Hassanali, Mahdi
(2026)
Relationality as the Condition of Physical Theory.
[Preprint]
Abstract
Every physical theory is constructed from observations performed within a physical frame, and this frame enters
the theory at a level antecedent to its equations — in the categorical structure through which observations are
organized into a formalism. This is a structural condition on physical theory as such, not a hypothesis about
any particular physical phenomenon; its character is analogous to the principle of general covariance, which
constrains the form of physical laws without predicting the behavior of any specific system. The condition
has a precise formal consequence in the geometric setting: for any non-invariant tensor field under a frame-
transformation group, the components specified in any single frame are insufficient to determine the underlying
geometric object without explicit specification of the frame. This consequence has been articulated four times
in the foundations of physics — in the tensor reformulation of electrodynamics, in the relativity of simultaneity,
in the unification of energy and momentum, and in the geometric unification of space and time — each time by
identifying a frame-dependence carried implicitly in the prevailing formalism and absorbing it into a geometric
object across the class of frames. Rovelli’s (1996) relational quantum mechanics is the most explicit contempo-
rary articulation of the structural condition: the frame is the physical system to which a quantum state is referred,
and the relational structure is exhibited directly at the level of the measurement interaction. The condition implies
that relationality must arise wherever current physics is examined at the level of its foundations — not because
relationality is a fundamental feature of the physics under description, but because it is a necessary feature of
any theory constructed from observations performed within physical frames, and open foundational problems
are most plausibly resolved by making implicit frame-dependences explicit rather than by eliminating them.
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