Clearly there's a forward momentum through time as we seem to experience time as a forward motion.
Now, what classical and relativistic physics gets wrong is that our rate of travel through time is not constant. We've all experienced occasions where time seemed to pass faster or slower. In order to change our velocity through time we must experience a temporal force which will create some sort of temporal acceleration. This is clear from laws of conservation of energy and momentum, both of which are the direct consequence of the degrees of symmetry in universal quantum fields (see
Noether's theorum). So there must be temporal forces that are acting upon us in order to change our velocity. Without a force our velocity would remain constant with respect to our reference frame.
Note that I mentioned our reference frame. It's also possible that the curvature of space time would actually change our relative velocity to our surroundings without actually exerting a direct force. Perhaps some people or events are just so temporally massive that their temporal gravity slows our relative speed? These could be modeled in classical chronodynamics as temporal forces, but that would be incomplete, just like gravity vs general relativity.
This is an intriguing line of thought that requires further analysis. I'd be curious to explore conservation of temporal properties and potential origins of temporal distortions/force.