The radiation of electromagnetic and mechanical waves depends not only on the intrinsic properties of the emitter but also on the surrounding environment. This principle has laid the foundation for the development of lasers, quantum optics, sonar, musical instruments and other fields related to wave–matter interaction. In the conventional wisdom, the environment is defined exclusively by its eigenstates, and an emitter radiates into and interacts with these eigenstates. Here we show experimentally that this scenario breaks down at a non-Hermitian degeneracy known as an exceptional point. We find a chirality-reversal phenomenon in a ring cavity where the radiation field reveals the missing dimension of the Hilbert space, known as the Jordan vector. This phenomenon demonstrates that the radiation field of an emitter can become fully decoupled from the eigenstates of its environment. The generality of this striking phenomenon in wave–matter interaction is experimentally confirmed in both electromagnetic and acoustic systems. Our finding transforms the fundamental understanding of light–matter interaction and wave–matter interaction in general, and enriches the intriguing physics of exceptional points.The modes of the radiation field generated from an emitter are usually determined by the eigenstates of the surrounding environment. However, this scenario breaks down in a non-Hermitian system, at the spectral degeneracy known as an exceptional point.