Paul A. Benioff

1930-2022

Biographical sketch

• 1959 Ph.D., University of California at Berkeley
• 1960 Weizmann Fellow
• 1961 Ford Fellowship, Niels Bohr Institute
• 1961-1995 Argonne National Laboratory
• 1995-present Post-retirement Research Participant, Argonne National Laboratory

Visiting appointments

• 1979 & 1982 Visiting Scientist, CNRS Marseilles
• 1979 Visiting Professor, Tel Aviv University

Awards

• 2000 Quantum Communication Award of the International Organization for Quantum Communication, Computing, and Measurement
• 2001 Fellow, American Physical Society
• 2002 Special University of Chicago Medal for Distinguished Perfomance at Argonne National Laboratory

Recent papers

1. Representation of natural numbers in quantum mechanics
   Paul Benioff
   Phys. Rev. A 63, 032305 (2001) [11 pages]
2. Efficient implementation and the product-state representation of numbers
   Paul Benioff
   Phys. Rev. A 64, 052310 (2001) [7 pages]
3. Towards a Coherent Theory of Physics and Mathematics
   Paul Benioff
   Foundations of Physics. 32, 989-1029 (2002)
4. The Representation of Numbers in Quantum Mechanics
   Paul Benioff
   Algorithmica 34, 529-559 (2002)
5. Cyclic networks of quantum gates
   Peter Cabauy and Paul Benioff
   Phys. Rev. A 68, 032315 (2003) [14 pages]
6. Tightening the Theory-Experiment Connection in Physics: $R_{n}$ Based Space and Time}
   Paul Benioff
   Int. J. Quantum Inform. 3, 1-8 (2005)
7. Representation of complex rational numbers in quantum mechanics
   Paul Benioff
   Phys. Rev. A 72, 032314 (2005) [11 pages]
8. Towards a Coherent Theory of Physics and Mathematics: The Theory-Experiment Connection
   Paul Benioff
   Foundations of Physics 35, 1825-1856 (2005)
9. Complex Rational Numbers in Quantum Mechanics
   Paul Benioff
   Int. J. Mod. Phys. B 20, 1730-1741 (2006)
10. A Representation of Real and Complex Numbers in Quantum Theory
    Paul Benioff
    Int. J. Pure and Appl. Math. 39, 297-339 (2007)
11. Fields of quantum reference frames based on different representations of rational numbers as states of qubit strings
    Paul Benioff
    J. Phys. Conf. Ser. 70, 012003-1:19 (2007)
12. Reference Frame Fields based on Quantum Theory Representations of Real and Complex Numbers
    Paul Benioff
    Advances in Quantum Computation, K. Mahdavi and D. Koslover, Eds., Contemporary Mathematics Vol. 482, pp125-163, (2009)
13. A Possible Approach to Inclusion of Space and Time in Frame Fields of Quantum Representations of Real and Complex Numbers
    Paul Benioff
    Advances in Mathematical Physics, Vol. 2009, ID 452738
14. New Gauge Field from Extension of Space Time Parallel Transport of Vector Spaces to the Underlying Number Systems
    Paul Benioff
    Int. J. Theor. Phys. 50, 1887-1907 (2011)
15. Representations of Each Number Type that Differ by Scale Factors
    Paul Benioff
    Advances in Pure Mathematics, Vol. 3, pp 394-404, 2013
16. New Gauge Fields from Extension of Parallel Transport of Vector Spaces to Underlying Scalar Fields
    Paul Benioff
    Proc. SPIE Int. Soc. Opt. Eng. 8057:80570X (2011)
17. Effects on quantum physics of the local availability of mathematics and space time dependent scaling factors for number systems
    Paul Benioff
    Chapter 2, in Quantum Theory, I. Cotaescu, Editor, Intech open access publisher, 2012
18. Local availability of mathematics and number scaling: effects on quantum physics
    Paul Benioff
    Proceedings Volume 8400, Quantum Information and Computation X; 84000T (2012)
19. Effects of gauge theory based number scaling on geometry
    Paul Benioff
    Proceedings Volume 8749, Quantum Information and Computation XI; 87490F (2013)
20. Effects of mathematical locality and number scaling on coordinate chart use
    Paul Benioff
    Proceedings Volume 9123, Quantum Information and Computation XII; 91230Q (2014)
21. Fiber bundle description of number scaling in gauge theory and geometry
    Paul Benioff
    Quantum Studies: Mathematics and Foundations volume 2, pages 289–313 (2015)
22. Principal fiber bundle description of number scaling for scalars and vectors: Application to gauge theory
    Paul Benioff
    Proceedings Volume 9500, Quantum Information and Computation XIII; 95000X (2015)
23. Space and time dependent scaling of numbers in mathematical structures: Effects on physical and geometric quantities
    Paul Benioff
    Quantum Information Processing volume 15, pages 1081–1102 (2016)
24. Effects of a scalar scaling field on quantum mechanics
    Paul Benioff
    Quantum Information Processing volume 15, pages 3005–3034 (2016)
25. Effect of number scaling on entangled states in quantum mechanics
    Paul Benioff
    Proceedings Volume 9873, Quantum Information and Computation IX; 98730D (2016)
26. The no information at a distance principle and local mathematics: some effects on physics and geometry
    Paul Benioff
    Theoretical Information Studies, M. Burgin and G. Dodig-Crnkovic, Eds., World Scientific Publishing Co. 2020, pp 115-138
27. Relation between observers and effects of number valuation in science
    Paul Benioff
    Journal of Cognitive Sciences, Vol.19-2, pp 229-251, (2018)

Selected previous papers