Science has a habit of asking stupid questions. Stupid, that is, by the standards of common sense. But time and time again we have found that common sense is a poor guide to what really goes on in the world.

So if your response to the question "Why does time always go forwards, not backwards?" is that this is a daft thing to ask, just be patient.

Surely we can just say that the future does not affect the past because (duh!) it has not happened yet? Not really, for the question of where time's arrow comes from is more subtle and complicated than it seems.

What's more, that statement might not even be true. Some scientists and philosophers think the future might indeed affect the past – although we would only find out when the future arrives. And it may be able to due to an emergent property of quantum mechanics.

To all intents and purposes, time seems to have a direction.

Our everyday experience insists that things only happen one way. Cups of coffee always get colder, never warmer, when left to stand. If they are knocked to the floor, the cup becomes shards and the coffee goes everywhere, but shards and splashes never spontaneously reassemble into a cup of coffee.

Yet none of this one-way flow of time is apparent when you look at the fundamental laws of physics: the laws, say, that describe how atoms bounce off each other.

Those laws of motion make no distinction about the direction of time. If you watched a video of two billiard balls colliding and bouncing away, you would be unable to tell if it was being run forwards or backwards.

The same time symmetry is found in the equations of quantum mechanics, which govern the behaviour of tiny things like atoms. So where does time's arrow come into the picture?

There is a long-standing answer to this, which says that the arrow only enters once you start thinking about lots and lots of particles.

The process of two atoms colliding looks perfectly reversible. But when there are lots of atoms, their interactions lead inevitably to an increase in randomness – simply because that is by far the most likely thing to happen.

Say you have a gas of nitrogen molecules in one half of a box and oxygen molecules in the other, separated by a partition. If you take away the partition, the random movements of the molecules will quickly mix the two gases completely.

There is nothing in the laws of physics to prevent the reverse. A mixture of the two gases could spontaneously separate into oxygen in one half of the box and nitrogen in the other, just by chance.

But this is never likely to happen in practice, because the chance of all those billions of molecules just happening to move this way in concert is tiny. You would have to wait for longer than the age of the Universe for spontaneous separation to occur.

This inexorable growth of randomness is enshrined in the second law of thermodynamics. The amount of randomness is measured by a quantity called entropy, and the second law says that, in any process, the total entropy of the Universe always increases.

Of course, we can decrease the entropy of a group of molecules, say by sorting them one from another. But doing that work inevitably releases heat, which creates more disorder – more entropy – somewhere else. Ordinarily, there is no getting around this.

However, the entropic arrow of time gets less well-defined at smaller scales. For example, the chances of three oxygen and two nitrogen molecules briefly "un-mixing" are pretty good.

This was illustrated by a 2015 study. Researchers studying single molecules found evidence that the growth of entropy is a good measure of how far the system was from being reversible in time.

This argument about entropy, which was worked out in the late 19th Century by the Austrian scientist Ludwig Boltzmann, is often seen as a complete and satisfying answer to the puzzle of time's arrow.

But it turns out the Universe holds deeper secrets. When you start looking at very small things, Boltzmann's neat story gets increasingly muddled.

In Boltzmann's picture, it takes a while for the arrow of time to find its direction. In the tiny fractions of a second after the partition between the two gases is removed, before any of the molecules have really moved anywhere, there is nothing to show which direction of time is forwards.

Entropy increases when collisions between atoms even out their energies, as for example when the heat of hot coffee spreads out into the surrounding air. This process, which washes away reservoirs of energy, is called dissipation.

Until dissipation starts to happen, a process looks much the same backwards or forwards in time. It does not really have a thermodynamic arrow.

But there is a one-way process in quantum mechanics that happens much faster. It is called decoherence.

At the quantum scale, particles behave as if they were waves. This has peculiar consequences.

For example, if you shoot individual electrons or whole atoms through two closely spaced slits in a screen , they will interfere with each other as if they were waves. But this does not happen with ordinary-sized objects. If you throw two coffee cups through two open windows, they do not interfere with each other.

Decoherence explains why objects on the everyday scale of coffee cups do not show the wave-like behaviour of quantum objects.

It arises because quantum particles can be coordinated in their quantum waviness, but if there are lots of them – like the countless atoms in a coffee cup – they rapidly lose any coordination. This means the object they constitute cannot show quantum behaviour.

Decoherence happens because of interactions between the objects and their environment: for example, the impact of air molecules on the cup. Quantum theory shows that these interactions rapidly cause a large object's quantumness to "leak" into its environment.

This means the object takes on unique characteristics. Quantum theory tells us that objects can show one of many possible properties when they are measured, but in our everyday world objects only have a single well-defined position, speed and so on. Decoherence is thought to be how this "choice" is enforced.

Quantum decoherence is incredibly fast, because interactions between particles are extremely efficient at dispersing quantum coherence.

For a dust grain one-thousandth of a centimetre across, floating in air, the collisions of other air molecules will destroy any quantum behaviour in around 0.0000000000000000000000000000001 seconds. That is a trillionth of the time it takes for light to cross the face of a single hydrogen atom.

