Physics of complex systems: Discovery in the age of Goedel

TL;DR

This paper explores the epistemological and decision-making limitations in modern physics through the lens of Gödel's Incompleteness Theorems, emphasizing the need for interdisciplinary synergy to advance understanding of complex systems.

Contribution

It highlights the open questions in physics related to certainty, decision-making, and reasoning limits, proposing interdisciplinary approaches for future progress.

Findings

Identifies the limits of certainty and decision-making in physics.

Connects Gödel's Incompleteness Theorems to physics epistemology.

Suggests interdisciplinary collaboration as essential for future discoveries.

Abstract

From the perspective of the physics of complex systems (1) we deal with the current state of mod-ern 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 s 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.