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
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
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...
To add a "funny" little nugget to the quest and to mysteriousness of alpha and its beautiful interplay with prime numbers.
ReplyDelete137 is 33rd in order on the list of prime numbers. 33 as 3×11 is a product of 2nd and 5th prime, which brings us to mysterious Wyler's (symmetry) group O(5,2) representing 7 dimensional hyperspace. 7 is 4th prime, while 5 (as spatial) and 2 (as temporal) are 3rd and 1st prime, which funnily brings in association to our (3,1) dimensional perceived world.
https://en.wikipedia.org/wiki/List_of_prime_numbers
Kind regards,
Saša
Inspired by the recent series of the posts here, and in honor to Armand Wyler and to our Mother Earth, here's the Octaves of Primes.
ReplyDeleten : 1 2 3 4 5 6 7 ... (709 numbers) ... 709 | (709th prime : 5381)
p(n) : 2 3 5 7 11 13 17 19 23 29 31 ... (127 primes) ... 709 | 5381
p2(n)=p(p(n)) : 3 5 11 17 31 ... (31 super-primes) ... 709 | ... 5381
p3(n) : 5 11 31 ... (11 super-super-primes) ... 709 | ... 5381
p4(n) : 11 31 127 277 709 | ... 5381
p5(n) : 31 127 709 | ... 5381
p6(n) : 127 709 | 5381
p7(n) : 709 | 5381
p8(n) : 5381 ...
p7(n) : 709 --- 5381 ...
p6(n) : 127 709 --- 5381 ...
p5(n) : 31 127 709 --- three elements followed by 5381 ...
p4(n) : 11 31 127 277 709 --- five elements before 5381 ...
p3(n) : 5 11 31 59 127 179 277 331 431 599 709 --- followed by 5381 ...
p2(n) : 3 5 11 17 31 ... 709 --- 31 element and 5381 ...
p(n) : 3 5 7 11 13 17 ... 709 --- 127 primes and keeping an eye on 5381 ...
n : 1 2 3 4 5 6 7 8 9 10 11 ... 709 ... 5381 ... - natural numbers
Kind regards,
Saša
Beauty of the patterns that like music emerged from the Octaves post above, called for a dance. A mathematical sort of a dance. And here it is.
ReplyDeleteWith Wolfram's Mathematica's help, a function returning multiple series of sort of a 'primed' primes, looked like this:
Priming[n_, k_] := NestList[Prime, Prime[n], k-1];
indicating iterative, repeated applications of Mathematica's function Prime[n], which returns prime number at n-th position.
In practice, for example Priming[1, 11], first series below, means that we took the first prime, p(1) which is 2, and then looked at the 2nd place within the infinite set of primes. There's 3, our second element of this series, so we look at 3rd place and there's 5, our third element. Then we check 5th position and there's 11, forth element. And so on we go until we collect 11 elements, the k value.
Here's the magic of first eleven primes, giving birth to six different/distinct series.
----------------------------------------------------------------------------
Priming[1, 11] = {2, 3, 5, 11, 31, 127, 709, 5381, 52711, 648391, 9737333}
Priming[2, 11] = {3, 5, 11, 31, 127, 709, 5381, 52711, 648391, 9737333, 174440041}
Priming[3, 11] = {5, 11, 31, 127, 709, 5381, 52711, 648391, 9737333, 174440041, 3657500101}
Priming[4, 7] = {7, 17, 59, 277, 1787, 15299, 167449}
Priming[5, 7] = {11, 31, 127, 709, 5381, 52711, 648391}
Priming[6, 7] = {13, 41, 179, 1063, 8527, 87803, 1128889}
Priming[7, 7] = {17, 59, 277, 1787, 15299, 167449, 2269733}
Priming[8, 7] = {19, 67, 331, 2221, 19577, 219613, 3042161}
Priming[9, 7] = {23, 83, 431, 3001, 27457, 318211, 4535189}
Priming[10, 7] = {29, 109, 599, 4397, 42043, 506683, 7474967}
Priming[11, 7] = {31, 127, 709, 5381, 52711, 648391, 9737333}
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We can see that if we take 1st, 2nd, 3rd, 5th and 11th prime as a starting point in creation of these Priming[n,k] series, we end up with the same series. And it's again the same series if we take 31st or 127th or 709th or 5381st prime as a1. In short :
Priming[1,n] ~ Priming[2,n] ~ Priming[3,n] ~ Priming[5,n] ~ Priming[11,n] ... ~ ... ;
where ~ stands for lower order series comprising higher order one. The same goes for Priming[4,n] ~ Priming[7,n] ~ Priming[17,n] and others alike.
