The Order of Time

by Carlo Rovelli

What alternatives do we have? Philosophers call ‘eternalism’ the idea that flow and change are illusory: present, past and future are all equally real and equally existent. Eternalism is the idea that the whole of spacetime, as outlined in the above diagrams, exists all together in its entirety without anything changing. Nothing really flows.

Eternalism

Let’s return to the question with which we began: what ‘is real’? What ‘exists’? The answer is that this is a badly put question, signifying everything and nothing. Because the adjective ‘real’ is ambiguous, it has a thousand meanings. The verb ‘to exist’ has even more. To the question ‘Does a puppet whose nose grows when he lies exist?’, it is possible to reply: ‘Of course he exists! It’s Pinocchio!’; or: ‘No, he doesn’t, he’s only part of a fantasy dreamed up by Collodi.’

Logic

We say that an event ‘is’, or ‘has been’, or ‘will be’. We do not have a grammar adapted to say that an event ‘has been’ in relation to me but ‘is’ in relation to you.

Relativity

What we need, if we want to do science, is a theory that tells us how the variables change with respect to each other. That is to say, how one changes when others change. The fundamental theory of the world must be constructed in this way; it does not need a time variable: it needs to tell us only how the things that we see in the world vary with respect to each other. That is to say, what the relations may be between these variables.

In respect with one another

The fundamental equations of quantum gravity are effectively formulated like this: they do not have a time variable, and they describe the world by indicating the possible relations between variable quantities.

No time variable required

There is nothing mysterious about the absence of time in the fundamental equation of quantum gravity. It is only the consequence of the fact that, at the fundamental level, no special variable exists.

The variables of the theory describe the fields that form matter, photons, electrons, other components of atoms and the gravitational field – all on the same level. Loop theory is not a ‘unified theory of everything’. It doesn’t even begin to claim that it’s the ultimate theory of science. It’s a theory made up of coherent but distinct parts. It seeks to be ‘only’ a coherent description of the world as we understand it so far.

Interesting. Loop theory

We cannot draw a complete map, a complete geometry, of everything that happens in the world, because such happenings – including the passage of time – are always triggered only by an interaction with, and with respect to, a physical system involved in the interaction. The world is like a collection of interrelated points of view. To speak of the world ‘seen from outside’ makes no sense, because there is no ‘outside’ to the world.

Main

The elementary quanta of the gravitational field exist at the Planck scale. They are the elementary grains that weave the mobile fabric with which Einstein reinterpreted Newton’s absolute space and time. It is these, and their interactions, which determine the extension of space and the duration of time.

planck scale

The relations of spatial adjacency tie the grains of space into webs. We call these ‘spin networks’. The name ‘spin’ comes from the mathematics which describe the grains of space.9 A ring in the spin network is called a loop, and these are the loops that give ‘loop theory’ its name. The webs, in turn, transform into each other in discrete leaps, described in the theory as structures called ‘spinfoam’.

Spin spinfoam

To determine a physical variable is not an isolated act; it involves interaction. The effect of such interactions depends on their order, and this order is a primitive form of the temporal order.

Temporal order

The entire difference between past and future may be attributed solely to the fact that the entropy of the world was low in the past.

Entropy low in the past

Speed is a property of an object with respect to another object. It is a relative quantity. The same is true for entropy. The entropy of A with regard to B counts the number of configurations of A that the physical interactions between A and B do not distinguish.

Entropy

The entropy of the world in the far past appears very low to us. But this might not reflect the exact state of the world: it might regard the subset of the world’s variables with which we, as physical systems, have interacted. It is with respect to the dramatic blurring produced by our interactions with the world, caused by the small set of macroscopic variables in terms of which we describe the world, that the entropy of the universe was low. This, which is a fact, opens up the possibility that it wasn’t the universe that was in a very particular configuration in the past. Perhaps instead it is us, and our interactions with the universe, that are particular. We are the ones who determine a particular macroscopic description.

Interaction

at the beginning of this one, the cards were in a random configuration. It was you who declared them to be particular, by taking note of which cards were in the front half of the pack at the beginning of the game. The same may be true for the entropy of the universe: perhaps it was in no particular configuration. Perhaps we are the ones who belong to a particular physical system with respect to which its state can be particular.

Example

there is also something curious about a text which refers to itself. What is it? It is what philosophers call ‘indexicality’: the characteristic of certain words which have a different meaning every time they are used, a meaning determined by where, how, when and by whom they are being spoken. Words such as ‘here’, ‘now’, ‘I’, ‘this’, ‘tonight’ all assume a different meaning depending on who utters them and the circumstances in which they are uttered.

