I don't use my real name for many reasons, most of which have to do with human nature. My avatar is, however, a self-consistent identity and unique enough for discussion.
As for the semantic argument, let me remind you that dimension is a rather loosely defined term and is often polluted by cultural meme when that isn't at all appropriate. When I use the term dimension, I do not mean to imply a philosophical dimension outside of this universe. For that reason, our universe is generally construed to be four-dimensional consisting of 3 dimensions of loci with one conflated dimension of space/time. I prefer the term causation to time, as time is a measurement between cause and effect.
I have no reason to believe in the philosophical idea of multiple dimensions or parallel universes. They may exist, or they may not exist, but for the purposes of science it is hardly observable or quantifiable merely speculative (at least at our current level of development).
Also, when dealing with physical reality there is absolutely no reason to assume an 'arrow of time'. Each observational frame has a context (or frame) of time specific to the context. Why then should we assume that the same causative frame must apply for partially closed systems? Why do so many assume that events at the nuclear and quantum scale must follow the same linear causal 'arrow of time'? When examining causation, how are we to assert that a causative event between frames (ex: a photon changing energetic state by bouncing off an atom and exchanging energetic potential) must have a direct correlative effect along OUR frame? Thermal transfer is a change in the energetic potential of the atom, but that is quantitative (i.e. the state of the entire closed system has changed relative our frame) yet the direct sequence of events within the closed system of the atom could travel at a tangent to our view of causality.
As an allegory, consider an atom as spherical time dimension all it's own. A causative event that changes the state of the atom changes the entire past and future of the atom. That change is observed (entangled observation) at the speed of light relative our frame, but attempting to assume that the previous state of the atom is preserved within its local frame violates the observations of t-symmetry. Saying that the atom was previously in a different state from within the quanta of the atom would be impossible, because the atom observes itself only as a standing wave where past, present, and future all change when the standing wave changes.