For all we know we may live in a world in which windows un-break and cold cups of coffee spontaneously heat up, we just don't remember. The explanation is quantum entanglement

Imagine if a cold cup of coffee spontaneously heated up as you watched. Or a cracked pane of glass suddenly un-broke. According to physicist Lorenzo Maccone at the Massachusetts Institute of Technology, you see things like this all the time – you just don't remember.

In a paper published last week in Physical Review Letters, he attempts to provide a solution to what has been called the mystery of "the arrow-of-time".

Briefly, the problem is that while our laws of physics are all symmetrical or "time-reversal invariant" – they apply equally well if time runs forwards or backwards – most of the everyday phenomena we observe, like the cooling of hot coffee, are not. They never seem to happen in reverse.

We have a statistical law that describes these everyday phenomena called the Second Law of Thermodynamics. This law tells us that the "entropy" or degree of disorder of a closed system never decreases. Roughly speaking, a process in which entropy increases is one where the system becomes increasingly disordered. Windows break, thereby increasing disorder, but they will not spontaneously unbreak. Gases will disperse but not spontaneously compress.

However, entropy describes what happens with large numbers of particles. We presume that it must arise from what happens with individual particles, but all the laws that govern the behaviour of individual particles are time-reversal invariant. This means that any process they allow in one direction of time, they also allow in the other.

So why will your coffee spontaneously cool down, but not heat up?

Maccone's solution is to suggest that in fact entropy-decreasing events occur all the time – so there is no asymmetry and no associated mystery about the arrow of time.

He argues that quantum mechanics dictates that if anyone does observe an entropy-decreasing event, their memories of the event "will have been erased by necessity".

Maccone doesn't mean that your memories will never form in the first place. "What I'm pointing out is that memories are formed and then are subsequently erased," he tells me.

When you observe any system, according to Maccone, you enter into a "quantum entanglement" with it. That is, you and the system are entangled and cannot properly be described separately.

The entanglement, Maccone says, is between your memory and the system. When you disentangle, "the disentangling operation will erase this entanglement, namely the observer's memory". His paper derives this conclusion mathematically.

While we cannot remember our cups of coffee re-heating, and hence cannot study them, Maccone thinks that entropy-decreasing events like that must happen.

"If transformations that increase the entropy do occur – and we know that they do – by symmetry we should expect also transformations that decrease the entropy – but we cannot see them."

I'm not convinced that Maccone has solved the dilemma of the arrow of time, and I'm not alone.

One problem is that, as he acknowledges, he cannot prove that entropy-decreasing events occur. Rather, he shows that if they do, we won't remember them.

Concerns about symmetry lead him to conclude that they must in fact happen. However, it is statistically very (very, very very) unlikely that the entropy of a macroscopic system will decrease.

It's all down to the way particles move around. In a gas, for example, there are many fewer ways in which the particles can be in a lower entropy state than there are ways for them to be in a higher entropy state. So the most likely state either before or after is one of higher entropy – simply because there are many more such states for the system to occupy.

Importantly, the statistics of entropy do not predict an asymmetry, because they suggest entropy should neither decrease towards the past nor decrease towards the future.

The mystery of the arrow of time is that entropy only increases towards the future. Put another way, why does entropy actually decrease towards the past, despite what the statistics predict?

Maccone says that "we should expect" entropy decreases towards the future since they occur towards the past. But the statistics show us that we should expect no such thing. It is enormously surprising that they happen towards the past and it would be doubly surprising if they happened towards the future. Symmetry is not a reason to expect what we know is statistically extremely unlikely.

Huw Price, head of the Centre for Time at the University of Sydney, thinks Maccone is simply trading one mystery for another.

"The proposal to explain the thermodynamic arrow in terms of the [quantum] effects of observers has an obvious flaw," he says. "It doesn't explain why all observers have the same orientation in time ... Why don't some observers remember what we call the future, and accumulate information towards what we call the past?"

A standard way of explaining why observers like us remember the past is by appealing to thermodynamics – the fact that entropy is increasing. This explanation is unavailable to Maccone since his theory takes that thermodynamic fact to depend on the existence of observers. Such an explanation, for Maccone, would thus be circular.

If Price is right, then Maccone has explained one temporal asymmetry at the expense of creating another that is equally hard to explain.

What's more, Price thinks that Maccone has made a hidden asymmetrical assumption. He argues that the quantum correlations Maccone relies on must be assumed to happen only in one temporal direction and not the other. "But that's just assuming the conclusion he wants to derive."

Whether or not Maccone has solved the mystery of the arrow of time is unclear. But to tell the truth, it would suit me just fine if my cold cup of coffee heated back up all on its own. I don't even care if I remember it happening or not.

Michael Slezak is a freelance journalist and teaches the philosophy of science at the University of Sydney, Australia