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A Many-Worlds Product Paradigm for Quantum Inertia and Quantum Gravity

By William D. Eshleman
(C) 1998-2007 by William D. Eshleman, All Rights Reserved
Permission to copy in its entirety granted for non-commercial purposes
April, 2007

Abstract. The conventional method for specification of a formalism for reality is to assume and determine for the chosen space, the following collection of mathematical objects: 1) the state as a vector in a vector space, 2) the observable as an operator that acts on the vector space, and 3) an algebra determined by the set of operators and certain constraints. Usually, this requires a detailed analysis of how vectors add in the chosen space. That is, the evolution of the state of a vector is a process whereby differential vectors are added to a vector. The original many-worlds interpretation took this approach and assumed the Hilbert space.

Detailed analysis of how vectors could magnify one another in the chosen space is usually avoided due to a change of the type of a vector upon multiplication; e.g., the product of two position tensors is not a tensor, but sums of tensors remain tensors. The report presented here attempts to investigate hypothetical mathematical products that predict equivalent results, as compared to conventional results, for relatively low-energy trajectories, and then to compare the differences for high-energy motion.

The assumed collection of mathematical objects for this report is: 1) state as a product of factors (resembling vectors) in a world of an observer, 2) observable as the logarithm of a particular factor that acts on the space of the observer, and 3) the algebra of convergent products, the notion of the equivalence of products, and the notion of the entropy of products. That is, the evolution of the state of a vector is a process whereby vectors magnify to produce change; the Product Paradigm.

This report claims the mathematical form for a Relativistic Hamiltonian consistent with the sub-factorization of Lorentz factors.

Preface reprinted from The Many-Worlds Interpretation of Quantum Mechanics (A Fundamental Exposition by HUGH EVERETT, III, with papers by J. A. WHEELER, B. S. DEWITT, et. al., and edited by BRYCE S. DEWITT and NEILL GRAHAM, 1973)


In 1957, in his Princeton doctoral dissertation, Hugh Everett, III, proposed a new interpretation of quantum mechanics that denies the existence of a separate classical realm and asserts that it makes sense to talk about a state vector for the whole universe. This state vector never collapses and hence reality as a whole is rigorously deterministic. This reality, which is described jointly by the dynamical variables and the state vector, is not the reality we customarily think of, but is a reality composed of many worlds. By virtue of the temporal development of the dynamical variables the state vector decomposes naturally into orthogonal vectors, reflecting a continual splitting of the universe into a multitude of mutually unobservable but equally real worlds, in each of which every good measurement has yielded a definite result and in most of which the familiar statistical quantum laws hold.

In addition to his short thesis Everett wrote a much larger exposition of his ideas, which was never published. The present volume contains both of these works, together with a handful of papers by others on the same theme. Looked at in one way, Everett's interpretation calls for return to naive realism and the old fashioned idea that there can be direct correspondence between formalism and reality. Because physicists have become more sophisticated than this, and above all because the implications of his approach appear to them so bizarre, few have taken Everett seriously. Nevertheless his basic premise provides such a stimulating framework for discussions of the quantum theory of measurement that this volume should be on every quantum theoretician's shelf.

"... a picture, incomplete yet not false, of the universe as Ts'ui Pen conceived it to be. Differing from Newton and Schopenhauer, ... [he] did not think of time as absolute and uniform. He believed in an infinite series of times, in a dizzily growing, ever spreading network of diverging, converging and parallel times. This web of time -- the strands of which approach one another, bifurcate, intersect or ignore each other through the centuries -- embraces every possibility. We do not exist in most of them. In some you exist and not I, while in others I do, and you do not, and in yet others both of us exist. In this one, in which chance has favored me, you have come to my gate. In another, you, crossing the garden, have found me dead. In yet another, I say these very same words, but am an error, a phantom."
Jorge Luis Borges, The Garden of Forking Paths

"Actualities seem to float in a wider sea of possibilities from out of which they were chosen; and somewhere, indeterminism says, such possibilities exist, and form a part of the truth."

William James


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