The nature of time is one of the most profound and longstanding problems in physics – one that no one can agree on. From our perspective, time seems to steadily progress forward with each tick of the clock.

But the closer we look, the more bizarre time becomes – from equations that state time should flow as freely backwards as it does forwards, to the strange quantum realm where cause and effect can flip on their heads.

Could it even be that time itself is an illusion?

What makes time so confounding is that we have three very different ways of defining it, which don’t easily fit together.

The first definition comes from the equations that describe how things change over time.

We have many such equations describing everything from the motion of tennis balls to the decay of atomic nuclei. In all these equations, time is a quantity, referred to as ‘coordinate time’.

Time is no more than a mathematical label to which we can assign a particular value.

The second definition of time comes from Einstein’s theories of relativity, where it’s a dimension in addition to the three we’re familiar with. It’s a direction in four-dimensional spacetime.

Our picture of reality then becomes one in which all times – past, present and future – are equally real and co-exist, just as all points in space are equally real.

More than that; time has a deep connection with gravity according to General Relativity, where the shape of spacetime is influenced by gravity.

Much of the effort at the forefront of theoretical physics over the past half-century has been devoted to unifying General Relativity with the strange world of quantum mechanics.

Mathematical frameworks that attempt to do this are known as theories of quantum gravity.

But how do we reconcile these two notions of time – the quantum mechanical idea, in which time is a mere parameter, versus the relativistic idea that time is a dimension in spacetime?

I call this ‘the first problem of physical time’.

Time in quantum gravity

The reason it’s so difficult to reconcile quantum mechanics with General Relativity is that their mathematics are fundamentally incompatible.

Not only that, but quantum effects primarily govern very small scales such as subatomic particles, while gravity impacts much larger scales such as planets and galaxies, so trying to create an experiment where both scales are not only relevant, but can be accurately measured, has proved exceedingly difficult.

Early attempts at unifying a quantum description of reality with the 4D spacetime of General Relativity led John Wheeler and Bryce DeWitt to come up with an equation – the Wheeler-DeWitt equation – in 1967, in which time no longer appears at all.

What they were attempting to describe is the quantum state of the entire Universe, independent of time. This, many physicists have suggested, means that time might just be an illusion.

But should we be so radical or dismissive about time? We’ve come a long way since then, so how does time enter current attempts to develop a theory of quantum gravity?

Here, things get very murky.

Some approaches still start from something like traditional coordinate time, but then add time again as part of a spacetime with more dimensions than the four we’re used to.

In other approaches, time emerges from more fundamental concepts about the Universe.

Time might even turn out to be ‘quantised’, meaning that if we were to zoom down to small enough scales, we would see both time and space as lumpy. So, we end up with quanta (atoms) of spacetime.

Combining quantum mechanics and General Relativity is all well and good, but there‘s one key mystery it doesn’t address: why does time only seem to flow in one direction?

This brings us to the third definition of time, stemming from thermodynamics, which describes the properties of large numbers of particles treated in terms of macro quantities like heat, temperature and pressure.

Here, time is neither a dimension nor a label, but a direction – pointing from the past to the future.

This is typically phrased as being in the direction of increasing entropy: our unwinding Universe, balls rolling downhill, ice cubes melting in a glass of water and so on.

However, despite all the irreversible processes we see around us, the fact is that, in all the fundamental equations of physics, reversing the direction of time doesn’t prevent the equations from working.

That is, time could point either way and we wouldn’t be able to tell the future from the past. Yet we see a clear difference between the past and the future.

This is ‘the second problem of physical time’. How do we reconcile the fact that our equations work just as well whichever way time is running with the irreversibility of time that we experience in the world?

For this, we might have to look towards the quantum domain and the strange phenomena of entanglement.

Read more:

• Could there be a time particle?
• Nuclear clocks: How ultra-precise measurements will let us probe the Universe like never before
• Why does time move so slowly when I’m at the gym?

Quantum entanglement

Quantum objects like electrons or photons can have properties that are not fixed before they’re measured, such as location, momentum, energy or spin direction.

That is, they can exist in a ‘quantum superposition’ of having a range of values at once, such as being spread out in space or spinning in two directions at the same time.

Only when we choose to observe a property do we force the quantum system to decide on one of the many options of that property it was co-existing in.

But if, before our measurement, an electron interacts with a second one, then this second electron can be ‘infected’ by the superposition of the first. It’ll also find itself in a limbo state prior to measurement.