Indexicality

In order to use a geographical map, it is not enough to look at it from the outside: we must know where we are situated in relation to what it represents. In order to understand our experience of space, it is not enough to think of Newtonian space. We must remember that we see this space from inside it, that we are localized. In order to understand time, it is not enough to think of it from outside: it is necessary to understand that we, in every moment of our experience, are situated within time.

Inside

Energy makes our engines run, helps plants to grow and causes us to wake up every morning full of vitality. But there is something that does not add up. Energy – as I was also told at school – is conserved. It is neither created nor destroyed. If it is conserved, why do we have to constantly resupply it? Why can’t we just keep using the same energy? The truth is that there is plenty of energy and it is not consumed. It’s not energy that the world needs in order to keep going. What it needs is low entropy.

Hmmmm

What makes the world go round are not sources of energy but sources of low entropy. Without low entropy, energy would dilute into uniform heat and the world would go to sleep in a state of thermal equilibrium – there would no longer be any distinction between past and future, and nothing would happen.

Low entropy

Near to the Earth we have a rich source of low entropy: the sun. The sun sends us hot photons. Then the Earth radiates heat towards the black sky, emitting colder photons. The energy that enters is more or less equal to the energy that exits; consequently, we do not generally gain energy in the exchange. (Gaining energy in the exchange is disastrous for us: it is global warming.) But for every hot photon that arrives, the Earth emits ten cold ones, since a hot photon from the sun has the same energy as ten cold photons emitted by the Earth. The hot photon has less entropy than the ten cold photons, because the number of configurations of a single (hot) photon is lower than the number of configurations of ten (cold) photons. Therefore, the sun is a continual rich source of low entropy for us.

The sun

Where does the low entropy of the sun come from? From the fact that, in turn, the sun is born out of an entropic configuration that was even lower: the primordial cloud from which the solar system was formed had even lower entropy. And so on, back into the past, until we reach the extremely low initial entropy of the universe. It is the growth of this entropy that powers the great story of the cosmos.

Lower entropy

A pile of wood, for example, lasts a long time if left alone. It is not in a state of maximum entropy, because the elements of which it is made, such as carbon and hydrogen, are combined in a very particular manner (‘ordered’) to give form to the wood. Entropy grows if these particular combinations are broken down. This is what happens when wood burns: its elements disengage from the particular structures that form wood and entropy increases sharply (fire being, in fact, a markedly irreversible process).

But the wood does not start to burn on its own. It remains for a long time in a state of low entropy, until something opens a door that allows it to pass to a state of higher entropy. A pile of wood is in an unstable state, like a pack of cards, but until something comes along to make it do so, it does not collapse. This something might, for instance, be a match to light a flame. The flame is a process that opens a channel through which the wood can pass into a state of higher entropy. There

Living beings are made up of similarly intertwined processes. Photosynthesis deposits low entropy from the sun into plants. Animals feed on low entropy by eating. (If all we needed was energy rather than entropy, we would head for the heat of the Sahara rather than towards our next meal.) Inside every living cell, the complex web of chemical processes is a structure that opens and closes gates through which low entropy can increase.

Interesting

Life is this network of processes for increasing entropy – processes which act as catalysts to each other.2 It isn’t true, as is sometimes stated, that life generates structures that are particularly ordered, or that locally diminish entropy: it is simply a process that degrades and consumes the low entropy of food; it is a self-structured disordering, no more and no less than in the rest of the universe.

Life

A stone falls to the ground. Why? One often reads that it’s because the stone places itself ‘in a state of lower energy’ that it ends up lower down. But why does the stone put itself into a state of lower energy? Why should it lose energy if energy is conserved? The answer is that when the stone hits the Earth, it warms it: its mechanical energy is transformed into heat. And there is no way back from there. If the second law of thermodynamics did not exist, if heat did not exist, if there existed no microscopic swarming, the stone would rebound perpetually; it would never land and be still.

Stone interesting take

The entire coming into being of the cosmos is a gradual process of disordering, like the pack of cards that begins in order and then becomes disordered through shuffling. There are no immense hands that shuffle the universe. It does this mixing by itself, in the interactions between its parts that open and close during the course of the mixing, step by step. Vast regions remain trapped in configurations that remain ordered, until here and there new channels are opened through which disorder spreads.

To disorder

Traces of the past exist, and not traces of the future, only because entropy was low in the past. There can be no other reason, since the only source of the difference between past and future is the low entropy of the past.

Traces

In order to leave a trace, it is necessary for something to become arrested, to stop moving, and this can happen only in an irreversible process – that is to say, by degrading energy into heat. In this way, computers heat up, the brain heats up, the meteors that fall into the moon heat it; even the goose quill of a medieval scribe in a Benedictine abbey heats a little the page on which he writes. In a world without heat, everything would rebound elastically, leaving no trace.

