Numbers, furthermore as archetypal structural constants of the collective unconscious, possess a dynamic, active aspect which is especially important to keep in mind. It is not what we can do with numbers but what they do to our consciousness that is essential.
The fine-structure constant is ubiquitous throughout physics. I’ve already noted its connection to the electromagnetic interaction. In atomic physics, the binding energy, fine-structure splitting, and Lamb shift are all proportional to powers of α. In condensed matter physics, α characterizes Josephson junction oscillations and quantum Hall resistance steps. In addition, α is an important component of our system of fundamental constants. [Physics Today]
Was Giza the mirror of the sky? In addition, what was the number 137 purpose? The number 137 has a very amazing meaning and it can range from modern Science to Kabbalah, from Archetypes numerology to Eastern philosophy, from smaller particles to the law of Universal Balance. ... Did the builders want to convey their scientific knowledge through the Pyramids proportions? ... Was their function connected to the number 137?
… there are no arbitrary constants ... nature is so constituted that it is possible logically to lay down such strongly determined laws that within these laws only rationally determined constants occur (not constants, therefore, whose numerical value could be changed without destroying the theory).
Take this neat little equation here. It tells me all the ways an electron can make itself comfortable in or around an atom. That's the logic of it. The poetry of it is that the equation tells me how shiny gold is, how come rocks are hard, what makes grass green, and why you can't see the wind. And a million other things besides, about the way nature works.
You too can make the golden cut, relating the two poles of your being in perfect golden proportion, thus enabling the lower to resonate in tune with the higher, and the inner with the outer. In doing so, you will bring yourself to a point of total integration of all the separate parts of your being, and at the same time, you will bring yourself into resonance with the entire universe....Nonetheless the universe is divided on exactly these principles as proven by literally thousands of points of circumstantial evidence, including the size, orbital distances, orbital frequencies and other characteristics of planets in our solar system, many characteristics of the sub-atomic dimension such as the fine structure constant, the forms of many plants and the golden mean proportions of the human body, to mention just a few well known examples. However the circumstantial evidence is not that on which we rely, for we have the proof in front of us in the pure mathematical principles of the golden mean.
As I regard physics and psychology as complementary types of examination, I am certain that there is an equally valid way that must lead the psychologist 'from behind' (namely, through investigating the archetypes) into the world of physics. As an example of background physics, I shall discuss a motif that occurs regularly in my dreams - namely, fine structure, in particular doublet structure of spectral lines and the separation of a chemical element into two isotopes.
There are considerable mysteries surrounding the strange values that Nature's actual particles have for their mass and charge. For example, there is the unexplained 'fine structure constant' ... governing the strength of electromagnetic interactions, ....
Today alpha equals 1/137.0359 or so. Regardless, its value makes the periodic table possible. It allows atoms to exist and also allows them to react with sufficient vigor to form compounds, since electrons neither roam too freely from their nuclei nor cling too closely. This just-right balance has led many scientists to conclude that the universe couldn’t have hit upon its fine structure constant by accident.
While twentieth-century physicists were not able to identify any convincing mathematical constants underlying the fine structure, partly because such thinking has normally not been encouraged, a revolutionary suggestion was recently made by the Czech physicist Raji Heyrovska, who deduced that the fine structure constant, ...really is defined by the [golden] ratio ....
Fine Structure Constant: Fundamental numerical constant of atomic physics and quantum electrodynamics, defined as the square of the charge of the electron divided by the product of Planck's constant and the speed of light.
Since only a narrow range of the allowed values for, say, the fine structure constant will permit observers to exist in the Universe, we must find ourselves in the narrow range of possibilities which permit them, no matter how improbable they are. We must ask for the conditional probability of observing constants to take particular ranges, given that other features of the Universe, like its age, satisfy necessary conditions for life.
The strength of the familiar electromagnetic force between two electrons, for example, is expressed in physics in terms of a constant known as the fine structure constant. The value of this constant, almost exactly 1/137, has puzzled many generations of physicists. A joke made about the famous English physicist Paul Dirac (1902-1984), one of the founders of quantum mechanics, says that upon arrival to heaven he was allowed to ask God one question. His question was: "Why 1/137?
Here the attention of the research workers is primarily directed to the problem of reconciling the claims of the special relativity theory with those of the quantum theory. The extraordinary advances made in this field by Dirac ... leave open the question whether it will be possible to satisfy the claims of the two theories without at the same time determining the Sommerfeld fine-structure constant.
