Abstract: We investigate the implications of the closure of the physical in the context of models and theories of consciousness. We prove that if and only if a model of consciousness does not describe the physical as closed, the induced physical evolution of that model is, to leading order in time, that of a dynamical quantum collapse model. This result sheds new light on the question of why and how consciousness and quantum theory are related. It contributes to the exploration of what consciousness does, independently of assumptions about what consciousness is. Our analysis is made possible by powerful theorems in quantum mathematical physics. From a mathematical perspective, the main achievement is to overcome the Markov requirement in these theorems.