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Proceedings Paper

Local availability of mathematics and number scaling: effects on quantum physics
Author(s): Paul Benioff
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Paper Abstract

Local availability of mathematics and number scaling provide an approach to a coherent theory of physics and mathematics. Local availability of mathematics assigns separate mathematical universes, x, to each space time point, x.. The mathematics available to an observer, Ox, at x is contained in x . Number scaling is based on extending the choice freedom of vector space bases in gauge theories to choice freedom of underlying number systems. Scaling arises in the description, in x, of mathematical systems in y . If ay or ψy is a number or a quantum state in y, then the corresponding number or state in x is ry,xax or ry,xψx. Here ax and ψx are the same number and state in x as ay and ψy are in y . If y = x+ μdx is a neighbor point of x, then the scaling factor is ry,x = exp( A(x) • μdx) where A is the gradient of a scalar field. The effects of scaling and local availability of mathematics on quantum theory show that scaling has two components, external and internal. External scaling is shown above for ay and ψy. Internal scaling occurs in expressions with integrals or derivatives over space time. An example is the replacement of the position expectation value, ∫ψ*(y)yψ(y)dy, by ∫x ryx* x(yx)yxψx(yx)dyx. This is an integral in x . The good agreement between quantum theory and experiment shows that scaling is negligible in a space region, L, in which experiments and calculations can be done, and results compared. L includes the solar system, but the speed of light limits the size of L to a few light years. For observers in L and events outside L, at cosmological distances, scaling is not limited by theory experiment agreement requirements.

Paper Details

Date Published: 8 May 2012
PDF: 15 pages
Proc. SPIE 8400, Quantum Information and Computation X, 84000T (8 May 2012); doi: 10.1117/12.917731
Show Author Affiliations
Paul Benioff, Argonne National Lab. (United States)


Published in SPIE Proceedings Vol. 8400:
Quantum Information and Computation X
Eric Donkor; Andrew R. Pirich; Howard E. Brandt, Editor(s)

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