This is not just quantum entanglement, this is hyperphysics!

The Allure of Myths

Myths are thrilling!

We humans are funny creatures. We like to think of ourselves as rational beings, guided by facts and truths, but let's be honest: we thrive on myths. Why? Because truth, for all its nobility, is often dull. Myths, on the other hand, are thrilling! They're the juicy stories that give us a little buzz, a sweet shot of adrenaline. Suddenly, the meaning of life doesn't seem so pressing—there's excitement to be had! Something to believe in! Whether it's faith in religion or faith in science, we cling to our myths like a lifeline. Yes, even science, the beacon of truth and logic, is not immune to the lure of a good myth.

The Quantum Quagmire

Take quantum entanglement, for example. Sounds fancy, right? Like something straight out of a sci-fi movie. But at its core, it's just an ordinary, mundane property of complex quantum systems. Nothing to write home about. Yet, this humble phenomenon has been glorified, named, and mythologized to the point where you can't attend a dinner party without someone dropping "quantum entanglement" like it's the latest celebrity gossip. And heaven forbid you don't nod sagely and pretend to understand.

I had a reader, a physicist no less, who wrote to me just the other day. Now, this guy doesn't even dabble in quantum theory, but he felt compelled to chime in:

A Physicist’s Perspective

"I think Bell's article should be known, regardless of one's sympathies. It is simply always good to look at any issue from the broadest perspective, to know all the important aspects. Bell's work is undoubtedly something important in the whole discussion of quantum entanglement. You can disagree with its message—but even then, you should know it, or at least know something about it.

In short: general culture requires knowledge of myths, regardless of whether one is involved in these myths or not."

Hard to argue with that, right? It's the intellectual equivalent of saying, "You should really read Shakespeare, even if you prefer binge-watching reality TV."

The Truth, The Whole Truth, and Nothing But...

But here's where it gets interesting. My physicist friend, for all his wisdom, doesn't seem too concerned with the truth. And that puzzles me. Why is it that people think we should be well-versed in myths, able to toss them around like party favors, yet so few are interested in the cold, hard truth? It's as if truth is less important, a party crasher that ruins all the fun. And maybe that's exactly it. The truth has a nasty habit of popping our mythological bubbles, leaving us suspended in a void with nothing but reality to hold onto. And who wants that?

The Daredevils of Truth

These fearless fighters, these daredevils of reality, are few and far between. 

There are, of course, those rare souls who dare to seek the truth, come what may. These fearless fighters, these daredevils of reality, are few and far between. They’re often ridiculed, ostracized, and sometimes even lose their jobs. Society doesn't take kindly to truth-tellers. They're like modern-day Fausts, selling their souls for a glimpse of the real deal. Why? Because our society is infected with a nasty little bug called narcissism. And one of the telltale signs of this disease? A preference for myths over truth. "I know!" people declare, and what follows is a string of their favorite myths, served up with a side of self-assuredness.

The Myth of Us

So, why do we cling to myths? Perhaps it's because they give us something to hold onto, something to believe in when the truth feels too slippery, too uncertain. Or maybe it's just because myths are more fun. After all, who wants to be the party pooper who ruins a good story with facts? But every now and then, it's worth asking ourselves: What are we really chasing? The thrill of a good myth, or the solid ground of truth? The answer, my friends, might just be another myth we tell ourselves. 

I was watching the video "The  impossible experiment"

Similar experiments with distant influence have been described in 2017 in a paper by Serge Kernbach: "Replication experiment on distant influence on biological organisms conducted in 1986", published in Issue #E2 of International Journal of Unconventional Science. The Introduction has this paragraph:

"...  modern experiments on quantum communication [4] confirm his vision and approach. In general, the quantum interpretation of observed phenomena, in particular the phenomenon of entanglement inmacroscopic systems, has now received numerous experimental confirmations [5], [6], [7], [8]. Therefore, in the above mentioned polemic, modern works confirm the correctness of A.E.Akimov, although with a slightly different interpretation.". 

"Slightly different" means moving from "torsion fields" of Akimov and Shipov to "quantum entaglement" - whatever it means! From attempts to find the truth to myths. How can we explain anything using quantum theory, which itself desperately needs an "explanation"?

The discussion under the Youtube video has an interesting comment by "technomirfuture2228". I quote this comment in extenso:

 

Guys, this is not just quantum entanglement, this is hyperphysics! You work with hyperfield effects. 

What are hyperfields? 

These are the same physical fields, but existing in more than 4 dimensions, in other words, they are hyperprojections of the field onto our 3D world, some of them can be called informational - for example, the field of Consciousness, it does not transfer force interaction, but information, and this happens instantly, and at the physical level this manifests itself in the synchronization of the states of molecules, atoms and even macro-objects. 

Vladislav is right about something, if we consider our world as a dense vesal world, then it should have a more subtle prototype that contains information about everything that happens at the material level. 

Studying quantum fields, it became clear that all elementary particles are not independent, isolated objects, but rather constantly interacting field clots with the field space surrounding them, which we call the 4-dimensional space-time continuum, but this is not limited to this!!! 

Time, like space, has 3 dimensions, it is not linear. A person only feels the 4th dimension, but cannot see. 

