There's egg on your face, literally. You tried to juggle some eggs, it all went wrong, and now you've got to shower and change your clothes.

Wouldn't it be faster to just un-break the egg? Breaking it only took a few seconds, so why not do that again, but in reverse? Just reassemble the shell and throw the yolk and the white back inside. You'd have a clean face, clean clothes, and no yolk in your hair, like nothing ever happened.

Why don't things happen in reverse all the time?

Sounds ridiculous — but why? Why, exactly, is it impossible to un-break an egg?

It isn't. There's no fundamental law of nature that prevents us from un-breaking eggs. In fact, physics says that any event in our day-to-day lives could happen in reverse, at any time. So why can't we un-break eggs, or un-burn matches, or even un-sprain an ankle? Why don't things happen in reverse all the time? Why does the future look different from the past at all?

It sounds like a simple question. But to answer it, we've got to go back to the birth of the universe, down to the atomic realm, and out to the frontiers of physics.

Like many stories about physics, this one starts with Isaac Newton. In 1666, an outbreak of bubonic plague forced him to leave the University of Cambridge, and move back in with his mother in the Lincolnshire countryside. Bored and isolated, Newton threw himself into the study of physics.

You might mix up east and west, but you would not mix up yesterday and tomorrow

He came up with three laws of motion, including the famous maxim that every action has an equal and opposite reaction. He also devised an explanation of how gravity works.

Newton's laws are astonishingly successful at describing the world. They explain why apples fall from trees and why the Earth orbits the Sun. But they have an odd feature: they work just as well backwards as forwards. If an egg can break, then Newton's laws say it can un-break.

This is obviously wrong, but nearly every theory that physicists have discovered since Newton has the same problem. The laws of physics simply don't care whether time runs forwards or backwards, any more than they care about whether you're left-handed or right-handed.

But we certainly do. In our experience, time has an arrow, always pointing into the future. "You might mix up east and west, but you would not mix up yesterday and tomorrow," says Sean Carroll, a physicist at the California Institute of Technology in Pasadena. "But the fundamental laws of physics don't distinguish between past and future."

The first person to seriously tackle this problem was an Austrian physicist named Ludwig Boltzmann, who lived in the late 19th century. At this time, many ideas that are now known to be true were still up for debate. In particular, physicists were not convinced – as they are today - that everything is made up of tiny particles called atoms. The idea of atoms, according to many physicists, was simply impossible to test.

He was ostracised by the physics community for his ideas

Boltzmann was convinced that atoms really did exist. So he set out to use this idea to explain all sorts of everyday stuff, such as the glow of a fire, how our lungs work, and why blowing on tea cools it down. He thought he could make sense of all these things using the concept of atoms.

A few physicists were impressed with Boltzmann's work, but most dismissed it. Before long he was ostracised by the physics community for his ideas.

He got into particularly hot water because of his ideas about the nature of heat. This may not sound like it has much to do with the nature of time, but Boltzmann would show that the two things were closely linked.

At the time, physicists had come up with a theory called thermodynamics, which describes how heat behaves. For instance, thermodynamics describes how a refrigerator can keep food cold on a hot day.

Boltzmann's opponents thought that heat couldn't be explained in terms of anything else. They said that heat was just heat.

Boltzmann set out to prove them wrong. He thought heat was caused by the random motion of atoms, and that all of thermodynamics could be explained in those terms. He was absolutely right, but he would spend the rest of his life struggling to convince others.

Boltzmann started by trying to explain something strange: "entropy". According to thermodynamics, every object in the world has a certain amount of entropy associated with it, and whenever anything happens to it, the amount of entropy increases. For instance, if you put ice cubes into a glass of water and let them melt, the entropy inside the glass goes up.

Rising entropy is unlike anything else in physics: a process that has to go in one direction. But nobody knew why entropy always increased.

Once again, Boltzmann's colleagues argued that it wasn't possible to explain why entropy always went up. It just did. And again, Boltzmann was unsatisfied, and went searching for a deeper meaning. The result was a radical new understanding of entropy — a discovery so important that he had it engraved on his tombstone.

Boltzmann found that entropy measured the number of ways atoms, and the energy they carry, can be arranged. When entropy increases, it's because the atoms are getting more jumbled up.

According to Boltzmann, this is why ice melts in water. When water is liquid, there are far more ways for the water molecules to arrange themselves, and far more ways for the heat energy to be shared among those molecules, than when the water is solid. There are simply so many ways for the ice to melt, and relatively few ways for it to stay solid, that it's overwhelmingly likely the ice will eventually melt.

Similarly, if you put a drop of cream into your coffee, the cream will spread throughout the entire cup, because that's a state of higher entropy. There are more ways to arrange the bits of cream throughout your coffee than there are for the cream to remain in one small region.

