The Concept of Infinity, A Key to the Keys

Background. Several pages have explored infinity over the years.

https://81018.com/infinitesimal/ From infinity to the infinitesimal, there are no less than 60.doublings of the Planck scale numbers prior to a “point particle” definition (June 2020)!

https://81018.com/redefining/  A nexus of transformations defines the Infinite-Finite relations and this is the most simple page to encapsulate that expression (May 2020).

https://81018.com/bridge/ Return to Newton’s absolute space and time and Leibniz relational view of space and time and then to the Silk-diValentino-Melchiorri.  November 4, 2019 publication, Planck evidence for a closed Universe and a possible crisis for cosmology (Nov. 2019).

https://81018.com/questions/  Determining the character, form, and functions of the very first instant of the universe is one the primary keys for understanding science, mathematics, and the meaning and value of life (August 2019).

https://81018.com/lemaitre-today/   A major ongoing investigation of this finite-infinite debate will be with theory of Kenneth Wilson to define phase transitions within a scale with known boundary conditions.  Also, the work of André Petermann (and Stueckelberg) will be analyzed (June 2019).

https://81018.com/nature/  Infinity is understood to be continuity, symmetry and harmony, light and other dimensionless constants that appear to create a bridge between the finite and infinite (July 2019).

https://81018.com/constant/  The Finite and the Infinite:  Dimensionless constants are either finite, infinite, or a bridge between them (April 2019).

https://81018.com/infinity/  To create our best possible world, the concept of infinity needs to be part of our conceptual richness. All possible historic questions about infinity need to be explored (Dec. 2018).

https://81018.com/infinitude/  A working summary of facts and guesses (Nov. 2017).

https://81018.com/infinite/ A looking at the infinite in light of the work of Stephen Hawking and Max Tegmark (MIT)  (October 16, 2017).

https://81018.com/facts/  A working summary of facts and guesses about infinity (Oct. 14, 2017).

https://81018.com/universeview/ Struggling with the concepts (December 2016).

In preparation of the in-depth study of renormalization:

• The Normalization Group in Quantum Theory, E.C.G. Stueckelberg and A.  Petermann, Helv. Phys. Acta 24, 317 (1951)
• Quantum Electrodynamics at Small Distances (PDF),
  M. Gell-Mann and F.E. Low, Phys. Rev. 95, 1300 (1954)
• Introduction to the Theory of Quantized Fields, N.N. Bogoliubov and D.V. Shirkov, Interscience Publishers, New York (1959);
• Renormalization and Symmetry: a review for Non-Specialists
  S. Coleman, in Properties of the Fundamental Interactions, Erice 1971, A. Zichichi (ed), Editrice Compositori, Bologna, 605 (1973);
• Renormalization Group and the Deep Structure of the Proton, A. Petermann, Phys. Reports 53, 157 (1979);
• Renormalization (PDF), J.C. Collins, Cambridge University Press, (1984).

See Freeman Dyson and Renormalization

NOTE: Oldstone Conference of 11 to 14 April 1949 was the third of three postwar conferences held to discuss quantum physics; arranged for the National Academy of Sciences by J. Robert Oppenheimer, chairman. It followed the Shelter Island Conference of 1947 and the Pocono Conference of 1948.