It follows from this that we perceive the world in an extremely limited way, we live in 3 dimensions on which the shadow of the 4th is cast. 

Phantoms, ghosts, plasmoids cannot always be explained by standard optical or psychic phenomena; these are objects not from our 3-dimensional world, these are objects of hyperspace that were able to penetrate our plane of existence. 

The hierarchy of dimensions is built not only from top to bottom - from the source to the most basic level, but also vice versa from the basic level to the source, and this process is the evolution of the Universe and spirit. 

Spirit is the primary idea of ​​the world, this is Logos in its broadest understanding, this initial world is very simplified, everything exists potentially in it, in the form of information or primary quantum potentials, in order for the world to begin to develop, the realization of this potential must occur, in other words, descending projection and division into levels, densities, matter and energy, elementary particles, protons and neutrons, electrons, atoms, molecules, etc. 

Only in addition to our physical. plan, there are many levels or subtle planes of existence where there are their own worlds and their own laws, and my assumptions regarding the fact that everything in our world is connected are confirmed by scientific research, I am very glad that now is the time to look at these ideas in a new way and move from theoretical, to their experimental implementation, your experiments are very valuable for science and society,

 I think the accumulated knowledge will help humanity reach a new level of knowledge not only of the world around them, but also of themselves.

This is a poetic vision. How to make real science out of this vision? 

P.S. 30-08-24 18:09 And what kind of science should it be? 

Oxford Mathematician DESTROYS Atheism In Less Than 15 Minutes

Supernatural - A Simple Charm

 The following text is translation from Russian to English of a story taken from the book "Сверхъестественное. Научно доказанные факты (Supernatural. Scientifically proven facts). ISBN: 978-5-906789-00-6, Algorithm. Moscow, 2015" by Serge Kernbach.

This story is about a charming little experiment with sympathetic magic—it's as simple as it is convincing.

So, I had a wart under my nail. If you've ever had one of these unpleasant things, you know exactly what I’m talking about. I tried the over-the-counter freezing treatment, following the instructions to the letter. But, alas, it didn’t deliver the results the box had promised.

Next, I visited the doctor, who gave me a little bottle of liquid (a weak acid solution) that I was supposed to apply to the wart daily. I diligently followed this routine for several weeks, but again, the wart stubbornly refused to budge. By this time, about five or six months had passed since the wart first appeared, and it was looking pretty nasty. Worse still, it had grown larger and spread to more of my skin.

At this point, in a mix of frustration and desperation, I decided to try a well-known folk remedy. Now, I didn’t really believe it would work, but I figured, why not give it a shot? Here’s how the experiment went down.

I took an apple, cut it in half, dipped a string into the apple juice, and tied a knot over the wart. In my mind, I visualized that the knot was strangling the wart, causing it to fall off. Then, I tied the apple halves together with the same string and buried them in a field. The whole process took no more than half an hour. Being quite skeptical, I quickly forgot about the whole thing.

 

About two or three weeks later—after I’d stopped all other treatments—I noticed that the wart had completely disappeared. I should point out that I wasn’t consciously thinking about the wart during this time, nor was I doing any mental exercises. The timing of the wart’s disappearance coincided with the possible rotting of the buried apple.

Interestingly, there’s another folk remedy that works similarly. You take a potato, cut it in half, rub the wart with both cut sides, then put the halves back together and bury them in the ground. When the potato rots, the wart is supposed to vanish. (Editor's note.)

My original intention was to write about another hypothesis of how to obtain the fine structure constant through  quantizing everything and using category theory, as in the following papers:

[1]  Lucian M. Ionescu, “e, pi,chi,...,alpha?”

https://vixra.org/abs/1912.0360

[2] Lucian M. Ionescu, “The Fine Structure Constant revisited”, https://vixra.org/abs/2308.0180

Then I thought, perhaps I will better write about gravity control and antigravity as in this paper:

[3] Lucian M. Ionescu, Alzofon-Ionescu Theory of Gravity, https://vixra.org/abs/2106.0056

But finally I decided that charming is more important. Question is: how exactly  it works?

P.S. 29-08-24 13:34 Simple charm:

Sailor Moon 「Moonlight Densetsu」

P.S. 29-08-24 18:49 Simple charm:

The Einstein Approach: When Persistence Becomes Stubbornness

Albert Einstein once shared a story that resonates deeply with me—perhaps it will with you, too.

"Einstein and an assistant, having finished a paper, searched the office for a paper clip. They finally found one, too badly bent for use. They looked for an implement to straighten it, and after opening many more drawers, came upon a whole box of clips. Einstein at once shaped one into a tool to straighten the bent clip. His assistant, puzzled, asked why he was doing this when there was a whole boxful of usable clips. 'Once I am set on a goal it becomes difficult to deflect me,' said Einstein."

'Once I am set on a goal it becomes difficult to deflect me...

This anecdote, borrowed from a story I encountered online, is a perfect example of a mindset I know all too well. It's about more than just stubbornness; it's about an unyielding focus that sometimes borders on the absurd.

The Moth and the Flame

Why do moths persistently fly into the flame? If that's truly the case, what drives this seemingly self-destructive behavior? 

