Fill a glass with hot water. If you let time pass, the water will cool down until it reaches the temperature of the surrounding environment. The same thing happens when you put an ice cube in a glass: little by little it melts until the water equals its temperature with the surroundings. This thermalization is a natural and irreversible phenomenon, because when we put two systems in contact, both tend to what experts know as thermal equilibrium .
Seemingly bland, this phenomenon introduces a fundamental asymmetry in physics: it defines an arrow of time . From our everyday experience, it flows from the past to the future, and it always is. “We can confuse east with west, but not yesterday with tomorrow,” explained Sean Carroll, a physicist at the California Institute of Technology (USA). Except in thermodynamics, this forward movement is irrelevant, a mute companion. “The fundamental laws of physics do not distinguish between past and future,” adds Carroll. For the Italian Carlo Rovelli, physics ignores the problem: “It is not described how things evolve in time, but how they evolve in their times,” Rovelli illustrates. From mechanics to electromagnetism to quantum theory, the equations are symmetric in that sense. For this reason, if they pass us a movie of two billiard balls colliding, we would be unable to know by simple observation if they are having a good time or backwards. However, if we see another video where the water in a glass is turning into an ice cube, we will know that they are giving us a hoot. This fundamental difference between the reality around us and the laws of physics seems to indicate that something is missing from us. But what?
The first person to take the problem seriously was Ludwig Boltzmann , an Austrian physicist in the late 19th century. He raised many revolutionary ideas in his time, such as that atoms really existed or that temperature was a consequence of movements and collisions between them. Short-sighted, Boltzmann perceived much further than his colleagues, but was scorned by them and committed suicide in 1906.
His ideas remained, and thermodynamics, the science that studies heat , could not be understood today without his insight. Among his efforts was to give an explanation to entropy, a strange concept that had appeared in 1865 from the hand of one of the fathers of thermodynamics, Rudolf Clausius (1822-1888). This German physicist and mathematician introduced it to explain why heat flows from a hot body to a cold one. Based on this, he formulated a fundamental principle, today known as the second law of thermodynamics: natural processes are those in which there is an increase in the entropy of the universe, and never the other way around . Clausius thus defined the direction of the arrow of time.
But what is entropy and why should it increase? These are the unknowns that Boltzmann solved. Starting from the assumption that the world is nothing more than “atoms and emptiness” – as Democritus said two millennia ago – Boltzmann reached the conclusion that the most probable state of any system is disorder . For example, if we mix some cards, the normal thing is to end up with a messy deck instead of grouped by suits and numbers. The same happens with gases: we could have all their molecules moving in the same direction; or two gases that, contained in the same container, are not mixed, but separated; or one that is compressed, without external influence, in a corner of the vessel that contains it, leaving the rest totally empty … There is no law that prevents any of these scenarios. However, it is highly unlikely, even more so that after mixing a deck it will come out organized by numbers and suits.
We must not forget this principle: there are a greater number of disordered combinations than ordered ones . Now we are in a position to understand what entropy is: a measure of disorder in nature. And since order is more likely, entropy tends to increase. This was Boltzmann’s great contribution, and the one that opened the door to the problem of the arrow of time: the future is different from the past simply because the entropy of the universe has increased.
If we now put into play cosmological evolution and the commonly accepted theory of its inception, the big bang, the universe must have been in a very low entropy –that is, very ordered– state when it was born. “The second principle of thermodynamics suggests that any system naturally evolves towards a typical and more probable state, but at the same time we are assuming that the universe began in an extremely atypical and improbable state,” Rovelli emphasizes. “If its configuration were chosen randomly among all the possible ones, it would be in a very high entropy state”, adds Carroll. How is it possible? “It’s something for which we have no answer,” says Carroll in his book From Eternity to Today. And it doesn’t sound too convincing that something very organized comes out of a big bang …
Now, in all this discussion there is something that we have not paid attention to. The universe is not a typical thermodynamic system, as it is governed by an external force: gravity. Although it must somehow affect entropy, we don’t really know how, since to do so we need a subatomic-scale gravitational theory, something we don’t yet have.
All these pitfalls must be solved in order to understand why the universe that emerged immediately after the big bang did so in a highly improbable state of order. And we are not even sure which answer would be the satisfactory one. Apparently, after half a century with us, the big bang hypothesis continues to put our best theories of physics at odds: without a way to describe exactly how the universe came into being, we cannot explain why it was low entropy and therefore So understand the arrow of time. And the million dollar question: what is a high entropy state like when gravity turns out to be a relevant piece of the system?
Roger Penrose has been working on this subject for decades. This eminent English physicist and mathematician argues that the formation of structures in the universe, such as galaxies, stars and planets, does not mean a decrease in entropy, but quite the opposite: “With gravity, things tend to be different [. ..]. High entropy is achieved when gravitating bodies pile up ”. Apparently, and according to different calculations, in the presence of gravitational forces, “the states of higher entropy are like empty space, with most of the particles scattered and progressively diluting,” says Carroll. In other words, just as the universe was in its beginnings.
To this whole panorama we must introduce an incredible phenomenon that happened in the very first moments of the universe’s life: inflation . Formulated by the American physicist Alan Guth in late 1979, it tells us that we will never know what happened just before the big bang , since the entire universe – or at least a region of it – experienced an exponential increase in volume. Such an expansion erased all the irregularities that might have existed at the beginning and made the cosmos flat – without curvature – and homogeneous. Although this astonishing mechanism explains many of the unknowns left by the initial big bang theory, it does not account for why the universe was born with such a low entropy.