Entropy, according to Boltzmann, is about what's probable. Objects with low entropy are tidy, and therefore unlikely to exist. High-entropy objects are untidy, which makes them likely to exist. Entropy always increases, because it's much easier for things to be untidy.

That may sound a bit depressing, at least if you like your home to be well-organised. But Boltzmann's ideas about entropy do have an upside: they seem to explain the arrow of time.

Boltzmann's take on entropy explains why it always increases. That in turn suggests why we always experience time moving forwards. If the universe as a whole moves from low entropy to high entropy, then we should never see events go in reverse.

The future looks different from the past simply because entropy increases

We won't see eggs un-break, because there are lots of ways to arrange the pieces of an egg, and nearly all of them lead to a broken egg rather than an intact one. Similarly, ice won't un-melt, matches won't un-burn, and ankles won't un-sprain.

Boltzmann's definition of entropy even explains why we can remember the past but not the future. Imagine the opposite: that you have a memory of an event, then the event happens, and then the memory disappears. The odds of that happening to your brain are very low.

According to Boltzmann, the future looks different from the past simply because entropy increases. But his pesky opponents pointed out a flaw in his reasoning.

Boltzmann said that entropy increases as you go into the future, because of the probabilities that govern the behaviour of small objects like atoms. But those small objects are themselves obeying the fundamental laws of physics, which don't draw a distinction between the past and the future.

Why is there an arrow of time at all?

So Boltzmann's argument can be turned on its head. If you can argue that entropy should increase as you go into the future, you can also argue that entropy should increase as you go into the past.

Boltzmann thought that, because broken eggs are more likely than intact ones, it was reasonable to expect intact eggs to turn into broken ones. But there's another interpretation. Intact eggs are unlikely and rare, so eggs must spend most of their time broken, very occasionally leaping together to become intact for a moment before breaking again.

In short, you can use Boltzmann's ideas about entropy to argue that the future and the past should look similar. That's not what we see, so we're back to square one. Why is there an arrow of time at all?

Boltzmann suggested several solutions to this problem. The one that worked best came to be known as the past hypothesis. It's very simple: at some point in the distant past, the universe was in a low-entropy state.

If that's true, then the flaw in Boltzmann's reasoning disappears. The future and the past look very different, because the past has much lower entropy than the future. So eggs break, but they don't un-break.

Within a decade, physicists accepted his ideas

This is neat, but it raises a whole new question: why is the past hypothesis true? Low entropy is unlikely, so why was the entropy of the universe in such a remarkable state sometime in the distant past?

Boltzmann never managed to crack that one. A manic-depressive whose ideas had been rejected by much of the physics community, he felt sure that his life's work would be forgotten. On a family holiday near Trieste in 1906, Ludwig Boltzmann hanged himself.

His suicide was particularly tragic since, within a decade, physicists accepted his ideas about atoms. What's more, in the decades that followed, new discoveries suggested that there might be an explanation for the past hypothesis after all.

In the twentieth century, our picture of the universe changed radically. We discovered that it had a beginning.

The universe began as an infinitely tiny speck, which exploded

In Boltzmann's time, most physicists believed that the universe was eternal – it had always existed. But in the 1920s, astronomers discovered that galaxies are flying apart. The universe, they realised, is expanding. That means everything was once close together.

Over the next few decades, physicists came to agree that the universe began as an incredibly hot, dense speck. This quickly expanded and cooled, forming everything that now exists. This fast expansion from a tiny hot universe is called the Big Bang.

This seemed to support the past hypothesis. "People said 'okay, the trick is clearly that the early universe had low entropy,'" says Carroll. "But why [entropy] was ever low in the first place, 14 billion years ago near the Big Bang, is something we don't know the answer to."

It's fair to say that an enormous cosmic explosion doesn't sound like something with low entropy. After all, explosions are messy. There are plenty of ways of rearranging the matter and energy in the early universe so that it is still hot, tiny, and expanding. But as it turns out, entropy is a little different when there's so much matter around.

Imagine a vast empty region of space, in the middle of which is a cloud of gas with the mass of the Sun. Gravity pulls the gas together, so the gas will get clumpy and ultimately collapse into a star. How is this possible, if entropy always increases? There are more ways to arrange the gas when it's wispy and scattered.

The importance of being clumpy

The answer is that gravity affects entropy, in a way that physicists still don't fully understand. With truly massive objects, being clumpy is higher entropy than being dense and uniform. So a universe with galaxies, stars and planets actually has a higher entropy than a universe filled with hot, dense gas.

This means we have a new problem. The sort of universe that emerged immediately after the Big Bang, one that is hot and dense, is low-entropy and therefore unlikely. "It's not what you would randomly expect out of a bag of universes," says Carroll.

