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...

The Secret of Room 137: Unlocking the Fine Structure Constant

In this post we explore the enigmatic journey of Swiss mathematician Armand Wyler, who attempted to unravel the fine structure constant, alpha, related to the number 137. It delves into historical attempts by physicists like Sir Arthur Eddington and Wolfgang Pauli to understand this dimensionless constant, connecting quantum theory, relativity, and electromagnetism. The post also highlights Wyler's geometric interpretation and the profound yet tragic impact of his work, which led him to a psychiatric clinic.

The Mysterious Journey of Armand Wyler

Wolfgang Pauli - Room 137

From the prestigious research institute to a psychiatric clinic—this was the price Swiss mathematician Armand Wyler paid for his attempt to unravel the geometric meaning of the fine structure constant, alpha. This mysterious dimensionless constant, whose reciprocal is close to 137, has long been the philosopher's stone for physicists. Wyler's formula was simple enough for a schoolboy to understand:

Wyler's Formula

Any student (not to mention engineers) with a calculator can easily calculate:

1/α=137.0360824482...

An Astonishing Agreement

Physicists' measurements, based on the theory of light and matter interaction, give the value of:

$1\mathrm{/}\mathrm{\alpha }= 137.03599976(50)$

The agreement is astonishing, especially since the value measured by physicists depends on the energy of the scattered electrons, so no one really knows what "exactly" it is.

Fundamental Constants of Nature

Let's start from the beginning. Physicists long ago discovered that certain values are constants. These constants, classified as fundamental, include the "Elementary charge e," "Planck's constant ℏ," and the "Speed of light c." In the commonly used system of units today, these constants have the following values:

$\mathrm{e }= 1.602176462(63)\times 1{\mathrm{0^(}}^{-\mathrm{19) }}C$

$$ℏ = 1.054571596(82) × 10^(-34) J s

$\mathrm{c }= 299,792,458\text{ m/s}$

The Magic of Alpha

There is also the "Vacuum Impedance ε₀":

ε₀ = 8.854187817...×10^(−12) F

Using the formula:

$e²/(2hε₀c)$

we get a dimensionless value, equal to $7.297352533(27)\times 1{\mathrm{0^(}}^{-\mathrm{3).}}$ This is α, the fine-structure constant. In the days of the CGS system, the expression was simpler:

$\alpha =\frac{\mathrm{e²/\hslash }c}{}$

Alpha connects quantum theory (constant h), relativity (constant c), and electromagnetism (constant e). If this constant could be calculated from purely geometric premises, it could revolutionize physics, possibly earning a Nobel Prize.

α is truly exceptional among physical constants. It is a pure number - it carries no meters or seconds or kilograms. And because it is a pure number, there is an overwhelming feeling that it must come out of pure math! Possibly of some pure geometry, like the number π.

The Eddington Affair

Astrophysicist and mystic Sir Arthur Eddington, in 1929, published speculative arguments suggesting $= 136$. In those days, measurements suggested this value. However, other physicists mocked Eddington, notably in a 1931 paper by Beck, Bethe, and Riezler, which "derived" $1\mathrm{/}\alpha$ from absolute zero temperature—a dubious joke for serious scientists.

Pauli's Obsession

Wolfgang Pauli, known for the Pauli Principle, also delved into this constant. Though he concluded Eddington's ideas were nonsense, Pauli himself was intrigued. When he was very ill, he requested room number 137 in a Zurich clinic, where he eventually died.

W. Pauli - Room 137

Quoting from Arthur I. Miller, "137: Jung, Pauli, and the Pursuit of a Scientific Obsession", W. W. Norton & Company, 2009:

"On Friday, December 5, 1958, as he was teaching his afternoon class, Pauli suddenly began to suffer excruciating stomach pains. Up until then he had been fine. The next day he was rushed to the Red Cross Hospital in Zürich. Charles Enz visited him the day after. Pauli was visibly agitated. Had Enz noticed the number of the room, he asked him?

“No,” replied Enz.

“It’s 137!” Pauli groaned. “I’m never getting out of here alive.”

