The divisors are 1, 137
The fine-structure constant is 1/137.
In physics, the fine-structure constant, also known as Sommerfeld's constant, commonly denoted α (the Greek letter alpha), is a dimensionless physical constant characterizing the electromagnetic strength between charged particles. It is related to the elementary charge e, which characterizes the strength of the coupling of a charged particle with the electromagnetic field.
Being a dimensionless quantity, it has the same numerical value of about 1/137 in ALL systems of units. (Keep the word "implications" in the back of your mind as you continue...so your subconscious starts metaphorically saving to file now)
It is a dimensionless constant which seems not to be directly related to any mathematical constant...and due to this face, has long fascinated physicists. What is a dimensionless constant? Well...this is lazy and not quite on point for this reference, but good enough for government work - think of the speed of light, or gravity - these are dimensionless constants for example.
The fine-structure constant intrigued physicist Wolfgang Pauli so much that he collaborated with psychoanalyst Carl Jung in a quest to understand its significance. (I find this quite logical, given Jung's obsession with synchronicities, definitely something I'll be looking into)
Similarly, Max Born (physicist who assisted in the original development of Quantum Mechanics) asserted that 1/137 is a law of nature.
“If alpha [the fine-structure constant] were bigger than it really is, we should not be able to distinguish matter from ether [the vacuum, nothingness], and our task to disentangle the natural laws would be hopelessly difficult. The fact however that alpha 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.”
— Max Born
Richard Feynman, one of the originators and early developers of the theory of quantum electrodynamics (QED), referred to the fine-structure constant in these terms:
Attempts to find a mathematical basis for this dimensionless constant have continued up to the present time. However, no numeralogical explanation has ever been accepted by the community.
In the early 21st century, multiple physicists, including Stephen Hawking in his book A Brief History of Time, began exploring the idea of a multiverse, and the fine-structure constant was one of several universal constants that suggested the idea of a fine-tuned universe.
There is a most profound and beautiful question associated with the observed coupling constant, e – the amplitude for a real electron to emit or absorb a real photon. It is a simple number that has been experimentally determined to be close to 0.08542455. (My physicist friends won't recognize this number, because they like to remember it as the inverse of its square: about 137.03597 with about an uncertainty of about 2 in the last decimal place. 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 pi 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!
— Richard P. Feynman (1985). QED: The Strange Theory of Light and Matter. Princeton University Press.
Attempts to find a mathematical basis for this dimensionless constant have continued up to the present time. However, no numeralogical explanation has ever been accepted by the community.
In the early 21st century, multiple physicists, including Stephen Hawking in his book A Brief History of Time, began exploring the idea of a multiverse, and the fine-structure constant was one of several universal constants that suggested the idea of a fine-tuned universe.
The mystery about α is actually a double mystery. The first mystery – the origin of its numerical value α ≈ 1/137 has been recognized and discussed for decades. The second mystery – the range of its domain – is generally unrecognized.
— Malcolm H. Mac Gregor, M.H. MacGregor (2007)
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