The Physics of Non-Material World?

 Return to the First Question: Information and Quantum Future

Once we have a preliminary answer to the question “How come quantum?”, we can return now to the first question: “How come existence?”. It may have something to do with “information”. But what is information? How is it related to physics? And is information sufficient? What about organization?

If energy and momentum have their own separate dimensions, should not information and organization have dimensions of their own as well? And if so, what would they be, “real” or “imaginary”? Physical or “non-physical”? These are vague questions; therefore I need to be more precise.

Physics, in spite of quantum mechanics and its excursions into subjectivism, essentially deals with a material world exclusively. Not only does it not show any interest in a non-material reality, but it also often ridicules such ideas, except, perhaps, when physicists engage in a dialogue with theologians, but even then it is at most a “philosophy” and not physics. But must it be so?

The Non-Material World

Can physics be extended in such a way that it can deal with non-material world and still be objective rather than falling into the subjectivity sinkhole? It appears that some people are doing it and being allowed to get away with it.

Military Interest?

One example is the duo of Elizabeth Rauscher and Richard Amoroso. According to Wikipedia:

Elizabeth A. Rauscher (1937–2019) was an American physicist and parapsychologist. She was born in Berkeley, California on March 18, 1937.[1] She died on July 3, 2019 (aged 82). (...) She was a former researcher with the Lawrence Berkeley National Laboratory, Lawrence Livermore National Laboratory, the Stanford Research Institute, and NASA

Richard Amoroso seems to be a Director of Noetic Advanced Studies Institute, has an education in psychology, and PhD in “Cosmology and Philosophy of Mind” – rather unusual domain, I’m sure you will notice. You may want to check their website to see what I mean.

Looking at one of their typical papers, with the title “The Physical Implications of Multidimensional Geometries and Measurement” I see that they are trying to include non-material reality by adding “imaginary dimensions” to those that are real. Tugging on this thread a little leads us to the fact that the US military seems to be interested in this kindof research by Prof. Rauscher:

Naval Surface Weapons Center, White Oak, 70-126, Silver Spring, MD 20910, 1982, R34-2- 0176 contract monitor E. Byrd, E.A. Rauscher, P.I. and W.L. Van Bise, P.I. Solving Maxwell’s equations in complex space relating to the space relating to the solutions to solitons and nonlinear Schrödinger equation and other nonlinear phenomena and the study of field phenomena.

What a surprise! Elizabeth Rauscher is also busy with “Modulating Brain Signals”:

E.A. Rauscher and W. Van Bise, Non-invasive Method and Apparatus for Modulating Brain Signals Through an External Magnetic or Electric Field to Reduce Pain, U.S. Patent Number 4,889,526, issued December 26, 1989.

But is it real, or is it a joke? I am inclined to think that it is, to a large extent, a joke, a red herring, so to say. Why do I think so? I am thinking that is a joke, because one of the works cited by Amoroso and Rauscher is “A Theory of Physical Vacuum” by G. I. Shipov, and this published monograph of Shipov is full of nonsense. I know it, because I checked it and also published a couple of  papers discussing Shipov's errors. I also had a private exchange with Shipov, and I did not change my opinion after this dialogue.

Nevertheless, with her military connections and funding, we may take it as a given that Rauscher and her colleagues are not doing what they do just for fun. They are searching, but, I guess, they have a really hard time finding the answer or they are not publishing the papers that do lead to the answer. The clue about what they are after is given in the last line of their paper. They say that just doubling the dimension, that is adding four imaginary dimensions to those four real dimensions of space and time, may not be enough. They want to go into twelve dimensions, not just eight.

Which leads us to Burkhard Heim.

"The theory of Heym has to be classified into the framework of a geometrization of physics. …” (STN INTERNATIONAL, 04 Jul 90).

Volume 3,  Structures of the physical world and its non-material side, was published in 1996 .

To be continued....

P.S.1. I pictured a rainbow, You held it in your hands, I had flashes, But you saw the plan. To my wife - The Whole of the Moon

The Whole of the Moon -  Lyrics.