What drives this seemingly self-destructive behavior? 

We see a similar stubbornness in a fly endlessly slamming against a glass window, desperately trying to escape. All it needs to do is take a step back, shift slightly to the right or left, and it would find the open window—freedom just a short distance away!

Freedom just a short distance away.

When Persistence Pays Off—And When It Doesn't

So, when is persistence a virtue, and when does it cross the line into stubbornness? Can we create guidelines for when to press on and when to pivot? Is there a philosophical underpinning to this dilemma?

I honestly don't know. What I do know is that, like Einstein, I am both stubborn and persistent. I also have a passion for fixing things that are broken. 

Fixing things that are broken.

I've written before about standing on the shoulders of giants, and this ties in here. There are moments when I feel I should be more creative, less dependent on the work of those who came before me. Maybe I should focus on creating entirely new things, rather than stubbornly fixing what others have messed up.

The Sunday Reflection

These are my thoughts on this Sunday, August 25th. As I reflect on Einstein’s story, I’m left wondering: when should we keep pushing, and when is it time to step back and try a different approach? Perhaps that’s a question worth pondering in all our lives.

P.S. 26-08-24 18:36 

Today I was fixing one of the two meteo stations (the white one). I have a separate stations for separate sides of the world. As you can see the winds on both sides blow in different directions. The bearing of the anemometer needed to be sprayed with a silicon lubricant. Tomorrow will be fixing causality relation on the doubly conformally compactified Minkowski space. Sabine Hossenfelder and Jean-Pierre Petit came close to a similar idea. I will try use their insights and to develop some of their ideas according to my own taste.  Standing on the Shoulders of Giants: The Unsung Path to Innovation!

P.S. 27-08-24 15:31  Laura has found it for me. You will enjoy it too: 

ChatGPT and Fake Citations

It is from March 2023, but nothing has changed, in this respect, since then. 

Life is at the boundary

A Sleepless Odyssey

For over a week, I've barely slept. I've barely eaten. Without my wife, I might not sleep or eat at all. Work has consumed me. My brain spins endlessly, processing algebraic symbols and the elusive objects from Plato's world. Something new is forming. At least, it's new to me.

My brain spins endlessly, processing algebraic symbols and the elusive objects from Plato's world. 

Will it be of use to anyone? Right now, I don't care. It's beautiful, and that's enough. A puzzle is unfolding before me. 

I don't know what the final picture will be. Many pieces are still missing. The box is vast, overflowing with possibilities. Strangely, I find myself returning to ideas from my doctorate. Back then, they were mysteries. Now, I understand them. Now, I develop them.

The Edge of Reality

To satisfy your curiosity, I'll share what I'm working on. Although, I doubt anyone will understand. But I’ll tell you anyway. Think of it as surrealist poetry.

On the edge, there’s a great concentration (critical density) of Black and White...

Our world—our entire reality—is a complex domain. This domain has an edge, and our lives unfold along this boundary. We have no clear view of its interior. Perhaps, just a glimpse. Deep within the domain, a spotlight of consciousness shines, like a lighthouse, illuminating the edge point by point.

A lighthouse, illuminating the edge point by point.

The Cycle of Time

Each point touched by light marks the passage of our "time." Time is cyclical. Reincarnations. For those who live only on the edge, with no insight into the interior, the cycle repeats endlessly. Every point on the edge has its opposite—somewhere, infinitely distant.

Within the domain, time does not flow. Inside, there is no difference between reality and imagination. Inside, Geometry dwells. Geometry akin to Escher’s devils and angels. Our edge is not the only one. There are others, adjacent to ours, with other "lives" existing in different dimensions.

Not only is our "time" cyclical, but our space also loops back on itself. It closes with a cap shaped like a truncated double  light cone.

The Operators of Existence

The domain is filled with operators. Our point on the edge, along with its opposite—the tip of the cap—is also an operator. This operator is anti-commuting with the lighthouse. It remains anti-commuting through all "time." The tangents to the edge are four Dirac gamma operators.

But there is a fifth gamma operator, anti-commuting with the four "normal" ones. Together, they span a five-dimensional space. The domain is "round." But if a "wind" distorts it slightly—it creates unstable gravity waves—that’s GRAVITY.

The Cosmic Mysticism of Sir Arthur Eddington: Exploring Mind-Stuff, E-numbers, and the Unseen World

 

Introduction: A Visionary Mathematician and His Enigmatic Quest

In my previous post, "Fine Structure Constant and Sir Michael Francis Atiyah," we explored the contributions of the great mathematician Sir Michael Atiyah and his intriguing approach to the fine structure constant, a mystery that has puzzled physicists for over a century. 

In [1] Atiyah  wrote

“There are now various ways of arriving at Eddington’s number, all by pure algebra, which appear in several different papers [5] and [9]. The simplest is

(7.2)  137 = 1 + 8 + 128 = 2⁰ + 2³ + 2⁷.

Eddington first proposed 136 = 8 + 128, based correctly on Clifford algebras as in [4], but he had difficulty justifying the additional 1 to get 137.

...

