¿Son los inobservables simples entidades teóricas construidas para mantener la consistencia interna de las teorías físicas?

Dear Ruth,

You asked so many good questions that it is probably worth discussing some of them. However, I have several suggestions to you. Before delving into ontology and epistemology of the possible beings and their relations to the "real world" you have to resolve the question of relationship between direct language you ask the question in and the "reality" you want to capture by the use of this language. You have to ask and decisively respond what observation means and what it means that something is not observable. Let me give you one example. In the "Standard Model" of elementary particles there are only very few so called particles that are stable. What does is mean that the remaining particles do not exist or there are only existing during observation, how about a random (stochastic) time of existence. I am even neglecting the fact that inthralls of the standard model involve introduction of around 275 arbitrary quantum fields. I am not even mentioning multitude of arbitrary parameters of unknown origin. I do not even mention a pure nonsense of infinities, and infinitesimally small, including a notion of singularities.

If you take into account that the Standard Model explains about 5% of observable cosmologically universe what existence or observability really means. Physics as any other human intellectual activity involving inquiry into the "real world" in the form of a mental exercise called "common" as it is commonly accepted idea, constitute only a mathematical model of this "observable" portion of the real world. So physics is a very, very soft science even though it is considered as one of the hardest. The main question is what is the relationship between this mathematical model and "reality" that you want to describe and understand.

There is not even a good definition of space, or of a material point, quantum fields, force, or any other notion of physics without it embodiment as a mathematical entity that we use for some kind of calculation. But really every experiment is eventually landing up with the interaction with one of our senses therefore how we interpret the result is to our discretion. Ontology and epistemology of this process is an expression of our belief and very little in it is as objective as classical philosophers would let us believe. If you have doubts in anything I wrote go back to Spinoza and you will discover that intellectual inquiry is almost independent of time as many of his thoughts are very platonian.

Internal consistency of any system of our thoughts is a historical requirement (like an internal logic of thought) borne out of our unfounded desire to understand something with our simplified notions that inevitably leads to reductionism. If somebody spends a long time in hard core science then in the end upon reflection, one have to conclude that very few real processes undergo successful reduction.

Not to be deterred from our rational inquiry I strongly believe in unlimited capacity of human intellect.

Happy theorizing.

Bog

Sobre su pregunta: "¿Son los inobservables simples entidades teóricas construidas para mantener la consistencia interna de las teorías físicas?"

Es el caso, por ejemplo, de la "materia oscura", que nunca se ha observada pero cuya existencia se presume para que la teoría de la Relatividad General no sea rechazada por inválida, y que fue concebida por Fritz Zwicky en 1933, cuando se dio cuenta de que el teorema del virial asociado a la RG no podía explicar la existencia de galaxias lejanas, ya que el cálculo de sus masas basado únicamente en su luminosidad era muy inferior al posible según la teoría de la Relatividad General. Esto le llevó a plantear la hipótesis de una cantidad de materia no luminosa que denominó "materia oscura", que había que añadir de manera ad hoc para llegar a masas razonables según esta teoría.

Obsérvese que la teoría gravitatoria de Newton permite calcular masas razonables para galaxias lejanas a partir únicamente de su luminosidad.

Saludos cordiales, André

Dear Andre,

Very wise answer but somewhat ordinary. In every science endeavor there must be something unknown but assumed. Even mathematicians realized that simple fact after a while that it must be so (vide Godel theorem). The point in my answer is somewhat different. The point is that even the simplest notions like existence of a point or existence of sun or a planetary system is never directly provable/observable and is always based on some kind of mathematical construct. The existence of a point cannot be demonstrated experimentally for a myriad of reasons which not the least is that it would require two assumptions: (1) infinite divisibility of material world (which is not), (2) it would require infinite energy (at least according to Heisenberg uncertainty principle, which is not attainable). Existence of any astronomical object can be only inferred from indirect observations that involve light signals (EM signals), so as a result something that does not "couple" (high energy lingo) to light would be invisible, therefore existence of dark matter. This can be interpreted not as existence of "dark matter" but rather internal inconsistency between experimentation based on EM and based on Gravitation mathematical theories. So this simple example illustrates how mathematical assumptions influence our vision of the world.

Cheers,

Bog

Dear Boguslaw Stec

Note that I am an experimentalist, and that this colors my perspective on scientific endeavors slightly differently with regard to assumptions, axioms, and particularly the "dimensionless point" issue.