P.S.2. New version of my notes on the conformal group.  Will add still more today

P.S.3. 

Only those thoughts are true the opposite of which is also

true in its own time and application; indisputable dogmas are

the most dangerous kind of falsehoods.

Sri Aurobindo

P.S.4 I know it's vanity, but it always feels nice. My old paper A. Jadczyk and K. Pilch, “Superspaces and Supersymmetries", Commun. Math. Phys. 78 (1981), 373–390, has been cited in a recent paper by R.R. Suszek (Warsaw), "Equivariant Cartan-Eilenberg supergerbes, the Kostelecký-Rabin defect and descent to the Rabin-Crane superorbifold"

Abstract: A concrete geometrisation scheme is proposed for the Green-Schwarz cocycles in the supersymmetric de Rham cohomology of the super-minkowskian spacetime, which determine standard super-σ-model dynamics of super-p-branes. The scheme yields higher-supergeometric structures with supersymmetry akin to those known from the un-graded setting - distinguished (Murray-type) p-gerbe objects in the category of Lie supergroups. These are shown to carry a canonical equivariant structure for the action of the discrete Kostelecký-Rabin subgroup of the target supersymmetry group on the target, and thus to resolve the `topology' of the corresponding Rabin-Crane soul superorbifold of the super-minkowskian spacetime. The equivariant structure is seen to effectively define a novel  σ-model of super-p-brane dynamics in the super-orbifold through the construction of the corresponding (gauge-)symmetry defect.

It has quite impressive graphics. Like for instance this one:

Figure 2. A Gσ-twisted field configuration x near a 2 → 1 junction υ of (oriented) edges ℓi,j , (i, j) ∈ {(1,2), (2,3), (1,3)} of a Gσ-jump defect. The edges separate patches ΣA, A ∈ {1,2,3} of the worldsheet, embedded by x in connected components of the metric bulk target space M and defined by the respective restrictions of the metric g and of the gerbe G. The field x maps the ℓi,j to the bi-brane worldvolume Q, from which it pulls back the respective restrictions of the gerbe bimodule Φ. Similarly, the junction υ is mapped to the component T (3) of the stratified inter-bi-brane worldvolume T , from which the 2-isomorphism φ is pulled back.

P.S.5. Recommended reading: Lies, damn lies and limited hangouts

P.S.6 30-06-23 12:20 . Suggested to me yesterday night by Laura, who, opposite to me,  remembers all she reads. From Umberto Eco, "The Name of the Rose"

“Precisely. But forget the machine for now. Thinking about the machine has led me to think about natural laws and the laws of thought. Here is the point: we must find, from the outside, a way of describing the Aedificium as it is inside. . . .”

“But how?”

“We will use the mathematical sciences. Only in the mathematical sciences, as Averroës says, are things known to us identified with those known absolutely.”

“Then you do admit universal notions, you see.”

“Mathematical notions are propositions constructed by our intellect in such a way that they function always as truths, either because they are innate or because mathematics was invented before the other sciences. And the library was built by a human mind that thought in a mathematical fashion, because without mathematics you cannot build labyrinths. And therefore we must compare our mathematical propositions with the propositions of the builder, and from this comparison science can be produced, because it is a science of terms upon terms. And, in any case, stop dragging me into discussions of metaphysics. What the Devil has got into you today?”

P.S.7. 30-06-23 12:44 Another Umberto's Eco quote suggested to me by Laura. This time from Foucault's Pendulum:

"Amid all the nonsense there are some unimpeachable truths... I invite you to go and measure [an arbitrarily selected] kiosk. You will see that the length of the counter is one hundred and forty-nine centimeters—in other words, one hundred-billionth of the distance between the earth and the sun. The height at the rear, one hundred and seventy-six centimeters, divided by the width of the window, fifty-six centimeters, is 3.14. The height at the front is nineteen decimeters, equal, in other words, to the number of years of the Greek lunar cycle. The sum of the heights of the two front corners is one hundred and ninety times two plus one hundred and seventy-six times two, which equals seven hundred and thirty-two, the date of the victory at Poitiers. The thickness of the counter is 3.10 centimeters, and the width of the cornice of the window is 8.8 centimeters. Replacing the numbers before the decimals by the corresponding letters of the alphabet, we obtain C for ten and H for eight, or C10H8, which is the formula for naphthalene.

