Maccone has taken a slightly different view of this problem by looking at correlations. Imagine I do something that increases entropy slightly, and my wife observes the results of my actions and records the consequent increase in entropy—we will leave the fight over who should tidy up the mess out of the story.
Now, I can choose a set of operations that can return the entropy to its previously low value. However, doing so involves not just reversing my actions, but also reversing all correlated systems. In other words, I have to wipe my wife's memory of the event and her subsequent recording of it. If she wrote it on a piece of paper, I have to wipe the paper clean etc, etc. But at the end of it, there would be no record of the event ever having occurred.
The upshot is that entropy-decreasing events can occur, but can never be observed from within the system.
Well, put simply, running time in one direction allows records to be kept and events to be observed. In the other direction, observation becomes impossible.
(Arstechnica: Quantum amnesia gives time its arrow )
"But if you analyse [the laws] carefully, you'll see that all the processes where things run backwards can happen, but they don't leave any trace of having happened," he says.
Maccone argues that in systems in which entropy has decreased, the connections or correlations between events and observers is wiped out. Lacking this information, observers like us cannot see such an event (Physical Review Letters, vol 103, 080401).
In the world of large-scale objects, increasing entropy is associated with the flow of heat, which always goes from a hot object to a colder one. Change in entropy can also be described as a flow of information: the higher the entropy of a system, the less information it contains.
An outsider who observes the box may become more entangled with it. This entanglement – which involves the loss of information in the particles – increases the information available to the observer.
(Newscientist: Quantum amnesia gives time its arrow )