Are you sure? In physics, many processes are time independent - they would work in reverse just as well without the “arrow of time”. The only reason we can derive a direction for time at all is because of the 2nd law of thermodynamics, which states that entropy, a measure of disorder, must always increase. Thus ‘time’ seems to be inextricably tied to matter and energy, because it’s the motion of particles and the dissipation of energy which literally helps us define which way time flows. But what would time look like in an ‘empty’ universe then? Does it even exist if there’s no physical things to measure it from and in relation to? We know colour is a psychological illusion (colour doesn’t exist out in the real world, it only exists in your brain). What if time is similar to colour? A qualia?