This is where many theoretical physicists raise their hands and point to string theory as a solution to the problem, but perhaps it is not. At the end of the last century, it was the star model of physics and its spokesmen, such as Brian Greene and Michio Kaku, raised it to the skies saying that we were before the theory of everything . But little by little it has been deflating. Some, like the Indian string physicist Shiraz Minwalla, already see it as a new way of doing science: “It has more to do with a mathematical theory inspired by physics than with classical physics,” says Minwalla. To all this we must add that, like almost any other fundamental physical theory, its equations do not establish a strong distinction between the past and the future, therefore the arrow of time does not arise naturally; it must be introduced ad hoc.
Some experts argue that we must look in another direction, towards where the competing hypothesis of the strings is: the quantum gravity of loops. Among those trying to solve the riddle is Canadian physicist Lee Smolin. According to him and his collaborator, the Portuguese Marina Cortês, the universe is made up of a series of completely unique events, which are never repeated. Each set of events can only influence the next, so the arrow of time appears naturally. “We hope we can get to the problem of the initial conditions [of the universe] and discover that they are not so special,” says Cortês.
Solving the problem of the initial entropy of the cosmos has triggered the imagination of theoretical physicists: some say that, although the physical laws that we know do not contemplate the existence of a temporal arrow, that is explained because they are not true, but only good approximations. When we discover the fundamentals, we will see how it appears naturally. For example, Penrose puts forward what he calls the Weyl curvature hypothesis : there is a natural law that distinguishes between space-time singularities of the past and those of the future, and that endows the universe with a time arrow.
At bottom, these are all attempts to explain the break between the laws of physics and reality. But whatever the correct hypothesis – or if it is a mixture of both – they all leave aside another fundamental question: when did time begin to flow?
It is at this point that the research published at the end of 2019 by Thomas Gasenzer and Jürgen Berges, physicists at the University of Heidelberg (Germany) enters. “If you start far from equilibrium, as the universe was born, how did the arrow of time appear?” Berges wonders.
What these researchers have developed is a whole theoretical construct to understand what happened at the subatomic level before the cosmos thermalization process began, that is, when entropy begins to rise. At that time things were not as we know them: the cosmos consisted of a vast ocean of quantum energy that “was in a state very far from equilibrium,” explains Gasenzer.
According to the calculations of the Heidelberg physicists, that energy field had fractal properties similar to what happens when we stir a cup of coffee. They were described in 1941 by one of the greatest mathematicians of the mid-20th century, the Russian Andrei Kolmogórov (1903-1987), when he was studying turbulent fluids. By stirring the coffee, we generate a vortex –flow in a spiral rotation– that causes the appearance of smaller ones, and so on. They feed on the energy transferred to them by the larger vortex, like in a waterfall, and at an exponential rate, which is known as the power law . Well, German scientists have found that the same phenomenon occurs in quantum systems very far from equilibrium . The difference between Kolmogórov’s coffee and the Berges and Gasenzer systems is that in the first case, this cascade of energy occurs in space –in different areas of the coffee–, while for the latter it is also produced in time. And this detail is essential, because it means that, if we could observe that ocean of primordial energy over time and, at the same time, at different scales, we would see that everything would remain exactly the same, as if frozen, in a state of no change, of no time.
And it would have remained like that for eternity if it weren’t for a sudden phase change similar to what happens when we have supercooled water – liquid, but below zero degrees – and we introduce a small impurity, like a speck of dust: then it freezes abruptly and instantly. Something like this happened to the universe, say the Heidelberg scientists. A very slight disturbance ended this non-time state governed by fractal dynamics and caused the appearance of a dense soup of quarks – the bricks of protons and neutrons – and gluons – the particles that hold the quarks together. It is from that moment that the universe is subject to the second law, and entropy begins to increase in an active process that will continue for billions of years.
The important thing to keep in mind is that before that phase change there was no time, there was no history. The universe arose from an initial singularity, from a great explosion, which was followed by an inflation that caused it to multiply its size by 1026 in an infinitesimal fraction of a second. That primal energy could well have remained that way indefinitely, without anything changing, without past, present, or future. Then all of a sudden there was a miniscule change that gave the energetic baby a direction to flow, an arrow of time.
Can this theory be tested experimentally? Markus Oberthaler, also from the University of Heidelberg, has taken a first step in that direction using 7,000 rubidium atoms. With them, and after two years of work, he formed a Bose-Einstein condensate, a state of aggregation of matter below the solid, at a temperature very close to absolute zero. Curiously, the properties of matter in this situation are similar to when it is found at very high temperatures, in the form of quartk-gluon plasma. In his article, published in September 2019, Oberthaler explained that during the forty seconds that the condensate was stable, they injected a large amount of energy into it and observed its evolution. It was in a very out of balance state, and they found that it was following the fractal dynamics of Gasenzer and Berges. “It seems to be a confirmation of the existence of this universal scale law,” Oberthaler summarized. Meanwhile, at CERN they are striving to design an experiment that creates a primordial plasma . Then it will be seen if we have finally discovered the origin of time.