...With numbers you can do anything you like. Suppose I have the sacred number 9 and I want to get the number 1314, date of the execution of Jacques de Molay—a date dear to anyone who professes devotion to the Templar tradition of knighthood.

...Multiply nine by one hundred and forty-six, the fateful day of the destruction of Carthage. How did I arrive at this? I divided thirteen hundred and fourteen by two, by three, et cetera, until I found a satisfying date. I could also have divided thirteen hundred and fourteen by 6.28, the double of 3.14, and I would have got two hundred and nine. That is the year Attalus I, king of Pergamon, ascended the throne

You see? ...The universe is a great symphony of numerical correspondences... numbers and their symbolisms provide a path to special knowledge. But if the world, below and above, is a system of correspondences where tout se tient, it’s natural for the [lottery] kiosk and the pyramid, both works of man, to reproduce in their structure, unconsciously, the harmonies of the cosmos."

Eco, Umberto, Foucault’s Pendulum, (San Diego, New York, London: Harcourt Brace Jovanovich 1988) pp. 288-289.

 P.S.8. 

P.S.9. 19:32 Managed to make the first image of the double infinity following the last Proposition in the file for a=1.5. Here it is

P.S.10 21:03 The same plot for a=5

P.S.11 01-07-23 19:41 Calculated the conformal structure on the infinity. It came out that it is  degenerated. While the lines connecting the two singular points have zero "length". There is no "time" there. Only space and light. I think.  Not sure about the interpretation. Will come out later on. Geometry on the circles (spheres) is standard Euclidean. Will write it down tomorrow.

Wheeler's Second Question: "How come the quantum?” Planck’s Constant

 This is a continuation of the previous post: Problems in Objectizing.

Wheeler's Second Question: "How come the quantum?”

John A. Wheeler at Princeton University in 1967.Credit...The New York Times

Let me consider the second question, which seems to me to be less abstract. Indeed, we do have “the quantum” It is embodied in the Planck constant

It has the physical dimension of a “Joule” multiplied by a “second”, energy multiplied by time – physicists call it “action”. This constant seems to be numerically rather small in our accepted human-size units, but it enters into almost every formula of quantum theory. 

Planck’s constant, by itself, indeed defines a “quantum”, but not a quantum of energy, as it sometimes written in popular books, but a quantum of action. Energy is not always quantized, there is no such thing as “quantum of energy”, except in some particular cases¹, but there is a “quantum of action”. Therefore we should pose another question: “How come action?” Evidently it is a very important quantity, but not directly observed or measured. Why?

Alexander Unzicker - Constants of Nature Explained: Planck's Quantum of Action

Energy and Momentum: Action

The physical dimension of action is that of energy multiplied by time, which happens to be the same as momentum multiplied by length. We all have a good general feeling or impression about what the time distance between, any two events is, and what the length distance between two points is. Energy and momentum seem to be more complicated and not so evident, and yet they happen to be fundamental in mechanics. Do they not deserve to have their own dimensions associated with them? Indeed they do, and they have.

Phase-space and Planck’s Constant

In mechanics, for quite some time now, we have been using not just space and time, and not just space-time, but also what is called “phase-space”. If space-time has four dimensions, three for space and one for time, then phase-space has these dimensions doubled. There are four dimensions added: three for momentum, and one for energy. Thus in relativistic mechanics, phase-space has eight dimensions.²

Things are somewhat more complicated when we are dealing with a system of particles rather than just one particle – we need a separate phase-space for every particle, but that can be thought of as a purely formal mathematical trick – we do it, because it makes calculation simple, and because “it works”.