Traces and heat

It is the presence of abundant traces of the past that produces the familiar sensation that the past is determined. The absence of any analogous traces of the future produces the sensation that the future is open. The existence of traces serves to make it possible for our brain to create extensive maps of past events. There is nothing analogous to this for future ones.

Interesting

The king replies cautiously that certainly ‘chariot’ refers only to the relationship between the ensemble of wheels, axle and chassis, to their working together and in relation to us – and that there does not exist an entity ‘chariot’ beyond these relations and events. Nāgasena triumphs: in the same way as ‘chariot’, the name ‘Nāgasena’ designates nothing more than a collection of relations and events. We are processes, events, composite and limited in space and time. But, if we are not an individual entity, what is it that founds our identity and its unity? What makes it so – that I am Carlo – and that my hair and my nails and my feet are considered part of me, as well as my anger and my dreams, and that I consider myself to be the same Carlo as yesterday, the same as tomorrow; the one who thinks, suffers and perceives?

What is a thing.

When we think of ourselves as persons, I believe we are applying to ourselves the mental circuits that we have developed to engage with our companions. The first image that I have of myself as a child is the child that my mother sees. We are for ourselves in large measure what we see and have seen of ourselves reflected back to us by our friends, our loves and our enemies.

Hmm

The experience of thinking of oneself as a subject is not a primary experience: it is a complex cultural deduction, made on the basis of many other thoughts. My primary experience – if we grant that this means anything – is to see the world around me, not myself.

Interesting

we are the reflection of the idea of ourselves that we receive back from our kind.

Interesting

there is a third ingredient in the foundation of our identity, and it is probably the essential one – it is the reason this delicate discussion is taking place in a book about time: memory.

Memory

In Book XI of the Confessions, Augustine asks himself about the nature of time and, despite being interrupted by exclamations in the style of an evangelical preacher that I find quite tiresome, he presents a lucid analysis of our capacity for perceiving time. He observes that we are always in the present, because the past is past and therefore does not exist, and the future has yet to arrive, so it does not exist either. And he asks himself how we can be aware of duration – or even be capable of evaluating it – if we are always only in a present which is, by definition, instantaneous. How can we come to know so clearly about the past, about time, if we are always in the present? Here and now, there is no past and no future. Where are they?

Main instantaneous

Proust could not be more explicit on this matter, writing in the first book: ‘Reality is formed only by memory.’13 And memory, in its turn, is a collection of traces, an indirect product of the disordering of the world, of that small equation written earlier, ΔS ≥ 0, the one that tells us the state of the world was in a ‘particular’ configuration in the past and therefore has left (and leaves) traces. ‘Particular’, that is, perhaps only in relation to rare subsystems – ourselves included.

Proust

We are stories, contained within the twenty complicated centimetres behind our eyes, lines drawn by traces left by the (re)mingling together of things in the world, and orientated towards predicting events in the future, towards the direction of increasing entropy, in a rather particular corner of this immense, chaotic universe.

Main

This space – memory – combined with our continuous process of anticipation, is the source of our sensing time as time, and ourselves as ourselves.14

Main

A present that is common throughout the whole universe does not exist (Chapter 3). Events are not ordered in pasts, presents and futures; they are only ‘partially’ ordered. There is a present that is near to us, but nothing that is ‘present’ in a far-off galaxy. The present is a localized rather than a global phenomenon.

Present

The closer we are to a mass (Chapter 1), or the faster we move (Chapter 3), the more time slows down: there is no single duration between two events; there are many possible ones.

The rhythms at which time flows are determined by the gravitational field,

But in our search for time, advancing increasingly away from ourselves, we have ended up by discovering something about ourselves, perhaps – just as Copernicus, by studying the movements of the heavens, ended up by understanding how the Earth moved beneath his feet.

Copernicus

Perhaps, ultimately, the emotional dimension of time is not the film of mist that prevents us from apprehending the nature of time objectively. Perhaps the emotion of time is precisely what time is for us.

Main

‘Every day countless people die, and yet those who remain live as if they were immortals.’1

But death does not alarm me. It did not scare me when I was young, and I thought at the time that this was because it was such a remote prospect. But now, at sixty, the fear has yet to arrive. I love life, but life is also struggle, suffering, pain. I think of death as akin to a well-earned rest. The sister of sleep, Bach calls it, in his marvellous cantata BWV 56.

Sister of sleep

Fearing the transition, being afraid of death, is like being afraid of reality itself; like being afraid of the sun. Whatever for?