What then is time? If no one asks me, I know what it is. If I wish to explain it to him who asks, I do not know.

(St. Augustine)

Time is a problem for us, trembling and demanding, perhaps the most vital problem of metaphysics; eternity is a game or an exhausted hope.

(Jorge Luis Borges)

The arrow of time is present in the entire living world, which is the product of evolution over time. It is also found in every organism that is constantly changing throughout its life. The past and the future represent totally different directions. Every living being goes from birth to death.

(François Jacob)

Is time definable?

In order to define something, the object must remain stable, and the moment I asked this question, is time definable? is already behind us. According to our common sense and scientific belief, time does not stand still, it can never be grasped. The passage of time is one of the main reasons for asserting that it cannot be defined, that it is fundamentally unknowable, and that it should probably be classified as a negative concept from which nothing constructive can be derived. Other concepts belong to this same class, for instance “chaos”, “indeterminacy”, “chance”. The concept of time only becomes clear if it is associated with motion, with number, with space or with causality. There is a science of space, geometry, but there is not, in an analogous way, a science of time, a chronometry.

Plato says that the creator could not build the world quite like its perfect model, i.e. eternal, because nothing sensible can be eternal, and so he managed to produce a moving image of eternity which he called “time”. Very early in rational thought, time was linked to movement, which is itself linked to space. If time is continuous, it is because motion is continuous, and motion is continuous because the space in which it takes place is continuous. For Aristotle, time is unreal or barely real. This shows that he who talks about time is in an uncomfortable position (as I am now). St. Augustine acknowledged that as long as no one asks him “What is time?” he knows, but if someone asks him the question, he does not know it any longer. This means, and this is true for all of us, that we know how to use the word “time” and other terms of the same family such as “before”, “after”, “at the same time”, etc., but we are unsettled, we have the impression of being caught off guard if we are asked for an explicit definition.

Time, duration and becoming

The distinction: scientific time / duration is probably the most important bifurcation within the concept of time. In order to progress, science needs both intuition and a formalism to fix ideas, verify them and improve them. This is probably what Aristotle understood so well when he defined time as “the number of movement according to before and after”. Newton and the early mechanists assigned to time the properties of the line of real numbers that represents it: both are homogeneous, one-dimensional, continuous and infinite. From this point of view, time is an absolute frame where each event can be uniquely indexed by a number, its time, and all correct clocks measure the same interval between two events. We know that the theory of relativity has modified this image: the temporal order of events depends on reference frames, and the notion of a 'universal present' no longer has any physical meaning, but it seems to accentuate the spatial character of time.

Some philosophers react by affirming that the time of physics is not the true, real time. This would be duration, a concrete phenomenon that cannot be reduced to the properties of its mechanistic representations. These are spatial and deprive time of its specificity, of its own quality: duration. Bergson insists on this. By interiorising it, he rejects its spatialisation, thinking that concrete and pure duration (la durée) is the true real time. And since the psychic has, among other properties, duration, this means that interiority, the psychic, is irreducible to the spatialisation presupposed by mathematics and physics. Duration, which gives itself in a much more faithful way to intuition than to scientific formalisms, would be intimate to things, a producer of novelty, of freedom, of natural diversity. It would thus be a fact that reason cannot accept because it is conservative, and consequently the idea of true creation is alien to it.

We have thus two concepts of time: one is scientific, abstract, mechanistic. It benefits from the clarity and accuracy of mathematics, as well as from all the operations it allows. The other concept, lived duration, is more biological, human and concrete, but somewhat less intelligible. This situation is unsatisfactory, and therefore an additional effort should be made to develop a single theory of time capable of harmonising all its aspects. The reason is that for us, realist and naturalist thinkers, nature is continuous, and respect for coherence requires the search for a unitary explanation of the world.

Irreversibility or reversibility of time. Mathematics and common sense

According to the philosophy of common sense developed by the Scottish school during the 18th and early 19th century, there are good reasons to trust the information obtained by sensation. This information is not just a set of ideas or a set of subjective impressions, but correctly conveys the qualities that belong to external objects. According to this school, the beliefs derived from sensation belong to both the common sense and reason of mankind. The philosophy of common sense is understood to be a kind of realism because it was a reaction to both scepticism and subjective idealism.

Let us remember now the distinction between scientific time and duration. Although the reversibility of time is symbolically conceivable, it clashes with our common sense. If from a scientific point of view we can conceive of a reversible time, it is mainly for some mathematical reasons. For example, the numerical line that represents time can be read from left to right or from right to left. That being said, we must recognise that the arrowed temporality of the biological and psychic world is an ultimate natural evidence that we cannot renounce. We can plant a tree, watch it grow, and if we live long enough, we can witness its death. However, no one has seen a mature tree gradually become its own seed. We remember our past, not our future. If there is inconsistency between reversible physics and irreversible biology and psychology, it is our physics that must be changed. The scientific conception of reversible time is an abstract speculation whose foundations must be re-examined. We will see that Einstein shares this reasonable attitude.

