We propose that information purity—a dimensionless scalar field I(x) taking values in (0, 1]—constitutes a fundamental physical field that couples to the energy density of spacetime. Motivated by Jaynes’ principle of maximum entropy, the potential term takes the unique form V(I)=−I ln I. From the action principle, we derive the energy density EL=Cφ² I ln I, where Cφ is a universal coupling constant. The theory is internally consistent, classically stable, and possesses a well-posed Cauchy problem. The global minimum of EL at I=1/e yields a constant negative energy density, making the I-field a natural candidate for dark energy. Crucially, the theory predicts a characteristic d⁶ correction to the Casimir pressure between parallel conducting plates, which is within reach of next-generation precision experiments. A null detection at the level of 10⁻⁷ relative accuracy would rule out the coupling down to the Planck scale. This work provides a concrete, falsifiable framework connecting local information content to observable physics.
Tianyu Liyuan Liu (Fri,) studied this question.