You wrote: "In every science endeavor there must be something unknown but assumed."

From my perspective, this is not so obvious. Scientific research to me simply boils down to try to understand and describe the various aspects physical reality as precisely as possible without any preconception as much as possible.

Historically, before the extent of the accumulated knowledge about Nature made it possible to identify absolute constants in Nature on which theories could be grounded to explain the identifiable processes observable in objective reality, the method used to ground theories consisted in establishing absolute axiomatic "principles" to be used as stable references to firmly ground rational explanations about the nature of energy, mass, electric charges, etc., such as the Principle of conservation of energy, the Pauli Exclusion Principle, the Principles of stationary action and of least action, etc.

I think that it is possible now to do away with these axioms and rebuild our models grounded on the stable constants and related processes that have now been understood and calculated as universally invariant. If any of those preset axiomatic principles initially set from logic only turn out to then be confirmed from models re-established from physically established constants, so much the better, otherwise, if such an ad hoc principle is found to be partially or totally lacking, it should simply be adapted or discarded as the case may be.

For example, the invariant relation ε0μ0=1/c2 and their experimentally confirmed invariant numerical values, and the thoroughly confirmed – in my view, of course – invariant 1/r2 force relation between two elementary charged particles were to me entirely trustable grounding element to revisit electromagnetism.

About the "point" issue, to me, it is just a mathematical place-holder representing the center of presence of any object, that we use in equations to calculate its trajectory or its relative location with respect to those of other objects in vector fields.

As an example, when calculating the orbit of the Earth about the Sun, the total mass of each body is assumed to be located in their respective centers of mass. We simply have no other means to represent objects in equations meant to calculate their trajectories. We have the same situation with elementary particles. But representing the centers of masses of the Earth and Sun as dimensionless points in our trajectory equations does not cause them to become physical points with infinite energy. In our maths, point representation turns out to be just a convenient place holder. The same for elementary particles. In this regard, limit point singularities of some equations belong to the mathematical language only, and can represent no real physically existing limit. Math function all can reach infinity, but I consider that the known physically observed and confirmed numerical limits should be applied when physical processes are actually being described.

In my analyses, I always pay close attention to this difference between mathematical concepts as such and whatever physically existing object or process that I am trying to understand and to mathematically describe with these mathematical concepts.

This mode of thinking led me in directions that I did not expect initially, effectively involving the reconsideration of some of these long standing axiomatic principles

Best Regards, André

Dear Andre,

It is a delight discussing with you. Your common sense approach to experimentation is laudable. However, as Einstein used to say, only theory can determine what is measurable. This is one of many symptoms of what I call an Einstein disease. He eventually got so enamored with his own success that he started to think that math is first and reality second. I never shared his views. Even he himself eventually got confused and said that God doesn't play dice, at least according to popular saying. Unfortunately, my view on this issue is simple; unfortunately God does play dice as this is the only view compatible with our existence, with religion and sense of free will.

I am in this very lucky position that I went through real ringer of science starting with mathematical physics and ending with experimental biology. Such a path teaches you sensitivities that are not available to other researchers. So I am absolutely with you in all your remarks but one.

You give this beautiful example of speed of light "c". You even give a very well known formula ε0μ0=1/c2 which can be understood as the definition of it. But almost everybody can easily imagine changeable values of ε0 and μ0 and therefore changeable speed of light (as ε0 and μ0 refer to known state of quantum vacuum) what on the face value contradicts many orthodox formulations of physics. I come to believe that most of these "absolute assumptions" must be questioned in order to get to a better description of the reality.

The final moral of this communication is that even in experimental science we must be very vigilant and cognizant of our assumptions. Weakening the orthodoxy of constant speed of light in the history of universe solves many fundamental problems faced by modern physics. If speed of light was very large at the beginning of the Universe (close to Big Bang) it avoids the problem of unjustified and ridiculous idea of inflation, if it constantly changing and diminishing in value, it avoids of problem of expanding universe, black energy and even some of the problems with black matter. It can explain mysterious results of early universe as they emerge in early photographs coming from the WEBB observatory. It finally messes up seriously the timeline of the lifetime of the universe and its 13.7B lifespan. What is ironic that changeable speed of light theories are present for a long time on the fringes of physics and recently (since 1998) they are approaching closer and closer to the mainstream.

So, I am always on the lookout for people like Ruth who try to get more insight into people's capacity in dissecting problems, including those that are blindly accepted and assumed. I would gladly hear what she has to say about our nice conversation.

