The Janus Point

CHAPTER 1

TIME AND ITS ARROWS

TIME FLOWS FORWARD. EVERYONE HAS THE FEELING. IT IS MORE THAN MERE feeling; it has a real counterpart in observable phenomena. Processes near and far in space and time all unfold in the same direction. All animals, us humans included, get older in the same direction. We never meet anyone getting younger. Astronomers have observed millions of stars and understand very well how they age—all in the same direction as us. On seashores around the world, waves build and break—they never ‘unbreak’.

We remember the past, not the future. There are arrows of time. A film run backwards confounds cause and effect: instead of divers making a splash on entering the water, they emerge from it while the splash disappears. Myriad arrows permeate our existence. They are the stuff of birth, life, and death. In their totality, they define for us the direction of time.

Three arrows are particularly important because they can be treated with a good degree of mathematical precision.

The first, with which we will be much concerned, is the common process of equilibration. To see an example and its end result, put a tumbler of water on a table and disturb its surface by stirring the water vigorously with your finger. Remove your finger. Very soon the disturbance subsides and the surface becomes flat. You have witnessed an irreversible process. You can watch the surface for hours on end and it will never become disturbed spontaneously. The observationally unchanging state reached through equilibration corresponds to equilibrium. This is an example you can see. More important for the subject of this book is one you can feel—the equalisation of temperature. Go from a warm room to a cold room and you immediately feel the difference because your body is losing heat to the air around it. Many similar examples could be given: hot coffee in a mug, if not drunk, cools to the ambient temperature of the room.

The next arrow relates to what are called retarded waves. Don’t worry about the name. You see a beautiful example whenever you throw a stone into a still pond and circular waves spread out from the point of entry. The waves are said to be retarded because they are observed after the impact of the stone—the effect follows the cause. You never see waves that mysteriously start in unison at the bank of the pond, converge on its centre, and eject a stone that then lands in your hand—although the laws of hydrodynamics and mechanics are perfectly compatible with the possibility. It is not only water waves that invariably exhibit retardation; so do the radio and TV signals that reach your home from transmitters.

The third example is in quantum mechanics and is the notorious problem of Schrödinger’s cat. In accordance with the quantum formalism, a certain wave function can describe a cat that is simultaneously both dead and alive. Only when an observation is made to establish the cat’s state is there collapse of the wave function and just one of the two possibilities is realised.

Arthur Eddington, the British astrophysicist who in 1919 made Einstein into a world celebrity overnight with a famous telegramme to the London Times that confirmed a prediction of the general theory of relativity, coined the expression ‘arrow of time’ in the 1920s. Eddington had in mind mainly the arrow associated with equilibration, but people often use it as a portmanteau expression to cover all the arrows, as I will.

BECAUSE THE ARROWS of time are so ubiquitous it’s easy to take them for granted, but since the early 1850s theoreticians have seen in them a major problem. It is easily stated: apart from a tiny temporal asymmetry in one single law that, just after the big bang, was one of the factors that prevented complete mutual annihilation of matter and antimatter but cannot have played any significant role in creating the currently observed huge asymmetry between past and future, all the remaining laws of nature make no distinction between past and future. They work equally well in both time directions. Take a very simple law, the one that governs billiard balls. Unlike divers plunging into water, a film that spans their impact does look the same forwards and backwards. Physicists say laws like that are time-reversal symmetric. By this, they do not mean that time is reversed but that if at some stage all relevant velocities are precisely reversed, the balls will retrace, at the same speeds, the paths previously taken. More complicated is the case of charged particles in a magnetic field; the direction of the field must also be reversed along with the particle velocities if the retracing is to occur. There is an even more subtle case related to electric charges, mirror reflection, and the single fortuitous rule-breaking exception which allowed a minuscule amount of matter to survive after the big bang and we who are made of it to come into existence billions of years later. In all cases, the problem is the same: if the individual laws of nature that count do not distinguish a direction of time, how does it come about that innumerable phenomena do?

