© 2002 Donald Briglia
© 2002 The Christian Fellowship of Students of The Urantia Book
Last year Joan and I visited Santa Barbara and met the Urantia Study Group there. I happened to mention something about the mystery of the three digit number, 137 , and its relation to quantum mechanics. (Please see the editorial in this edition, “God’s Little Three-Digit Joke on Quantum Science”). Veteran Urantians should quickly note the relationship of 137 to the Urantia Papers … one being the First Source and Center, three the Trinity, and seven the limit of different associations of the Trinity. Donald Briglia, a physicist, happened to be in the Santa Barbara group. On that wonderful California evening Donald gave the group an elegant scientific explanation of “137,” far beyond my lay abilities. He kindly consented to expand upon this explanation in our Journal. Donald’s commentary follows.
Larry Mullins
Acknowledging the huge information content contained in even a single image, vision is considered to be the primary sense. Light, the visible portion of the electromagnetic spectrum [UB 42:5.10], is the ready facilitator of visual information and is produced whenever electrons change their energy relationship in an atom or molecule in the relevant energy range, i.e., the outer shells of the structure, so they are known as optical electrons.
All visible light results from electron energy dynamics, optical electrons changing their state. More energetic electromagnetic signals come from inner shell transitions, e.g., “x rays.” [UB 42:5.1]
As the facilitator of the primary and most important of the senses, light conveys to the eye or optical instrument images of very high information content through the action of photons, tiny bundles of “wavy” energy that travel faster than anything else, and whose velocity represents an upper limit to the velocity of material matter (theorized first by Einstein in his special theory of relativity). Most of what is known about the cosmos comes from observations of light and the other non-visible photons of the electromagnetic spectrum. Our earliest mathematical knowledge of the submicroscopic makeup of matter, atomic theory, was developed from observations of light, produced when electrons become dynamic.
The science that analyzes light dispersed into its spectral components and interprets these spectra is known as optical spectroscopy and this branch of physics produced not only our first mathematical knowledge of atomic structure but also led to quantum theory and most of the rest of the “new physics.” For example, when light from the simplest atom, Hydrogen, a single proton and a single electron bound together by their mutual electrical attraction, was analyzed into its spectral components no agreement with classical electromagnetic theory was found. Classical (in this case) means pre-quantum and prerelativity theoretical physics. An early quantum approach by N. Bohr produced a theory that provided some agreement and led to our earliest mathematical model of atomic structure. (Of course, there were earlier models, probably going back to the Greeks, and Rutherford had a model previously, the so-called “Rutherford nuclear model of the atom,” which was derived from alpha particle scattering by a nucleus, but since the fast and far more massive alphas are hardly affected by the electrons, there is no knowledge provided by this type of experiment about the electronic structure of atoms.) “The formation of all matter is on the order of the solar system. … Within the atom the electrons revolve about the central proton …” [UB 42:7.1]
Not accounted for by the Bohr theory are subtleties of the spectra, such as spectral components that are split into more than one signal, called fine structure. A. Sommerfeld added features to the Bohr model that took into account Einsteinian special relativity (the electron moves fast in this model) and the apparent spinning of the electron. This expanded model produced a theory that did agree with most of the observations. “The electronic axial revolutions and their orbital velocities about the atomic nucleus are both beyond the human imagination …” [UB 42:7.3]
When calculations are performed to theoretically predict the spectral features, the number 137 appears, the reciprocal of which Sommerfeld named the “fine structure constant” and denoted with the Greek letter alpha. In the technical literature, both 137 and its reciprocal are referred to as the fine structure constant (fsc).
The expression for the fsc involves the value of the charge of a single electron (electrodynamics), the velocity of light (relativity) and Planck’s constant (quantum theory), all of which have dimensional units, e.g., meters per second. Yet the fsc is dimensionless, so 137 is a pure (and prime) number.
This interesting and what some consider unexpected numerical result which includes considerations of electrical charge, relativistic motion and quantum effects appears in physics calculations from the sub-microscopic to the cosmologic which has given the number 137 almost cult status.
