Since the theory of relativity tells us that time is a dimension, and we are always moving forward along that dimension, doesn’t it follow that at the quantum level there must be some kind of boson pushing matter forward through time? (In the same way that all motion through the 3 spatial dimensions requires force bosons).  

Since acceleration of fermions (matter) to near-light speeds results in a relative slowing of passage through time, and if it was possible (I know it isn’t) to actually accelerate matter to the speed of light, that their relative speed through time would stop, doesn’t it follow that fermions move through the 4-dimensions of space-time at a constant speed of light, and that that some of that velocity through time gets shifted to velocity through the spatial dimensions at relativistic speeds? The speed of light isn’t simply the maximum speed for particles: it’s the only speed.
The Standard Model of quantum physics tells us that the motion in the spatial dimensions requires bosons, so doesn’t the time dimension need them too? If entropy is somehow that force, how does it push us forward along the time dimension … doesn’t it still need to be a boson particle? We assume the existence of gravitons as a way of keeping quantum mechanics in alignment with all 4 of the classical forces. The same way we exist in a Higgs field and a Gravity field, perhaps we also exist in a Time field.  

As I’ve never seen this issue directly discussed, I assume that I must be somehow terribly way off base (perhaps ignorant of critical equations), but I would love to know why I’m wrong.