Physics of complex systems: Discovery in age of Goedel

TL;DR

This paper explores the foundational limits of physics in the context of complex systems, highlighting the influence of Gödel's Incompleteness Theorems on certainty, decision-making, and reasoning, and emphasizing interdisciplinary collaboration.

Contribution

It links the epistemological challenges in physics to Gödel's theorems and advocates for interdisciplinary approaches to advance understanding of complex systems.

Findings

Identifies limits of certainty and decision-making in physics

Highlights the need for interdisciplinary synergy

Provides research examples illustrating these concepts

Abstract

From the perspective of the physics of complex systems (1) we deal with the current state of modern physics including the crisis in physics demonstrated through its epistemological, psychological, economical as well as the social context; (2) considering the strength of the Goedel Incompleteness Theorems we point out the following open questions in physics: (i) the limits of the precision of certainty, (ii) the limits of making decisions on information and (iii) the limitations of reasoning that sometimes affect progress, (3) since further advances will necessarily require synergy between physics and seemingly distinct fields - mathematics, information science, chemistry, biology, medicine, psychology, and art. We illustrate this relation by providing examples based on our research. Point (1) is discussed in Ch1 while Ch2-Ch5 encompasses the point (2) and point (3) is covered in Ch6-Ch10.