The Order of Time

by Carlo Rovelli

as useful approximations for the clumsy and bungling mortal creatures we are: aspects of our perspective, and aspects, too, perhaps, that are decisive in determining what we are. Because the mystery of time is ultimately, perhaps, more about ourselves than about the cosmos.

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.

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.

In the elementary equations of the world,13 the arrow of time appears only where there is heat.* 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 backward, there is something that is heating up.

Thermal agitation is like a continual shuffling of a pack of cards: if the cards are in order, the shuffling disorders them.

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

The difference between past and future does not lie in the elementary laws of motion; it does not reside in the deep grammar of nature. It is the natural disordering that leads to gradually less particular, less special situations.

if we look at all of its details, since every configuration always has something about it that characterizes it in a unique way. Just as, to its mother, every child is particular and unique.

certain configurations being more particular than others (twenty-six red cards followed by twenty-six black, for example) makes sense only if I limit myself to noticing only certain aspects of the cards (in this case, the colors). If I distinguish between all the cards, the configurations are all equivalent: none of them is more or less particular than others.18 The notion of “particularity” is born only at the moment we begin to see the universe in a blurred and approximate way.

entropy exists because we describe the world in a blurred fashion. He has demonstrated that entropy is precisely the quantity that counts how many are the different configurations tha...

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.

all the phenomena that characterize the flowing of time are reduced to a “particular” state in the world’s past, the “particularity” of which may be attributed to the blurring of our perspective.

entropy, as Boltzmann fully understood, is nothing other than the number of microscopic states that our blurred vision of the world fails to distinguish.

“Proper time” depends not only on where you are and your degree of proximity to masses; it depends also on the speed at which you move.

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

A partial order establishes a relation of before and after between certain elements, but not between any two of them.

Special relativity is the discovery that the temporal structure of the universe is like the one established by filiation: it defines an order between the events of the universe that is partial, not complete. The expanded present is the set of events that are neither past nor future: it exists, just as there are human beings who are neither our descendants nor our forebears.

Every event has its past, its future, and a part of the universe that is neither past nor future,

It is the curious local structure of the present that produces black holes.

Don’t take your intuitions and ideas to be “natural”: they are often the products of the ideas of audacious thinkers who came before us.

There is no single time: there is a different duration for every trajectory; and time passes at different rhythms according to place and according to speed. It is not directional: the difference between past and future does not exist in the elementary equations of the world; its orientation is merely a contingent aspect that appears when we look at things and neglect the details. In this blurred view, the past of the universe was in a curiously “particular” state. The notion of the “present” does not work: in the vast universe there is nothing that we can reasonably call “present.” The substratum that determines the duration of time is not an independent entity, different from the others that make up the world; it is an aspect of a dynamic field. It jumps, fluctuates, materializes only by interacting, and is not to be found beneath a minimum scale. . .

the world is a network of events.

The fundamental equations do not include a time variable, but they do include variables that change in relation to each other.

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.

If by “time” we mean nothing more than happening, then everything is time. There is only that which exists in time.

changes are not arranged in a single orderly succession:

The distinction between past, present, and future is not an illusion. It is the temporal structure of the world. But the temporal structure of the world is not that of presentism.

Change, what happens—this is not an illusion. What we have discovered is that it does not follow a global order.63

To describe the world, the time variable is not required. What are required are variables that actually describe it:

Quantities and properties that we see continuously changing. In these changes there are regularities:

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.

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.

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 theory does not describe how things evolve in time. The theory describes how things change one in respect to the others,72 how things happen in the world in relation to each other. That’s all there is to it.

As human beings, we live by emotions and thoughts. We exchange them when we are in the same place at the same time, talking to each other, looking into each other’s eyes, brushing against each other’s skin. We are nourished by this network of encounters and exchanges. But, in reality, we do not need to be in the same place and time to have such exchanges. Thoughts and emotions that create bonds of attachment between us have no difficulty in crossing seas and decades, sometimes even centuries, tied to thin sheets of paper or dancing between the microchips of a computer. We are part of a network that goes far beyond the few days of our lives and the few square meters that we tread. This book is also a part of that weave. . . .

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.

a “quantum spacetime” that is fluctuating, probabilistic, and discrete.

the spacetime of the quantum collapse of a black hole passes through a phase in which time fluctuates violently, there is a quantum superposition of different times, and then, later, a return to a determined state after the explosion. For this intermediate phase, where time is wholly indeterminate, we still have equations that tell us what happens. Equations without time. This is the world described by loop theory.

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.

A generic macroscopic state determines a time.

quantity. What clocks measure is the proper time along a line of the universe γ,

In order to make advances in our understanding of the world, it is not always necessary to have new data. Copernicus had no more observational data than Ptolemy: he was able to deduce heliocentrism from the data available to Ptolemy by interpreting it better—as Einstein did with regard to Maxwell.

The choice is between forcing the description of the world so that it adapts to our intuition, or learning instead to adapt our intuition to what we have discovered about the world. I have few doubts that the second strategy is the most fruitful one.

There is only a single straight line between two events in spacetime, from A to B: it’s the one along which time is maximum, and the speed relative to this line is the one that slows time.