A mathematical identification of F_jk with the curl of a gauge potential does not establish causal efficacy; formal equivalence in a geometric model underdetermines the physical mechanism responsible for clock rate differences.
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An underlying mathematical description that physicists use to calculate observable forces and fields; it's not directly observable itself, but it's useful for making predictions.
Geometric model(as used in physics and mathematics)
A mathematical description of how objects relate to each other in space using shapes and spatial concepts.
Physical mechanism(as used in philosophy of science)
The actual process or chain of events that explains how and why something happens in the real world.
causal efficacy(Vaibhāṣika causal theory of cognition)
The capacity of an object to serve as a real cause, which nonexistent objects are held to lack
underdetermines(logic and language)
Doesn't fully decide or pin down; leaves open multiple possible interpretations because there isn't enough information visible to choose just one.