Mysteriousness surrounding this 'primed' series deepens as elements of this first Priming[1,n] series are the exact same primes we encountered in the Octaves post above. Moreso, those are the very first elements in the sets above. This 'primed' series resembles something more fundamental that just being a prime or super-prime or super-super-prime. In fact, these are the primes that would still be present within the infinite set of primes, after repetitive application of returning primes out of them.
Meaning, the p9(n) as prolongation of priming operation in the Octaves post, would start with 9th element of Priming[1,n]; p(10) with 10th and p(11) with 11th element, 9 737 333, a number being 11 times actually primed.
Another mystical thing revolves around number 4. As 4th place among the primes is given to 7, series Priming[4,n] opens the floor to Priming[7,n], so to speak. And as far as Priming[22,n] went, by eye inspection of first 7 members of the series up to 22nd order, those two were the only ones basically the same.
The mysteriousness around number 4 grows as this Priming[4,n] series at its 4th place holds 277, the 'lonely' prime not being 'primed', that stands at the 4th place in the five members large p4(n) set from the Octaves : (11 31 127 277 709).
And an intrigue at the end of the dance.
What to think about the fact that first 11 primes exactly 5 times created 'primed' series, and exactly 2 times the lovely 4-7 one, which brings to association Wyler's symmetry group, mysterious O(5,2)?
Kind regards,
Saša
Well, looking at the first 11 Priming[n,k] series on wider view, another relation popped up : columns of such a matrix are elements of the actual priming operation, p1(n) p2(n) ... p7(n) an so on from the Octaves post.
ReplyDeleteMeaning, for example, first 5 elements of 4th column of Priming[n,k] matrix are the p4(n) set in Octaves post : (11 31 127 709).
In other words, transposed matrix of Priming[n,k] gives elements to the sets of primes that are k times actually primed. Interesting.
Is there something like p_n series, n times primed primes, like n times super-super...super-primes series, like p4(n) or p(2) series, 4 times and 2 times primed numbers, as described in the Octaves post?
Kind regards,
Saša
Another mysterious thing that adds to mysteriousness of number 4, is that 'lonely' prime 277 from lovely p4(n) set in Octaves post, stands also on the main diagonal of the Priming[n,k] matrix.
ReplyDeleteMaybe it's feeling lonely in p4(n), but here stands in the company of some real prime giants of the main diagonal : (2 5 31 277 5381 ...).
So, what do you think of this little mathematical dance with the primes?
Kind regards,
Saša
I think the main question is: "What these beautiful prime numbers DO?"
DeleteWell, first of all apologies for usurping your blog for this.
DeleteRegarding the question : I don't know, yet. Need to think about the application. Would like to learn, that's for sure.
Just dancing with them like that in posts above, brought peace in the heart, and opened the mind, sort of, made it lighter, sort of illumined it.
Well, in a way, it seems they bring light where it's needed, not wanted, but really needed.
On the other hand, impact on the state of awareness and consciousness due to learning and knowing this Priming dance is rather notable, like noted about the illumined mind.
Kind regards,
Saša
"What these beautiful prime numbers DO?"
DeleteThey can bring order into chaos, balsamic healing to open wounds and bleeding scars, tranquility and relief to troubled minds. No evil kind of application comes to mind and it seems like it would be a hard work to come up with one.
But also Ibn al'Arabi's words come to mind and his warning that souls easily get enamored and entranced when being in the realms of the Names of God. Following that line, it would seem that the resulting states depend on which of the Names given person aligns herself with, i.e. on the quality of the energy of the Names that person resonates with.
Which, in a roundabout way, brings us back to the matters of the heart, because it seems that the quality of the energy person's resonating with, reflects that what's already there, in that person's heart.
So, what do these dwellings of the mystics do, you ask? One possible answer would be :
They sing to the soul the music that soul most joyfully dances to.
Kind regards,
Saša