Now, once we have phase-space, eight or six dimensional, depending on whether we respect the special theory of relativity or not, we can measure the volume of a region in this space. Then the Planck constant tells us that there is something like a “fundamental volume” – this phase-space has a kind of granular structure. That is to say, there is a discreteness at the fundamental level, though it has nothing to do with space or with time alone, but rather with a more complicated space that we are not immediately aware of – the phase-space. Energy and momentum, the additional coordinates of the phase-space have, intuitively, to do with frequencies and wave-lengths, not just time and position.

Are we somehow sensitive to frequencies and wavelengths, not just to positioning of objects in space and time? I think that in order to answer these questions the theory should be developed a little bit further. So, let me continue with my speculations about a possible shape of future physics.

To be continued...

1 An ideal harmonic oscillation, with a fixed frequency. is one such example.

2 U.S. Army seems to be interested in extending Einstein’s general theory of relativity to phase space: Howard E. Brandt, U.S. Army Research Laboratory,  “Finslerian Quantum Field Theory”, 

P.S.1. To my wife. She likes it.

P.S.2. 

"If mankind could but see though in a glimpse of fleeting experience what infinite enjoyments, what perfect forces, what luminous reaches of spontaneous knowledge, what wide calms of our being lie waiting for us in the tracts which our animal evolution has not yet conquered, they would leave all & never rest till they had gained these treasures. But the way is narrow, the doors are hard to force, and fear, distrust & scepticism are there, sentinels of Nature, to forbid the turning away of our feet from her ordinary pastures."

Sri Aurobindo

P.S.3. The video below was taken 10 days ago in our yard. 

Coincidence? Synchronicity? Or electromagnetic resonance?

P.S.4. I wish I would have such muscles:

https://twitter.com/RobertKennedyJr/status/1673053159172833280

P.S.5. Here’s What Happened To The Bodies When The Titanic Submersible Imploded

Problems in Objectizing

 Bernard d’Espagnat

Here I would like to mention one particular physicist and philosopher: Bernard d’Espagnat. In his paper “Problems in Objectizing”, d’Espagnat opts for “Mind-Independent Reality”, and, in particular, he also supports Hans Primas’s proposals which EEQT developed into a full-fledged mathematical model. 

Direct realism is often thought of as the common sense theory of perception.

That is an example of a totally subjective view.

But even d’Espagnat is somewhat pessimistic about the final results of such an approach. He ends his paper with the comment:

…although we cannot know Mind-Independent Reality, still we get, through physics, not fully deceitful glimpses of it. I feel Primas’s optimistic guess somehow strengthens my position in this matter.

Waves and Things: Information!

In EEQT we are dealing with two kinds of objects: material objects about the existence of which we have no doubts, and which are necessary if we want to tell engineers what to do; but also we have “wave functions” that are necessary for modeling quantum phenomena - two different categories of objects. These two kind of objects are coupled together – there is an exchange of information between them. That is why in our theory we have not only “dynamics” – exchange of forces, but also, what we called, “binamics” – exchange of “bits of information”. Therefore our theory can be considered as one step towards an introduction to the active role of information in physics.

I was already well-situated in my career as a scientist when I made the decision to follow this path so it was not so easy to attack me – it was enough to just ignore my work. 

The Three Questions of John Archibald Wheeler

Here comes the important term that is rather new in physics: Information. It has become more popular since John Archibald Wheeler published his famous “It from Bit” article "Information, Physics, Quantum: The Search for Links", and asked three important questions:

How come existence?

How come the quantum?

How come the “one world” out of many observer-participants?

The simplest answer to the first question, “How come existence”, is, I would say, existence comes from “timeless information”.

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What does John Wheeler mean by his famous 'It from bit' idea?

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John Wheeler's "It from bit" idea is a concept that suggests that all physical reality is ultimately based on information. In other words, the physical world can be thought of as being made up of bits of information rather than physical particles. This idea is rooted in the field of quantum mechanics and suggests that the universe is fundamentally digital in nature.

