We know how time will end, but not how it started

The mystery around the origin of time's arrow

Times arrow

The arrow of time appears to be pointing in one very specific direction. Natural processes, from rivers flowing downhill, never uphill, to eggs always breaking, never spontaneously reassembling, to cups of coffee always cooling down, show us that direction.  Yet the laws of physics that govern the motion of all matter are time-symmetrical: they don’t distinguish between past and future. What give time’s arrow its direction is the initial conditions of each situation: an orderly state of affairs which then disintegrates into a disorderly state. The question then is, what was that original orderly state of the entire universe, giving the whole of time its direction, asks Paul Davies.

 

Take a movie of an everyday scene and play it backwards to an audience. People are sure to notice: rivers flowing uphill, broken eggs reassembling themselves, footprints washed into existence by the retreating tide… In daily life we have no trouble telling past from future, so it’s easy to spot the deception when sequences are reversed. The directionality inherent in natural phenomena is dubbed ‘the arrow of time.’ It is such a familiar part of experience that it often comes as a shock to learn that its origin is shrouded in mystery.  

Thermodynamics and the arrow of time

Physicists first got to grips with the problem of the arrow of time in the middle of the nineteenth century by considering the behavior of gas molecules rushing around and colliding. Imagine a box of gas with a barrier down the middle. Suppose the gas on the left is hotter than on the right. If the barrier is removed, the faster-moving molecules on the left collide with the slower ones on the right, redistributing the energy. Soon the gas reaches a uniform temperature, a condition known as thermodynamic equilibrium. This process is irreversible. You never see the opposite happening. Without external interference, heat always flows from hot to cold. It’s an example of the so-called second law of thermodynamics.

Although this result seemed straightforward, there was a troubling paradox lurking. The laws of physics governing the motion of molecules are time-symmetric – they make no distinction between past and future. If by some magic all the molecules in a box of gas had their velocities simultaneously reversed, the box of gas would heat up at one end and cool at the other. There is nothing in the laws of motion themselves to prevent heat flowing from cold to hot, in violation of the second law of thermodynamics. The reason we don’t see such bizarre sequences of events is because of the initial conditions. The gas in the above example started out in an ordered state, with heat energy distributed unevenly. To explain the arrow of time in the box of gas we need to explain how it attained its initial state.

There is nothing in the laws of motion themselves to prevent heat flowing from cold to hot, in violation of the second law of thermodynamics.

In 1852, the physicist Lord Kelvin applied the second law to cosmology and delivered what is undoubtedly the gloomiest conclusion in the history of science. The universe, proclaimed Kelvin, is slowly dying, stuck on a one-way slide towards a final state of total degeneration in which all sources of available energy are used up and nothing further of interest will happen.

Kelvin’s prediction of a cosmic heat death is easy to understand. We need look no further than the sun, which is busily pouring out heat lost to the cold depths of space at the prodigious rate of about 1020 megawatts. That will continue so long as the sun has reserves of nuclear fuel. But sooner or later the fuel will run out and the sun will die. Same story for all stars, and indeed the cosmos as a whole. It cannot go on forever in its present state. Like a gigantic clock ticking away, epoch by epoch, the universe will eventually run down.

But that leaves us with a profound puzzle. How did the great cosmic clock get wound up in the first place? Think back to the box of gas. The origin of its arrow of time was traced to the initial conditions: there was a temperature difference built in at the outset. The gas started out in a state of what is known as thermodynamic disequilibrium: hot at one end of the box and cooler at the other. So, is something similar true about the initial conditions of the universe?

Like a gigantic clock ticking away, epoch by epoch, the universe will eventually run down. But that leaves us with a profound puzzle. How did the great cosmic clock get wound up in the first place?

The answer comes from the fading afterglow of the big bang that gave birth to the universe we know. This cosmic microwave background radiation still bathes the universe today, and has been meticulously mapped by satellites. Contrary to the box of gas, however, the  distinctive pattern of density variations observed in the cosmic background radiation bear the distinctive hallmark of thermodynamic equilibrium, that is, a uniform temperature everywhere, right across the sky.

Where, then, is the all-important original thermodynamic disequilibrium needed to explain the arrow of time today?

