The Order of Time

by Carlo Rovelli

the whole of our physics, and science in general, is about how things develop ‘according to the order of time’.

they are two currencies which have value relative to each other.

There is no truer time. There are two times that change relative to each other.

We do not describe how the world evolves in time: we describe how things evolve in local time, and how local times evolve relative to each other.

What distinguishes the past, its having been, from the future, its not having been yet, in the folds of the mechanism of the world?

The difference between past and future, between cause and effect, between memory and hope, between regret and intention … in the elementary laws that describe the mechanisms of the world, there is no such difference.

All of the sons of Adam are part of one single body, They are of the same essence. When time afflicts us with pain In one part of that body All the other parts feel it too. If you fail to feel the pain of others You do not deserve the name of man.

if nothing else around it changes, heat cannot pass from a cold body to a hot one.

This is the only basic law of physics that distinguishes the past from the future.

In the elementary equations of the world,5 the arrow of time appears only where there is heat.fn1 The link between time and heat is therefore fundamental: every time a difference is manifested between the past and the future, heat is involved. In every sequence of events that becomes absurd if projected backwards, there is something that is heating up.

The growth of entropy is nothing other than the ubiquitous and familiar natural increase of disorder.

The notion of ‘particularity’ is born only at the moment we begin to see the universe in a blurred and approximate way.

Heat, entropy and the lower entropy of the past are notions that belong to an approximate, statistical description of nature.

We often say that causes precede effects and yet, in the elementary grammar of things, there is no distinction between ‘cause’ and ‘effect’.

There are regularities, represented by what we call physical laws, that link events of different times, but they are symmetric between future and past. In a microscopic description, there can be no sense in which the past is different from the future.

For now, I will end with the mind-boggling fact that entropy, as Boltzmann fully understood, is nothing other than the number of microscopic states that our blurred vision of the world fails to distinguish.

There is no special moment on Proxima b that corresponds to what constitutes the present here and now.

Our ‘present’ does not extend throughout the universe. It is like a bubble around us.

The ‘present of the universe’ is meaningless.

Time is the measure of change:8 if nothing changes, there is no time.

Aristotle: time is nothing other than the measurement of change.

Newton: there is a time that passes even when nothing changes.

the place of a thing is what surrounds that thing.

That which seems intuitive to us now is the result of scientific and philosophical elaborations in the past.

The time it seems to capture is just the movement of its hands …

The entire evolution of science would suggest that the best grammar for thinking about the world is that of change, not of permanence. Not of being, but of becoming.

The world is not a collection of things, it is a collection of events.

The basic units in terms of which we comprehend the world are not located in some specific point in space. They are – if they are at all – in a where but also in a when. They are spatially but also temporally delimited: they are events.

‘Things’ in themselves are only events that for a while are monotonous.

If by ‘time’ we mean nothing more than happening, then everything is time.

People like us who believe in physics, know that the distinction between past, present and future is only a stubbornly persistent illusion.

The theory does not describe how things evolve in time. The theory describes how things change one in respect to the others,6 how things happen in the world in relation to each other. That’s all there is to it.

The world without a time variable is not a complicated one. It’s a net of interconnected events, where the variables in play adhere to probabilistic rules which, incredibly, we know for a good part how to write.

The fields manifest themselves in granular form: elementary particles, photons and quanta of gravity – or rather ‘quanta of space’. These elementary grains do not exist immersed in space; rather, they themselves form that space. The spatiality of the world consists of the web of their interactions. They do not dwell in time: they interact incessantly with each other, and indeed exist only in terms of these incessant interactions. And this interaction is the happening of the world: it is the minimum elementary form of time that is neither directional nor linear. Nor does it have the curved and smooth geometry studied by Einstein. It is a reciprocal interaction in which quanta manifest themselves in the interaction, in relation to that with which they interact.

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.

On a small scale, the theory describes a ‘quantum spacetime’ that is fluctuating, probabilistic and discrete. At this scale, there is only the frenzied swarming of quanta that appear and vanish.

In a theory of this kind, time and space are no longer containers or general forms of the world. They are approximations of a quantum dynamic that in itself knows neither space nor time. There are only events and relations. It is the world without time of elementary physics.

In these examples, something that is real – a cat, a football team, high and low, the surface of clouds, the rotation of the cosmos – emerges from a world that at a much simpler level has no cats, teams, up or down, no surfaces of clouds, no revolving cosmos … Time emerges from a world without time, in a way that has something in common with each of these examples.

The usual way of interpreting the relation between time and the state of equilibrium is to think that time is something absolute and objective; energy governs the time-evolution of a system; and the system in equilibrium mixes all configurations of equal energy. The conventional logic for interpreting this relation is therefore: time → energy → macroscopic state5 That is: to define the macroscopic state we first need to know the energy, and to define energy we first need to know what is time. In this logic, time comes first and is independent from the rest. But there is another way of thinking about this same relationship: by reading it in reverse. That is, to observe that a macroscopic state, which is to say a blurred vision of the world, may be interpreted as a mingling that preserves an energy, and this in its turn generates a time. That is: macroscopic state → energy → time

a generic macroscopic state determines a time.

a macroscopic state (which ignores the details) chooses a particular variable that has some of the characteristics of time.

it is not the evolution of time that determines the state, it is the state – the blurring – that determines a time.

The intrinsic quantum indeterminacy of things produces a blurring, like Boltzmann’s blurring, which ensures – contrary to what classic physics seemed to indicate – that the unpredictability of the world is maintained even if it were possible to measure everything that is measurable.

Speed is a property of an object with respect to another object. It is a relative quantity.

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. The initial low entropy of the universe, and hence the arrow of time, may be more down to us than to the universe itself. This is the basic idea.

How can a particular interaction between us and the rest of the world determine a low initial entropy? It’s simple. Take a pack of twelve cards, six red and six black. Arrange it so that the red cards are all at the front. Shuffle the pack a little and then look for the black cards that have ended up among the red ones at the front. Before shuffling, there are none; after, some. This is a basic example of the growth of entropy. At the start of the game, the number of black cards among the red in the first half of the pack is zero (the entropy is low) because it has started in a special configuration. But now let’s play a different game. First, shuffle the pack in a random way, then look at the first six cards and commit them to memory. Shuffle a little and look to see which other cards have ended up among the first six. At the start, there were none, then their number grew, as it did in the previous example, together with the entropy. But there is a crucial difference between this example and the previous one: 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.

But why should we belong to one of these special systems? For the same reason that apples grow in northern Europe, where people drink cider, and grapes grow in the south, where people drink wine; or that I was born where people happen to speak my native language; or that the sun which warms us is at the right distance from us – not too close and not too far away. In all these cases, the ‘strange’ coincidence arises from confusing the causal relations: it isn’t that apples grow where people drink cider, it is that people drink cider where apples grow. Put this way, there is no longer anything strange about it. Similarly, in the boundless variety of the universe, it may happen that there are physical systems that interact with the rest of the world through those particular variables that define an initial low entropy. With regard to these systems, entropy is constantly increasing. There, and not elsewhere, there are the typical phenomena associated with the flowing of time: life is possible, together with evolution, thought and our awareness of time passing. There, the apples grow that produce our cider: time. That sweet juice which contains all the ambrosia and all the gall of life.

Every glance that we cast towards the world is made from a particular perspective.

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.

At the fundamental level, the world is a collection of events not ordered in time. These events manifest relations between physical variables that are, a priori, on the same level. Each part of the world interacts with a small part of all the variables, the value of which determines ‘the state of the world with regard to that particular subsystem’.