Tell me more

P.S.1. To my wife: The Air That I Breathe - The Hollies

Lyrics.

P.S.2. 

"When I speak, the reason says, “This will I say”; but God

takes the word out of my mouth and the lips say something else

at which reason trembles."

Sri Aurobindo

P.S.3. New version of my notes on the conformal group.  Will add still more today.

P.S.4. 25-06 12:45 Finished Sec. 6.7 "Calculating the conformal structure". Updated the file.

P.S.5. A Reader has sent me a link to a paper by Alexander Prahauser "Hegel in Mathematics"

At the end of this paper I am finding, in particular, these gramatically correct sentences:

"From this fermionic superpoint, through a series of canonical extensions, emanates a piece of 11-dimensional spacetime R 10,1|32 , which has precisely the properties that are demanded by M-theory, the joint generalization of string theory and supergravity. Our physical universe would then be determined by some manifold in ∞ − SF S or some extension thereof, with some force field on it that is the unified fundamental force which manifests as the four fundamental forces of our universe after M through a process called KK-compactification, which yields the four-dimensional spacetime we all know and love. At this point mathematics becomes difficult to avoid. However, it should be noted that a conjecture by Sati and Schreiber called Hypothesis H, based on the observations by Sati in [21], states that such a field would be described by a cycle in the fourth differential equivariant J-twisted cohomotopy on X, so a differential equivariant refinement of a section of the J-morphism into the 4- dimensional spere. Given the importance of the n-dimensional spheres and the J-morphism in homotopy theory (and in general), this result would be highly satisfying."

Frankly speaking I consider it as a "word salad" that has nothing to do with Reality. Escapism into total abstraction - that is how I call it.

EEQT: Things Exist and Events Happen!

 In our theory of EEQT we start with a fundamental and simple fact that material things (like chairs) exist, and that events happen (for instance a chair breaks). Any theory that does not have a place for these simple data will not be able to account for what happens. It will have to, for instance, imply that these things happen only in our minds, and then resign, because our minds do not belong to physics. That is what many of the so called “quantum philosophers” say. It’s a load of nonsense.

Quantum Fluctuations

One of the speculations made by theoretical physicists is that the “space-time metric fluctuates”. Time somehow becomes space, space somehow becomes time – in a way that is still speculative within the context of the orthodox quantum theory.

Alexsander K. Guts, a Russian physicist and mathematician from the State University of Omsk wrote an entire book entitled “Elements of the Theory of Time”¹, where he discusses, in particular, possible scenarios of four and five-dimensional space vs. time fluctuations. According to him (and his collaborator, Marina S. Shapovalova²) the idea goes back to John Archibald Wheeler in 1960-1970, then followed by the famous Russian physicists, A. D. Sakharov, and an Italian iconoclast physicist G. Modanese. Modanese also became famous for his work on “antigravity”. According to the English Wikipedia:

Giovanni Modanese is a professor at the Free University of Bozen-Bolzano, Italy.

He is the author of several publications in General Relativity and Quantum Gravity. He collaborated with Eugene Podkletnov, devising a device that reportedly generates a "repulsive" gravity-like beam that is several orders of magnitude stronger than the aforementioned experiments. This work has been published in a peer-reviewed journal but has not yet been confirmed by others. (Italics, mine.)

Evidently there is something dangerous about these ideas; not all is revealed to the public, probably because the military are interested in this kind of work. But from my private correspondence with Modanese I know that he is quite serious.

Bu no one  has yet addressed the fundamental problem of “what are quantum fluctuations?”

Many physicists are using this term – “quantum fluctuations” - in a misleading way, in a way that suggests that quantum theory can explain “fluctuations”, while instead of explaining it, a rather involved mathematical apparatus is being proposed that actually only serves to hide the real problem. Nothing can really “fluctuate” except in a theory that describes “quantum jumps”, and this is still a speculative idea, except, I would say, in EEQT, where it is described as a real process that can be simulated even on a personal computer.

