© 2003 Donald Briglia
© 2003 The Christian Fellowship of Students of The Urantia Book
This is a continuation of Donald Briglia’s comments on the mystery of the three digit number, 137, and its relation to quantum mechanics. (Please see the Fall and Winter Journal, including the editorial: “God’s Little Three-Digit Joke on Quantum Science.”) While some readers found the piece difficult, many others found the article enthralling. The three digit number, 137 has long confounded quantum physics experts, including Werner Heisenberg, father of the famous uncertainty principle, who declared that all the quandaries of quantum physics would shrivel up if this same three-digit number was ever explained! It should be noted by veteran Urantians that the relationship of 137 to the Urantia Papers is obvious … one being the First Source and Center, three the Trinity, and seven the limit of different associations of the Trinity. However, Donald Briglia, a California physicist, takes us beyond the obvious into the deeper water of quantum mechanics. I urge you to take the plunge with him. You will find it well worth the effort.
Larry Mullins
In Part I, a simplified model of the origin of “all” light quanta, optical electrons changing their state of energy, was presented to highlight the historically important role of light spectroscopy in elucidating atomic structure. As stated in Part I, “when calculations are performed to theoretically predict the spectral features, the number 137 appears, the reciprocal of which Sommerfeld named the ‘fine structure constant’(fsc), 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.”
“The fact that alpha 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]
To expand our characterization of light beyond everyday experience, there are other sources of photons whose wavelengths are within the visible region of the electromagnetic spectrum and are technically the same as light. These include “radioactive decay, triboluminescence, bioluminescence, sonoluminesence, particle-antiparticle annihilation,” and acceleration of free charged particles (electrons, protons, positive and negative ions, etc.) which may produce "cyclotron/ synchrotron radiation, Bremsstrahlung radiation or Cherenkov radiation.” [See, e.g., http://www.wikipedia.org/wiki/light]
“Wavelike energy manifestations also attend upon the performances of positive bodies and the other members of the electronic group.” [UB 42:5.6] Photons produced by these sources are indistinguishable from those resulting from atomic spectral emission of the same wavelength.
So a more robust characterization is that light results from electrical charge dynamics, or, commonly, electrodynamics. Yet, at some deeper level, even these apparently non-electron sources of light may be due to virtual electrons that flash into existence briefly and radiate electromagnetic energy and then disappear, keeping energy levels at the minimum values that nature prefers and behaving so that energy is conserved. This is suggested by the extremely high mobility of the electron whose very light mass relative to the proton (yet possessing the same magnitude of electrical charge, thereby being as “forceful”) make it the ideal candidate for very rapidly “zipping around” (accelerating almost two thousand times faster than a proton experiencing the same electrical force!). The electron is generating photons in its role of maintaining energy balance in the relentless realization of minimum energy states while conserving energy, characteristic of all energymatter system processes. The concept of virtual particles and photons flashing in and out of existence is not uncommon in describing quantum phenomena. For example, results from experiments have been interpreted to reveal that as the particle’s central core is approached, the electron may exert a stronger force than would be expected from the magnitude of its electric charge, according to Purdue University physicists [http://www.purdue.edu/UNS/html4ever/970110.Koltick.electron.html]; while surrounding this core is a fuzzy “cloud” of virtual particles, which wink in and out of existence in pairs. (Could this be ultimatonic activity? [UB 42:6.2] )
If the effective charge of the electron increases as the interaction distance decreases to those low values characteristic of high energy collision physics conditions, then so does the effective value of alpha , as will be seen later. So has a dependence on collision energy which in principle provides an analytical tool that may lead to increased experimentation at various energies to further elucidate the nature of this important quantity.
While it may seem that physicists are being mystical or unscientific when using concepts such as mysteriously appearing virtual energy units and mathematical devices like the “creation operator” in quantum calculations and considerations, the special theory of relativity requires the use of these concepts. The famous special relativity expression of Einstein, , energy is equal to the mass (amount) of matter times the speed of light squared [UB 42:5.4], predicts that matter and energy may interchange, so the quantum theory must be applicable to a process in which, for example, radiation changes into particles. This is exactly what happens when an electron and its charge opposite, a positron, are created when a sufficiently energetic cosmic ray photon is converted into two particles by the very strong energy field of an atom’s nucleus in a process known as pair production. Of course, no new energy is created by the process, merely an interchange between radiation (electromagnetic) and material energies.
