Christian Baumgarten

75.08 · Paul Scherrer Institut

Dear Arturo,

what, if you express the Zeeman constant in inch/Gauss? I guess, the remarkable coincidence is purely random. The value of constants with dimensions depends on the chosen unit system, e.g. is completely arbitary.

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Arturo TozziArturo Tozzi

39.27 · University of North Texas

Dear Christian, thanks a lot for your wise interpretation. Probably you are right, but, on the other side, also the Monster Moonshine conjecture seemed arbitrary, until somebody discovered the Umbral Moonshine...

Sep 4 · 1 LikeEdit · Remove · Reply

Peter EndersPeter Enders

34.09 · Abai Kazakh National Pedagogical University

Arturo,

Your answer to Christian misses his point. You were right, if you would compare sequences of numbers.

For instance, if you consider a simple symmetric random walk in 1+1 dimensions as a discrete model for a diffusion process. Then, the _relative_ occupation numbers of the walk are related to Pascal's triangle. This is independent of the chosen units of measurement, because these units cancel in the ratios of the occupation numbers.

For this, I propose to explore Zeeman spectra for testing your conjecture (and similar ones).

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Vasiliy Fedorovich KomarovVasiliy Fedorovich Komarov

4.67 · Donetsk University

Although the process of splitting of the lines in the sense of looking for traces of dynamic chaos - it's interesting.

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Vasiliy Fedorovich KomarovVasiliy Fedorovich Komarov

4.67 · Donetsk University

Of course, there may be interest in the matching sequence numbers, because both values are in the same number system. But I also agree with Christian, when it comes to dimensions, it is difficult to hope for direct regularities.

Feigenbaum constants are dimensionless. It makes sense to search for comparing it with warious similitude parameters and it combinations. In this sense, Dirac large numbers may have more interest. At least, I'm thinking about them for a long time in this aspect.

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Arturo TozziArturo Tozzi

39.27 · University of North Texas

Dear Peter, thanks for your precius suggestion!

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Arturo TozziArturo Tozzi

39.27 · University of North Texas

Dear Vasiliy, the correlation, at least, gave me the idea to try to think to the plots of Feigenbaum bifurcations as if there is something splitting and deforming the linear paths between 3 and 4. It could be something magnetic, but also something different... What do you think?

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Vasiliy Fedorovich KomarovVasiliy Fedorovich Komarov

4.67 · Donetsk University

Dear Arturo, I decided to read a little bit about the Feigenbaum constant again. It took away me from the topic (as usual). Am feeling that have little experience directly in bifurcation theory and little practical contact with a variety of data about the behavior of particular systems.

Perhaps the main problem is to establish the parameter of dependency, also whether it is single parameter at all? I also think, he's one only in some "neighborhood" (magnetic). It is necessary to pay attention at least for the emitted photons, a process linked with them on a mechanical level.

The complex Zeeman effect, effect of the Paschen-Buck and hyperfine splitting may give some key points for the restructuring of the system. It is necessary build a hierarchy. I am afraid that it drags along rest in system due to integrity. But this should be expected.

PS: Side thoughts. All organic cellular life on earth in this way seems clearly identifiable section of the ordered "doubling period". And there is still a lot more blurry macrostructures, which is also interesting for similar search. For example, the alternation of planetary orbits to the asteroid belt, Oort cloud, etc.

Sep 9 · 1 LikeLiked · Report

Arturo TozziArturo Tozzi

39.27 · University of North Texas

Furthermore, concerning the dimensions of the Feigenbaum constant, take into account that: https://www.researchgate.net/publication/284171808_TOPOLOGY_PLUS_LOGISTIC_MAPS_NONLINEAR_CHAOTIC_SYSTEMS_EXPLAINED

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Zeraoulia Elhadj (www.arctbds.com)Zeraoulia Elhadj (www.arctbds.com)

26.14 · Université de Tébessa

I think that a true relation holds true if the origin of these two constant have some logical relations.

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Arturo TozziArturo Tozzi

39.27 · University of North Texas

Dear Zeraoulia, thanks for your comment.

However, I think that the logic is useless in this case, as in other scientific cases (think about the quantum entanglement). I like logic very much, I love and read Frege, Wittgenstein, Russell, Carnap, Godel, but... there are severe limitations in the application of logic laws to scientific matter, unless you do not think... in a scarcely logical way! see: https://www.researchgate.net/publication/306012510_A_TOPOLOGICAL_BRAIN_ELUCIDATES_SYNTACTIC_AND_SEMANTIC_PROCESSING?ev=prf_pub

6d agoEdit · Remove

Vasiliy Fedorovich KomarovVasiliy Fedorovich Komarov

4.67 · Donetsk University

Dear Arturo,

I think, we need to pay attention to the sequences of the coupling constants. Gauge theories allows to sew areas of regular processes. Crosslinking points are likely connected with system restructuring. In addition, they are already dimensionless and therefore unified. In addition, I interested in it for a long time because of "abnormal" trend of four-variable in all areas and scales from microworld to GR. In addition, they are interesting because indirectly related to the angular momentum (Planck's constant and speed of light).