Here I will illustrate quantum fluctuations with a simple toy model that involves six Schrödinger’s cats that are continuously monitoring the simplest possible quantum system, so called “spin ½”. Quantum states of such a system (so called “pure states”) can be represented as points of the surface of an ordinary sphere. Each point on the sphere represents a direction of the spin (of an electron, for example). I have chosen six points on this sphere, points located at the vertices of two pyramids joined at their bases. These vertices form a regular octahedron – one of the five Platonic solids. At each vertex I put one of Schrödinger’s cat that monitors the direction of the spin, whether it points in his direction or not.

If the direction of the spin points in the direction of the cat – the cat dies. But, because I adore cats, my cats are immortal. Right after their deaths they get resurrected and start watching again. When a given cat dies, quantum state jumps – usually in the direction of the cat that got hit by the spin. Since the other cats are observing as well, we have a sequence of jumps. Each time when the quantum state jumps I note the new position of the direction of the spin state by a white point on a black sphere of quantum states. The jumps are random, according to a particular algorithm proposed by EEQT. And yet, after ten million random jumps, simulated on a PC, a strange (and not fully understood yet) fractal pattern appears.

Two things are “fluctuating” here. First there are cats that repeatedly get killed and resurrected, but I am not interested in their reincarnation histories here. I am interested in the fluctuating state of the quantum system – the pattern drawn on the invisible “quantum sphere”. The Russian physicist from Omsk, Guts, also has an idea of fractality that may be important for space and time fluctuations. In EEQT, in this example with six cats, one of the well known quantum dogmas is being questioned, since according to the textbook quantum theory my arrangement of cats is not allowed by Heisenberg’s uncertainty principle. But Heisenberg was not God, and a textbook should not be considered as a Holy Bible. To have some fun I published my paper in the Chinese Journal of Physics,

1Aleksandr Guc), “Elementy teorii vremeni”, Art&fakt jelektronnyj al'manah Omsk: Nasledie. Dialog-Sibir', 2004 (in Russian)

2Alexander K. Guts, Marina S. Shapovalova, “Large fluctuations of time and change of space-time signature”.

EEQT - an eccentric theory

 This post is a continuation of previous posts about the birth of the Event Enhanced Quantum Theory - EEQT

Heide Narnhofer to the Rescue

Our Event Enhanced Quantum Theory of 1993 was, however, essentially incomplete. It was describing an “statistically averaged” history, and it was not yet able to provide a mechanism that is responsible for our particular and unique history, answering the question "How Nature does what She does?". Finding such a mechanism, finding the unique algorithm that, when repeated, would reproduce our “average behavior” was not easy. I finally found it by a "directed chance", and then I was able to prove its uniqueness owing to the enlightening comments of a renowned Austrian physicist, Heide Narnhofer, when I was giving a talk on the early version of EEQT  at the Schrödinger’s Institute (ESI) in Vienna in 1994. 

Gloriette stands on higher ground in Schönbrunn Palace park, Vienna

The rest followed rather easily. Not without obstacles, but already downhill.

Our formalism allowed us to derive, instead of just to postulate, Max Born’s probabilistic interpretation of the wave function. 

We were now able to simulate, on a classical computer, real world quantum processes, including tracks left by elementary particles in particle detectors, and even Schrödinger’s cats.

"Everyone who claims that there is a Schrödinger cat paradox would first have to justify the assumption that a superposition of any two quantum states is always meaningful. As far as I know, this is just an arbitrary assumption. If it leads to a paradox, there is only one logical conclusion: the assumption must be wrong."

Quantum Paradoxes and Fritz Zwicky

Thus, with EEQT, we succeeded in removing “quantum paradoxes”. Since then we have published about 20 papers describing our theory as applied to both simple and complicated cases, but no one paid any attention. Everybody was busy with their own pet theories driven by what had been made fashionable to the Authoritarian followers - which is not a surprise in Science. Let me give just one example from the history of “Dark Matter”:

The first suspicion of dark matter came in the 1930s, when Fritz Zwicky suggested that clusters of galaxies contained dark matter. He used the average motion of the galaxies in the cluster to measure the total mass, and found out that it was much more than the number of galaxies.

