One of the motivations for S4 physics was objective metaphysics. I have exerted an enormous amount of personal effort to understand this through my own metaphysical or internal experiences. Standard three-dimensional physics would suggest that all internal experiences are due to brain activity but I believe that this is an experience in a four space dimensional universe with matter that is not tabulated by the Standard Model of physics. This is not a completely new idea: Nietzsche had suggested that the universe is composed of atoms of ‘will to power’ which jibes with the sort of matter with which one can interact with. I can sometimes hear voices from either specific people or beings unknown — it is possible that these are self-delusional but I am a careful observer of my own conscious thought and those that are quite alien to me. One analogy is Julian Jaynes’ theory of development of consciousness from auditory hallucination. These are fleeting but distinct. Sometimes they could be the judgment or opinion of individuals that I have interacted with in the physical world. For example, it could be a private judgment like ‘psychopathic’ about me and I can hear that. Sometimes there are clear images of human beings in symbolic caricature.
What does S4 universe have to do with this phenomenon? First, the mathematical picture of an S4 universe is very abstract and might lead one to suspect that a four dimensional universe is ‘open and empty’ but the actual experience of four dimensional reality is quite dense and difficult to traverse. I can describe the voices in my head in terms of passage through tight tunnels where I can literally hear some judgments or thoughts. Thus I suspect that telepathy is possible but not simple to describe. I have no experiemental knowledge whatsoever that this is reproducible in controlled experiments but nevertheless I can make the reasonable deduction still that telepathy cannot be understood with a theory of electromagnetism that is a gauge theory, essentially because metaphysics exists in the lack of a gauge symmetry in an S4 universe.