Traduction simplifiée
Que le temps s’écoule dans une seule direction, du passé vers le futur, est un constat que nous faisons quotidiennement. De plus la science le confirme tous les jours : nous ne pouvonns pas remonter le temps. Dès que le Big Bang s’est produit, les particules de matière ont évolué dans un seul sens. C’est ce que l’on nomme la flèche du temps
Aujourdhui, un certain nombre de scientifiques cherche à comprendre ce phénomène. Plus précisément, ils se demandent pourquoi dès le Big Bang ne sont pas apparues deux flèches du temps opposées.
Pour répondre à la queston, on évoque un phénomène nommé entropie. Pour celle-ci, la flèche du temps manifeste l’impossibilité pour l’univers d’échapper au désordre résultant de la création d’entités de plus en complexes. Mais ne s’agirait-il pas plutôt de la conséquence d’une loi fondamentale de la nature. Il s’agirait de la nature quantique de la gravité.
Les hypothèses actuelles sur le temps découlent de la théorie générale de la relativité due à Albert Einstein. Les trois dimensions de l’espace et celle du temps aboutissent au concept d’espace-temps. On peut se déplacer dans l’espace comme l’on veut mais pas dans le temps, où l’on est obligé de se déplacer du passé vers le futur. Il n’y a cependant aucune loi naturelle imposant au temps une direction du passé vers le futur, au contraire des autres lois naturelles qui peuvent toujours être appliquées à l’envers.
Afin d expliquer ce paradoxe, les physiciens font appel à la seconde loi de la thermodynamique . Celle-ci, qui n’a rien de fondamental, dispose que dans un système clos, l’entropie augmente toujours. Elle le fait parce qu’il y a a toujours statistiquement plus d’états de désordre que d’ordre . Le terme de statistique signifie que le désordre n’est pas obligé par une loi fondamentale de la nature.
Mais notre univers est-il un système clos ? Il semble au contraire être infini en taille et peut-être même être en expansion.
En 1772 le mathématicien Joseph-Louis Lagrange avait montré que dans un système composé de trois particules interagissant selon la loi de la gravitation de Newton, chaque particule attire les autres avec une force proportionnelle à sa masse et inversement proportionnelle au carré de leur distance
Suite non traduite faute de temps
Lagrange’s result, which extends to any number of particles, showed that if a system’s total energy (potential plus kinetic) is either zero or positive then its size, essentially its diameter, passes through a unique minimum at just one point on the timeline of its evolution. This process runs just as well backwards as forwards, Newton’s gravity being time-symmetric. And with one fascinating exception to which I will return, the size of the system grows to infinity both to the past and future.
Interestingly, the uniformity with which the particles are distributed is greatest around the point of minimum size. It has long been known that a uniform distribution of particles is gravitationally unstable and breaks up into clusters. What nobody seems to have realised, however, is that when you run the evolution of the particles’ motion backwards from the clustered state to the minimum, most uniform state and then take it beyond this point, it goes on to become clustered again.
In a paper I published in 2014, together with Tim Koslowski at the National Autonomous University of Mexico and Flavio Mercati at the University of Naples, Italy, we showed that this is the case in a simple proxy of the universe. A computer simulation of a thousand particles interacting under Newtonian gravity showed that pretty much every configuration of particles would evolve into this minimum state and then expand outwards, becoming gradually more structured in both directions. I call the minimal state the Janus point, after the Roman god who looks simultaneously in opposite directions of time.
What would this mean for us? If we lived in the model universe I have just described, we must be on one side or the other of the Janus point. We find Newton’s time-symmetric law governs what happens around us, but also a pervasive arrow of time that defines our future. In our past direction, we can just make out fog – what we call the big bang – and nothing beyond it. Not realising the fog is a Janus point, we invoke a past hypothesis to explain the inexplicable. But Newton’s laws say the special point must be there, so there is no need to invoke the past hypothesis. Instead, we can mathematically define a quantity that reflects the evolution of our system of particles into something that looks like structure. Let’s call it “complexity”.
Complexity is calculated using all the masses of the particles and all the ratios of the distances between any two of them. It has nothing to do with the statistical likelihood of possible states and differs from entropy in that its growth reflects an increase in structure, or variety, rather than disorder. I argue that it should take the place of entropy as the basis of time’s arrow.
In my recent book The Janus Point, I take things further. I propose that, ultimately, our model suggests that the history of the universe isn’t a story of order steadily degrading into disorder, but rather one of the growth of structure or complexity, as we define it.