“Throughout the Thirties and Forties, the greatest scientists of the day tried and failed to figure out the magic number 137. The great Werner Heisenberg told his friends that the problems of quantum theory would disappear only when 137 was explained, and spent years trying to explain it; fortunately, the problems did go away despite his failure. One of Heisenberg’s friends, theorist Wolfgang Pauli, wasted endless research time trying to multiply pi by other numbers to get 137; Edward Teller, now a prominent advocate of star wars, derived alpha from gravitation; and a Japanese showed that the difference in the masses of the proton and delta particle is equal to alpha. All this shows is that there are many ways you can multiply and add a bunch of numbers to get 137 . The closest any of these people got to the answer, perhaps, was when Pauli died-in hospital room 137.” [http://www.137.com/137]
It is a subject of great interest and much has been written about its significance in science and elsewhere. For example, 137 is the number associated with the kabala, the book of Jewish mysticism, which may be merely a coincidence but that has heightened the interest in the fsc.
“The best explanation of the mystery ever given to Victor Weisskopf, another leading theorist from that time, was provided by Gershom Scholem, one of the most eminent scholars of Jewish mysticism. When Scholem met Weisskopf, he asked about the prominent unsolved problems in physics. Weisskopf said, ”Well, there’s this number, 137…“ And Scholem’s eyes lit up! He said, ”Did you know that one hundred thirty-seven is the number associated with the Cabala?"
Another example is found in considerations of the four different lengths used to characterize electrons in atoms, the classical radius of an electron, the radius of the first Bohr orbit, the electron Compton wavelength, and the Rydberg length. These quantities differ respectively by successive powers of 137 . Little wonder that there is great and ongoing interest. Some scientists in the past wanted to consider the number 137 to be a fundamental aspect of nature, and notwithstanding that the fsc is not exactly 137 (nor completely constant) they wanted to adjust the constants in its calculation so that it is exactly that.
When a free electron captures a free proton that was initially at rest at an infinite separation, the two may become bound together to form a hydrogen atom by releasing energy, the so called binding energy. When the mechanism is that of radiative recombination to the ground state, that of lowest energy, (there are other mechanisms that may also stabilize the binding, e.g., collisional deactivation with a third particle, which has a much higher probability of occurrence, except in very sparse media), a photon is emitted that carries off the recombination energy.
This is the same amount of energy that must be expended to separate the two at rest at a very large separation, called the ionization potential (energy).
“The quantity of energy taken in or given out when electronic or other positions are shifted is always a ‘quantum’ or some multiple thereof, but the vibratory or wavelike behavior of such units of energy is wholly determined by the dimensions of the material structures concerned. Such wavelike energy ripples are 860 times the diameters of the ultimatons, electrons, atoms or other units thus performing.” [UB 42:4.14]
License has been used here (it is usually stated that the nuclear proton captures the electron) to draw attention to the observation that the electron is dimensionally so much larger than the proton in models of atomic optical processes/structures though it is so much smaller in mass. The more correct way of stating the recombination is that they capture each other to form their union. Using the planetary model of this simplest of atomic systems, and calculating how fast the electron moves, the result is that the electron velocity is only slightly relativistic, less than one percent of the velocity of light, as light travels 137 times faster. Interpreting the phrase “wavelike energy ripples” to mean “wavelengths,” logical consistency results. The reason 860 is stated as a dimensionless number is it is the ratio of two lengths, a wavelength and a diameter.
The reader has perhaps anticipated that there is a connection between these two numbers. Yes, 860 is two pi times 137 , two pi being the ratio of the circumference to the radius of every circle. The details of the applicability of this 860 rule is beyond the scope of this article, but it would presumably apply to the various transitions which take place when atoms are excited by energetic processes like high temperatures or electrical excitation, thereby producing the observed optical spectra. At the time the Papers were being revealed, some physics books considered Planck’s constant to be a quantity, represented by the symbol “h”, while others considered it to be . If the latter had been referenced in the Papers, the number would have been 137 and not 860 .
“A note on calculating alpha: If you look up these constants in a textbook, and form the indicated ratio, you may or may not get the advertised number. This is because in some systems of units, one must additionally divide by and in others by a constant denoted by . This does not mean that, , depends on the system of units. Rather, it means that in different systems of units one must define the same physical constant, , in different ways.”
“Here is a rule that will give you, , using the constants in a randomly chosen physics text: find the expression for Coulomb’s law, and use this to give you the magnitude F of the force between 2 electrons separated by a distance R. The expression will have the form .”
“What is will depend on the system of units the book is using. But whatever it is, the way to extract the fine structure constant from the numbers in the book is to calculate .”