There is only one universal language, which is the language of numbers and proportions that are so striking and stunningly built into the Great Pyramid and to which our current science has no appropriate response. We can no longer ignore that this ancient civilization was aware of our units used in modern mathematics and physics and were even aware of our metric system. Our metric system originating in the eighteenth century, designed and implemented by a committee of mathematicians and physicists commissioned by the French revolutionary government.
God is a pure mathematician!' declared British astronomer Sir James Jeans. The physical Universe does seem to be organised around elegant mathematical relationships. And one number above all others has exercised an enduring fascination for physicists: 137.0359991.... It is known as the fine-structure constant and is denoted by the Greek letter alpha (α).
We have one real candidate for changing the rules; this is string theory. In string theory the one-dimensional trajectory of a particle in spacetime is replaced by a two-dimensional orbit of a string. Such strings can be of any size, but under ordinary circumstances they are quite tiny, ... a value determined by comparing the predictions of the theory for Newton's constant and the fine structure constant to experimental values.
The significance of [the fine-structure constant] goes far beyond atomic physics, however. It is the smallness of 1/137 compared to unity that enables us to treat the coupling between the electromagnetic field and a charged particle such as an electron as a small perturbation, a fact of great computational importance. [Forces of Nature]
The theoretical determination of the fine structure constant is certainly the most important of the unsolved problems of modern physics. We believe that any regression to the ideas of classical physics (as, for instance, to the use of the classical field concept)cannot bring us nearer to this goal. To reach it, we shall, presumably, have to pay with further revolutionary changes of the fundamental concepts of physics with a still farther digression from the concepts of the classical theories.
The unsolved problems of the physical world now seem even more formidable than those solved in the twentieth century. Though in application it works splendidly, we do not even understand the physical meaning of quantum mechanics, much less how it might be united with general relativity.We don't know why the dimensionless constants (ratios of masses of elementary particles, ratios of strength of gravitational to electric forces, fine structure constant, etc.) have the values they do, unless we appeal to the implausible anthropic principle, which seems like a regression to Aristotelian teleology.
The power of the deductive network produced in physics has been illustrated in a delightful article by Victor F. Weisskopf. He begins by taking the magnitudes of six physical constants known by measurement: the mass of the proton, the mass and electric charge of the electron, the light velocity, Newton's gravitational constant, and the quantum of action of Planck. He adds three of four fundamental laws (e.g., de Broglie's relations connecting particle momentum and particle energy with the wavelength and frequency, and the Pauli exclusion principle), and shows that one can then derive a host of different, apparently quite unconnected, facts that happen to be known to us by observation separately ....
Highly complex numbers like the Comma of Pythagoras, Pi and Phi (sometimes called the Golden Proportion), are known as irrational numbers. They lie deep in the structure of the physical universe, and were seen by the Egyptians as the principles controlling creation, the principles by which matter is precipitated from the cosmic mind.Today scientists recognize the Comma of Pythagoras, Pi and the Golden Proportion as well as the closely related Fibonacci sequence are universal constants that describe complex patterns in astronomy, music and physics. ...To the Egyptians these numbers were also the secret harmonies of the cosmos and they incorporated them as rhythms and proportions in the construction of their pyramids and temples.
The prime number 137 had continuously occupied Pauli's mind. It is an approximate value for a constant appearing in the fine structure theory of atomic spectra which in its theoretical expression ties together electromagnetism, relativity and quantum theory. Pauli saw the fine structure theory of spectra as a key in understanding the deepest contemporary problems of theoretical physics. For that reason the number 137 possessed a mysterious attraction for him.
The bridge between the electron and the other elementary particles is provided by the fine structure constant. ... An expanded form of the constant leads to equations that define the transformation of electromagnetic energy into electron mass/energy, ...
In his first philosophical lecture on modern physics that Pauli gave in November 1934 to the Zurich Philosophical Society he said that only a formulation of quantum theory would be satisfactory which expresses the relation between the value of [the fine structure constant] and charge conservation in the same complementary was as that between the space-time description and energy-momentum conservation.
