ssrn-id1296854

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Unformatted text preview: Electronic copy available at: http://ssrn.com/abstract=1296854 Constants of Nature from the Dynamics of Time Michael A. Sherbon e-mail: michael.sherbon@case.edu November 5, 2008 Abstract An archetypal model for the constants of nature is found from the ancient geometry of the the Cosmological Circle and is related to Platos cosmology, with its dynamics and harmonics of time cycles. The inverse fine-structure constant and the proton-electron mass ratio are calculated, connecting fun- damental mathematical constants of geometry with the latest theoretical and experimental values of these physical constants. Continuing in the tradition of George Gamows suggestion, Since the works of Sir Arthur Eddington, it has become customary to discuss from time to time the numerical relations between various fundamental constants of nature. Although until today such discussions have not led to any practical results - that is, to any valuable road signs toward further development of the theory of the still unclear fundamen- tal facts in physics - it may be of some interest to survey the present status of this clairvoyant branch of science. 1 1 Introduction From ancient times harmonic proportion was considered to mediate between basic duali- ties of nature such as finite/infinite, part/whole, etc., and number itself was a phenomena of time and energy [2]-[5]. Today we have a more advanced mathematical language that has been developed over the centuries, the errors of Aristotles physics have mostly been corrected, and what remains incomprehensible has largely been forgotten [6]. Recently, mathematician Andy Hone has said, The whole of physics can be described by the equation S = 0 [7]. Beginning as something of a play on Feynmans U = 0 equation for unifying physics, Hone then gets serious and explains the principle of least action. The principle of least action belongs to the general class of variational principles which include the principle of least time [8]. Finding theaction S is common to almost 1 Electronic copy available at: http://ssrn.com/abstract=1296854 all branches of physics except perhaps the clairvoyant branch, where some say there is no action. At the foundation of the calculus of variations is the brachistochrone problem and the cycloid curve as its solution. The cycloid, a curve traced by a point on the circumference of a rolling circle [9] and given its name by Galileo, was the most studied curve in the 17th century; and was so controversial it was often called theHelen of Geometers. Simon Gindikin says, What was most striking was that the cycloid appeared again and again in the solution of very different problems where it was not a part of the original formulation [10]....
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This note was uploaded on 10/24/2011 for the course SCIENCE PHY 453 taught by Professor Barnard during the Winter '11 term at BYU.

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