Luca,
I think the problem we have with understanding time is that since we are individual beings, we experience change as a particular sequence of events and so think of it as this point of the present moving from past events to future ones. Physics then distills this to measures of duration between these sequences.
The actual reality is the changing configuration of what exists turns future into past. For example, tomorrow becomes yesterday because the world turns, not that we travel some dimension from yesterday to tomorrow. Since this means time is an effect of action, its irreversibility is due to the physical inertia of the actual actions. The world isn't going to stop and go the other direction.
Duration is just what is happening between the occurrence of the events, like the rest of the wave happening between the peaks.
It makes time similar to temperature, rather than space. Time is to temperature what frequency is to amplitude. We think of temperature as a cumulative effect, but it's based on lots of specific amplitudes/velocities. With time we measure the specific actions, but cannot find a universal rate of change. That is because it also is a cumulative effect of lots of little actions. The present is simply that which physically exists. We are just one molecule, bouncing from one encounter to the next, in this thermodynamic medium.
We cannot measure precise locations of objects in motion, whether it is a subatomic quantum of light, or a car driving down the road. To do so, we would have to freeze all the motion which makes them what they are. Like a temperature of absolute zero, there would be no normal reality to measure and no way to measure it, since our devices and their atomic structure would also be motionless.
Faster clocks don't move into the future more rapidly, as they age/burn quicker, they recede into the past more rapidly. The hare is long dead, but the tortoise is still plodding along. Keep that in mind, the next time you are rushing about.
If we go along that narrative vector from past to future, we either think the future must be determined, because we know only one outcome will happen and the laws governing it are firm. Or we think the past must remain probable and branch off into multiworlds, because some element of probability remains. Now if we view it as the process by which future becomes past, then probability precedes actuality. The laws determining the outcome might be set, but the input into the equation of the event only arrives with its occurrence.
Now I find most physicists simply ignore this observation, because it does raise questions which are not permitted, but you might consider it when trying to figure out time.
Regards,
John Merryman