Cheers,

Bog

Dear Boguslaw Stec

Note that I had not read your first contribution to Ruth's question before I answered her specific question, and had only glancingly read her complete intro. After I answered your direct message to me, I then got to reading your first message to Ruth.

I noticed that you are aware that only a few of the particles in the Standard Model are stable. Then you rhetorically ask "What does is mean that the remaining particles do not exist or there are only existing during observation?"

Actually it only means that they are unstable and have very short half-lives before decaying into the very few stable forms as they convert to those stable forms in typical and well documented cascades of intermediary unstable steps while releasing their extra energy as photons or neutrinos depending on the case. All documented in resources such as the Handbook of Chemistry and Physics, or the European Physical Journal C – Review of Particle Physics, for example, and other formerly published references that have now gone out of fashion these last few decades even in mainstream since accessing general info direct on the internet has replaced careful study of each case. And this is quite likely to worsen even more with the advent of AI apps like ChatGPT.

The ultimate outcome of all these decay/conversion processes of absolutely all these metastable overexcited states is always one of the stable states plus release of the excess energy.

But back to the stable states, it occurred to me that all atoms in the universe are actually made of only these stable states, it was to the historical findings about these stable states at the subatomic level that I restricted my analyses of the historical papers and books of the original discoverers and experimentalists, generally.

Since you are aware of the stable set, you may be interested in my little analysis on this issue, first formally published as an article in 2017, and then republished in slightly expanded form upon invitation as a book chapter in 2021:

Article The Last Challenge of Modern Physics: Perspective to concept...

All of the formal references analyzed are given in reference, with links to those directly available on the Net.

About Einstein remark "God does not play dice!" It was not due to any confusion on his part. It is a remark that he uttered on his way out of the 1927 Solvey Congress to mark his dismay of the seeming acceptance by the assembly of the Heisenberg and Bohr arguments that nothing could be established with certainty at the subatomic level.

They were satisfied that all that could ever be determined was related to the then defined wave function and that the most that could be hoped for was calculating the precise momentum energy of the electron in the various orbitals statistically mapped over by Heisenberg's method.

What I think he meant was that not enough was known at the time to really understand the subatomic level, while Heisenberg and Bohr were convinced of the opposite, and had given up clarifying further. At least, this is what I concluded. And effectively, we have learned quite a bit more since.

About the equation ε0μ0=1/c2, you comment: "But almost everybody can easily imagine changeable values of ε0 and μ0 and therefore changeable speed of light"

Yes, but not only "imagine", actually "define" such different sets of values for ε and μ, but then they do not carry the 0 subscript, and apply to media denser than vacuum. The ε0μ0 product applies only to vacuum and is the only value derivable from second partial derivatives of the E and B field equations, as established by Maxwell. It is the fundamental reference for the whole range of other ε and μ values applicable to denser media in engineering, a table of which can be found in reference works such as Reference Data for Radio Engineers, last reprinted in 1967 to my knowledge by the ITT Corporation.

Since you drifted to experimental biology, then you certainly are aware of the ATP producing electron transport chain, driven by this extraordinary rotating proton engine. This is allowed only by precisely the invariant stability of the properties of the stable set of elementary particles of which all atoms are made. So there are in nature stable numerical references on which theorizing can be grounded. At least, it is from this conviction that I made my analyses.

You wrote: "I come to believe that most of these "absolute assumptions" must be questioned in order to get to a better description of the reality."

I completely agree. But as mentioned, there comes a point at which certainties can be established about physical reality. For example, the simple fact that electric motors of all types have been successfully designed for the past couple of hundred years with perfectly controlled characteristics, is a confirmation to me that the underlying electromagnetic equations reflect certainty of correct understanding of the electromagnetic interactions involved. From this also you can ground coherent models.

As for the far reaches of the universe, and how it all began, I think that we do not know enough to draw final conclusions, contrary to the bad habit in mainstream to feel so certain that they have bagged it all, like Heisenberg and Bohr, and that nothing further can be clarified. To me, any inconsistency in whatever theory or model is a telltale that more needs to be learned before concluding.

A pleasure for me also to discuss with you.

Best Regards, André

Como mencionó Bog, nos interesaría mucho, estimada Ruth Castillo, saber lo que piensa de nuestra conversación.

Saludos cordiales, André

yes, you can add any number of alternatives.

