The arrow of time and causality are not the same thing. Ask yourself; Does yesterday cause today? Does one rung on a ladder cause the next? Causality is energy transfer, not sequence. The sun radiating on a rotating planet creates the effect called "days."
Time, the measure of units of change, is an effect, similar to temperature. As an analogy, time is to frequency, as temperature is to amplitude. Circumstances determine the amount of energy and the rate it accumulates and disperses.
The deep seated problem in physics is that after recognizing that time is an effect of change, physics obsesses over measuring such units of change, rather than the action which causes change. Two prominent examples of this tendency, in entries submitted to FQXi contests, are Julian Barbour's winning entry in the Nature of Time contest and because he is an FQXi awardee on the issue of time, I include Edward Anderson's entry in this recent contest. Both first ascribe to a Machian view of time, then focus on how to measure intervals.
The reason for this disconnect is because rationality is a serial effect, rather than a causal effect. We do not have a 360 degree perspective of cause, only the linear progression through a sequence of events. Change is not the present(our point of view) moving from one event to the next, but the configuration of the present changing, such that it is the events going from future potential to residual past. The earth doesn't travel the fourth dimension from yesterday to tomorrow. Tomorrow becomes yesterday because the earth rotates.
Time dilation is simply due to processes developing at different rates in different situations. If time were really a vector from past to future, logically a faster clock rate would move into the future faster, but the opposite is true. It ages/burns faster, so it moves into the past faster. Consider in the twins paradox, the one in the faster frame has died by the time her slower frame twin returns. And with every passing day, her life recedes ever further into the past.
Duration is not external to the present, but is the state of the present between occurrences.
As for the cat, the problem is quantum theory does rely on that external clock and its infernal measure, so it tries to fit a probabilistic future into the confines of a determined past and concludes all probabilities must happen. Ha. Get rid of the clock and just let the events happen. Future probability collapses into present actuality and being replaced, recedes into past circumstance.
Then again, the social momentum behind current models will have to dissipate considerably before viable new ideas will rise above the froth. Until then it's multiworlds and multiverses and whatever thought bubbles the establishment dreams up.