“Complexity doesn’t just give time its direction – it literally is time”
The suggestion for this comes in the first place from Newton’s theory of gravity. It isn’t yet clear it can be extended to a general relativistic description of gravity. But in many cases, Newtonian gravity predicts behaviour almost identical to relativity, so there is a hint to look for a similar effect in Einstein’s theory.
This brings me to the fascinating exception to Lagrange’s result I mentioned earlier. In everything discussed so far, the minimum size of the “universe”, at the Janus point, isn’t zero but finite. But general relativity at the big bang leads to a zero size of the universe, known as a singularity, where the equations break down.
It has been known since a remarkable paper by Frenchman Jean Chazy in 1918 that singular events called total collisions can also occur in Newton’s theory. In them, all the particles come together and collide simultaneously at their common centre of mass. At this point, Newton’s equations break down; they can’t be employed to continue any solution past a total collision. Instead of two-sided solutions, we have one-sided solutions.
If we take this exception seriously, we cannot say time has two opposite directions but, significantly, it doesn’t rule out complexity giving time a direction.
The equations for Newton’s gravity are still time symmetrical, so the solutions that terminate at a total collision can run the other way. They become Newtonian “big bangs” in which all the particles suddenly fly apart from each other. Right at the start, the particles are arranged in a remarkably uniform way, but they soon begin to look like the motions on either side of the Janus point we saw in our calculations.
As they emerge from zero size, their configuration, characterised by the complexity, satisfies a very special condition. There are plenty of configurations, or shapes, that satisfy the condition but just one has the absolutely smallest possible value of the complexity. It is more uniform than any other shape the universe could have.
This is where a radical twist in the tale was all but forced on me, during the final stages of writing my book. The fact that the universe had an extremely uniform shape immediately after the big bang set me thinking. Could the special shape I’ve identified, which I call Alpha, serve as a guide to a new theory of time – and also point the way to arguably the biggest prize in physics, a quantum theory of gravity?
Quantum theory describes the often counter-intuitive behaviour of subatomic particles. For all its successes, it has always relied on an essentially classical conception of a time that exists independently of and outside the system. But surely any attempt to create a quantum theory of the universe, and with it gravity, should start without the notion of a pre-existing external time. Time has to originate somewhere, and where else but the quantum realm.
My ideas about complexity can help. What I’m proposing might be called Newtonian quantum gravity because it unifies aspects of Newton’s theory of gravity, above all this value of complexity, and the two key novel features of quantum mechanics: probabilities for the state a system finds itself in, and an entity known as a wave function that determines how these probabilities evolve.
The idea is that a wave function of the universe determines the probabilities of all the possible shapes it can have. This is relatively conventional. What I’m suggesting, however, is how that happens: I put the birth of time at Alpha, this uniquely uniform configuration of particles, and make complexity time itself.
Heaps of time
I said my granddaughter could sort the shuffled snapshots into the correct order. Now suppose I give her snapshots of all possible shapes of the universe to sort into heaps, one for each value of their complexity. In the first heap there will be just that one most uniform shape: Alpha. After that, there will be infinitely many for each value of complexity. The wave function determines relative probabilities for each of the shapes within each heap.
This is what standard quantum mechanics does for the probabilities of a system’s possible states at different external times. My proposal includes something similar but with invisible, external time replaced by complexity, which is visible in the sense that it is directly determined by the shape of the universe. Hence, complexity doesn’t just give time its direction – it literally is time.
The picture I have sketched matches the known history of the universe, but is only a start. The good news for next steps is that there is, at least in principle, an observational test.
Scrutiny of the first light in the universe, known as the cosmic microwave background (CMB), indicates that very soon after the big bang the distribution of matter in the universe was extremely uniform, while also revealing tiny fluctuations of a very specific structure. Inflation, a theory that suggests the universe underwent a huge expansion in its first split second, can explain the form of those fluctuations rather well. But it doesn’t tell us how inflation began and key parameters must be fitted to match observations.
According to my idea, the universe must begin as uniform as it possibly can and then develop small nonuniformities. This might sound like an arbitrary assumption, but it is a direct consequence of the simplest quantum law one can propose for the universe, which forces the wave function to evolve from a necessarily unique condition at its most uniform shape. It is possible we could use first principles to directly predict the form of the fluctuations, which we could at some point verify or rule out by further scrutinising CMB.
This idea could go either way. I am hopeful, and not only because Newtonian complexity has a counterpart in Einstein’s theory. I also find encouragement in the thoughts of Niels Bohr, a founder of quantum mechanics, who said any new quantum idea needs to be crazy. The idea that complexity is time is certainly that – and it could be transformative. If time really is complexity, and it is a big if, it will kill two birds with one stone: provide a new starting point from which to formulate a quantum theory of gravity and show, on the basis of simple first principles, how time gets its direction.
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