This question throws up such basic issues that we cannot hope to answer it unless we identify secure foundations for our theorising. One such foundation is that all meaningful statements in science are about relationships. This applies to the very notion of the direction of time. We recognise one because all around us we have those multitudinous unidirectional arrows. Without their constant presence, a single diver emerging backwards out of turbulent water, leaving it smooth and flat, would not appear to violate the normal course of nature. Also important are the nature and precision of observation. Wearing night-vision spectacles sensitive to infrared light, we would not see the collision of billiard balls as the same backwards and forwards—we would see hot spots appear on both balls after the collision, while the film run backwards would show those spots disappearing. In cricket, infrared imaging cameras are used when umpires are in doubt whether the ball has nicked the bat or pad and, through friction, raised the temperature at a localised spot.

This sensitivity to the means of observation raises a critical question: are the laws of nature truly time-reversal symmetric? The answer almost universally given is that yes, they are at the fundamental level of elementary particles—there is no microscopic arrow of time, only one at the macroscopic level. This was the conclusion that scientists reached in the second half of the nineteenth century. It came about in the first place through one truly remarkable study. Towards the end of the eighteenth century, people started to investigate seriously the properties of heat. A large part of the stimulus for this was to understand the workings of steam engines and how to make them as efficient as possible. In 1824, the young French engineer Sadi Carnot published a book, remarkable for its profundity and brevity, on this problem. Initially it passed unnoticed, but in 1849 a paper by William Thomson (later Lord Kelvin) brought Carnot’s work to the notice of Rudolf Clausius, with dramatic effect: together with Thomson, Clausius played a key role in the creation of an entirely new science, for which Thomson coined the name thermodynamics.

Its first law states that energy can be neither created nor destroyed. Within physics, this formalises the long-held belief reflected in Lear’s warning to Cordelia: “Nothing will come of nothing”. The second law of thermodynamics introduces the fundamental concept of entropy, a great discovery by Clausius, who introduced the name. Entropy is, to say the least, a subtle notion that, since Clausius’s discovery, has been formulated in many different ways. Indeed, a search through the technical literature throws up about twenty different definitions of the second law. Some of them include entropy; others do not. Despite that, entropy is one of those scientific concepts that have entered common parlance along with energy, the big bang, the expansion of the universe, black holes, evolution, DNA, and a few more. In a non-technical simplification that can mislead, entropy is widely described as a measure of disorder. The most common formulation of the second law states that, under controlled conditions that allow proper definition, entropy cannot decrease and generally will increase. In particular, entropy always increases in any process of equilibration in a confined space. Among the various arrows of time, entropy’s growth is the one that the majority of scientists take to be the most fundamental. The second law, often referred to without the addition ‘of thermodynamics’, has acquired an almost inviolable aura. In quite large part this is due to Clausius, who knew how to make sure that, deservedly, his results lodged securely in the mind. The paper of 1865 in which he coined ‘entropy’ ends with the words “Die Entropie der Welt strebt einem Maximum zu” (the entropy of the universe tends to a maximum). This statement had the impact that Clausius intended and was taken to mean that the universe will eventually expire in the heat death of thermal equilibrium. In human terms, there’s a near anticipation of this in the final quatrain of Shakespeare’s Sonnet 73:

Not surprisingly, the second law is grist for the mill of all pessimists. For many scientists, the growth of entropy, and with it disorder, is the ineluctable arrow that puts the direction into time. The mystery then is how the arrow gets into things so profoundly if the laws give no indication that it should.

THE DIFFICULTY RESIDES in the structure of the laws. By themselves they do not tell you what will happen in any given situation. You have to specify an initial condition. In the billiard example, you need to say where the two balls are at an initial time and the velocities they have at that moment. The law will then tell you what subsequently happens. It will give you a solution. The situation is this: Law + Initial Condition → Solution. In the simplest billiard example, the solution is time-reversal symmetric, just like the law that creates it. But the examples of processes with which I began this book most definitely are not. As I indicated then, scientists have not yet been able to resolve the mismatch between the symmetric laws and the asymmetric solutions.

