I was explaining basis vectors to my brother, I said that in quantum mechanics that when you have a number of dimensions, each dimension being an eigenket in vector space, that every dimension is independent of all the other basis vectors. It is however interesting to think that if this is the case, then time would not qualify as an eigenbasis but as rather transform or observable on your eigenkets. Is time suppose to be a unitary operator or something? This would mean time cannot be the 4th dimension. I suppose this would effect relative quantum mechanics given that all states of a particle must be in the same time state making time negligible as an eigenbasis. I suppose my question is, what is time considered to be(a dimension or unitary operator) and how is it treated in quantum relativity ( a course I have yet to take ).