In a sense, theorists are “getting even” with the restrictions of quantum level uncertainty dictates. Those virtual energy units postulated, and whose activities the theory describes as quantum level interactions, exist for such short periods of times that the principle of conservation of energy is not violated, thanks to a “license” from the Heisenberg uncertainty principle!
Quantum Electrodynamics (QED), “the strange theory of light and matter” (Feynman), is the very successful and highly regarded science that specializes in the interaction of light and matter. It was developed as an advanced quantum theory to overcome the problems ordinary quantum theory (itself an extension of classical mechanics and electromagnetic theory to overcome their problems) had in its treatment of radiation. QED is a “field theory of relativistic electromagnetism at the quantum level” (meaning the field of electromagnetic energy is quantized and relativity is incorporated in the calculations) which includes classical electrodynamics in the limit of high fields. Calculations from QED are considered to be the most reliable, and one property of the electron (anomalous magnetic moment) predicted by QED has been experimentally confirmed to 11 decimal digits!
QED also predicts the value of the fsc to numerous decimal digits, and this has led to a whole new group of measurements in non-optical contexts. Thus, there is ongoing active experimental and measurement interest in the fsc, though first defined in early 20th century work. Measurements are being made in the diverse fields of atom interferometry, precision laser spectroscopy, single ion mass spectrometry, ion cyclotron resonance, quantum hall effect, AC Josephson effect, electron & positron magnetic moment, and neutron interferometry/ photon recoil. The value of the fsc as given by QED is widely accepted, so each of these fields must submit to the test of comparison of its results with this champion of theories.
How constant should a physical constant be? Analysis of light from astronomic sources is a way of looking back in time and has been used to check on the constancy of the fsc over cosmic time periods.
“Physicists measure the values of basic quantities like the speed of light and the charge of the electron. Cosmologists use the results in studies of the origin of the universe, some 12 billion years ago, and they assume the numbers have not changed over this time.”
“Alpha specifies how strongly electromagnetic waves (like light or x-rays) affect charged particles (like electrons and protons). Alpha is actually a dimensionless ratio-all units cancel outinvolving three quantities:”
— the charge on the electron
— the speed of light
— a fundamental constant from quantum mechanics.
“The idea that one or more of these quantities changes over time is generally most unappealing, although a few theories actually have suggested that it might happen. Since the observed effect is small, many physicists have decided to await further results before making any judgements.”
“Quasar spectra recorded at the Keck Observatory in Hawaii imply that a fundamental physical constant may have been increasing slightly over the past six billion years.”
“But now comes a result that could stand this assumption on its head. A research group claims that the fine structure constant, written as the Greek letter alpha , has increased over the last six billion years or so. Admittedly, the increase is only one part in 100,000 — pretty small — but that’s enough to be plenty unsettling.” [http://www.physicscentral.com/action/action-02-2-print.html]
Perhaps the very small change in alpha should not be viewed with surprise. Our sun is a variable star. Our galaxy evolves. The entire cosmos is constantly changing. Space is expanding. Thus the space within matter is expanding. It is not surprising that all these variations and expansions will result in minor changes of physical constants over cosmic time intervals. “Paradise is motionless, being the only stationary thing in the universe of universes.” [UB 0:4.12] “The eternal Isle is absolutely at rest; all other organized and organizing energy is in eternal motion;” [UB 105:3.4] “Pervaded space is now approaching the mid point of the expansion phase” [UB 11:6.4], “one billion years.” [UB 11:5.8] “…the space content of an atom [is not] empty.” [UB 42:5.16]
Whether an expansion of space would be consistent with the slight increase of alpha depends upon evolving knowledge of the inner structures of electrons and atoms. Since the Coulomb force constant (the “ k ” in Part I, The Value of Alpha) which contains in its expression “epsilon subzero,” the permittivity of free space, enters into the formula for the fsc, this might be a candidate for a long term variation leading to the cosmic evolution of alpha.
