Researchers at IPhT (CEA, CNRS) and the Universitat Autònoma de Barcelona have shown that gravity—and with it, supersymmetry—emerge as logical necessities whenever a massive spin-3/2 particle exists in nature. Two principles are enough: causality, the fact that no signal can travel faster than light, and unitarity, the requirement that probabilities are conserved in quantum mechanics. The structure of supergravity is not assumed: it bootstraps itself.

In fundamental physics, gravity is usually thought of as an ingredient one adds to a theory. But could it instead be forced by the internal consistency of the quantum world? This is what a study published in the Journal of High Energy Physics demonstrates.

The starting point is disarmingly simple: a single massive spin-3/2 particle. The authors show that such a particle simply cannot exist in isolation within a consistent theory. Its scattering amplitudes grow too fast with energy, clashing with positivity inequalities—the mathematical encoding of causality (the speed of light as an absolute limit) and unitarity (the conservation of probabilities in every quantum process). The theory breaks down barely above the particle’s own mass.