At quantum levels, quantum indeterminacy renders the "arrow of time" obsolete. I'll try and find some citations for you by tomorrow. I'm out of time here.
Not necessarily obsolete, but perhaps a function of perspective and perception. An illusion, in effect. Quantum physicist Carlo Rovelli argues this in his book The Order of Time. Let’s see if I’ve understood Rovelli well enough to explain it (without calculus, which I wouldn’t be able to follow anyway and have to take on faith. Apparently Boltzmann’s equation is pertinent though);
We start by observing that the 2nd Law of Thermodynamics is the
only law of science which distinguishes between past and future. We can also observe that in conditions of thermal equilibrium, there would be no directional flow of time; no transfer of energy from hot to cold objects, no increase in entropy, no linear flow of time. But park that here for now.
As the entropy of the universe increases, the configurations at quantum level, as at the macro level, become less ordered, more disordered. At this point we may use the analogy of a pack of cards. When a new pack of playing cards is unwrapped, they are ordered according to colour and suit, and each suit is ordered numerically. This is a state of low entropy, with obvious order and structure. When the cards are shuffled, these obvious configurations can no longer be observed; order is lost, the pack is now in a state of high entropy.
However, what we observe of the cards is precisely that; an observation. The reality may be that there are an equal number of particular configurations in the cards both before and after shuffling, if we perceive and calculate all of them. The particular configurations before and after shuffling are in fact equivalent, though it does not seem that way to the naked eye, because the naked eye noticed the obvious particularities like colour, but would not be aware of all the numeric particularities that would need to be calculated to be observed.
This in itself may be enough to upend our perception of the direction of time, but there’s more; in the swirling maelstrom of information with which the quantum world surrounds us, we have access only to a handful of variables. We exist within a subset of the universe, and our experience of it is defined by the particular sets of variables we have access to. And within this subset, entropy was low in the past and increasing in the present, the second law pertains, time is linear. But if we had access to all the information contained within the universe around us, the intricate webs of causality would not be linear, they would be multi dimensional. Entropy would not increase in linear manner, time would not be unidirectional - they would fluctuate in all directions, and none.
So much for Rovelli, though I urge anyone and especially any lay person interested in the fundamentals of QM, to read him. Gerard t’Hooft and Yakir Aharanov are two other Quantum Physicists whose work on Superdeterminism, The Aharanov/Bohm effect, and Weak Values, have radical implications for the nature of time. Bell’s Theory is another reference worth pursuing, in particular the revelations regarding non-locality which Bell uncovered.
A final observation; in his popular book A Brief History of Time, Stephen Hawking posits not one time’s arrow, but three. The Thermodynamic Arrow, as we’ve been discussing; the Cosmic Arrow, moving in the direction of the expanding universe (this may go into reverse, if the universe begins to contract), and the Psychological Arrow, by which we are able to remember the past, but have no foreknowledge of the future. Hawking, who makes no claims at least in the chapter on Time’s Arrow in his Brief History, makes no claims challenging the linear progression of time, but he does make the observation that
all three arrows must be aligned in order for conditions to pertain that allow for the existence of intelligent life (us). Philosophically, this observation from the workd of astrophysics seems to have some bearing Rovelli’s preposition that we exist within a peculiar subset of the quantum universe configured by the information to which we have access.
in summary; our experience of time is linear. It must be so, in order for us to construct narratives that allow us to make sense of our lives. But this probably has nothing to do with the true nature of time; everything we thought we knew about time was probably wrong, as Einstein told us over 100 years ago.