It was noted in Part I that the constant is slightly higher than 137, which is its value at low energies of interaction. The value of this constant decreases at the very high energies reached with modern particle accelerators: “It is worth noting that the finestructure ‘constant’ isn’t really a constant. The effective electric charge of the electron actually varies slightly with energy so the constant changes a bit depending on the energy scale at which you perform your experiment. For example, 1/137 is its value when you do an experiment at very low energies (like Milliken’s oil drop experiment) but for experiments at large particle-accelerator energies its value grows to 1/128.” [http://www.physlink.com/Education/AskExperts/ae186.cfm]
“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]
Why is 860 (= two pi times ) times the diameter equal to the wavelength? [UB 42:4.14] This is a very important conceptual relationship as it relates the wave and particle aspects of energy units. A relatively simple and straightforward (but long) mathematical derivation starting with the equation which states the conservation of energy as applied to the system of atom and photon leads to the 860 rule [wavelength equals 860 times the diameter (L=860 d)] and shows that it applies exactly to the light radiated when an electron and a proton combine to form a hydrogen atom in the ground state (discussed in Part I) from two initially infinitely separated particles. (There are possible short cuts in the derivation but it is more rigorous to start with the principle of energy conservation; in this case that is a necessary starting point since a new energy unit that did not previously exist is created in the process, the photon.)
Radiative combination of an electron and a positive ion to form an electrically neutral atom or molecule is an example of a process that is "thus performing” [UB 42:4.14], and the formula can be applied directly. What must have been thought to be useful about this expression is that the wavelength can be easily measured very accurately (the handy result of centuries of developments in optics). So the diameter of the atom, which can not be measured directly, can be determined or at least estimated by dividing the wavelength by 860 , as a rule of thumb. Since atoms do not have rigid boundaries or well defined dimensions, estimates of their size are often very useful.
For example our eyes are most sensitive in the green region of the spectrum, where the wavelength is on the order of 5000 Angstroms. The light from the electron/proton combining to form the electrically neutral hydrogen atom is about 5.5 times as energetic and the wavelength is about 909.1 Angstroms, which is well into the ultraviolet region of the spectrum, beyond human vision but easily measured with instruments. So the diameter of the atom is given by the rule as d = 909.1 / 860 Angstroms or 1.0571 Angstroms, which would yield as the radius of the first Bohr orbit, corresponding to quantum number one, 0.5285 Angstroms, which is to be compared with the accepted value of 0.5291 Angstroms. [See http://physics.nist.gov/cgi-bin/cuu/Value?bohrrada0#mid] The agreement is very good, within about one tenth of one percent.
This expression is thus a link between the particle and wave concepts, and in addition shows that “looking at the light” provides a very practical way of effecting a magnification of atomic dimensions, otherwise unknowable directly.
The 860 rule provides what is known in optical spectroscopy as a term. Each term corresponds to a different quantum energy level of the atom. For a more general case of interlevel electronic transitions [UB 42:5.6], the 860 rule can be applied to each of two terms, corresponding to the two energy levels involved in the transition, and a difference taken, which is standard spectroscopic procedure. When this is done, the reciprocal of the wavelength is given by the difference in the reciprocals of the atom’s (electron orbit) diameters, corresponding to the two energy levels, divided by 860 . [For details, see, for example, Tallqvist. http://www.vtt.fi/tte/samba/staff/st/no860.htm]
Our example was chosen for simplicity so that one of the terms was zero, corresponding to the selection of the zero of energy being the state of infinite separation and negligible initial velocities of the electron and proton, chosen as initial conditions in the energetics.
It was stated in Part I: “At the time the Papers were being revealed, some physics books considered Planck’s constant to be a quantity, represented by the symbol “”, while others considered it to be . If the latter had been referenced in the Papers, the number would have been 137 and not 860.” Does this mean that there then would have been a two pi uncertainty? Possibly, but more likely the logic of the derivation which led to the mathematical relation, L = 860 d, (wavelength equals 860 times the diameter) would lead to the two pi factor being incorporated in the stated dimension, e.g., “the crest to trough of the wavelike energy ripples are 137 times the circumference ( C ) of the…atoms…thus performing,” or, , is an equivalent statement, but very wordy and not as simple compared to the statement in the Urantia Papers, which terseness is notable and typical. (The assumption that the unit has a circumference is inferable from the use of “diameters” in the formula, “860 times the diameters of the …” [UB 42:4.14])
To derive a formula which shows the relation of the wavelength of the emitted photon and the approximate size of the atom in our example of the radiative forming of a ground state hydrogen atom, using a simple physical model rather than the lengthy mathematical conservation of energy approach, consider that the radiated light travels 137 times faster than the electron does in its orbit (see Part I). Thus in the time that the radiating electron goes around once, covering a distance of pi times the diameter (the circumference of the orbit), the electromagnetic emission extends 137 times that distance, or 137 times pi times the diameter, or, wavelength equals 860 times the radius.