In the context of physics, 137 is equal to the integer part of the inverse of the fine structure constant ... The fine structure constant α is the key to the physicist’s quest for a Grand Unified Theory ... The number 137 has intrigued numerous prominent theoretical physicists ... All told, we believe that it is much easier, and more motivating, to remember a number that has deep significance in numerous disciplines, ... with the following terse ode to 137:Bethe was mischievous with 137Bohr was intrigued by 137Born was mystified by 137Fermi was frisky with 137Feynman was mesmerized by 137Heisenberg was fascinated by 137Lederman was enchanted by 137Pauli was consumed by 137Turing was matched by 137
Quite obviously, a theoretical determination of the numerical value of α would signify great progress in our understanding of fundamental interactions. Many physicists have tried to find it, but without significant success to this day. Richard Feynman, the theory wizard of Caltech in Pasadena, once suggested that every one of his theory colleagues should write on the blackboard in his office: 137 -- how shamefully little we understand!
We can measure the fine structure constant with very great precision, but so far none of our theories has provided an explanation of its measured value. One of the aims of superstring theory is to predict this quantity precisely. Any theory that could do that would be taken very seriously indeed as a potential 'Theory of Everything'.
We present a series of hypotheses and speculations, leading inescapably to the conclusion that SU(5) is the gauge group of the world — that all elementary particle forces (strong, weak, and electromagnetic) are different manifestations of the same fundamental interaction involving a single coupling strength, the fine-structure constant. Our hypotheses may be wrong and our speculations idle, but the uniqueness and simplicity of our scheme are reasons enough that it be taken seriously.
True, the Standard Model does explain a very great deal. Nevertheless it is not yet a proper theory, principally because it does not satisfy the physicists naive faith in elegance and simplicity. It involves some 17 allegedly fundamental particles and the same number of arbitrary and tunable parameters, such as the fine-structure constants, the muon-electron mass ratio and the various mysterious mixing angles.
To calculate 'the' fine structure constant, 1/137, we would need a realistic model of just about everything, and this we do not have. In this talk I want to return to the old question of what it is that determines gauge couplings in general, and try to prepare the ground for a future realistic calculation.
In short, the idea dawns that the one universal principle which possibly ... between force and structure, the embodiment of the Principle of Least Action and the (unknown) force, which in mathematics is known as the attractor which pulls ... in the direction of the most optimal and relatively stable self-organized criticality, could very well be the Golden Ratio dynamic. the universal principle which as the balance between finiteness and infinity, stability and flexibility underlies self-similar fractal forms emerging at the 'edge of chaos' indeed seems to be the Golden Ratio Spiral.
Dirac's equation not only accounted for the spin of the electron and its observed magnetic moment, but also correctly explained the fine structure of the hydrogen atom. If the derivation of the Sommerfeld-like formula for the spectrum of the hydrogen atom was one of the striking successes of the Dirac equation, some of its other features were very troublesome.
QED [quantum electrodynamics] reduces ... "all of chemistry and most of physics," to one basic interaction, the fundamental coupling of a photon to electric charge. The strength of this coupling remains, however, as a pure number, the so-called fine-structure constant, which is a parameter of QED that QED itself is powerless to predict.
I introduce the subject of fine structure with a mini-calendar of events. ...Winter 1914-15. Sommerfeld computes relativistic orbits for hydrogen-like atoms. Pashcen, aware of these studies, carefully investigates fine structures, ....January 6, 1916. Sommerfeld announces his fine structure formula, citing results to be published by Paschen in support of his answer.February 1916. Einstein to Sommerfeld: "A revelation!"March 1916. Bohr to Sommerfeld: "I do not believe ever to have read anything with more joy than your beautiful work."September 1916. Paschen publishes his work, acknowledging Sommerfeld's "indefatigable efforts.
But some numbers, called dimensionless numbers, have the same numerical value no matter what units of measurement are chosen. Probably the most famous of these is the "fine-structure constant," .... Physicists love this number not just because it is dimensionless, but also because it is a combination of three fundamental constants of nature.
Following the path of earlier unificationists, one of Eddington's aims was to reduce the contingencies in the description of nature, for example, by explaining the fundamental constants of physics rather than accepting them as merely experimental data. One of these constants was the fine-structure constant ..., which entered prominently in Dirac's theory and was known to be about 1/137.
The bridge between the electron and the other elementary particles is provided by the fine structure constant, a ~ 1/137, as manifested in the factor-of-137 spacings between the classical electron radius, electron Compton radius, and Bohr orbit radius. ... An a-quantized mass-generation grid extends accurately from the electron all the way to the top quark t, and leads to a corresponding a-quantized particle lifetime grid.
As Sommerfeld said in his famous text "Spectral Lines and Atomic Constitution," on which a generation of physicists learned the subject, "In the fine structure constant e is the representative of the electron theory, h the appropriate representative of the quantum theory, c comes from relativity and characterizes it in contrast to classical theory.