“Another tricky point to note is that many books define something they call Planck’s constant and denote it by rather than (h bar). The relation between these two is that .” [http://www.physicscentral.com/action/action-02-2c.html]
“The Number is well-known throughout the physics community as the approximate inverse of the Fine Structure constant. It even has a name alpha — which seems to be a supernatural coincidence given the context in which this number appears — John 1.1-5 — and the numerous highly significant identities associated with the Greek word ”. [http://www.biblewheel.com/GR/GR_Frame.asp?GRRef=FineStructure]
“The value of alpha can be found on the U.S. Government’s site: http://www.nist.gov/. The current value reported from NIST is: , ”
“The value of alpha is extremely well established, with an uncertainty of about — i.e. about three parts in 100 billion. It appears in Quantum Electrodynamics (aka QED) as the probability of interaction between Light and Matter. It has been the subject of intense study — many of the best physicists have felt that there must be some connection between alpha and the underlying structure of the Universe. A light hearted review of some of the more famous attempts are described at: http://www.137.com/137.”
“Without doubt, the most famous quote concerning alpha comes from Nobel Laureate Richard Feynman. In his comment on page 129 of his book QED, he refers to the “coupling constant, e” — the charge of the electron — which is proportional to alpha:
“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 d—n 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!” [http://www.nobel.se/physics/laureates/1965/feynmanbio.html]
“There are many reasons great minds have been strongly attracted to this number. Not only is it prime, but is a beautiful prime made up of Unity (1, God) and a prime division of Ten (10 = 3 + 7), with echoes of the Trinity and Perfection, Fullness, Seven Spirits of God. Three united divine digits — — so different from the directional composites 4 (2D) and 6 (3D). To find this as the large prime factor governing the structure of the Divine Prologuethe premier text linking Creation and Light-is certainly intriguing, to say the least. This is all greatly amplified by the concepts associated through its value, such as The God of Truth, Miracle of the Lord, Kabbalah, Wheel, and Crucifix." [http://www.biblewheel.com/GR/GR_Frame.asp?GRRef=FineStructure]
“The fine structure constant, alpha (), describes how electromagnetic radiation affects charged particles. It has the numerical value 0.007297351 , with an uncertainty of 6 in the last decimal place, and as such is one of the best-measured numbers in physics.”
“Note that a is quite a small number, very nearly 1/137. This makes theoretical physicists happy, because it is much easier to calculate things when the forces are not very strong. The theory of radiation and charged particles, called Quantum Electrodynamics (or QED for short), is probably the best understood and the most successful theory in all of physics. Some of its predictions have been verified experimentally to twelve decimal places.”
“Another important property of a is that it is dimensionless. It is formed as a ratio of three of the fundamental constants of Nature: the electric charge of the electron, e; the speed of light, c; and Planck’s constant, which is usually written as , and which is necessary to describe quantum phenomena. Each of these 3 constants has dimensions, that is, it changes when you change your system of units. For example, the speed of light is very close to meters per second, but if we want to know it in miles an hour, the answer is a different number, . However, when we form alpha by taking the ratio , all the dimensions cancel out. The result is a dimensionless number, whose value is 0.007297351 no matter what system of units we use.”
“The fact that a is dimensionless has led some physicists to speculate that its value has some fundamental significance. It describes a fundamental property of the universe, and the question is whether its value is just an accident of how the universe happened to be put together, or whether its value is determined by some deep principle that we have yet to discover.” [http://www.physicscentral.com/action/action-02-2c.html]
Part II of this article will be published in the next issue of Spiritual Fellowship Journal and will feature expanded information on the fine structure constant. Among the issues for further consideration will be:
(1) The number is actually not exactly 137 and it is not constant under all conditions.
(2) Cosmic evolution of alpha.
(3) Numerous ways to measure it.
(4) Modern relevancies; QED, etc.
(5) Operationalism (remarks on the philosophy of physics)
Donald Briglia has been a casual reader of the Urantia Papers for fifteen years. After three years of military service, mostly in Germany, he studied Physics at Cornell and UCLA and Computer Engineering at Stanford. He did some Physics research (electron collision processes), then Engineering Physics in Scientific Instrument field (mostly semiconductor measurement instruments).
“Matter-energy is recognized by the mathematical logic of the senses; mind-reason intuitively knows its moral duty; spirit-faith (worship) is the religion of the reality of spiritual experience. These three basic factors in reflective thinking may be unified and coordinated in personality development, or they may become disproportionate and virtually unrelated in their respective functions. But when they become unified, they produce a strong character consisting in the correlation of a factual science, a moral philosophy, and a genuine religious experience. And it is these three cosmic intuitions that give objective validity, reality, to man’s experience in and with things, meanings, and values.” [UB 16:6.10]