Ironically, Eddington was later laughed out of court, when 137 was found to need a long string of corrections. In fact these corrections just arise from the iterative process that defines Ж , so Eddington’s two mistakes cancel each other out. Stability helps the tricky initial stage. A wobbly start acquires stability from subsequent motion in a very precise sense as on a bicycle.”

Sir A. Eddington: "A wobbly start acquires stability from subsequent motion in a very precise sense as on a bicycle."

Atiyah's work, particularly in "The Fine Structure Constant" [1], highlights the legacy of Sir Arthur Eddington, a profound figure in the realms of astronomy, physics, and mathematics. Eddington’s work delves into the mystical and mathematical fabric of the universe, revealing dimensions of thought that continue to inspire and challenge modern science.

Eddington’s Algebraic Mysticism: Unveiling the E-numbers

Sir Arthur Eddington (1882–1944), an English astronomer and physicist, was not merely a scientist; he was a visionary who sought to uncover the sacred algebraic structures governing the universe. In "The Fine Structure Constant," Atiyah praises Eddington for his exploration of these structures, notably his "E-numbers," which Eddington believed were not just mathematical curiosities but divine symbols of a higher-dimensional reality intertwined with spacetime.

Einstein and Eddington seated together at the Cambridge Observatory in 1930
(Photo: Royal Astronomical Society)

Eddington’s fascination with the number 137, the fine structure constant, is particularly noteworthy. He proposed that 137 could be derived algebraically, and while his methods were initially met with skepticism, modern physics acknowledges the importance of such dimensionless numbers in understanding the universe's fundamental laws. Eddington’s work, though often overlooked, laid the groundwork for future explorations into grand unified theories, where the echoes of his mystical insights can still be heard.

Mind-Stuff: The Foundation of Reality

Eddington's philosophical inquiries extended beyond the physical constants to the very nature of reality itself. In "The Nature of the Physical World" [2], he introduces the concept of "mind-stuff," a fundamental substance that he posits as the true basis of existence. According to Eddington, what we perceive as the physical world is a construct derived from this more basic form of reality.

This "mind-stuff" is not to be confused with our conscious minds; instead, it is a generalized substrate that underlies all reality. Eddington argues that our material world is shaped by this mental substance, much like how a college's activities are represented in bursar accounts. Consciousness, in his view, arises from this mind-stuff, challenging the traditional physicalist perspective that considers space and time as fundamental entities. Instead, Eddington suggests that they too are products of this deeper mental reality.

Science and the Unseen World: A Cosmic Perspective

In his 1929 Swarthmore lecture, "Science and the Unseen World" [3], Eddington challenges conventional notions of existence and reality. He argues that the obsession with proving the existence of entities—whether they be gods, deities, or even friends—is an intellectual trap that distracts from a more profound understanding of our relationships and the universe.

Eddington proposes that our connection with the divine, or any higher entity, transcends logical validation. He likens it to our friendships, where the need for proof is absurd. Eddington proposes that, in the highest form of spiritual experience, the soul and God share a cosmic joke, laughing together at the absurdity of trying to "prove" something so inherently beyond proof.

the soul and the divine share a cosmic joke, laughing at the futility of trying to "prove" something inherently beyond proof.

This perspective invites us to move beyond sterile metaphysical arguments and embrace the realization that some aspects of reality are beyond the dichotomy of existence and non-existence—they simply are. Eddington’s insights offer a potential reconciliation between science and spirituality, suggesting that both domains might find common ground in the shared joy of a deeper understanding of the cosmos.

Egregors and Mind-Stuff: Beyond the Reach of Science

In [3] Eddington addresses the “unseen world” hiding behind the symbols of science as follows:

“Natural  law  is  not  applicable  to  the  unseen world behind the symbols, because it is unadapted to  anything  except  symbols,  and  its  perfection is  a  perfection of symbolic linkage.  You cannot apply such a scheme to the parts of our personality which  are  not measurable  by symbols  any more than you can extract the square root of  a sonnet." 

Here I do not fully agree with Eddington. While it is true that attempting to take square root of a sonnet is not very productive, it is also not productive to take a square root of of the equality sign “=”. But sonnets can be analyzed in other, more productive and scientific ways. We can analyze the information contained in a sonnet, its complexity, its impact on the consciousness level. We can analyze its “egregor” character, even if egregors are still beyond the reach of science. 

While Eddington’s notion of the "unseen world" behind the symbols of science might seem esoteric, it opens the door to exploring concepts that are currently beyond the reach of modern science. One such concept is the "egregor," a collective consciousness or psychic entity that emerges from the shared beliefs and intentions of a group.

An egregor is more than just the sum of individual thoughts; it is a dynamic, influential presence shaped by collective human activity. This idea brings us back to Eddington’s mind-stuff—an enigmatic substance that, while not fully understood, might one day be accessible through new scientific methodologies. Just as quantum theory is used in daily life without being fully comprehended, the mind-stuff could become a tool for future scientific exploration and control.

Mind-Stuff - an enigmatic substance that, while not fully understood, might one day be accessible through new scientific methodologies.