Another area of research - identification of the parameters of universal laws of Goldilocks zones sequences in star systems, galaxies. These points have a direct link to the area of ordered organic (life). This is also directly related to the structure of the solar system, which is mentioned in my previous one comment.

3d ago · 1 LikeLiked · Reply · Report

Arturo TozziArturo Tozzi

39.27 · University of North Texas

Dear Vasiliy, your ideas are very interesting, in particular the issues of the angular momentum and the requirement of just a single order parameter. Give me a couple of days to finish another ongoing manuscript, then I will be back. I have indeed an idea, but it requires a lot of mathematics: give me the time to focus the thoughts... Ciao!

2d ago · 1 LikeEdit · Remove

Vasiliy Fedorovich KomarovVasiliy Fedorovich Komarov

4.67 · Donetsk University

Dear Arturo. I consider the angular momentum as a consequence/cause of constant stabilization for the system at all. The lack of observations of neutron stars at low rotational speed give the cue of absence of the phenomenon called non-rotating black holes (Schwarzschild solution). In addition, all attempts to calculate the rotational speed of black holes in the observations lead to the direct connection of rotation speed with the speed of light. This, incidentally, is well agreed with the concept of Hypothesis.

Furthermore, it should provide the spins of particles for standard model. Angular momentum is a candidate of the system parameter which is independent of the dynamical details of the system. This is the first landmark.

In general, I provisionally imagine the process on the edge of chaos for such a system on the principles like Centrifugal Governor of James Watt. Positive feedbacks inside and negative outside must provide continuous "before the catastrophic" state for internal coherence structure (this, incidentally, is very similar to thinking processes in biological systems). Approximately like this.

The entropy of the system, as a single "time" parameter of the unitary evolution of coherent structure is the second landmark.

The phase characteristics can be left for the freedom of the system.

The hardest ever part is turned inside out hyperbolic (fractal) geometry. How to approach to it? This is a separate procrastinated question.

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Arturo TozziArturo Tozzi

39.27 · University of North Texas

Dear Vasiliy, concerning your hypotesis about nonlinear chaotic dynamics, take into account that the entropy, during such bifurcations, might not change. Contrarily to symmetry breaks in other systems, in chaotic systems the bifurcations not necessarily lead to changes in entropy. Concerning the angular momentum, there is a problem: the bifurcation plots are reversible if you change the phase parameter from 3 to 4 and then back from 4 to 3, while the angular momentum (both orbital and spin) breaks the T-symmetry, and therefore is irreversible. We need to think to other possible parameters...

1d agoEdit · Remove

Vasiliy Fedorovich KomarovVasiliy Fedorovich Komarov

4.67 · Donetsk University

In addition, a situation, where two different configurations of system have same entropy, involves the concept of information. Does this mean some "hidden" parameter (these states differ in their position in the phase space)? We can not see it in "disassembled" parts of the system. Parameter looks like an integral property of the holistic system.

Usually, time plays role of such a parameter, which can distinguish two states of the system. It is always external parameter to the system. It can only exist in relations of objects. We can say, in the evolving system time accumulates in the form of information. This means that something external to the system is converted into a topological spatial configuration within the system as the system evolves.

Amount of ignorance of information about the system (entropy) and the information in the system must be interconnected and connected to process of evolution (i.e., to process of interaction of the system with the environment).

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Vasiliy Fedorovich KomarovVasiliy Fedorovich Komarov

4.67 · Donetsk University

Dear Arturo, I fully agree with you regards to entropy. I think this option is important because of the uniqueness outside of unitary evolving object (not for some selected degrees of freedom within).

On symmetry for bifurcations: may be that the system in question on any scale is fundamentally not insulated from the environment provides irreversible global process. In this case entropy of unitary process can manifest itself as unique parameter. By the way, the emission and absorption of photons is one example of such a reversible process within the system. We can remember still many examples, especially of artificial origin, among the products of human activities (they all need external support or complete isolation model).

Integrity forced me to think about the eligibility of the application of symmetric laws without looking back at environment of application area. In this sense, "other systems" must also located within our desired model (they are just the Universe subsystems). For this reason, entropy and its dynamic must be fragmented in the system. It may be useful to localization of relevant subsystems at finding patterns of interest to us.

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Preprint TOPOLOGY PLUS LOGISTIC MAPS: NONLINEAR CHAOTIC SYSTEMS EXPLAINED

Preprint A TOPOLOGICAL BRAIN ELUCIDATES SYNTACTIC AND SEMANTIC PROCESSING

Apparently the unit of the Zeeman effect constant is not dimensionless, and therefore a resemblance with any mathematical constant can only be a mere coincidence, since the constant depends on the arbitrary choice for the units (meter, Tesla). Sorry, but keep up the good work.