Quantum theory of time perception: phases,clocks and quantum algebra

Experience of time is one of the primordial human experiences which is deeply tied to human consciousness. But despite this intimate relation of time with human conscious experience, time has proved to be very elusive. Particularly in physics, though there is already some understanding of time, there are still so many paradoxes that plague this understanding. In this paper we take rather a different route to question of time. We first attempt to come up with a theoretical understanding of time perception. Quite interestingly we find that quantum theory provides an algebraic formulation within which we can understand some essential aspects of time perception by human mind. We then ask whether a similar formalism can furnish the understanding of time as well and find connections of our formulation of time with similar works by other researchers. Our underlying approach to question of time has been inspired by R. W. Hamilton who considers algebra as science of pure time. Hence our work has an extensive algebraic flavor. Our work also incorporates another approach based on Kauffman's iterant algebra which relates time to underlying recursions and oscillations. We believe that our work will initiate more investigations in this direction.