Conclusion: Eddington’s Legacy and the Future of Science

Sir Arthur Eddington’s work, spanning the mystical and mathematical realms, continues to challenge and inspire. His exploration of the fine structure constant, mind-stuff, and the unseen world invites us to reconsider the foundations of reality and the limits of scientific inquiry. Eddington’s insights suggest that the universe is not merely a physical construct but a profound interplay of mind and matter, hinting at dimensions of existence that remain largely unexplored.

As we advance in our scientific endeavors, it is crucial to remember Eddington’s legacy. His work reminds us that the pursuit of knowledge is not just about understanding the material world but also about embracing the mysteries that lie beyond. In doing so, we might one day bridge the gap between science and spirituality, uncovering deeper truths about the nature of reality and our place within it.

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References

1. M. Atiyah, “The Fine Structure Constant” (2018).
2. A.S. Eddington, “The Nature Of The Physical World”, Cambridge University Press 1929. Link.
3. A.S. Eddington, Swarthmore lecture, “Science and the Unseen World”, George Allen & Unwin Ltd 1929. Link.

Fine Structure Constant and Sir Michael Francis Atiyah

 Sir Michael Francis Atiyah (22 April 1929 – 11 January 2019) wasn't just a mathematician; he was a magician of numbers, a wizard whose work could turn the most abstract mathematical ideas into something akin to pure magic. His groundbreaking contributions linked geometry and topology in ways that fundamentally transformed modern mathematics. Atiyah was not just any mathematician; he co-developed the Atiyah-Singer Index Theorem - a concept so profound that it's like discovering a hidden treasure map using nothing but a mathematical compass. This theorem creates a bridge between differential equations and the topological properties of shapes, making it one of the most intriguing ideas in the mathematical universe. Along the way, Atiyah collected nearly every top prize in mathematics, from the prestigious Fields Medal to the Abel Prize, firmly establishing himself as one of the grand wizards of the mathematical world.

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The Enchanted Forest of Mathematics: Atiyah's 2018 Abel Prize Talk

In his 2018 Abel Prize talk at the International Congress of Mathematicians (ICM), Michael Atiyah did more than just give a lecture; he took his audience on a mesmerizing journey through the enchanted forest of mathematics. With the skill of a master storyteller, he wove together tales of numbers, geometry, and physics, revisiting some of his greatest mathematical adventures, including the renowned Atiyah-Singer Index Theorem. All that he did with humor.

Michael Atiyah at ICM 2018 Rio de Janeiro (in my personal vision)

Atiyah reflected on how these seemingly abstract concepts have surprising and deep connections to the real world, musings that felt like whispers of the universe's deepest secrets. With the charisma and flair of a seasoned wizard, he suggested that the most profound truths in mathematics are like hidden spells, waiting to be discovered by those brave and curious enough to explore them. It was a fitting farewell from one of the most brilliant minds to ever grace the field of mathematics.

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The Fine Structure Constant: A Bold and Controversial Proposal

Atiyah's talk was not just a stroll down memory lane. He also presented a bold and speculative idea about one of the most mysterious constants in physics: the fine structure constant. This constant is crucial because it governs the strength of electromagnetic interactions, yet its precise value has long puzzled physicists.

Atiyah proposed an innovative approach to deriving the value of this constant, one that intertwined deep mathematical concepts with the mysteries of the physical universe. He traced his ideas back to the work of Euler, von Neumann's theory of factors, and Clifford algebras, seamlessly blending his lifelong passion for mathematics with his curiosity about the physical world. His discussion was both intriguing and controversial, sparking debate and reflecting his enduring spirit of exploration, even in his later years.

Abel Lecture — The future of mathematical physics: new ideas in old bottles — M. Atiyah — ICM2018 

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The Calculations: No Cigar, But Still a Magical Journey

Atiyah's proposal stirred quite a bit of discussion, particularly on forums like the Physics Forum, where physicists debated whether he had uncovered new links between arithmetic and physics. Viktor T. Toth, a notable contributor to the discussion, analyzed Atiyah's 2018 preprint using Maxima software, ultimately concluding that Atiyah's proposal did not match the expected value of the fine structure constant. Undeterred, I decided to dive into the calculations myself using Mathematica.

Using Atiyah's formula, the value of the inverse of the fine structure constant, 1/α (which he denoted by the Cyrillic letter Ж), came out as 0.160262—significantly different from the expected 137.0359992, making it about 854 times smaller than the expected value. In short, no cigar here. In fact, it was a true disaster.

But Atiyah's story doesn't end with a simple miscalculation. His paper delves into much more advanced mathematics, suggesting that Ж might be similar in nature to π. Atiyah speculated that just as Euler’s formula

links π with complex numbers, there might be a similar elegant formula for Ж involving noncommutative quaternions. From there, he ventured into von Neumann factors, traces, and infinite products, sketching ideas that are as challenging to comprehend as they are fascinating. While he didn’t provide all the answers, Atiyah’s speculations open up tantalizing possibilities that invite further exploration.

