Testing Mass-Sign Dependent Gravity via Atom Interferometry in a Rb BEC

onformal bimetric gravity in the geometric algebra Cl(4, 2) predicts that thegravitational coupling of a particle may depend on its internal quantum state througha discrete Z2 mass-sign inversion symmetry [18]. We propose a tabletop experimentto test this prediction using a 87 Rb BoseEinstein condensate (BEC). Within theCl(4, 2) framework, we identify the mass-sign operator with the dilatation bivectorn ∧ n̄ and its physical realization with a microwave π -pulse exchanging two hypernestates of 87 Rb. The central hypothesis is that if the conformal bimetric structure isphysically realized, the gravitational acceleration of an atom depends on its hypernestate, and the π -pulse should produce a measurable anomaly in the gravitationalphase accumulated during free fall. We present a complete experimental protocol,parameterize the deviation from standard physics by a coupling constant ϵ, andshow that current atom interferometers (δg/g ∼ 10−12 ) can detect or exclude ϵdown to the 10−12 level with one day of data. The experiment is a precision testof the weak equivalence principle for internal states, requiring no exotic equipment.A null result establishes new bounds on internal-state-dependent gravity; a positivedetection would constitute evidence for the conformal bimetric structure predictedby Cl(4, 2).