This is much faster than the time it takes for heat in a dust grain to get redistributed in the environment. In other words, decoherence is faster than dissipation – and it seems to only work one way. That means decoherence reveals the arrow of time faster than dissipation.

This implies that the arrow of time really comes from quantum mechanics, not thermodynamics as Boltzmann thought.

In a sense it has to, because everything is made of atoms, and quantum mechanics is the right theory to use for atoms. "The thermodynamic arrow of time must emerge from the quantum one," says George Ellis of the University of Cape Town in South Africa.

Yet in the end, the quantum and thermodynamic explanations amount to the same thing: the scrambling of information.

It is easy to see that the mixing of two types of gas molecule is a kind of scrambling, a destruction of orderliness.

But decoherence involves scrambling too: of the coordination between the "waves" that describe quantum objects. In effect, decoherence comes from the way interactions with atoms, photons and so on in an object's environment carry away information about the object and scatter it around. This is, in fact, a quantum version of entropy.

In both the classical and the quantum cases, then, time's arrow comes from a loss of information.

This offers a better way to think about time's arrow. It points in the direction in which information is lost and can never be retrieved.

A process is only truly irreversible when the information about the change is lost, so that you cannot retrace your steps. If you could keep track of the movement of every single particle, then in principle you could reverse it and get back to exactly where you started. But once you have lost some of that information, there is no return.

"The loss of information is a key aspect," says Ellis. "At the macroscopic scale this gives the second law."

It is still not entirely clear when, in the quantum world, the information is truly lost.

Some researchers think that decoherence alone is enough. But others say that the information, although smeared and dispersed in the environment, is still recoverable in principle. They think an additional, rather mysterious process called "collapse of the wave function" – in which the quantum waviness is irreversibly lost – takes place. Only then, they say, does the arrow of time point unambiguously in one direction.

In either case, in quantum physics we can only really say that an event has happened if we have lost the option of making it "unhappen".

The arrow of time seems to reflect a process of the Universe "committing itself" to something, rather than hedging its bets by allowing for many different outcomes. It is this "crystallising" of the classical present from the quantum past, says Ellis, that produces a direction in time.

This idea fits neatly with one of the most famous thought experiments in physics.

The second law of thermodynamics says that things tend to become more random, but only because randomness is so likely. In the late nineteenth century, the Scottish physicist James Clerk Maxwell came up with what looked like a way to get around this.

Maxwell imagined a tiny intelligent being that could observe the random motions of molecules. This "demon" could un-mix two gases, by opening and closing a door at just the right moments.

Maxwell's demon seems to violate the second law, but in fact it cannot. The reason is that the demon has to accumulate information in its brain as it observes the molecular motions. To keep this up, it has to delete the older information, and that increases the entropy.

It is the act of erasure, of forgetting, that guarantees the thermodynamic arrow of time. Once again, the key thing is loss of information.

However, the quantum-mechanical picture of time's arrow leads to something deeply peculiar. In some experiments, it looks as though influences can work backwards in time. The future can affect the past.

Take the double-slit experiment, in which a quantum particle such as a photon of light is fired at two narrow slits in a screen.

Suppose we do not measure which way the particle went, and so cannot tell which slit it went through. In this case, we see an interference pattern – a series of light and dark bands – when the particles emerge on the far side.

This reflects the wave-like character of quantum particles, because interference is a wave property. The interference even persists when the particles pass through the slits one at a time, which only "makes sense" intuitively if we imagine each particle passing, wave-like, through both slits at once.

However, now suppose we place a detector by the slits to reveal which one the particle passes through. In this case the interference pattern disappears, and the particles act more like sand grains being fired through holes. Measuring a particle's path destroys its waviness.

Here is the really strange thing. We can set up the experiment so that we only detect which slit a particle passed through after it has done so. And yet we still see no interference.

How does the particle "know" that it is going to be detected after passing through the screen, so that when it reaches the slits it "knows" whether to go through both slits or just one? How can the later measurement seem to affect the earlier behaviour?

This effect is called "retrocausality", and it seems to imply that the arrow of time is not as strictly one-way as it seems. But does it really?

Most physicists think that retrocausality in these delayed-choice experiments is an illusion created by the counterintuitive nature of quantum mechanics.

Detecting a particle "after" it has passed through the slits does not really influence the path it takes, they say. That is just the way we are forced to imagine what is happening when we try to apply our classical intuition to quantum events.

"Post-selection is like a parlour trick that makes it seem like there is backwards causation where there actually is none," says Todd Brun of the University of Southern California. "It's like the guy who shoots at the side of a barn and then goes and draws a target around the bullet hole."

However, others say that backwards effects in time are a perfectly valid way of interpreting such processes.

According to Ellis, we can regard retrocausality as a kind of fuzziness in the "crystallisation of the present". "Quantum physics appears to allow some degree of influence of the present on the past, as indicated by delayed-choice experiments," he says.

