I think it's no mystery at all if you consider Heisenberg's uncertainty principle. To reverse the arrow of time would mean that all particles reversed their mom

I think it's no mystery at all if you consider Heisenberg's uncertainty principle. To reverse the arrow of time would mean that all particles reversed their momentum. Observing that maybe in a limited area of space would tell us that the arrow of time has clearly been reversed since things move towards more organization rather than less. The observed entropy would decrease. But since particles do not even have precise momentum it makes no sense that you could precisely reverse it. This imprecision is everywhere and as it interacts with its surroundings it can only grow larger. Therefore entropy can never decrease and time can never flow backwards.