Observers, observations and referencing in physics theories

TL;DR

This paper explores how the role of observers and observations, especially self-reference, impacts the completeness of physical theories, suggesting that a universal theory may inherently be incomplete due to G"{o}delian self-reference.

Contribution

It introduces a novel perspective linking G"{o}del's incompleteness to the role of observers and observations in physics, highlighting the hierarchical and self-referential nature of physical theories.

Findings

Observers and observations are inherently self-referential in physics.

Self-reference leads to inherent incompleteness in universal physical theories.

Hierarchical referencing prevents a fully complete theory of the universe.

Abstract

Is it possible to encompass the full extent of the universe within a theory based on a finite set of first principles and inference rules? The r\^{o}le of observers and observations in physics theories is considered here in the light of G\"{o}del's incompleteness theorem. Physics theories are the sum-total that we -- humans, scientists, physicists -- can make in interpreting our observations of the universe. We are integral part of the universe, together with our observations, therefore acts of observation are also observables and should become part of the phenomena considered by the theory, especially in view of the fact that arbitrarily chosen modes of observations may essentially determine empirical results. Incompleteness arises in G\"{o}del's theorem with self-referential propositions. Observations and interpretations are acts of referencing, and self-referencing occurs in physics whenever the observer is recognized as being part of the observed system. If self-reference appears in physics in simile to G\"{o}del's theorem, then incompleteness seems unavoidable in physics. The article discusses observers and observations as referencing in physics, culminating with the understanding that they are hierarchically inter-related so that a universal physics theory cannot be complete.