Success, as ever, is destined to be short-lived—even great success. Einstein writes the equations of the gravitational field in 1915, and barely a year later it is Einstein himself who observes that this cannot be the last word on the nature of time and space, because of the existence of quantum mechanics. The gravitational field, like all physical things, must necessarily have quantum properties.
5 QUANTA OF TIME
There’s an amphora
of old wine in the house
of nine years’ vintage.
There is in the garden, Phyllis,
laurel for braiding crowns
and much ivy . . .
I invite you to celebrate
this day in mid-April—
a festive one for me,
dearer than my own birthday. (IV, 11)
The strange landscape of the physics of relativity that I have described so far becomes even more alien when we consider quanta and the quantum properties of space and of time.
The discipline that studies these is called “quantum gravity,” and this is my own field of research.50 There is not yet a theory of quantum gravity that has been generally accepted by the scientific community, or has obtained experimental support. My scientific life has been largely dedicated to contributing to the construction of a possible solution to the problem: loop quantum gravity, or loop theory. Not everyone is betting on this turning out to be the right solution. Friends who work on string theory, for instance, are following different paths, and the battle to establish who is right is still raging. This is good—science also grows thanks to fierce debates: sooner or later, it will become clear which theory is correct, and perhaps it will not be long.
Divergences of opinion regarding the nature of time, however, have diminished in the last few years, and many conclusions have become reasonably clear to most. What has been clarified is that the residual temporal scaffolding of general relativity, illustrated in the previous chapter, also falls away if we take quanta into account.
Universal time has shattered into a myriad of proper times, but if we factor in the quanta, we must accept the idea that each of these times, in turn, “fluctuates” and is dispersed as in a cloud—and can have only certain values and not others. . . . They can no longer manage to form the spatiotemporal sheet outlined in the previous chapters.
The three fundamental discoveries that quantum mechanics has led to are these: granularity, indeterminacy, and the relational aspect of physical variables. Each one of these demolishes further the little that was left of our idea of time. Let’s consider them one by one.
GRANULARITY
The time measured by a clock is “quantified,” that is to say, it acquires only certain values and not others. It is as if time were granular rather than continuous.
Granularity is the most characteristic feature of quantum mechanics, which takes its name from this: “quanta” are elementary grains. A minimum scale exists for all phenomena.51 For the gravitational field, this is called the “Planck scale.” Minimum time is called “Planck time.” Its value can be easily estimated by combining the constants that characterize phenomena subject to relativity, gravity, and quantum mechanics.52 Together, these determine the time to 10-44 seconds: a hundred millionth of a trillionth of a trillionth of a trillionth of a second. This is Planck time: at this extremely minuscule level, quantum effects on time become manifest.
Planck’s time is small, much smaller than any actual clock is today capable of measuring. It is so extremely small that we should not be astounded to discover that “down there,” at such a minute scale, the notion of time is no longer valid. Why should it be? Nothing is valid always and everywhere. Sooner or later, we always come across something that is new.
The “quantization” of time implies that almost all values of time t do not exist. If we could measure the duration of an interval with the most precise clock imaginable, we should find that the time measured takes only certain discrete, special values. It is not possible to think of duration as continuous. We must think of it as discontinuous: not as something that flows uniformly but as something that in a certain sense jumps, kangaroo-like, from one value to another.
In other words, a minimum interval of time exists. Below this, the notion of time does not exist—even in its most basic meaning.
Perhaps the rivers of ink that have been expended discussing the nature of the “continuous” over the centuries, from Aristotle to Heidegger, have been wasted. Continuity is only a mathematical technique for approximating very finely grained things. The world is subtly discrete, not continuous. The good Lord has not drawn the world with continuous lines: with a light hand, he has sketched it in dots, like the painter Georges Seurat.
Granularity is ubiquitous in nature: light is made of photons, the particles of light. The energy of electrons in atoms can acquire only certain values and not others. The purest air is granular, and so, too, is the densest matter. Once it is understood that Newton’s space and time are physical entities like all others, it is natural to suppose that they are also granular. Theory confirms this idea: loop quantum gravity predicts that elementary temporal leaps are small, but finite.
The idea that time could be granular, that there could be minimal intervals of time, is not new. It was defended in the seventh century by Isidore of Seville in his Etymologiae, and in the following century by the Venerable Bede in a work suggestively entitled De Divisionibus Temporum (“On the Divisions of Time”). In the thirteenth century, the great philosopher Maimonides writes: “Time is composed of atoms, that is to say of many parts that cannot be further subdivided, on account of their short duration.”53 The idea probably dates back even further: the loss of the original texts of Democritus prevents us from knowing whether it was already present in classical Greek atomism.54 Abstract thought can anticipate by centuries hypotheses that find a use—or confirmation—in scientific inquiry.
The spatial sister of Planck time is Planck length: the minimum limit below which the notion of length becomes meaningless. Planck length is around 10-33 centimeters: a millionth of a billionth of a billionth of a billionth of a millimeter. As a young man at university, I fell in love with the problem of what happens at this extremely small scale. I painted a large sheet with, at its center, in red, a glittering:
I hung it up in my bedroom in Bologna and decided that my goal would be to try to understand what happens down there, at the very tiny scale where time and space cease to be what they are—all the way to the elementary quanta of space and time. Then I spent the rest of my life actually trying to achieve this.
QUANTUM SUPERPOSITIONS OF TIMES
The second discovery made by quantum mechanics is indeterminacy: it is not possible to predict exactly, for instance, where an electron will appear tomorrow. Between one appearance and another, the electron has no precise position,55 as if it were dispersed in a cloud of probability. In the jargon of physicists, we say that it is in a “superposition” of positions.