Arnold Sommerfeld generalized Bohr's model to include elliptical orbits in three dimensions. He treated the problem relativistically (using Einstein's formula for the increase of mass with velocity), ... According to historian Max Jammer, this success of Sommerfeld's fine-structure formula "served also as an indirect confirmation of Einstein's relativistic formula for the velocity dependence of inertia mass.
Alpha sets the scale of nature -- the size of atoms and all things made of them, the intensity and colors of light, the strength of magnetism, and the metabolic rate of life itself. It controls everything that we see. ... In 137, apparently, science had found Nature's PIN Code.
The measured magnetic moment, together with fine structure constant determined by a different method, is the most stringent test of QED and the Standard Model of particle physics. The measured magnetic moment and QED theory together yield the most precise measured value of the fine structure constant.
[The fine structure constant] ... defines how firmly atomic nuclei bind together and how all the atoms on Earth were made. Its value controls the power from the Sun and, more sensitively, how stars transmute hydrogen into all the atoms of the periodic table.
At his "World of Physics" Web site, Eric W. Weisstein notes that the fine structure constant continues to fascinate numerologists, who have claimed that connections exist between alpha, the Cheops pyramid, and Stonehenge!
If the deep logic of what determines the value of the fine-structure constant also played a significant role in our understanding of all the physical processes in which the fine-structure constant enters, then we would be stymied. Fortunately, we do not need to know everything before we can know something.
Realizing its fundamental importance in understanding spectral lines, in atomic physics and in the theory of how light and electrons interact, quantum electrodynamics, Pauli and Heisenberg were determined to derive it from quantum theory rather than introducing it from the start. They believed that if they could find a version of quantum electrodynamics capable of producing the fine structure constant, it would not contain the infinities that marred their theories.
Let us begin with the fine-structure constant. ... The fine-structure constant is really the ratio of two natural units or atoms of action. ... We obtain action when we multiply energy by time. ... We are challenged to find a unified theory of electric particles and radiation in which the electrostatic type of action and the quantum type of action are traced to their source.
One hundred thirty-seven is the inverse of something called the fine-structure constant. ...The most remarkable thing about this remarkable number is that it is dimension-free. ...Werner Heisenberg once proclaimed that all the quandaries of quantum mechanics would shrivel up when 137 was finally explained.
Through Jung [Pauli] became very interested in various kinds of mysticism, including Jewish mysticism. This led Pauli to develop a friendship with Gershom Scholem, the world's greatest authority in that field and in the Cabala, .... On one occasion Scholem asked me to tell him about unsolved problems in modern physics. .... When I mentioned this number --137-- to Scholem, .... He told me that in Hebrew .... The number corresponding to the word 'cabala' happens to be 137.
All integral laws of spectral lines and of atomic theory spring originally from the quantum theory. It is the mysterious organon on which Nature plays her music of the spectra, and according to the rhythm of which she regulates the structure of the atoms and nuclei.
Physicists love this number not just because it is dimensionless, but also because it is a combination of three fundamental constants of nature. Why do these constants come together to make the particular number 1/137.036 and not some other number?
For [Wolfgang] Pauli the central problem of electrodynamics was the field concept and the existence of an elementary charge which is expressible by the fine-structure constant ... 1/137. This fundamental pure number had greatly fascinated Pauli, .... For Pauli the explanation of the number 137 was the test of a successful field theory, a test which no theory has passed up to now.
It is shown that the golden ratio plays a prominent role in the dimensions of all objects which exhibit five-fold symmetry. It is also showed that among the irrational numbers, the golden ratio is the most irrational and, as a result, has unique applications in number theory, search algorithms, the minimization of functions, network theory, the atomic structure of certain materials and the growth of biological organisms.
The focus of history and philosophy of science scholar Arthur Miller’s (2010) "137: Jung and Pauli and the Pursuit of Scientific Obsession" is Jung and Pauli’smutual effort to discover the cosmic number or fine structure constant, which is a fundamental physical constant dealing with electromagnetism, or, from a different perspective, could be considered the philosopher’s stone of the mathematical universe.This was indeed one of Pauli and Jung’s collaborative passions, but it was not the only concentration of their relationship. Quantum physics could be seen as the natural progression from ancient alchemy, through chemistry, culminating in the abstract world of subatomic particles, wave functions, and mathematics. [Ancient Egypt and Modern Psychotherapy]