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Conclusion: The Legacy of a Mathematical Wizard

Michael Atiyah's work remains a testament to the power of curiosity, creativity, and courage in the world of mathematics. While his attempt to link the fine structure constant to deep mathematical ideas may not have yielded the expected results, it exemplifies the adventurous spirit that drove him throughout his life. Atiyah's legacy is not just in the theorems he proved or the prizes he won, but in the magical way he connected different realms of mathematics and physics, inspiring future generations of mathematicians to explore the unknown. Whether or not his ideas about the fine structure constant will stand the test of time, they will undoubtedly continue to provoke thought and inspire wonder.

In the end, Sir Michael Atiyah leaves behind a legacy that, like all great magic, will continue to captivate and challenge those who dare to dream big in the world of mathematics.

Related links

• M. Atiyah , “The Fine Structure Constant” (2018)
• M. Atiyah, “Arithmetic Physics – Abel Lecture” (2018)
•  “Atiyah and the Fine-Structure Constant“ on Sean Carroll's blog
• “Riemann hypothesis, the fine structure constant, and the Todd function” post on John D. Cook blog
• "A fantastic journey through Atiyah's mathematical mind", IMPA blog

P.S. 18-08-24 I thank to Viktor T. Toth for pointing it to me that Atiyah's  Ж was supposed to denote 1/α, and not α, as I had it in the original version of this post. 

The Fine Structure Constant - the Curious de Vries formula

The Fine Structure Constant - Adventure Plus

Roughly 20 years ago, on October 4, 2004, Hans de Vries made a subtle yet significant contribution to physics by posting his recursive formula for the fine structure constant, α, on his Chip Architect website. This formula, which can be described as implicit or even recursive, sparked interest and debate among physicists and mathematicians alike.

Here is the formula;

Hans de Vries formula

Who is Hans de Vries?

If you’ve never heard of Hans de Vries, allow me to introduce him. According to his LinkedIn profile, de Vries is a High Tech Consultant and Physics Software Engineer with a solid background in Electrical Engineering, Computer and Telecommunication Technology. He’s also the mind behind the Physics Quest website, where he is currently working on a graduate-level physics book titled “Understanding Relativistic Quantum Field Theory.” Some chapters are available online for the curious reader.

 A Formula in the Spotlight

Fast forward to last year, and de Vries’ formula became a topic of extensive discussion, particularly in German-speaking circles and on the math.stackexchange forum. This formula caught the attention of Gudlaugur Kristinn Ottarsson (GKO), who took a serious approach to calculating α using de Vries’ formula. In July 2018, GKO published a preprint titled “The Fine Structure Constant and Discrete Calculus – GKO2018,” where he rewrote the de Vries formula in a closed form and tested it numerically.

Crunching the Numbers

Out of sheer curiosity, I decided to verify GKO’s results. Ottarsson’s method involves rewriting de Vries’ formula by taking the square roots of both sides and then putting it to the test with a high-precision calculation engine capable of handling 100 decimal digits. 

GKO version of de Vries formula

His results? The fine structure constant to 27 significant digits:

1/α = 137.035999095829799489647400 + ε ;  ε < 10^(-24).

However, GKO also noted that current experimental values are a bit perplexing. It seems we’ll need to wait a while before experiments consistently align with the numbers predicted by de Vries’ formula. For now, we can only be confident up to about 8 digits: 137.035999.

experimental values taken from Wikipedia

 Beyond that, things start to get a bit fuzzy. It’s also important to remember that α is a "running constant," meaning its value depends on the energy levels involved in the measurement, while de Vries’ formula likely provides the low-energy limit for α.

A Personal Dive into the Calculation

Never one to pass up an opportunity for some intellectual exercise, I decided to put Ottarsson’s calculations to the test using Wolfram's Mathematica. My no-brainer code churned out the exact same high-precision number that Ottarsson had obtained. 

But I didn’t stop there—I also estimated the error by limiting the series on the right-hand side to the sixth power of α. Thankfully, the series converges rapidly, much faster than a geometric series, making this task a breeze. However, these are minor details, and I’ll spare you the nitty-gritty.

Reflecting on the Formula

There are a couple of points worth mentioning. First, de Vries’ formula aligns much more closely with the experimental value of α than the mysterious Wyler’s formula, which is discussed in TheSecret of Room 137: Unlocking the Fine Structure Constant. Wyler’s formula results in 1/α=137.03608245, which is further from the mark. However, de Vries’ formula, while more accurate, doesn’t exactly unravel the deep mystery of α. It seems more like a "balance equation" inspired by the perturbative methods of Quantum Electrodynamics rather than a key to new physical insights. Unlike Wyler’s excursions into hyperdimensional physics and conformal symmetry, de Vries’ formula doesn’t open up new adventures in the realms of light and matter.

Second, de Vries’ formula isn’t a one-trick pony - it has more than one solution. By tweaking the last line of my Mathematica code, I found a second possible value of α, roughly 1576.56 times larger than the "correct" one. 

Second solution for α

The significance of this fact remains unclear. Luke Kenneth Casson Leighton noticed the multiple solutions in his paper "An Explanation of the de Vries Formula for the Fine Structure Constant" (January 2017), but he didn’t delve into the potential consequences.