Dear André Michaud and Boguslaw Stec

I have followed very carefully the development of your conversation, which I find marvellous. Certainly, the problem of the nature of unobservables in physics involves a large number of questions: objectivity in science, the problem of observation, the problem of measurement, the subjectivity-objectivity dichotomy, the nature and influence of mathematical structures on our description of the real world, the problem of the conceptual framework on physical theory and experiments, etc.

Reichenbach argued that our representations of reality are laden with "theory." The history of philosophy and philosophy of science until today may even be considered as a struggle to grasp theory-ladenness in human knowledge. The same may be said about the physical sciences, where the conceptual framework of mathematics has been the master. I am of the opinion that mathematical structures have been used so mindlessly in physics that too many unobservables and theoretical entities were created merely on the strength of the mathematics. As if they said: ‘The mathematics requires it, hence, this unobservable and this theoretical entity is necessary, whether it exists or not!’ My work questions this attitude, by using Husserl and other thinkers.

Boguslaw Stec, I think you are in tune with this line of argument. Like Hans Grelland, for whom mathematical structures influence our descriptions of reality. He also makes an analysis of how our limited language does not allow further progress in our postulations in science. But, if the unobservables are then only "theoretical entities" built to give internal consistency to our theories, then how is it possible that we can empirically "evidence" the existence of the unobservables which are in harmony with our mathematical conceptions? This is yet another area in which I have spent a long time researching, including in my doctoral dissertation. My answers are not only physical. I suggest also a “Scientific Realist Processualism” (in my PhD dissertation) that attempts to identify the ways to differentiate between unobservables and theoretical entities in physical sciences. I believe this may later be extended to the social sciences too.

Of course, facing this question, it could be argued that our detections in physical cosmology respond not to direct observation but rather to the use of scientific and technological instruments which too, by the way, is subscribed to our "eyes loaded with theory".

However, this argument is confronted with another, but simple, question: Is it not true that physics has been successful in its predictions? While it is true that we cannot deny the influence of our mental and/or theoretical representations due rightly to both language and our mathematical preconceptions, the unobservables in many cases have provided evidence of their existence – through the right instrumentation that obeys the right aspects of theory.

Such is the case, for example, of the neutrino. Postulated as a "theoretical particle", its existence was evidenced, and the prediction in particle physics has shown and until today supported the existence of neutrinos.

Similarly, the question of dark matter and dark energy. We are precisely at one of the high points within physical cosmology that has challenged the standard ΛCDM model, and which, on the other hand, has opened the possibility of postulating the ΛMOF cosmological model. However, both for physical cosmology and for the philosophy of physics, the question about the existence (or not) of dark matter/energy is an open matter. Assuming (on my part) a vertical position in this regard seems risky to me.

I am of the following opinion about the existence of unobservables. As long as their existence can be "detected", in the sense of their being susceptible to future instrumentation, I may consider, for the time being and perhaps as a permanent interim solution, that the Weylian vision about the symmetry of the world and reality could shed light on this blind spot.

Assuming that all our descriptions, and even more, indirect detections or observations (due to scientific-technological instrumentation) in many cases "collapse" our orderly descriptions, nevertheless, the necessity to account for a symmetry of reality still needs to be understood and considered. Perhaps this is in tune with Boguslaw Stec where he supported the necessary consideration of the ideas of Spinoza or Plato (Penrose also points in this direction). But it is also in harmony with André Michaud when he argued that physics has given objective and tangible results.

So, is there a meeting point? I believe that the example of symmetry breaking could shed some light on this question. But in effect what is symmetry breaking? When the unification between the electromagnetic force and the weak nuclear force (1/m2) was established, it was observed that the photon did not comply with the conservation principles when violating F=1/m2 and then the so-called "symmetry breaking" is assumed to have occurred. But this is nothing more than conceiving another level of symmetry. In this way, every time we talk about a symmetry breaking, what we are talking about in the name of symmetry are (1) the necessary rupture in our way of describing and (2) the need to move on to understanding (describing) reality in more complex forms. These descriptions must always respond to an order (principles of conservation).

In the search for this more complex form of understanding, entities appear (which were inconceivable until then, and hence are called "unobservable"). These entities provide the necessary internal consistency in the theory. Thus, in the example of electroweak unification and symmetry breaking, the Higgs Boson and the so-called Higgs Fields were postulated.