This simple physical model agrees within a factor of two with the exact expression derived from the very much longer and burdensome conservation of energy approach. (The short cut taken here is to assume the correctness of the result, light travels 137 times faster than the electron, from the hydrogen atom calculations, see Part I, The 860 (in the Urantia Papers) Connection. Since the derivation leading to is so straightforward and transparent, it is unlikely that the assumption is challengeable. It is well accepted and has been incorporated widely in physics calculations, and often “ ” appears as “ .”) The interesting result obtained suggests that the photon is emitted when the electron is at a greater distance from the proton than assumed in our model.
The assumption has been made that the photon is synchronously emitted, the emission starting as the electron reaches a position very close to the ground state orbit radius (but still in the interelectronic space where the model allows radiation) and ending (is fully emitted) when the electron has completed one full cycle of its motion after the start, some one hundred billionth billionth (ten to the minus eighteenth) of a second later, at which time it is exactly at its ground state radius. This is a reasonable assumption and must be made because the model does not provide any details on the specifics of light emission, just the energy levels of the atom from which are calculated the wavelengths of the light that results from transitions between those energy levels. So one is on one’s own here with respect to just how the photon is emitted and any of the details of just what the electron does as it radiates electromagnetic energy. (Recall that it was after the fact analysis of light spectra which led to the model.)
The result shows that the general nature of the assumption is OK and it is worth fine tuning. We now specify conditions such that the photon is emitted while the electron is in the interelectronic space further out than the first Bohr orbit but closer than that corresponding to the energy level. The photon is assumed to be emitted during a 360 degree electron transit around the atom at a radius where the electron is 58.7% further out than, and where the electron velocity is 25.9% lower than, that of the first Bohr orbit (compared to 50% lower for the n = 2 orbit). These percentages result from considerations of the hydrogen atom mathematical description and are not arbitrary, and lead to the factor (two to the minus one third power) in the numbers for the velocity of the electron and its radius, and radius, . The resulting electron path length is $1.587 \pi d, so the light wavelength is 137 times 1.259 times the electron path or , so . The choice of the larger radius, suggested by the first simple analysis of this model of the radiative combination of electron and proton to form a neutral ground state hydrogen atom, gives the correct result.
This choice of radiating orbit diameter equal to (two to the minus one third power times d, the diameter of orbit n = 1 ), results in the electron rotational frequency being exactly equal to the frequency of the emitted light, the classical-physics relation between source and signal, providing further confidence in the approach taken here. [For another approach on how to establish the 860 relation, see D. Massey, http://www.ubfellowship.org/archive/science/doc093.htm.]
Models are very important at the discrete level since we can then start off with an approximate calculation and by comparison with experiment improve upon the results by refinement of the model. But do these models represent reality? Does the electron orbit the proton as in the Bohr-Sommerfeld model? We do not and can not know, as at the quantum level indeterminacies rule. The uncertainty principle of Heisenberg prevents the simultaneous accurate measurement of position and velocity. This same uncertainty principle shows that the Compton electron wavelength mentioned in Part I represents an inherent uncertainty in position or “spread” of a particle, even when at “rest.” In a quantum approach, the position of an electron even at rest cannot be localized closer than this wavelength, regardless of what the intrinsic size may be. The electron Compton wavelength, h/mc, is the wavelength of a photon having the same rest energy as the electron. The Compton electron wavelength is much larger than the classical electron diameter and in atomic phenomena the electron has an effective size of the order of this wavelength. As we saw in Part I, the Compton wavelength (normalized by ) is 137 times the classical electron radius. The electron Compton wavelength is 0.0243 Angstroms (as referenced in Part I, is actually this number over ). This indicates a 5% “fuzziness” in the orbit radius. The orbit length calculates to be 137 electron Compton wavelengths . ).