Zwicky turned out to be correct, but no one believed him since he had a reputation of being eccentric and sometimes over-interpreting results. He found that galaxies in the cluster represented less than 10% of the total cluster mass.

Zwicky had a reputation of being eccentric and so no one believed him

Zwicky had a reputation of being eccentric and so no one believed him – can you imagine? Is Science about believing? I don’t think so. It should not be a question of believing, but the question of simply checking whether Zwicky was correct or not. But no one cared. Why? Because Zwicky’s observations were against the accepted dogma. Scientists indeed tend to be authoritarians.

We're sailing on a strange boat. Heading for a strange shore. 

P.S.1 My wife likes this song. So this is for her>

Lyrics: "Strange Boat"

We're sailing on a strange boat
Heading for a strange shore
We're sailing on a strange boat
Heading for a strange shore
Carrying the strangest cargo
That was ever hauled aboard

We're sailing on a strange sea
Blown by a strange wind
We're sailing on a strange sea
Blown by a strange wind
Carrying the strangest crew
That ever sinned

We're riding in a strange car
We're followin' a strange star
We're climbing on the strangest ladder
That was ever there to climb

We're living in a strange time
Working for a strange goal
We're living in a strange time
Working for a strange goal
We're turning flesh and body
Into soul

P.S.2. New version of my notes. Removed the last part of the previous version. Added beginning of "Important subgroups...."

I noticed that for these notes to make sense x must be dimensionless. That is probably how the radius R of the sphere S^3 is participating. We are choosing units in which this radius R=1.

P.S.3. 21:47 UFO clouds over us  20 minutes ago

P.S.4. 21-06 8:12 

There are two allied powers in man; knowledge & wisdom. Knowledge is so much of the truth seen in a distorted medium as the mind arrives at by groping, wisdom what the eye of divine vision sees in the spirit.

Jnana, Sri Aurobindo

P.S.5. 16:49 Unfortunately the method of finding the SO(4,2) matrix implementing translations, as described in my notes,  is not working. Don't know why? Can't find an error. I am stuck. We have a problem.

P.S.6. 21:07 Found the answer. Checked also the group property.  Updated the file.  

I thank my Readers for the emotional support and good intentions, the point is, however, that the matrix L(a) must depend only on a, and not on x. And this part was tricky.

Here is the Beauty

P.S.7. 22-06 8:30  Sri Aurobindo on free will:

“Our highest Self which possesses and supports this universal Power is not our ego-self, not our personal Nature; it is something transcendent and universal of which these smaller things are only foam and flowing surface. If we surrender our conscious will and allow it to be made one with the will of the Eternal, then and then only shall we attain to a true freedom; living in the divine liberty, we shall no longer cling to this shackled so-called free will, a puppet freedom ignorant, illusory, relative, bound to the error of its own inadequate vital motives and mental figures.”

So, according to the above we do have free will: we can freely choose whether we want to follow the "will of the Eternal" or to follow our whimsical  "ego-self". From my observations I deduce that the amount of our free will, defined as above, fluctuates. Sometimes we have it, some other times we do not have it at all.

P.S.8. 17:33 Added to the notes: Lorentz rotations, dilations, and conformal inversion.

P.S.9. My attention has been drawn to the following very interesting research project:

Stan kwantowy: informacja, wolny wybór, losowość 

Quantum Sate: information, free choice, randomness

Somehow EEQT is addressing similar questions, but from mathematical and physical rather than from a philosophical perspective. I would like to keep in touch with one of the participants of this project.

 P.S.10. Added special conformal transformations. Though unfinished.

An Open Universe: Heresy?

 As I have mentioned above, in our formalism “superselection charges” are not necessarily conserved (though they may be, that depends on the details of the dynamics). Is it a Big Heresy? 