While preparing this post, I kept an old saying in mind: "Follow the clues, stick to the shadows, and most importantly - trust no one." In my quest for knowledge, I checked out other papers by GKO on ResearchGate. 

https://www.researchgate.net/profile/Gudlaugur-Ottarsson

Some of the titles immediately piqued my interest:

• Unified Horizons of Electricity and Gravity

• Matter as Poisson Degeneracy in Natural Space

• The Equations of Maxwell and Gauss in Natural Space

• Operations in d+i Dimensional Natural Space and Einstein's Quest for Asymmetric Tensors

These titles are tantalizing, and I’m planning to dive into them soon. The mystery deepened when I learned that GKO’s education spans Polytechnic Engineering, Mathematical Physics, Computer Science, and Fine Art. To top it all off, he’s also an accomplishedmusician, according to Wikipedia!

Conclusion

The exploration of the fine structure constant, α, through Hans de Vries’ formula is a journey full of numbers, curiosity, and a dash of mystery. While it may not solve the enigma of α, it certainly adds a fascinating chapter to the ongoing quest to understand one of the most fundamental constants in physics. As I continue to follow the clues, I’m reminded that in science, as in life, the answers often lead to more questions—and that’s what makes the journey so exciting.

To be continued...

The Cosmic Love Affair: Chasing the Enigmatic Beauty of Alpha

After “The Secret of Room 137: Unlocking the Fine Structure Constant”, “Standing on the Shoulders of Giants: The Unsung Path to Innovation” and “The Fine Structure Constant - Unraveling the Mystery”, this is the third post in the fine structure constant series. 

In the hidden corridors of physics, there lies a secret - Room 137. Not an actual room, but a number, a constant that whispers the delicate harmony of the universe. This number, the fine structure constant, often denoted as α, is a seemingly simple figure - 0.0073 in one form, but its inverse, close to 137, captures the imagination of the greatest minds. This is not just a number; it's the key to the dance of light, matter, and energy. The giants of science have all felt its pull, grappling with its mystery, and today, we explore their love affair with this enigmatic beauty.

Feynman’s Forbidden Romance

 You might say the ‘hand of God’ wrote that number, and ‘we don't know how He pushed his pencil.’ 

Richard Feynman, the physicist known for his playful wit and deep curiosity, saw in alpha a forbidden romance. He described it as a mystery—a magic number handed down by the cosmos itself, one that tantalizes but refuses to reveal its secrets. Feynman likened it to the "hand of God," a divine scribble that even the most brilliant minds couldn't fully decipher. His frustration mingled with awe, as he admitted that while we can measure this number with exquisite precision, the dance required to understand its origins remains elusive.

Quote: "It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it. Immediately you would like to know where this number for a coupling comes from: is it related to π or perhaps to the base of natural logarithms? Nobody knows. It's one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man. You might say the ‘hand of God’ wrote that number, and ‘we don't know how He pushed his pencil.’ We know what kind of a dance to do experimentally to measure this number very accurately, but we don't know what kind of dance to do on the computer to make this number come out, without putting it in secretly!"

Source: Feynman, R. P. (1985). QED: The Strange Theory of Light and Matter. Princeton University Press, p. 129.

Pauli’s Existential Yearning

For Wolfgang Pauli, alpha was an obsession that reached beyond the grave. He famously quipped that upon death, his first question to the devil would be about the meaning of the fine structure constant. Pauli's relationship with alpha was tinged with frustration and an almost existential urgency, as if understanding this number was the key to unlocking the deepest truths of existence. It was a riddle that haunted him, a love unrequited, driving him to the brink of metaphysical inquiry.

Quote: "When I die, my first question to the devil will be: What is the meaning of the fine structure constant?"

Source: Popular wisdom.

Dirac’s Elegant Seduction

Paul Dirac, with his belief in the mathematical elegance of the universe, viewed alpha as a puzzle that begged to be solved through pure logic and numbers. He was optimistic, seeing the fine structure constant not as a random figure but as a ratio that could one day be explained entirely through mathematics. For Dirac, alpha was like a beautiful equation waiting to be balanced, a seduction that promised the ultimate revelation of nature's underlying order.

Quote: "The fact that the fine structure constant has turned out to be a pure number and not a dimensional quantity would suggest that it could be a pure ratio, one which could be constructed purely from mathematical constants and not depending on any arbitrarily chosen quantity."

Source: Popular wisdom.

The Giants’ Chorus

Max Born, another giant in physics, echoed the sentiment that the fine structure constant is a central enigma, a major unsolved problem in modern physics. 

Quote: “If   [the fine structure constant] were bigger than it really is, we should not be able to distinguish matter from ether [thevacuum, nothingness], and our task to disentangle the natural laws would be hopelessly difficult. The fact however that   has just its value 1/137 is certainly no chance but itself a law of nature. It is clear that the explanation of this number must be the central problem of natural philosophy.”

Source: A. Miller, 137 Jung, Pauli, and the Pursuit of a Scientific Obsession, W.W. Norton Company 2009.

Quote: "Is  this  state  of  affairs  satisfactory?  I  think  not  in  tile  least.  We should expect  that  numerical coefficients in  physical laws  are  always mathematical numbers like 3/4 or π or something of the  kind.  If this  here  seems to be  different  it  must  mean  an  incompleteness  of  the  theory.  A  perfect theory should  be  able to derive the number a by purely mathematical reason-ing without recourse to  experience.  

