An analysis and extension of Eddington's unified theory of physics
Mulhern, John Edward Jr
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This thesis is divided into three parts. In the first part Eddington's algebra of E-numbers is outlined and the Dirac matrices are introduced. At this point .it becomes possible to relate specific entities that the two men treat in common. In particular, the derivation of the interchange operator from the point of view of wave tensor calculus is given in full. The reason for this method of treatment is that Eddington's interchange operator is more general than Dirac's, since it contains Dirac's interchange operator as one factor. The additional factor in Eddington's operator helps to form the basis of his nuclear theory. With the introduction of Lorentz rotations it becomes possible to show that many of the E-numbers have their exact counterpart in the work of Dirac. Part Two deals with certain general relationships which are shown to exist between the wave tensor calculus and the bra and ket vector algebra. Tho Heisenberg and Schrödinger formulations are presented. against the more general background or Dirac's algebra. Procedures are then set up to relate the bra and ket vectors to Eddington's wave vectors. Within the wave tensor algebra it is possible to build wave tensors of higher order from a group of wave vectors. One can, in turn, relate the elements of a second-rank wave tensor with a vector, and the element of a fourth-rank wave tensor with a second-rank tensor. This means that Dirac's bra and ket vectors can be related to a second-rank tensor. This is illustrated through the tenaors of electromagnetic theory and the Einstein law of gravitation. The purpose of Part Two is to show the tremendous scope possessed by the E-numbers. Part Three contains a more general type of discussion. Here, for example, the concept of an observable ia scrutinized from both Dirac's and Eddington's point of view. Although at first they look entirely different, they can be shown to be compatible. Eddington's argument for an absolute standard of length is also discussed. Here the particular application of Eddington's concept of a basic uncertainty in position appears. This argument applies to the field of quantum electrodynamics when one deals with an electron of zero dimensions. If the basic uncertainty in position is of the order of 10^-13 cm, then distances of less than this value cease to have physical significance, as their measurements cannot be taken. This helps to remove certain of the divergences inherent in a point particle theory. A step by step analysis leading to Eddington's exclusion principle is given, starting from the Pauli exclusion principle, because it gives insight as to the vantage point from which Eddington views physical theory.
Thesis (Ph.D.)--Boston University
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