In fundamental relativistic physics, where no variable plays a priori the role of time, we can reverse the relation between macroscopic state and evolution of time: it is not the evolution of time that determines the state, it is the state—the blurring—that determines a time.
Time that is determined in this way by a macroscopic state is called “thermal time.” In what sense may it be said to be a time? From a microscopic point of view, there is nothing special about it—it is a variable like any other. But from a macroscopic one, it has a crucial characteristic: among so many variables all at the same level, thermal time is the one with behavior that most closely resembles the variable we usually call “time,” because its relations with the macroscopic states are exactly those that we know from thermodynamics.
But it is not a universal time. It is determined by a macroscopic state, that is, by a blurring, by the incompleteness of a description. In the next chapter, I will discuss the origin of this blurring, but before I do, let’s take another step by bringing quantum mechanics into consideration.
QUANTUM TIME
Roger Penrose is among the most lucid of those scientists who have focused on space and time.83 He reached the conclusion that the physics of relativity is not incompatible with our experience of the flowing of time but that it does not seem sufficient to account for it. He has suggested that what’s missing might be what happens in a quantum interaction.84 Alain Connes, the great French mathematician, has pointed out the deep role of quantum interaction at the root of time.
When an interaction renders the position of a molecule concrete, the state of the molecule is altered. The same applies for its speed. If what materializes first is the speed and then the position, the state of the molecule changes in a different way than if the order of the two events were reversed. The order matters. If I measure the position of an electron first and then its speed, its state changes differently than if I were to measure its velocity first and then its position.
This is called the “noncommutativity” of the quantum variables, because position and speed “do not commute,” that is to say, they cannot exchange order with impunity. This noncommutativity is one of the characteristic phenomena of quantum mechanics. Noncommutativity determines an order and, consequently, a germ of temporality in the determination of two physical variables. 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.
Perhaps it is the very fact that the effect of these interactions depends on the order in which they take place that is at the root of the temporal order of the world. This is the fascinating idea suggested by Connes: the first germ of temporality in elementary quantum transitions lies in the fact that these interactions are naturally (partially) ordered.
Connes has provided a refined mathematical version of this idea: he has shown that a kind of temporal flow is implicitly defined by the noncommutativity of the physical variables. Due to this noncommutativity, the set of physical variables in a system defines a mathematical structure called “noncommutative von Neumann algebra,” and Connes has shown that these structures have within themselves an implicitly defined flow.85
Surprisingly, there is an extremely close relation between Alain Connes’s flow for quantum systems and the thermal time that I have discussed above. Connes has shown that, in a quantum system, the thermal flows determined by different macroscopic states are equivalent, up to certain internal symmetries,86 and that, together, they form precisely the Connes flow.87 Put more simply: the time determined by macroscopic states and the time determined by quantum noncommutativity are aspects of the same phenomenon.
And it is this thermal and quantum time, I believe,88 that is the variable that we call “time” in our real universe, where a time variable does not exist at the fundamental level.
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.
Both the sources of blurring—quantum indeterminacy, and the fact that physical systems are composed of zillions of molecules—are at the heart of time. Temporality is profoundly linked to blurring. The blurring is due to the fact that we are ignorant of the microscopic details of the world. The time of physics is, ultimately, the expression of our ignorance of the world. Time is ignorance.
Alain Connes has coauthored with two friends a short science fiction novel. Charlotte, the protagonist, manages to have for a moment a totality of information about the world, without blurring. She manages to “see” the world directly, beyond time:
I have had the unheard-of good fortune of experiencing a global vision of my being—not of a particular moment, but of my existence “as a whole.” I was able to compare its finite nature in space, against which no one protests, with its finite nature in time, which is instead the source of so much outrage.
And then returning to time:
I had the impression of losing all the infinite information generated by the quantum scene, and this loss was sufficient to drag me irresistibly into the river of time.
The emotion that results from this is an emotion of time:
This re-emergence of time seemed to me like an intrusion, a source of mental confusion, anguish, fear and alienation.89
Our blurred and indeterminate image of reality determines a variable, thermal time that turns out to have certain peculiar properties which begin to resemble what we call “time”: it is in the correct relation with equilibrium states.
Thermal time is tied to thermodynamics, and hence to heat, but does not yet resemble time as we experience it, because it does not distinguish between the past and the future, has no direction, and lacks what we mean when we speak of its flow. We have not yet reached the time of our own experience.
The difference between the past and the future that is so important to us:
Where does that come from?
10 PERSPECTIVE
In the impenetrable night
of his wisdom
a god closes
the strip of days
that’s to come
and laughs
at our human trepidation. (III, 29)
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.90 Why was entropy low in the past?
In this chapter I will give an account of an idea that provides a possible answer, “if you will hear my answer to this question and its perhaps extravagant supposition.”91 I am not sure that it is the correct answer, but it’s the one with which I have become enamored.92 It might clarify many things.
WE ARE THE ONES TURNING!
Whatever we human beings may be specifically, in detail, we are nevertheless pieces of nature, a part of the great fresco of the cosmos, a small part among many others.