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.

"(2) Every new physical theory requires some new mathematics which is not an evident extension of the previous one." The birth of quantum mechanics coincided approximately with an explosion in discrete mathematics (logic) beginning around Frege and Cantor and developing through Russel and Whitehead, Goedel, Turing and Shannon to the internet and its denumerable and non-denumerable (theoretical) extensions.

"(3) The goals of physicists are very different from those of mathematicians." Mathematicians want consistent and interesting symbolic structures; physicists want to explain how the amazingly complex structure of the universe grew from the initial singularity. Cantor's construction of the transfinite numbers from the natural numbers could be a starting point here.

"(4) New theories are best developed as answers to pressing questions." Both physics and theology are currently moribund. It may even be true that the physics community is as hidebound as the theological community. How might we measure hideboundness? Maybe by the lag in coming to terms with reality, a lag in perception. The principal absurdity of physics is the belief that one can encode information in a continuum. We cannot observe a continuum, since there is nothing to see. It is not surprising that every physical observation without exception is a quantum, a discrete, marked, event.

"(5) The unification of theories takes place automatically once the correct mathematical structure has been identified." See above and below.

"(6) Two theories cannot be unified until they have been finalized and characterized by principles." As you say, "Special and general relativity are, but quantum mechanics is defined only by technical axioms. It is therefore not ready for unification. Postponing unification, we must first search for the 'principle of quantum mechanics' which implies the axioms of the latter. As I see it, the 'principle of quantum mechanics' is that it describes a denumerable communication network.

Without going into detail we see that the concrete foundation of information theory is the same as a quantum source: a source that emits a statistically normalized sequence of orthogonal letters from an alphabet. In quantum mechanics we represent this alphabet by a basis of a Hilbert space of suitable dimension.

By seeing the world as a communication network we get an explanation for quantization. As Shannon showed, the strategy for defeating error in communication is to encode messages into long strings or packets whose letters are equiprobable. We can place these packets so far apart in message space that the chances of confusion are negligible. This is quantization. Messages with no overlap (confusion) are orthogonal, like orthogonal quantum mechanical states.

We may see quantum mechanics as a method for computing the traffic in various channels in the universal network. It may be that an abstract denumerable description can go no further. The Löwenheim-Skolem theorem tells us denumerable theories are are unable to control the cardinality of their infinite models. The only way to get into one-to-one correspondence with infinite reality is to be it.

How does all this relate to relativity? An answer might be be that gravitation is the lowest physical level in the universe and is not quantized. Gravitation sees only energy, so that it is not prone to error. Quantization (packetization) is not necessary. Such complexity as we see in gravitational theory is a result of the subsequent differentiation of the universe into discrete packets of energy moving in 4D spacetime. In a practical layered network, any communication between peers involves all the lower layers down to the physical layer.

All the best,

Jeffrey

Emile Grgin

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:

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

[deleted]

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

[deleted]

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

Emile Grgin

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.

[deleted]

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

Emile Grgin

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 (I hope not). Even so, they go a very long way. So far in fact that the major current impediment to progress is the cost of new observational insights in astrophysics and particle physicse. By contrast, theology had complete answers to all questions from day one, but different theologies had different answers -- all demonstrably wrong. Not only for not agreeing with observations (we definitely don't live on the back of a tortoise), but because the usual underlying idea of an almighty creator is an antinomy. The trouble comes from the lack of qualifications to the part "all" in "all-mighty".

Concerning my book, I think you will enjoy the long introduction. It is written in a conversational style which, some details aside, will probably not go over your head. I don't know what your background in physics and math is, but if you are familiar with special relativity and some not terribly advanced math, you might be able work your way through the chapter on the Schroedinger equation. A warning: It is Minkowski's geometric version of relativity that must be well understood; Einstein's original version in terms of trains passing each other has played out its historical role as a stepstone to Minkowski's view.

The reason for my suggesting Chapter 15 (very little of what comes before is needed) is its philosophical implication.

The Schroedinger equation is the fundamental equation of quantum mechanics. Together with the classical structure od space-time, it conceptually explains all of chemistry, and hence all of biology. I say "conceptually" because fast growing complexity limits the reach of exact computations -- but this does not imply that preternatural agencies are stirring the brew. Now, please note the following two points:

(1) Schroedinger's equation and the Galilean structure of space-time have been extracted from observations.

(2) Schroedinger's equation is about a complex function (the wave function). Since our observations in physics are formulated in terms of real numbers, an interpretation is needed to relate the complex wave function to real observations. It is "Born's interpretation".

Compare this with the quantionic approach to structural unification:

(a) Let us assume that the algebra of quantions is the underlying number system of physics. (This is not an outrageous assumption because the algebra of quantions is the structurally nearest generalization of the complex numbers.)

(b) If the quantions are to replace the complex numbers (we don't know how a priori), an interpretation will be needed. My colleague Nikola Zovko suggested the most natural one there is, so I call it Zovko's interpretation. (It slides into Born's interpretation when we reduce the quantions to complex numbers.)

Please note that quantions are purely mathematical object (just like complex numbers), and that Zovko's interpretation contains no specific information about physics. Yet, lo and behold, (a) and (b) taken together yield Schroedinger's equation (along much else) as a theorem.

Thus, the physics of our daily lives stems exclusively from a mathematical number system and an idea about how to relate it to what we see. Experiments confirm this insight, but are not its source.

A theologian friend of mine is delighted by this idea, but, unfortunately, my book is way above his head. Maybe I should translate it into Latin for his benefit.

All the best, Emile.

Emile Grgin

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.

[deleted]

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 [math]\alpha = \dfrac{h_e}{h}[/math]

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

Emile Grgin

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.

[deleted]

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

[deleted]

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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