Although physics claims to be close to a “Theory of Everything”, there are two features of the Universe that are far from understood: time and consciousness. The problem with time is that its role is very different in relativity theory and quantum theory, so its status in any final theory is unclear. The problem with consciousness is that most physicists neglect it altogether, even though there are several indications from physics itself that consciousness is a fundamental rather than incidental feature of the Universe. Since a key feature of consciousness is the flow of time, these two problems are clearly connected. However, the relationship between physical time and psychological time is still not understood and poses a profound mystery. The resolution of this mystery may require a new psychophysical paradigm, in which consciousness interacts with the Universe on a hierarchy of levels, each associated with a different specious present. The implications of this picture for normal, paranormal and mystical states of consciousness will be discussed.