In a sense, the electron’s path may be thought of as being made up of 137 steps, each step being that size that the electron assumes as a particle in atomic interactions. So at best, the concept of a well defined orbit that is measurable must be modified, until different (and radical) methods are available. The planetary model is, however, extremely useful, and is still widely taught. But the actual dynamics is far more complicated than a simple orbital rotation of a spinning point charge. “The interelectronic space of an atom is not empty. Throughout an atom this interelectronic space is activated by wavelike manifestations which are perfectly synchronized with electronic velocity and ultimatonic revolutions” [UB 42:8.2] (busy ultimatons!)
While the concept of an electron as a definite point of charge circulating in a fixed orbit is a good starting point, other considerations and experiments lead to the concept of a rapidly changing electrical charge cloud, surrounding the nucleus, forming somewhat of a shell structure. “The wavelike energy extension of an electron may so spread out as to occupy the whole of the lesser atomic orbits; especially is this true of electrons nearest the atomic nucleus.” [UB 42:7.8] The good agreement with spectroscopic data that the simple planetary model gives, suggests that perhaps the assumed motion of the electron in the model is some sort of an average of elaborate, incredibly fast, atomic size steps in a dance that the agile electron performs with its partner, the proton. The resulting energetics (energy states) of this averaged motion agrees with that given by the model based on spectroscopic data and that is the great success of this important construct.
Nature’s limitations on measurement ability in the atomic domain and the proper regard for and inclusion of relativity implications dictate that a theory deals with “observables,” those things measurable in the laboratory by “operations.”
This is a philosophy most physicists are comfortable with, though not at the exclusion of metaphysical elements in their beliefs. Only quantities that can be defined as the objective result of certain prescribed laboratory operations and not necessarily by intuitive understanding are dealt with. Examples are the quantities of charge, mass, temperature, and length. The basis of the philosophy is this operational viewpoint. Relationships between operationally defined quantities that always occur when certain experiments are performed lead to physical laws.
Theory gives a simple description of as many experiments as possible, using as few hypotheses as possible. Less useful theories and hypotheses are replaced by more useful ones when found.
Does that mean if we can not measure it we can not consider it? Not necessarily, as long as we can deduce operationally definable quantities in a logical way that we can measure. For example, in the quantum mechanics of Schrödinger, the electron is represented by a wave function whose amplitude is not measurable, and which only leads to a probability of a measurement result, not to the exact location of the particle. Many find this troubling, but this is what must be settled for at the discrete level of reality, given the quantum uncertainties, when the wavelike behavior of the particle is incorporated into its characterization.
Physicists consider the operational view so fundamental that when Pauli postulated the existence of the neutrino, a tiny uncharged massless energy unit that was implied by the experimental data to be carrying off energy in interactions, he declared that he had committed an unforgivable sin for a theorist, to invent a particle that had no measurable properties!
How is the fsc to be viewed from this philosophically tough-minded perspective of operationalism? “God is no respecter of numbers” is a likely comment, rather than to seek mystical import in its ubiquitous occurrence. This comes from considerations such as electrons are pervasive in the universe. We live in a “sea of electrons” (P. Dirac), literally. It is difficult to imagine any activity in daily life that does not reduce down to electron activity or anything else that is electron-free, other than purely gravitational or nuclear processes. (In fact, electrons perform so many functions that it takes 100 ultimatons per electron [UB 42:6.5] to provide all the special capabilities that electrons must possess. Nature is conservative and would not use 100 ultimatons to make up each electron if not necessary.) So in all of our experiences, electron interactions dominate. Thus the fsc is pervasive in our physics. The number 137 is the sign of the electron. If it comes up, there is an electron involved, real, virtual or both. That is one view of the operational perspective on the fsc.
At the same time, holders of this view would likely have some metaphysical foundation of beliefs to evaluate what pervasiveness of the fsc means. In Part I and the editorial by Larry Mullins preceding it, two distinguished Nobel laureate physicists, Feynman and Lederman were quoted showing their puzzlement over this ubiquitous three digit number and its meaning, but leaving it in the domain of God. This is reminiscent of the oft quoted comment of Einstein on the probabilistic description of the quantum theory, with its intrinsic uncertainties, "I can not believe that God plays dice with the universe.”
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).