When the doctors operated, they found a massive pancreatic carcinoma. Pauli died in Room 137 on December 15. His last request had been to speak to Carl Jung."

Einstein and Feynman's Insights

Einstein, in 1950, expressed his belief that there should be no dimensionless constants in the laws of nature. Richard Feynman famously said every theoretical physicist should have a sign on their door saying, "137 - how little we know."

Wyler's Geometric Interpretation

Armand Wyler

In 1968-1969, Zurich mathematician Armand Wyler published papers suggesting alpha has a geometric interpretation, related to higher-dimensional geometry. Physicists couldn't understand his mathematics but took it seriously. Freeman Dyson invited Wyler to IAS, Princeton to explain his ideas, but reportedly, Dyson understood nothing. After three months, Wyler returned home and ended up in a psychiatric clinic, publishing nothing more.

IAS Princeton

An Unexpected Encounter

I inquired AI (Perplexity, having access to online resources) about Wyler's work and his fate  after his return from IAS. Here is what I got:

#### **Focus on Pure Mathematics**

- **Topological Singularities**: Wyler's dissertation at ETH Zürich focused on topological singularities, employing rigorous mathematical tools from algebraic topology, differential topology, and singularity theory. This work was more aligned with pure mathematics and the theoretical aspects of topology.

- **Mathematical Foundations**: His work in Switzerland was heavily grounded in the mathematical foundations laid by his advisor Heinz Hopf and other prominent mathematicians. This period was characterized by a deep dive into the mathematical structures and their properties.

#### **Initial Forays into Theoretical Physics**

- **Proton/Electron Mass Ratio**: Wyler applied Clifford algebra for spinors and Green functions for the Shilov Boundaries $ Q^5 $ and $ Q^4 $, calculating the proton/electron mass ratio to be $ 6\pi^5 = 1836.118 $, which is remarkably close to the actual value[1]. This work hinted at his interest in bridging mathematics and physics.

...

Before his time at Princeton, Armand Wyler was in a stable and productive mental state, marked by academic success and innovative research. However, his experience at the Institute for Advanced Study significantly deteriorated his mental health. The hostile and isolating environment, combined with intense scrutiny and lack of recognition, led to a nervous breakdown upon his return to Switzerland. This tragic outcome highlights the importance of a supportive and inclusive academic environment for researchers, especially those working on groundbreaking and unconventional ideas.

Armand Wyler is no longer living. According to the information gathered, Wyler passed away in 1971. This is confirmed by multiple sources, including a blog post that discusses his work and mentions his tragic destiny, stating explicitly "Armand Wyler -1971" and detailing his life and contributions up until his death[1].

Citations:

[1] https://physicalgeometry.wordpress.com/2016/08/30/armand-wyler/

[2] https://www.e-periodica.ch/cntmng?pid=swo-001%3A1940%3A0%3A%3A1080

[3] https://academic.oup.com/book/25794/chapter-abstract/193393218?redirectedFrom=fulltext

[4] https://www.scirp.org/journal/paperinformation?paperid=31409

[5] https://www.math.columbia.edu/~woit/wordpress/?p=272

[6] https://en.geneanet.org/fonds/bibliotheque/?country=CHE&go=1&nom=WYLER&page=1&size=50

[7] https://cosmosmagazine.com/science/mathematics/the-number-that-fascinates-physicists-above-all-others/

[8] https://www.physicsforums.com/threads/the-7-strangest-coincidences-in-the-laws-of-nature-s-hossenfelder.1062281/

In 2007, a journalist from Zurich approached me for material on Wyler. The last message I received was that Wyler had been seen on the street. Thus we have a real mystery.

My colleague at CNRS in Marseille and I have worked on similar issues, citing Wyler's work [2,3]. Years later, Laura and I visited my colleague in Marseille and stayed in Cassis, where we were assigned room number 137. Jung would have laughed at the coincidence.