Ellis has argued that the past is not always fully defined at any instant. It is like a block of ice that contains little blobs of water that have not yet crystallized.

Even though the broad outline of events at a particular instant has been decided, some of the fine details remain fluid until a later time. Then, when this "fixing" of the details happens, it looks like they have retrospective consequences.

It is hard to find the right words to describe this situation.

Certainly we should not imagine a "force" reaching back through time and altering earlier events. Instead, those things are slow to acquire the true status of events – of stuff that has actually "happened" – at all.

Alternatively, perhaps those past events really did happen at the time, but the laws of quantum mechanics forbid us from seeing them until later. "If the future detector choice causes the particle to behave a certain way in the past, one should consider the past behavior 'real' when it originally happened," says Ken Wharton of San José State University in California.

Quantum retrocausality crops up quite naturally if, instead of trying to force an arrow of time onto quantum theory, we simply let quantum mechanics work equally well in both directions in time. Wharton's colleague Huw Price of the University of Cambridge in the UK has argued that such a theory really would allow backwards causation.Still, Wharton admits that such retrocausal theories are speculative.

Only a handful of physicists and philosophers have embraced retrocausality. Most consider backwards causality "too high a price to swallow", says Wharton.

But he feels that we only resist this idea because we are not used to seeing it in daily life.

"The view that the past does not depend on the future is largely anthropocentric," says Wharton. "We should take apparent backwards causation more seriously than we usually do. Our intuition has been wrong before, and this time symmetry on quantum scales is a reason to think we could be wrong again."

If time's arrow is not quite as one-way as it seems, that raises one last question: why do we perceive it as always pointing one way? Why should the "psychological arrow of time" be aligned with the physical ones?

Again, it might sound like an odd question. If the laws of physics dictate an arrow of time, surely our perception of it should follow quite naturally? But that is not as obvious as it sounds.

Suppose you have some particles moving around in a box according to physical laws. If you know all the exact positions and speeds of the particles right now, you can predict the future exactly.

In principle, there is nothing in the future that could not be known in the present. Why could that not be experienced as a "memory" of the future; a little like a master chess player seeing well in advance how the game will inevitably end?

This question is usually swept under the carpet. "Since biology rests on a foundation of chemistry, which rests in turn on foundations of quantum mechanics and thermodynamics, I think most people believe that the biological arrow of time is a consequence of the thermodynamic arrow," says Brun.

But this is not a foregone conclusion. Brun and his colleague Leonard Mlodinow at the California Institute of Technology in Pasadena have argued that the psychological and thermodynamic arrows of time are actually independent. They only coincide because of how our memories work.

The first part of the argument was put forward by David Wolpert of the Santa Fe Institute in New Mexico. He said that, before you can remember something, you must initialize your memory in some standard starting state; like wiping your hard drive to make space for new data.

But as Maxwell's demon showed us, erasing information always increases entropy. This means initialization is an irreversible process, and so only works forward in time.

However, Mlodinow and Brun say that this argument is not quite complete. In principle, you can eliminate any need for erasure and initialization just by remembering everything. Then, recording information in the memory can be fully reversed, and has no arrow of time.

In this case, they argue that the psychological arrow of time is still preserved, by something they call "generality".

The problem with remembering the future now is that there can always be "surprise" events that wreck the link between the system's state now and its state in the future. I can "remember" that my clock will show 11 o'clock in an hour's time – but if the battery runs out in ten minutes, my "memory" will be wrong.

A real memory cannot be contingent on the system behaving a certain way, Mlodinow and Brun say. It has to remain general, meaning it is true whatever happens. So even if memory is recorded in a reversible system, the requirement of generality imposes a directionality in time.

In this case, says Brun, the reason we cannot remember the future is not simply because it has not happened yet. Instead, it is because the "memory" would really only be a prediction, which might or might not be correct. And it is not a true memory unless it is correct.

In other words, a putative "future memory" is fine-tuned to a particular outcome, and must be readjusted if any slight change occurs between now and the appearance of the "remembered" future state. That means it is too fragile to count as a genuine memory.

Not everyone is convinced that Brun and Mlodinow have cracked the problem.

Some think their argument is circular. They had to put in the asymmetry of time by hand, making it possible for contingent events to intervene in the future but not the past – which some feel is a bit of a cheat.

All the same, simply by posing the question, Brun and Mlodinow have shown that the answer is not as obvious as we might suppose. Our perception of time may not have much to do with the actual passage of time.

What is clear is that the arrow of time, which seems like such a common-sense fact of life, is actually a profoundly tricky concept. The closer we look, the less we can be sure that the arrow is really always one-way.

Join over five million BBC Earth fans by liking us on Facebook, or follow us on Twitter and Instagram.

If you liked this story, sign up for the weekly features newsletter called "If You Only Read 6 Things This Week". A handpicked selection of stories from BBC Future, Earth, Culture, Capital, Travel and Autos, delivered to your inbox every Friday.