The Burning of Master John Rogers

Even if it is a heresy, I am not the only heretic in this world. John Archibald Wheeler stated explicitly, though it is not often quoted:

John Wheeler Principle of mutability (Part 2)

Well somebody might very well say "What about electric charge?" Yes, we don't know any process that violates the Law of Conservation of Electric Charge, so if one believes in the principle of mutability, you'll keep looking for a process where electric charge is not conserved. I'm not immediately animated to go on a raging tearing search for such a process because I don't envisage it right now.

The point is that in our theory the Universe is “open” rather than “closed”, as it is usually assumed. And why should it be “closed”? Experience indicates that it is open. Assuming that it is closed leads to inconsistencies, so why be afraid of letting it be open? There is always some “unknown” lurking somewhere, and so open minds seem to have advantages over closed minds, and open societies seem to have advantages over closed societies. Therefore an open Universe may have some significant advantages over a closed one!

P.S.1. This song about the electric/magnetic charge is for my wife - she likes it!

Judith Edelman - Magnetic

It's the buzz when I'm full
Of your sweet magnetic pull
It's the tug that I crave
It's how opposites behave
Is electricity all there is to you and me?

In the field, in the field
Where the static is revealed
If the north isn't true
Will I lose my way to you?
Is electricity
All there is to you and me?

What's gonna happen when the magnetism fails?
Will we burn up on bright day?
Will the aurora borealis give us one last show?
You can't leave love to science when you go.

There's a deep molten heart
Where these strange attractions start
If we are passionate
Will this rock remember it?
Is electricity all there is to you and me?

What's gonna happen when the magnetism fails?
Will we burn up one bright day?
Will the aurora borealis give us one last show?
You can't leave love to science when you go.

What's gonna happen when the magnetism fades?
Will we burn up on bright day?
Will the aurora borealis give us one last show?
You can't leave love to science when you go.

It's the buzz when I'm full
Of your sweet magnetic pull

P.S.2. The Illusion of Consensus

P.S.3. Laura brought to my attention this interesting report:  Man’s Biological Clock Set Back 10 Years After 93 Days Living Under the Ocean in a Research Station

P.S.4 18-05 17:14 Actually I am stuck and can't move forward with my notes on conformal compactification. It all got complicated and at the moment I do not see a way out. Don't know how long it will take before all comes out exactly the way I want it to come. Therefore a break for God only knows how long?

P.S.5 19-08 7:46 Yesterday my three daughters surprised me with a Father's Day gift. They gave me five VW cars (+flowers and cookies + food for the Cat)!  The third on the left looks almost exactly as the one I used to have as my first car - an orange beetle:

I think the one on the picture is pink rather than orange, but for me (and for Pikabu the Cat) it makes no difference.

P.S.6. About Purity (Beer, Protestantism, Kant) - suggested to me by Laura:

P.S.7. Today  I received a nice long email from a mathematical physicist in Lisbon, Portugal (PhD from DAMPT Cambridge). starting with:

"I've had a long-time interest in old-fashioned, geometrical Kaluza-Klein. While I was in academia I did not work on it, spending my time with other geometrical topics in field theory. Recently, however, I've had enough time to finish a draft describing some observations that, perhaps, may be relevant to KK.

Your book about Kaluza-Klein was an important learning reference for me. On the other hand, nowadays very few people are interested in the traditional version of those theories. So I would be very interested and grateful if you could let me know your opinion about these observations, even if only at a general high level.:

And then there is an attached paper - 100 pages long. At first look - quite interesting, And yes - it is done in a "traditional way" - which I like! In the past he even wrote a paper on vortices, degenerate metric and conformal transformations - I like them all.

P.S.8. 

Inspiration is a slender river of brightness leaping from a vast & eternal knowledge, it exceeds reason more perfectly than reason exceeds the knowledge of the senses.

Jnana, Sri Aurobindo

P.S.9. 19-06 19:23 Concerning P.S.4: No real progress. Have found today several new ways how not to build the bulb.