Cassis

References

1. Astrophysics, Clocks and Fundamental Constants, S. G. Karshenboim and E. Peik (Eds), Lecture Notes in Physics 648, Springer Heidelberg – New York 2004
2. Born's Reciprocity on a Conformal Domain, A. Jadczyk, in "Spinors, Twistors, Clifford Algebras and Quantum Deformations”, Z. Oziewicz, B. Jancewicz, and A. Borowiec (Eds), Kluwer Academic, Dordrecht, 1993
3. Conformal Theories, Curved Phase Spaces, Relativistic Wavelets and the Geometry of Complex Domains", R. Coquereaux, A. Jadczyk, Rev. Math. Phys. 2, (1990), p. 1-44
4. Wyler, A., On the Conformal Groups in the Theory of Relativity and their Unitary Representations, Arch. Rat. Mech. and Anal., 31:35-50, (1968)
5. Wyler, A., L'espace symetrique du groupe des equations de Maxwell' C. R. Acad. Sc. Paris, 269:743-745 (1969)
6. Wyler, A., 'Les groupes des potentiels de Coulomb et de Yukawa', C. R. Acad. Sc. Paris, 271:186-188

P.S.1. The following excerpt from the freely available and eye opening book "AGAINST THE TIDE  A Critical Review by Scientists of  How Physics and Astronomy Get Done", Martín López Corredoira &  Carlos Castro Perelman (Eds.), 2008.

In the chapter  "Is Ethics in Science an Oxymoron?", by Castro Perelman, we find an additional take on the mystery:

"A particular example of the detrimental psychological effects of the “silence treatment” on a scientist is the story about Armand Wyler's sabbatical leave from the University of Zurich to the Institute for Advanced Study at Princeton University in the early 1970's. He was invited to Princeton by F. Dyson based on his interest on Wyler’s work in bounded complex homogeneous domains and his geometrical derivation of the fine structure constant (1/137) involving the Electro-Magnetic interaction, and whose value is crucial for the emergence of life in our Universe. According to a personal communication with Frank Tony Smith (another blacklistee by the Cornell arXiv.org e-archives) the atmosphere under which Wyler had to live during his sabbatical leave at Princeton was filled with such hostile silence that Wyler felt utterly invisible. His “silence treatment” was so detrimental to Wyler’s mental health that when he returned back to Zurich he basically experienced a nervous breakdown. Even worse, it seems that F. Dyson himself might have felt this hostile silence treatment towards Wyler to the point that he gave R. Gilmore (a Group theory expert) the only copy of Wyler’s work during his Princeton stay. Wyler gave a copy of his recent work at the time (in June 1972) to Dyson. It was related to Operations of Symplectic and Spinor Groups and the Complex Light Cone. At the top of the page one can see Wyler’s warm words (in French) thanking Professor Dyson. However, in the right hand margin one can read Dyson’s words to R. Gilmore saying: “This seems to be the only copy I have. Don’t tell Wyler that I gave it to you, F. D.”. Perhaps F. Dyson did not wish to hurt Wyler’s feelings and this is why he asked R. Gilmore not to tell Wyler that he had dispensed of the only copy he had (containing the warm words of gratitude from Wyler to Dyson). Frank Tony Smith posted in his website the 57 pages of Wyler’s two articles at Princeton. This was possible since R. Gilmore gave the alleged copy to Frank Tony Smith  later  on.  One  of  the  reasons  why  Frank  Tony  Smith  has  been  blacklisted  is  because  he  extended Wyler’s  derivation  of  the  fine  structure  constant  to  the  weak  and  strong  couplings  (in  addition  to  other parameters of the Standard Model). Ideas that have been ridiculed so many times by so many very powerful individuals  (David  Gross,  for  example).   

P.S.2. Even with the help of AI I was unable to find the year of birth of Armand Wyler.

P.S.3. A complementary reading on the subject can be found in the article "The number that fascinates physicists" by Paul Davis.

P.S.4 The paper by Robert Coquereaux and myself  [3], where we, in particular, referred to the works of Armand Wyler, was recently (June 27, 2024) cited by Martin Ammon, Jakob Hollweck, Tobias Hossel, and Katharina Wolfl in "Conformal Blocks in Two and Four Dimensions from Oscillator Representations".