Of course, Boguslaw Stec could object to me by saying that the detection of the Higgs boson was carried out in a controlled manner and that this demonstrates his point of view. And he will be right about it. However, controlled or not, the boson exists. Undoubtedly, this leads us to the problem of the observational question in physical cosmology and in particle physics: Do we really observe objectively? Is "detect" really "observe"? Will we not be seeing with the "loaded eyes" of theory" as Reichenbach maintained? The debate opens up again.

But not everything is "dark" in the face of the unobservable. Recently, a certain research initiative (on the hippocampus) in neuroscience (2014) obtained the renowned Nobel for its findings in terms of time and space. This opens a new horizon. SPACE AND TIME CEASED TO BELONG TO THE GROUP OF UNOBSERVABLES. According to the current empirical evidence in neuroscience, space and time are cognitive conditions, that is, they are in the subject. So, our Newtonian representations (even physical ones "represent" space-time Newtonian-style despite Einstein's theory) break down. There is no "space" or "time" outside the subject. They are in the subject. So, this gives a point in favor of Galileo, Kant and Husserl. In this sense, following neuroscience, we would already have a clear definition of space and time, but not of energy and matter. It seems that studying the unobservables involves attending to these two foundational conceptions: matter and energy. Not just dark matter and dark energy, but in all its general aspect.

So, the question of unobservables is much more complex than we think. Of course, I do not intend to give a definitive answer to the problem, but analyzing it together with André Michaud and Boguslaw Stec sheds light on the question. I am pleased with the discussion, among other things, because few researchers take up the challenge of studying this issue, despite the enormous importance it involves. I believe that many researchers simply do not delve into this due to the demands put on the researchers.

I await your comments.

Dear Ruth Castillo

Note that I will not address all of the issues that you raised, even if I also have an opinion on those issues, since my contribution would become way too long to maintain interest.

I could not agree more than with your remark "The mathematics requires it, hence, this unobservable and this theoretical entity is necessary, whether it exists or not!" with regard to the attitude of many mathematicians in their attempts to smooth out inconsistencies that are observed in theories with respect to observation.

I observed that not many seem aware of the fact that mathematics is only a universally intelligible idealized "descriptive language" that we developed across the centuries that can be used to clearly describe and measure the confirmed observed physical processes, that we can then use and control to our benefit; but which is a language that can just as easily be used to describe arbitrarily established theories that become the source of endless arguments as to whether or not they match reality.

Just yesterday, I fell perchance on the opinion of Eli Maor, author of the so interesting book "e – The story of a number", Princeton University press, 1994, that perfectly summarizes the difference in research philosophies between "pure" mathematicians and "applied" mathematicians:

"Pure mathematicians pursue their profession with little concern for practical applications (some even claim that the more removed mathematics is from practical matters, the better for the profession). To some members of this school, mathematical research is much like a good game of chess, an activity whose main reward is the intellectual stimulus it affords; others pursue their research for the freedom it allows, freedom to create one's own definitions and rules and erect on them structure held together solely by the rules of mathematical logic.Applied mathematicians, by contrast, are more concerned with the vast range of problems arising from science and technology. They do not enjoy the same degree of freedom as their "pure" counterparts, for they are bound by the laws of nature governing the phenomenon under investigation." (On page 50 of his book)

Isn't then the question that now comes to mind: Was GR and other currently popular theories, with their menagerie of unobservables, conceived of and elaborated on by "pure" or by "applied" mathematicians?

With regard to Hans Grelland's opinion that "...our limited language does not allow further progress in our postulations in science.", I beg to differ, because languages are not statically frozen in their current state, including mathematics.

I also analyzed the function of language in conceptual thinking, and observed that across the ages, a plethora of new words and definitions were progressively introduced as needed to clearly describe issues and processes newly discovered that the previous state of languages could not accommodate, for articulated languages as well as for the mathematical language.

Newton used "fluxion" for what we now more precisely name "indefinite integration" – source: the book by Eli Maor previously mentioned – that also mentions many other such cases across history, such as the case of Archimedes, who never used the term "infinity" to refer to what he described as "a finite process that could be repeated again and again until the desired accuracy was achieved".

If interested in my analysis of this issue, an example is given early in the development identifying the language issue that differentiates the ability of a lay person to understand a complex issue with respect to that of an expert in this article, first published in 2017 and republished in final version in 2021 as a book chapter:

Article Relating the Comprehension Ability to the Neocortex Verbal A...