So how did our universe start in such an unlikely state? It's not even clear what kind of answer to that question would be a satisfying one. "What would count as a scientific explanation of the initial state [of the universe]?" asks Tim Maudlin, a philosopher of physics at New York University.

One idea is that there was something before the Big Bang. Could that account for the low entropy of the early universe?

Carroll and one of his former students proposed a model in which "baby" universes are constantly popping into existence, calving off from their parent universe and expanding to become universes like our own. These baby universes could start out with low entropy, but the entropy of the "multiverse" as a whole would always be high.

Our best theories of physics can't actually handle the Big Bang

If that's true, the early universe only looks like it has low entropy because we can't see the bigger picture. The same would be true for the arrow of time. "That kind of idea implies that the far past of our big-picture universe looks the same as the far future," says Carroll.

But there's no wide agreement on Carroll's explanation of the past hypothesis, or any other explanation. "There are proposals, but nothing is even promising, much less settled," says Carroll.

Part of the trouble is that our best theories of physics can't actually handle the Big Bang. Without a way to describe what happened at the universe's birth, we can't explain why it had low entropy.

Modern physics relies on two major theories. Quantum mechanics explains the behaviour of small things like atoms, while general relativity describes heavy things like stars. But the two can't be made to combine.

Nobody has managed to come up with a theory of everything

So if something is both very small and very heavy, like the universe during the Big Bang, physicists get a bit stuck. To describe the early universe, they need to combine the two theories into a "theory of everything".

This ultimate theory will be the key to understanding the arrow of time. "Finding that theory will ultimately let us know how nature builds space and builds time," says Marina Cortês, a physicist at the University of Edinburgh in the UK.

Unfortunately, despite decades of trying, nobody has managed to come up with a theory of everything. But there are some candidates.

The most promising theory of everything is string theory, which says that all subatomic particles are actually made of tiny strings. String theory also says that space has extra dimensions, beyond the familiar three, that are curled up to microscopic size, and that we live in a kind of multiverse where the laws of physics are different in different universes.

String theory might not help explain the arrow of time

This all sounds quite outlandish. Nevertheless, most particle physicists see string theory as our best hope for a theory of everything.

But that doesn't help us explain why time moves forwards. Like almost every other fundamental physical theory, the equations of string theory don't draw a strong distinction between the past and the future.

String theory, if it turns out to be correct, might not help explain the arrow of time. So Cortês is trying to come up with something better.

Working with Lee Smolin of the Perimeter Institute in Waterloo, Canada, Cortês has been working on alternatives to string theory that incorporate the arrow of time at a fundamental level.

Time isn't really an illusion

Cortês and Smolin suggest that the universe is made up of a series of entirely unique events, never repeating itself. Each set of events can only influence events in the next set, so the arrow of time is built in. "We are hoping that if we can use these types of equations to do cosmology, we can then arrive at the problem of the initial conditions [of the universe] and find they're not as special," says Cortês.

This is completely unlike Boltzmann's explanation, in which the arrow of time emerges as a kind of accident from the laws of probability. "Time isn't really an illusion," says Cortês. "It exists and it's really moving forward."

But most physicists don't see a problem with Boltzmann's explanation. "Boltzmann pointed the correct direction to the solution here, a long time ago," says David Albert, a philosopher of physics at Columbia University in New York. "There's a real hope that if you dig carefully enough, the whole story is in what Boltzmann said."

Carroll agrees. "If you have that low-entropy Big Bang, then we're done," he says. "We can explain all the differences between the past and the future."

One way or another, to explain the arrow of time we need to explain that low-entropy state at the beginning of the universe. That will take a theory of everything, be it string theory, Cortês and Smolin's causal sets, or something else. But people have been searching for a theory of everything for 90 years. How do we find one? And how do we know we have the right one once we've got it?

Our best hope lies with the largest machine in human history

We could test it using something very small and very dense. But we can't go back in time to the Big Bang, and regardless of what a recent blockbuster movie suggested, we also can't dive into a black hole and send information back about it. So what can we do, if we really want to explain why eggs don't un-break?

For now, our best hope lies with the largest machine in human history. The Large Hadron Collider (LHC) is a particle accelerator that runs in a 27km circle under the border of France and Switzerland. It smashes protons together at nearly the speed of light. The phenomenal energy of these collisions creates new particles.

The LHC has been closed for repairs for the last two years, but in the spring of 2015 it will turn back on — and for the first time, it will be operating at full power. At half-strength in 2012, it found the long-sought-after Higgs boson, the particle that gives all the others mass. That discovery led to a Nobel Prize, but the LHC could now top it. With any luck, the LHC will catch a glimpse of new and unexpected fundamental particles that will point the way to a theory of everything.

It will take several years for the LHC to collect the necessary data, and for that data to be processed and interpreted. But once it's in, we may finally understand why you can't get that stupid egg off your face.