Paul Benioff 
LOCAL MATHEMATICS FOR LOCAL PHYSICS 
From Number Scaling to Gauge Theory and Cosmology

The language of the universe is mathematics, but how exactly do you know that all parts of the universe ‘speak’ the same language? Benioff builds on the idea that the entity that gives substance to both mathematics and physics is the fundamental field, called the ‘value field’. While exploring this idea, he notices the similarities that the value field shares with several mysterious phenomena in modern physics: the Higgs field, and dark energy.

The author first introduces the concept of the value field and uses it to reformulate the basic framework of number theory, calculus, and vector spaces and bundles. The book moves on to find applications to classical field theory, quantum mechanics and gauge theory. The last two chapters address the relationship between theory and experiment, and the possible physical consequences of both the existence and non-existence of the value field. The book is open-ended, and the list of open questions is certainly longer than the set of proposed answers.

Paul Benioff, a pioneer in the field of quantum computing and the author of the first quantum-mechanical description of the Turing machine, devoted the last few years of his life to developing a universal description in which mathematics and physics would be on equal footing. He died on March 29, 2022, his work nearly finished. The final editing was undertaken by Marek Czachor who, in the editorial afterword, attempts to place the author’s work in the context of a shift in the scientific paradigm looming on the horizon.

Contents:

• In Memory of Paul Benioff


• Foreword by Seth Lloyd


• Local Mathematics and Value Fields:
  
  
  
  • Introduction
  
  
  • Fiber Bundles and Connections
  
  


• Effects of Local Mathematics and the Value Field on Physical and Geometric Quantities:
  
  
  
  • Introduction
  
  
  • Gauge Theories
  
  
  • Quantum Mechanics
  
  
  • Geometry
  
  
  • The Theory Experiment Connection
  
  
  • The Basic Role of the α Field
  
  


• Afterword by Marek Czachor


• References


• Index

Readership: For use by academics, particularly at graduate level, interested in the foundations of physics and the philosophy of mathematics.

Key Features:

• A scientific testament left behind by an outstanding and recognized scientist


• A pioneering work on an original concept that has no equivalent on the market