Affiliation:
1. Artwork Conversion Software Inc. , 509 N. Sepulveda Blvd, Manhattan Beach , CA 90266 , USA
Abstract
Abstract
Following the results of our recently published book [F. Lev, Finite Mathematics as the Foundation of Classical Mathematics and Quantum Theory. With Applications to Gravity and Particle Theory, Springer, 2020, ISBN 978-3-030-61101-9], we discuss different aspects of classical and finite mathematics and explain why finite mathematics based on a finite ring of characteristic
p
p
is more general (fundamental) than classical mathematics: the former does not have foundational problems, and the latter is a special degenerate case of the former in the formal limit
p
→
∞
p\to \infty
. In particular, quantum theory based on a finite ring of characteristic
p
p
is more general than standard quantum theory because the latter is a special degenerate case of the former in the formal limit
p
→
∞
p\to \infty
.
Reference17 articles.
1. E. Wigner, The unreasonable effectiveness of mathematics in the natural sciences, Commun. Pure Appl. Anal. 13 (1960), no. 1, 1–14, https://doi.org/10.1002/cpa.3160130102.
2. F. Lev, Finite Mathematics as the Foundation of Classical Mathematics and Quantum Theory. With Applications to Gravity and Particle Theory, Springer, Cham, Switzerland, 2020, ISBN 978-3-030-61101-9.
3. F. G. Dyson, Missed opportunities, Bull. Amer. Math. Soc. 78 (1972), no. 5, 635–652.
4. O. Consa, Something is wrong in the state of QED, arXiv preprint (2021), https://arxiv.org/abs/2110.02078.
5. S. Weinberg, The Quantum Theory of Fields, vol. I, Cambridge University Press, Cambridge, UK, 1999.