**The Mysterious 137**

*If you have ever read **Cargo Cult Science* by Richard Feynman, you know that he believed that there were still many things that experts, or in this case, physicists, did not know. One of these ‘unknowns’ that he pointed out often to all of his colleagues was the mysterious number 137. This number is the value of the fine-structure constant (the actual value is one over one-hundred and thirty seven), which is defined as the charge of the electron (q) squared over the product of Planck’s constant (h) times the speed of light (c). This number actually represents the probability that an electron will absorb a photon. However, this number has more significance in the fact that it relates three very important domains of physics: electromagnetism in the form of the charge of the electron, relativity in the form of the speed of light, and quantum mechanics in the form of Planck’s constant. Since the early 1900’s, physicists have thought that this number might be at the heart of a GUT, or Grand Unified Theory, which could relate the theories of electromagnetism, quantum mechanics, and most especially gravity. However, physicists have yet to find any link between the number 137 and any other physical law in the universe. It was expected that such an important equation would generate an important number, like one or pi, but this was not the case. In fact, about the only thing that the number relates to at all is the room in which the great physicist Wolfgang Pauli died: room 137. So whenever you think that science has finally discovered everything it possibly can, remember Richard Feynman and the number 137.

Dr. Bill Riemers writes: classical physics tells us that electrons captured by element #137 (as yet undiscovered and unnamed) of the periodic table will move at the speed of light. The idea is quite simple, if you don’t use math to explain it. 137 is the odds that an electron will absorb a single photon. Protons and electrons are bound by interactions with photons. So when you get 137 protons, you get 137 photons, and you get a 100% chance of absorption. An electron in the ground state will orbit at the speed of light. This is the electromagnetic equivalent of a black hole. For gravitational black hole, general relativity comes to the rescue to prevent planets from orbiting at the speed of light and beyond. For an electromagnetic black hole, general relativity comes to the rescue and saves element 137 from having electrons moving faster than the speed of light. However, even with general relativity, element 139 would still have electrons moving faster than light. According to Einstein, this is an impossibility. Thus proving that we still don’t understand 137.

Dr. James G. Gilson contributes more with his *Solution to a 20th Century* *Mystery: Feynman’s conjecture of a relation between a, the fine structure*

*constant, and n.*

**Feynman’s Conjecture**: A general connection of the quantum coupling constants with p was anticipated by R. P. Feynman in a remarkable intuitional leap some 40 years ago as can be seen from the following much quoted extract from one of Feynman’s books.

*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 p 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!
*

**The Solution**: It will here be shown that this problem has a remarkably simple solution confirming Feynman’s conjecture. Let P(n) be the perimeter length of an n sided polygon and r(n) be the distance from its centre to the centre of a side. In analogy with the definition of p = C /2r we can define an integer dependent generalization, p(n), of p as p(n) = P(n) / (2r(n)) = n tan(p / n). Let us define a set of constants {a(n^{1},n^{2})} dependent on the integers n^{1} n^{2} as a(<n^{1}, n^{2}) = a(n^{1}, ∞) p(n^{1} x n^{2}) /p, ………………………* where a(n^{1},∞) = cos(p / n^{1}) / n^{1}. The numerical value of a, the fine structure constant, is given by the special case n^{1} = 137, n^{2} = 29. Thus a = a(137,29) = 0.0072973525318… The experimental value for a is a^{exp} = 0.007297352533(27), the (27) is +/- the experimental uncertainty in the last two digits.

The very simple relation * between a, the fine structure constant, p and p(n) confirms Feynman’s conjecture and also his amazing intuitional skills.

**Link**: For details of how the formula * was obtained and some of the consequences arising from it visit the website: http://www.fine-structure-constant.org/.

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