According to the modern conception which transforms the causal relationship into a constant succession of causes and effects, the cause always precedes the effect. Each cause is the invariable antecedent of its effect. On the other hand, this requirement of succession, passage or transition is absent in Aristotle for whom cause and effect are simultaneous. For moderns it is unthinkable that the cause does not precede the effect and this property serves to define causality, just as modern science has retained the Galilean definition that the presence of the cause is always followed by the effect, and if the cause disappears, the effect disappears as well.

Does the cause always precede the effect? Relativistic physicists, including Einstein, hesitated, and the situation became more complicated with Gödel's physicomathematical developments in this respect. Gödel's discovery is not simple. It cannot be reduced to the idea that if we conceive of instants as points on a one-dimensional continuum, then we prove that mathematically there is nothing to prevent us from conceiving of closed curves: what was will be, the cause precedes the effect, the effect precedes the cause. What Gödel has shown is that there are semi-Riemannian varieties (R4, g) such that the metric g is an exact solution of the Einstein field equations and in which closed curves exist. If certain ways of solving the equations of the general theory of relativity allow the existence of closed curves (this, as I said, was achieved by Gödel) it means that it is possible to pass over and over again through the same spacetime points, that one can return to a previous state: time would be reversible. (See Kurt Gödel, “A Remark About the Relationship Between Relativity Theory and Idealistic Philosophy”, in Albert Einstein, Philosopher-Scientist, edited by Paul A. Schilpp, Open Court, La Salle, Ill., 1949).

I spare here the reader Einstein's considerations about the paradox discovered by Gödel. His answer is, in a word, that it would be interesting to assess whether such paradox should not be excluded on physical grounds, which shows Einstein's sound common sense. But it would be much fairer and more convincing to say that reversibility must be excluded on biological grounds. In fact, says François Jacob, the requirement of a time parameter represents one of the characteristic differences between biology and most aspects of physics. For, curiously enough, there is no arrow of time in the basic theories of physics. “Contrary to most branches of physics, biology makes time one of its main parameters. The arrow of time is present in the entire living world, which is the product of evolution over time. It is also found in every organism that is constantly changing throughout its life. The past and the future represent totally different directions. Every living being goes from birth to death.” (François Jacob, Le jeu des possibles. Essai sur la diversité du vivant, Ch. 3 Le temps et l’invention de l’avenir, Fayard, Paris, 1981).

Time, geometrical images, death and myth

Our concept is not that of prehistoric man or that of societies that see time as a cyclical reality. Who knows if the man of the future, once he is used to interplanetary travel, will still talk about time in the same way as we do. We modern Westerners have assimilated the classical physics conception of time which is based, in part, on the Jewish myth of linear time directed towards an end. Except that for us it is infinite. The cultural consequences of myths are very important because if time has a circular structure, if what was will be in a perfectly determined way, then one does not believe in progress or development, life is not a task that consists in producing a better world. On the other hand, a linear and open conception of time allows for the belief in progress in every order of things, but it is also partly responsible for the excessive value placed on work that leads to fatigue and anxiety.

Man is aware of his life and of the inexorable arrival of his own death, and he finds it hard to imagine himself becoming nothing. “Neither the sun nor death can be looked at fixedly” (La Rochefoucauld). Man is quite uneasy about time, about its passage, its irreversibility, and sometimes, dramatically, invents myths to console himself. He tries to imagine that he may have an immortal soul separable from its flesh and blood, that we can relive our past, be reincarnated or resurrect. These fabulous stories, born of a deep desire and thanks to the inventive power of imagination, have a poetic value, but their truth value is something else. Now, since we do not have the appropriate concepts to describe the causal continuum from the mathematical, physicochemical and biological strata to the consciousness resulting from the activity of the brain, this series of empty words, I mean the belief in a soul separable from the body of flesh and blood, still has a long time before it.

We do not know what “existing outside of time” means. As I have recalled, time is an aspect of motion, and motion takes place in space, so there is no time if there is no motion and no space.

The only reasonable survival is the one we pass on to our children as well as the one described by the Chinese wisdom: man can survive thanks to his works, to the example he can leave.

The appearance of animal and human consciousness, which also exists to an elementary degree in plants, and in particular the awareness of time, of suffering and of death, intrigues us in a supreme way. Finally, and not surprisingly, biologists are uncomfortable with the question of what the selective advantage of consciousness might possibly be.