Source:  Max Born, The Mysterious Number 137, Lecture  delivered  to  the  South  Indian  Science  Association,  Bangalore, the  9th  of  November  1935. 

Arnold Sommerfeld, who introduced alpha into quantum theory, lamented that despite its clear importance, its true nature remains shrouded in mystery. 

Quote: " The universal nature of the elementary charge was mirrored in a mysterious way in the fine-structure constant and extended to the entire domain of electromagnetic interaction. “It is not only the coupling of the electrons with the light quanta that is determined by the fine structure constant, but the coupling of any  arbitrary  elementary  particle  with  the  electromagnetic  radiation  fields."

Source: Quoted in Sommerfeld: Science, Life and Turbulent Times 1868-1951 by Michael Eckert (2013), Chapter 14.3 The  Fine-Structure Constant.

These pioneers recognized alpha as a constant that governs the very fabric of reality, yet it slips through the fingers of understanding like sand.

Mathematician Michael Atiyah pondered the deeper connection between mathematics and physics, suggesting that alpha hints at a relationship between the abstract and the concrete that we have yet to grasp. Similarly, 

Quote: "The fine-structure constant α is a dimensionless number that is ubiquitous in physics, but has remained an enigma for over a century. Does it have mathematical significance analogous to π? Its numerical value is now known accurately to 12 significant figures but it has no satisfactory mathematical explanation as shown by the following opinions...  

Finally, this explanation of α should put an end to the anthropic principle, and the mystery of the fine-tuning of the constants of nature. Nobody has ever wondered what the Universe would be like if π were not equal to 3.14159265... "

Source: Atiyah, M. (2004). The Fine Structure Constant. Preprint.

John D. Barrow mused on the fine structure constant as a number that seems almost magical, as if placed by a deity to be discovered, but never fully explained. It’s a cosmic tease, drawing physicists and philosophers alike into a dance of discovery.

Quote: "Many other scientists were completely mystified and some, like Vladimir Fock, were moved to poetry about it all

"137 - 1840 

Though we may weigh it as we will, 

It is the number of (says he)

The world's dimensions. Can it be?!-

The world enfolding you and me?

The world that holds Sir Arthur E.?

The very world we smell and see?-

Oh come, he can’t be serious!

Well, here's a number of my own

(In tit for tat I revel):

One-thousand-eight-four-oh. I've shown

It's strictly on the level.

Sir Arthur, keep your puny sum,

It's yours from now to Kingdom Come!

My 1 and 8 and 4 and 0

Will fit a world we've yet to know-

So on and upward with the show!

And on my cauldron down Below

Let these four figures shine and glow,

Bewildering the Devil!"

Source: Barrow, J. D. (2002). The Constants of Nature: The Numbers that Encode the Deepest Secrets of the Universe. Vintage, p.89; G. Gamow, The Great Physicists from Galileo to Einstein, Dover (1988), p. 327. 

A Poetic Interlude

Even outside the realm of physics, the allure of alpha is felt. Borges, with his poetic mind, captured the essence of an elusive harmony in the universe, a formula that forever escapes comprehension. 

Time carries him as the river carries

A leaf in the downstream water.

No matter. The enchanted one insists

And shapes God with delicate geometry.

Source: Luis Borges, "Baruch Spinoza", as translated in Spinoza and Other Heretics: The Marrano of Reason (1989) by Yirmiyahu Yovel 

 

T.S. Eliot's exploration of the never-ending journey of discovery resonates with the quest to understand alpha—a journey that ends where it begins, with the mystery intact. 

Quote: "We shall not cease from exploration,

And the end of all our exploring

Will be to arrive where we started

And know the place for the first time."

Source: Four Quartets (1943).

 

The Constant Whisper

A riddle etched in starlit sand,

The fine structure, by nature’s hand. 

In the end, alpha remains a whisper in the cosmic haze, a number that binds the stars and guides the beams of light, yet refuses to fully reveal its secrets. It is the subject of a cosmic love affair—scientists and thinkers across generations drawn to its mystery, seduced by its elegance, and frustrated by its elusiveness. Here is AJ's (assisted by AI)  little poem on the subject:

In the dance of light and shadow's trace,

A number sings in silent space,

Not too strong, nor weak, it stays,

A whisper in the cosmic haze.

It binds the stars, it guides the beam,

A thread within the physicist’s dream.

Mysterious, it holds the key,

To secrets of eternity.

The universe in balanced form,

By this constant, softly worn,

Yet who can tell, who dares to see,

The hand that set its value free?

So we ponder, minds entwined,

With thoughts that stretch, yet cannot bind.

A riddle etched in starlit sand,

The fine structure, by nature’s hand. 

 

 Epilog

As we ponder this enigmatic constant, we are reminded of the delicate balance of the universe, a balance maintained by this humble number. The fine structure constant is more than just a figure in an equation; it is a reminder of the beauty and mystery that lie at the heart of reality, a love story that continues to unfold in the minds of those who dare to seek its truth.

To be continued...