For the gyromagnetic factor g e , both the integer value 2 resulting from the Dirac
equation and the shift of measured values from 2 have theoretical explanations: the
integer value is ultimately the expression of the duality matter/antimatter, and the
corrections listed in Eq. (24) express the interactions with the quantum vacuum. For
the electric parameter a, no such understanding is available, neither for the integer
value 137 nor for the measured shift of ∼ 0.26 ppt (Eq. 26). Feynman referred to
the constant a in these terms:
It has been a mystery ever since it was discovered more than fifty years ago […]. 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 is 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 […]. 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 Feynman, The Strange Theory of Light and Matter (Princeton UP, 1985).
Over the years, a kind of mystic has developed about the peculiar value a ≈ 137,
as illustrated in the quotation below:
The fine-structure constant holds a special place among cult numbers: [it] seduces otherwise
sedate people into seeking mystical truths and developing uncollaborated theories …. The
cult of 137 began with scientists who already had quite a reputation, including Pauli, Jung,
Heisenberg, and most notably Eddington […]. In more recent years, the tradition has spread
to the larger community of science theory hobbyists ….
Robert Munato, http://www.mrob.com/pub/num/n-b137_035.html.
However, although Eddington’s speculations about the integer 137 are disputable, this number has, even more than 2, a number of mathematical properties
that make it rather unlikely that its physical occurrences be merely due to chance. In
addition to being the 33rd prime number, it is a superadditive prime in base 10
(1 + 3 + 7 = 11 and 1 + 1 = 2). It is also a Chen prime (twinned with 139), a
Stern prime (the 4th among 8), an Euler prime, an Eisenstein prime, a Pythagorean
prime, a binary quadratic prime, and an optimal primeval prime (the 10th of the 15
primes generated with its 3 digits).
It has been shown [27] that a and 137 are related to the conspicuous numbers π
and e (related themselves through the magic relation: e
iπ = −1), and to the harmonic sum 137/60 and golden ratio Φ (defined from the equation: Φ = Φ
− 1 + 1),
through the relations (precise within ∼ 0.24 ppm, 0.15 ppm, 0.33 ppt and 0.15 ppt,
respectively):
a
2
≈ 137
2 + π
2 ; Log a ̸ Log 137 ≈ a
2
̸ a
2
− 1
À
Á
; 3 a ≈ 60 Φ
4 ; Φ
137 ̸ 60
≈ 3.
Sanchez [27] has also disclosed puzzling occurrences of a (or 137) in the mass
distributions of nucleotide bases and amino-acids in terms of the hydrogen mass
m H . For instance, every amino-acid being coded by three couples of nucleotide
bases (in pairs A-T and G-C), the average mass M C of all codons appears to be
(within <0.2%):
The Dirac Electron and Elementary Interactions …
369
equation and the shift of measured values from 2 have theoretical explanations: the
integer value is ultimately the expression of the duality matter/antimatter, and the
corrections listed in Eq. (24) express the interactions with the quantum vacuum. For
the electric parameter a, no such understanding is available, neither for the integer
value 137 nor for the measured shift of ∼ 0.26 ppt (Eq. 26). Feynman referred to
the constant a in these terms:
It has been a mystery ever since it was discovered more than fifty years ago […]. 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 is 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 […]. 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 Feynman, The Strange Theory of Light and Matter (Princeton UP, 1985).
Over the years, a kind of mystic has developed about the peculiar value a ≈ 137,
as illustrated in the quotation below:
The fine-structure constant holds a special place among cult numbers: [it] seduces otherwise
sedate people into seeking mystical truths and developing uncollaborated theories …. The
cult of 137 began with scientists who already had quite a reputation, including Pauli, Jung,
Heisenberg, and most notably Eddington […]. In more recent years, the tradition has spread
to the larger community of science theory hobbyists ….
Robert Munato, http://www.mrob.com/pub/num/n-b137_035.html.
However, although Eddington’s speculations about the integer 137 are disputable, this number has, even more than 2, a number of mathematical properties
that make it rather unlikely that its physical occurrences be merely due to chance. In
addition to being the 33rd prime number, it is a superadditive prime in base 10
(1 + 3 + 7 = 11 and 1 + 1 = 2). It is also a Chen prime (twinned with 139), a
Stern prime (the 4th among 8), an Euler prime, an Eisenstein prime, a Pythagorean
prime, a binary quadratic prime, and an optimal primeval prime (the 10th of the 15
primes generated with its 3 digits).
It has been shown [27] that a and 137 are related to the conspicuous numbers π
and e (related themselves through the magic relation: e
iπ = −1), and to the harmonic sum 137/60 and golden ratio Φ (defined from the equation: Φ = Φ
− 1 + 1),
through the relations (precise within ∼ 0.24 ppm, 0.15 ppm, 0.33 ppt and 0.15 ppt,
respectively):
a
2
≈ 137
2 + π
2 ; Log a ̸ Log 137 ≈ a
2
̸ a
2
− 1
À
Á
; 3 a ≈ 60 Φ
4 ; Φ
137 ̸ 60
≈ 3.
Sanchez [27] has also disclosed puzzling occurrences of a (or 137) in the mass
distributions of nucleotide bases and amino-acids in terms of the hydrogen mass
m H . For instance, every amino-acid being coded by three couples of nucleotide
bases (in pairs A-T and G-C), the average mass M C of all codons appears to be
(within <0.2%):
The Dirac Electron and Elementary Interactions …
369