The material discussed in this article is related to a recent discovery of a theoretical formula for the fine structure constant α and a prediction for its value of great accuracy. This prediction and the formula that made it possible represents a substantial step forward in the solution of the α mysteries which are fundamental and pervade the whole of theoretical physics from the smallest systems, elementary particles, to the very largest one, the universe. This is no mere speculative fantasy or science fiction extrapolation of imagination about the importance of α . The fine structure constant impacts on our every day life here and now through the physics of the semi-conductor devices via the Hall effect that is for example exploited in electronic switches. The fine structure constant's ubiquitous influence in such every day objects of the electronic arena is now an all pervasive adjunct to the human environment. This influence in our society extends our philosophical view of the world by the possibility making explorational tools such as computer controlled telescopes, microscopes, digital photo devices, fibre optical light communication channels all of which involve, at some stage of their operational systems, the coupling of the electromagnetic field with electrons and thus α. Our primary personal interface with the world, our eyes are such photonic-electronic coupled biological signal conversion devices. The fine structure constant, has been for many years a source of scientific and philosophical questions regarding its numerical value and significance and as a fundamental object of theory, it has an unavoidable place in our attempted explanations of those extraordinary images of distant galaxies returned by the Hubble telescope. Thinking persons cannot ignore those new spectacular views of our world such as that of the Eagle Nebula which have recently been returned by Hubble. They jolt us back to the age old question of what is it all about ? The mass of such an object relative to the mass of a human observer may be greater than ≈1040 an incredible and overwhelming comparison. When we think about the relative scale of those distant monolithic and magnificent assembles of raw particles, fields and atomic systems, how can we have any doubt that molecular, biological and social structures are out there in abundance. However, it largely depends on α and its contribution to the strength of the Coulomb potential. If α where to suddenly be switched off, here on earth out there in those massive astronomical objects and indeed everywhere, atomic systems would shed all their orbiting electrons as the Coulomb attraction reduced to zero. All those bound electrons would slingshot tangentially out of orbit into a universal orgy of randomness. All atomic, molecular, biological systems would be destroyed in the process. All life including our own, all human aspirations, society and institutions would be consumed in the instant catastrophic fireball and there would be no record left that they had ever existed. It might not be The End of The World but it would certainly be the end of us.
Technical astronomical, spectroscopic information about the properties of α at great distances from earth is being obtained by examining light that started on its journey to earth some six billion years ago to arrive currently at the world's largest telescope, the 10-metre Keck facility in Hawaii. The team of scientists involved in that project, Chris Churchill et al, are questioning the constancy of α over cosmological time and what bearing this might have on light velocity in distant places or in the distant past. Answers to such questions are essential if we are to make real progress with our fundamental scientific view of the universe. A full understanding of the significance of α will transform present day science at the technical and practical device level and greatly help with finding the answers to those many fascinating philosophical questions in physics and cosmology of existence, meaning, significance and beginnings generally. My objective in writing this short note about α has been to bring out how central and important the study if the fine structure constant is to our Scientific and Philosophical View of the World.
The resolution of the big philosophical problems will likely only come about when the more technical aspects of α are fully clarified. With that thought in mind, let us return to the technical question of the correctness of the prediction for the value of α. The predicted value published by the present author was confirmed by the value given in CODATA's latest report, the one that appeared in 1999, on the experimental and recommended values of the fundamental constants. Effectively, the prediction added four additional decimal places to the eight decimal places that were previously accepted as correct. The theoretical formula for α is an inevitable consequence of the kinematics and geometry of the cyclic group of order 29×137 . However, the value of α is a special case obtained from a general formula α(n1,n2) which yields the values for various other quantum coupling constants depending on the integer pair (n1,n2) input. The geometry resides in a simple relation between α(n1,n2) and an integer dependent generalization π(n) of π, the n=n1×n2 order cyclic group and an unusual application of the idea of projection quantization, a concept from orthodox quantum mechanics. Coupling here will mean the tendency for a coupled object to remain in some specific locality by cyclically visiting some defined region over some period of time. This is not necessarily the same as an object being attracted to some position by a force such as the Coulomb field generated by a proton. However, these two aspects of coupling are related. The cyclicity implies that π plays a central role. A result derived from this theory is that the fine structure constant α has the same value that characterises a relation, denoted by α137(29 ×137), between a representation of the cyclic group of order 29×137 and the induced representation for the cyclic subgroup of order 137. The value of this characteristic is α137(29×137) =0.007297352532....... A second result is that the complementary characteristic α29(29×137)=0.034280626357...... for the cyclic subgroup of order 29 represents the gauge theory electro-weak coupling quantity g2/4π. A third such result that can be obtained from this theoretical structure is a generalized version of the Weinberg electro-weak mixing angle θW. These are the more technically orientated results that come from the formula for α. However, as remarked earlier, the mysteries of α are very much also in the domain of the philosophy of science and while the technical progress that has occurred is a first step there is still a long way to go with those more tantalising philosophical aspects of what the fine structure really represents and how understanding it can help with the big questions of space-time and such issues as Mach's Principle.
More information about this area of research can be obtained here Fine Structure Constant
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