To the question: "Is it not true that physics has been successful in its predictions?"

History shows that it was true only of models elaborated from experimental data – that is, established by applied mathematicians, such as Newton, Maxwell, Lorentz, for example, who developed mathematical formulations derived from the analysis of experimentally collected data.

To the point that you raise that "... the unobservables in many cases have provided evidence of their existence", I would add this little shade of meaning: "... the unobservables in many cases "seemed to" have provided evidence of their existence".

The example that comes to mind is the so-called "proof" of time dilation provided by the Hafele-Keating experiment with their atomic clock experiment, grounded on the increase in rate with altitude of the reference frequency used, an increase in rate with altitude easily explainable from very standard electromagnetic interaction between electronic escorts and nuclei of the emitting caesium atoms.

With regards to the neutrino issue. Note that its existence was postulated not from theory, but from observation that some energy of the initial isolated neutron state could not be accounted for by the sum of the energies of the proton and electron that are the end products of neutron decay. In 1934, Fermi then made the hypothesis that this missing energy could possibly be related to a particle as of yet undetected by having no mass nor charge, which was required for direct detection.

By then stretching the definition of the concept of "direct detection" in a very clever manner, Reines and Cowan succeeded in definitely proving the existence of such a "particle" with no mass and no charge from the decay of the very unstable muon particles.

If interested, this very interesting case is analyzed in the first part of this article published in 2013:

Article The Mechanics of Neutrinos Creation in the 3-Spaces Model

All historical formal references are provided.

On the issue of dark matter and dark energy, I for one do not hesitate in observing that both concepts were postulated in an ad hoc manner in attempts at explaining why GR strayed so far from proven classical kinematic mechanics as applied here on Earth.

For symmetry breaking, my own analyses of the subatomic level do not hint at any such issue. If you were interested in an example of the symmetry that I perceive as pervading the subatomic level from the electromagnetic perspective, the remainder of my analysis of the neutrino is specifically grounded on the symmetry of the neutrino emission process that I hypothesized from the data historically collected.

I will stop here due to length considerations, hoping that my comments are not found to be too much off the wall.

Best Regards, André

Dear André Michaud I appreciate such interesting and accurate comments, as well as the bibliographical references, which I will have the pleasure of reviewing. As I have previously commented, the problem of unobservables opens up new and intense debates that are still open. I would not risk assuming a vertical position in relation to the existence (or, supposed existence) of the unobservables wherever an unobservable is posited by theory.

I consider that this subject still requires a lot of analysis and arduous and deep studies. However, I will also not assume that physics is founded on theoretical assumptions alone. I consider that even today the light that we have on this point is not enough.

As you say, the history of science is full of examples through which the first theoretical postulations were subsequently empirically verified. And, of course, this also happened in the opposite way. From this point further on, I think there is no further solid discussion that we can take for granted in the experimental and theoretical practices of physics.

In relation to Hans Grelland, I think that I do not explain Grelland's point of view well and in this regard it seems fair (for Grelland) to clarify it. Grelland assumes that our conceptions, definitions, labels, etc., "shape" our form of representation and, with it, our way of thinking. Of course, language is evolutionary and dynamic. I don't think there is anyone who doubts this fact. Also our conceptions "influence" our mental representations. Of course, since language is evolutionary and dynamic, our terms are extended, enriching our specialized languages (take the example of "variety", "Gaussian", "covariance", among many others).

But the confusion with respect to Grelland is precisely in the expression: "limitation of our language for the representation of reality", but this statement is precisely in harmony with the history of science. You mention Newton, but before him Galileo in his astronomical observations could not find a term to describe sunspots. So at this point, I think Grelland is wise. It is not a secret that as science advances, it (science) requires new terms that of course go on to enrich scientific terminology.

In relation to the notion of symmetry, certainly, there are many scientists and scholars who analyze what is inherent in the concept of symmetry exclusively at the quantum level, leaving aside physical cosmology and the consequences in the problem of gravitation.

Symmetry and its study have much more to show if we leave the microworld or particle physics and "dive" into macro levels. In this regard, I could recommend the excellent book by Hermann Weyl, "Symmetry". I myself have studied the notion at levels of physical cosmology and the problem of gravitation, as well as the asymmetric nature of the so-called "Planck constant". However, I do not want to make this answer very extensive. I consider, dear André, that we have a lot to talk about and of course it will be a pleasure to continue with such an interesting dialogue. ruth