What they have been able to do is at best give a partial solution. To illustrate this, one needs a game with more balls than billiards: snooker. The game begins with the white cue ball striking the triangle of fifteen reds. Successive impacts send the balls flying in all directions. No individual two-ball impact distinguishes a direction of time. But what then happens does. That’s where the law which at the elementary two-ball (microscopic) level describes a phenomenon without an arrow is able to create a many-ball effect with a macroscopic arrow. Theoreticians are universally in agreement that many dynamical ‘agents’ (the balls in snooker, elementary particles in fundamental physics) must be present if a macroscopic arrow is to emerge from time-symmetric microscopic laws.

However, this is at best a necessary condition; by itself it is not sufficient. To understand this, make a film of the initial impact in a game of snooker, its explosive effect, and a few bounces off the table walls. Run it backwards. Each individual impact again satisfies the reversible billiard law. But, in a seeming miracle, reds with apparently random speeds and directions of motion conspire in the midst of their chaos to come to rest in a perfect triangle and eject the white.

Of course, there is no miracle. The game begins with a special initial condition. That singles out a special solution. Only the tiniest fraction of all possible solutions is like that. But the example does at least show that reversible laws are compatible with solutions like ‘unbreaking’ waves, provided that sufficiently many objects are involved. There is no absolutely irreconcilable conflict with the laws of nature even if one has to invoke something close to divine intervention. De facto, this is what physicists are forced to do. They have to assume that at some time in the distant past, most probably at the big bang, the universe was in a special state of extraordinarily high order, the ultimate origin of all time’s arrows.

The philosopher of science David Albert has dubbed this assumption the ‘past hypothesis’. It was first proposed by the great Austrian physicist Ludwig Boltzmann in the 1890s as one possible way to explain what is now called the arrow of time. But it’s a stopgap he did not favour because it does not respect temporal symmetry. Science aims to explain phenomena by laws, not by inexplicable initial conditions arbitrarily imposed. By that criterion, the hypothesis fails, as I think Albert himself would not deny. But this leaves us in a very uncomfortable place: the most profound aspects of existence are attributed not to law but to a special condition ‘put in by hand’. It’s not a resolution; it’s an admission of defeat. However, I would not be writing this book if that were all I had to say. Plenty of other writers have already done a good job of describing the problem; their books are included in the bibliography and there are brief comments about them in the notes to this chapter.

INSTEAD, I’M GOING to suggest that the problem could have a genuine—and surprisingly simple—resolution. My collaborators and I stumbled on it a few years ago while working on a different problem. In this chapter I will give you an outline of our proposal and then fill out the necessary details in the chapters that follow. If the proposals that I present are on the right lines, I think that, taken together, they do amount to a new theory of time itself and not just its arrows. While the arrows by themselves represent a major aspect of time and a huge part of our deepest and most intimate experience, a proper understanding of their nature is impossible without a radical transformation of our notion of time. Accordingly, this book has two parts. The first sets the scene with a brief history of thermodynamics, formulates its principles, and explains why they fail to solve the problem of time’s arrows. The second presents the proposed solution; it takes up the bulk of the book.

We need the history because thermodynamics grew out of a specific problem which arose at a particular point in time: the industrial revolution and Sadi Carnot’s search for the most efficient way to operate steam engines. In that slim booklet published in 1824 he laid down principles of remarkable robustness—they have stood now for almost two hundred years—but they all apply in a ‘box scenario’, that is, to steam, gas, or any fluid in an impermeable and insulating container. Despite this critical condition, it is widely assumed that the laws of thermodynamics and the notion of entropy can be carried over more or less unchanged to cosmology. But the universe is not in a box; it is expanding, seemingly without impediment.