A Sleepless Quest
After posting "The Secret of Room 137: Unlocking the Fine Structure Constant" just a week ago, the puzzle I uncovered has haunted me relentlessly. My nights have been filled with restless thoughts, consumed by this enigmatic question. Driven by an insatiable curiosity, I’ve started digging into the mystery, and the further I go, the deeper the hole becomes, branching off in unexpected directions. I glimpse glimmers of what could be diamonds—perhaps genuine, perhaps not. But the real answers remain buried, and the excavation is far from over.
Back to 1971: A Fateful Invitation
Let’s turn the clock back to 1971, when Armand Wyler, the enigmatic figure at the heart of "The Secret of Room 137," found himself thrust into the limelight. That year, Wyler was invited to the prestigious Institute for Advanced Study (IAS) at Princeton, an invitation that would mark a pivotal moment in his life and career. There is still an official record documenting his nearly year-long stay at IAS, evidence of a chapter in his life shrouded in both honor and controversy.
Before Wyler set foot in Princeton, a significant event unfolded. In August 1971, Gloria B. Lubkin, then a senior editor for Physics Today, penned an article that would cast a spotlight on Wyler's work. Her piece, featured in the "search & discovery" column, bore the intriguing title "A Mathematician's Version of the Fine-Structure Constant." [1]
The Article That Sparked a Debate
Lubkin’s article introduced the world to Wyler’s groundbreaking papers, which proposed a mathematical formula predicting the fine-structure constant—a fundamental physical constant—with astonishing precision. Wyler’s formula was nothing short of miraculous: it predicted a value for the fine-structure constant within a half part per million of the experimental figure, using only simple rational powers of integers and Pi.
Lubkin noted the widespread discussions his work had sparked among theorists, many of whom admitted they struggled to grasp the theory’s complexities. Despite the confusion, one thing was clear: Wyler's results were astonishing, and his upcoming year at Princeton only added to the anticipation.
Wyler’s Radical Approach
Wyler's work [2], [3], revolved around the mysterious O(5,2) group—a concept that needs a bit of unpacking. In the language of mathematicians and physicists, a "group" like the Lorentz or Conformal group refers not to a corporation but to a set of symmetries in a specific space.
Note: The largest discrete finite sporadic simple group in mathematics carries the name "Monster Group" and has
elements.
In corporative world there is also a monster group "The Alphabet Group" - the parent company of Google.
On 26 April 2024, Alphabet surpassed a market valuation of $2 trillion for the first time.
In Wyler's case, O(5,2) represented the symmetries of a seven-dimensional space, with five space-like and two time-like dimensions.
The group itself, one of the orthogonal symmetry groups, was defined by 21 parameters. Wyler’s genius was in extending the 15-parameter conformal group O(4,2) into something far more complex, hinting at possibilities yet to be fully explored. Lubkin astutely noted that many physicists had long suspected that the conformal group would play a more significant role in the future of physics—a prediction that has indeed come to pass.
Skeptics and Counterarguments
But as with any groundbreaking theory, Wyler’s work attracted its share of critics. In the November 1971 issue of Physics Today [4], the skeptics made their voices heard.
Ralph Roskies of Stanford pointed out that in just 30 seconds, using the 360-91 computer,
he had derived five alternative formulas similar to Wyler’s, each yielding values close to the experimental fine-structure constant.
Asher Peres from the Israel Institute of Technology weighed in with a pointed letter to the editor, titled "A New Pastime: Calculating Alpha to One Part in a Million." He argued that Wyler’s result could merely be a numerical coincidence, akin to how the irrational number Pi is eerily close to the simple formula: the cube root of 31. Another critic, D. D. Reilly Jr., offered yet another simple formula:
The Complexity of Alpha
One crucial point to understand is that the fine-structure constant, denoted as alpha (α), is not a fixed value. It is a "running constant," meaning its value changes depending on the energy at which it is measured. For instance, at very high energy levels, the value of approaches 128, while at low energies, it hovers around 137. This nuance suggests that Wyler’s theory—and similar mathematical approaches—might apply specifically to the low-energy limit of alpha.
The Ongoing Adventure
As I continue my exploration into this mathematical labyrinth, I find myself drawn deeper into the abstract realms that Wyler once navigated. The adventure is far from over, and with each new discovery, the puzzle of the fine-structure constant becomes ever more intriguing. But those revelations will have to wait for future posts.
For now, the mystery deepens, and the story of Armand Wyler’s forgotten formula is far from complete.
P.S. The article by Gloria Lubkin ends with a photo of Armand Wyler smiling. That was before Wyler visited IAS. From "The Secret of Room 137: Unlocking the Fine Structure Constant" one can easily imagine Wyler's face after this adventure:
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References
[1] Gloria B. Lubkin, A mathematician's version of the fine structure constant, Physics Today, August 1971; doi: 10.1063/1.3022875
[2] Armand Wyler, Theorie de la Relativité - L’espace symétrique du groupe des équations de Maxwell, Acad. Sci. Paris, Comptes Rendus 269A, 743 (1969).
[3] Armand Wyler, Les groupes des potentiels de Coulomb et de Yukawa, Comptes Rendus de l'Académie des Sciences, Sér. A, Vol. 271 (1971), pp. 186-188.
[4] Letters, Physics Today, November 1971 doi 10.1063/1.3022455
P.S. 12-08-24 16:17 Scientists Discovered Something Kinda Alarming: The Universe Shouldn't Actually Exist Story by Jackie Appel
"For instance, at very high energy levels, the value of 1/α approaches 138, while at low energies, it hovers around 137."
ReplyDeleteIt seems the trend is the opposite: with the increase of available interaction energy the alpha also increases, i.e. in perturbation theory, at the scale of Z boson mass (~90 GeV), the alpha value measured is cca 1/127. FWIW.
https://en.m.wikipedia.org/wiki/Coupling_constant
Thank you for sharing your 'digging notes', they're very intriguing.
Kind regards,
Saša
Thanks. I made a very bad typo writing 138 instead of 128. Corrected now.
DeleteTony uses the volumes below to get Wyler's equation (and the gravity, weak and color force analogs). The only other thing Tony uses is the idea of gravity and color forces as 4-dim, weak force as 2-dim and EM as 1-dim. This produces the raised to the 1/4 part of Wyler's equation. It's basically an EM to geometric gravity force strength ratio so the 4 is from gravity and the 1 for EM just raises to the 1 power so it keeps something the same.
ReplyDeleteThe geometric force strength for gravity is one since it is the ratio with itself and an effective mass factor (the Planck mass) makes it a small valued force. The weak force has a real effective mass since its bosons have mass. Tony does have the formula at a characteristic energy which for EM he has at 4 KeV. A lot of the EM values are effectively one so the volumes used except for one from EM come from gravity.
From Tony's site https://www.valdostamuseum.com/hamsmith/Sets2Quarks8.html
The geometric volumes of
the target Internal Symmetry Space MISforce,
the link volume Qforce,
and the bounded complex domains Dforce of which
the link volume is the Shilov boundary,
mostly taken from Hua, are:
Force M Vol(M) Q
gravity S4 8 pi^2 / 3 RP1xS4
color CP2 8 pi^2 / 3 S5
weak S2xS2 2x4 pi RP1xS2
e-mag T4 4x2 pi -
Force Vol(Q) D Vol(D)
gravity 8 pi^3 / 3 IV5 pi^5 / 2^4 5!
color 4 pi^3 B^6(ball) pi^3 / 6
weak 4 pi^2 IV3 & pi^3 / 24
e-mag - - -