Gravitational order as the source of time’s arrow

Our current understanding of what is usually taken as the origin of the universe, the big bang, suggests that the early universe was one of almost perfect simplicity and order, with matter spread nearly uniformly through space, expanding at the same rate everywhere. It is this primordial structural simplicity that is the source of time’s pervasive arrow. All the structure we observe in the universe – galaxies, star clusters, stars, planets – were sculpted from a smoother earlier state by the action of gravity. Our sun, for example, formed when a cloud of gas was pulled inwards by its own gravity, raising the temperature until nuclear reactions were triggered. The seeds of this large-scale structure were the very slight departures from uniformity – just a few parts per million – etched into the overall distribution of matter in the universe, which show up in a distinctive pattern of temperature variations observed in the CMB. These variations are thought to be the product of quantum fluctuations in the first split second after the big bang. According to this picture, gravity is the fountainhead of cosmic order from which all subsequent irreversible thermodynamic processes proceed. 

But the mystery doesn’t end there, for we are bound to ask, why was the universe born in a state of near-perfect gravitational order? A partial answer comes from the standard explanation for why the big bang was so big: inflation. The idea here is that a split second after the universe came into being, it leapt in size by a huge factor. Any gravitational irregularities present before this inflationary burst would have been smoothed out in the same way that inflating a balloon removes its wrinkles. This exceedingly brief but dramatic growth spurt was driven, according to the theory, by a huge pulse of antigravity, which served to both ’ignite’ the big bang and explain its extraordinary simplicity and near-perfect uniformity.

Gravity is the fountainhead of cosmic order from which all subsequent irreversible thermodynamic processes proceed.

Inflation driven by antigravity is more than a cosmic “just-so” story. Antigravity has a designated place in Einstein’s general theory of relativity, our best current understanding of gravity. Indeed, Einstein himself first proposed it in 1917. These days, cosmologists envision space to be pervaded by some sort of quantum field that produced a powerful antigravity force responsible for the early inflation of the universe.

Although the existence of this field is still speculative, most physicists and cosmologists find the basic idea plausible, and forms the subject of many theoretical research projects. We can ignore the technicalities here, because in terms of explaining the arrow of time, all that matters is that some form of lawlike physical process underpinned inflation. And therein lies the root of all the problems about time’s arrow. The laws assumed to govern inflation, like the laws of physics underpinning everyday irreversible processes such as heat flow, are symmetric in time – they don’t discriminate between past and future. The only way time asymmetry, the direction of the arrow of time, can be derived from time symmetric laws is by appealing to special initial conditions. In the case of inflation, that means declaring that the universe was born with the inflation field in a special state at the outset.

Accepting that the laws governing the very early cosmic epoch were indeed time symmetric means shifting the burden for time’s arrow to the very beginning – the ultimate initial conditions: the coming into existence of the universe itself. Here we really are in unknown territory. Did the universe come from nothing, that is, was the big bang the origin of space and time as well as matter? Or was something there before the big bang?

Suppose time started with the big bang. Then declaring that the universe began in a special highly-ordered state is no more a leap of faith than declaring that it started at all. On the other hand, if the big bang was just a phase, a cosmic punctuation mark so to speak, then the universe may have had no ultimate beginning at all. What then of time’s arrow?

The only way time asymmetry, the direction of the arrow of time, can be derived from time symmetric laws is by appealing to special initial conditions.

One old idea is that the big bang was really just a big bounce, and the expanding universe was preceded by a contracting one in which the arrow of time was reversed. That would make the big bang a symmetry point of high gravitational order, with the arrow pointing forwards in our epoch but backwards in the epoch on the other side of the big bang. A similar speculation that keeps coming around is that in the far future the universe may cease expanding and start to contract, faster and faster, culminating in a big crunch like the big bang in reverse. During the contracting phase, so the conjecture goes, time’s arrow is flipped. Although observations don’t currently favour a re-contracting universe, it can’t be ruled out. A third possibility is known as the multiverse. It posits that our universe is merely one of an infinite number, and that taking a god’s-eye-view - outside all of the universes -  there would be some with time’s arrow pointing forwards and an equal number with it pointing backwards, although the designation ‘forwards’ and ‘backwards’ here is arbitrary.

All these somewhat outlandish cosmological models are an attempt to permit the totality of existence to reflect the underlying time symmetry assumed to be inherent in the laws of physics. But a handful of scientists wonder whether physicists have been too fixated on symmetry and that maybe the laws of physics break the symmetry in time, perhaps by a tiny amount. In fact, they do. Some obscure processes in subatomic particle physics are observed to display a tiny preponderance of processes going in one direction of time over their inverses. Perhaps these minute effects provide a window into a deeper level of physics in which time itself comes with an inbuilt arrow, intrinsic to its nature. If so, then applying this deeper level to the birth of the universe could finally explain the centuries-old mystery of time’s arrow.

Only time will tell.

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Rupak Dey 14 December 2021

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