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

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