We say the two electrons are quantum entangled and we have to describe them as a single quantum entity.

The strange feature of entanglement is that observing just one of the two electrons also forces the second to snap into one of the available options in its superposition. This will happen at the same time, however far apart they are.

And it’s not even the entanglement between two electrons that needs to be considered. The entire Universe can become – indeed will inevitably become – quantum entangled with its surroundings.

In fact, we should stop thinking of quantum entanglement as some sort of bizarre phenomenon that only rarely happens in nature, or that it’s ‘spooky’, as Einstein once said.

Rather, it’s one of the most, if not the most prevalent process in the Universe. So, how can it help us demystify the nature of time?

In 1983, Don Page and William Wootters first suggested a link between time and quantum entanglement, rescuing time from the timeless Wheeler-DeWitt equation.

Imagine that some hypothetical quantum clock is entangled with its environment.

Instead of thinking of the clock being in a superposition of two locations in space, we can combine them into an entangled clock+environment system in a superposition of states at different times.

Now, when we measure the clock by reading the time, it forces the clock’s environment to snap into what it was doing at that time only.

So, what if we think of the overall state of the Universe, which might be timeless, as being composed of two parts: (1) a clock and (2) everything else?

For us, embedded within the ‘everything else’, perceiving a particular time amounts to measuring the clock at that time, so we perceive reality – the clock’s environment, aka the Universe – at that moment.

But, viewed from ‘outside’ the Universe, all times co-exist and there’s no ‘passage’ of time, as Wheeler and DeWitt argued.

Quantum causality

If quantum mechanics tells us that a system can be in a superposition of states at two different times, then this has an even more fascinating consequence when we consider the ordering of cause and effect.

That is, for something to occur, the cause must come before the effect.

Consider two events, A and B, such as flashes of light made by two sources in different places.

Cause and effect means there are three possibilities: 1) Flash A happened before flash B, and via some mechanism, could have triggered B; 2) Flash B happened before Flash A and could have triggered it; 3) Neither one could have triggered the other because they are too far apart in space and too close in time for a triggering signal to have been sent from one location to the other.

Now, Einstein’s Special Theory of Relativity states that all observers, no matter how fast they’re moving relative to each other, see light travelling at the same constant speed.

This strange but simple fact can lead to observers seeing events happening in different orders.

For option (3) above, two observers moving relative to each other close to the speed of light might disagree on the ordering of flashes.

Thankfully, there’s no danger of an effect coming before its cause (known as a ‘violation of causality’) since the events are too far apart for either to cause the other.

However, what if options (1) and (2) coexisted in a quantum superposition? The causal order of the two events would no longer be fixed.

They would exist in a combined state of Flash A happening before and triggering Flash B, and of B happening first. We see then that cause and effect can become blurred when we bring quantum mechanics and relativity together.

It gets even weirder when we introduce gravity via General Relativity.

Here’s an interesting thought experiment. Imagine two quantum entangled clocks, each in a superposition of different heights above Earth’s surface.

According to General Relativity, this would mean the two clocks tick at slightly different rates, due to the slight difference in the gravitational field.

The superposition here is a combination of State 1 in which clock A is higher than clock B, and so ticking a little faster, and State 2 in which the clocks are swapped over.

Until this combined entangled state is measured by reading the time on one of the clocks, it’s not possible to determine the ordering of any events recorded by the two clocks.

And if we can’t determine which events are in the future and which are in the past, we arrive at the possibility of events acting backwards in time to cause events in their past.

If, at the quantum level, events in the past can be affected by events in the future, then all bets are off.

While some physicists argue that causality is sacred and must be preserved at all costs, others have argued in favour of the idea of retrocausality (the future affecting the past) and even of quantum time travel.

It may well be the case that even if we find our true theory of quantum gravity, time will turn out not to be one single concept, but rather a multi-faceted, complex thing.

Perhaps it really does retain its different properties depending on how we’re using it: a dimension of spacetime, a coordinate to be measured against, and an irreversible arrow.

All of these are only meaningful in the approximate, zoomed-out way we subjectively perceive time. Maybe that’s the best we can hope for.

Or maybe, just maybe, we need to dig even deeper into the mysteries of time.

Read more:

• How to change your perception of time (and make life seem longer)
• If time travel were possible, should you really avoid contacting yourself?
• Animals can experience time very differently to humans. Here’s why