In the beautifully naïf hubris of youth, as I was about to begin my studies in physics, I thought that what waited for me at the other end of the tunnel was a deep understanding of the universe and of all its secrets. However, as the semesters passed, that goal seemed to slip further and further away. Sure, I was learning a great deal of fascinating things, and studying many of the theories we have to explain the universe we observe, but, lecture after lecture, one thing above all others became clear to me: we are ridiculously far from understanding everything, and the deepest secrets of the universe are as well hidden and out of reach as they’ve ever been. And, you’ve probably guessed it, one of these elusive mysteries is time itself, the very thing our watches are built to measure.
In this article, I’d like to share with you what I’ve learned so far about time, and what makes it so fascinating and mysterious. Bear with me along this ride, and your mind might be blown along the way, and, at the end, you will hopefully also see time with new eyes.
Newton, Einstein, and beyond
Let’s start with the question: what is time? ‘What an odd question!’ — some might say — ‘Time is… well, time! It’s that thing that clocks measure and that moves forward, and in which things happen!’. This is, indeed, a legit reaction, as, for all practical purposes of our everyday life, time is just there, flowing undisturbed, and carrying everything end everyone with it. And this is, understandably, also the view that people had for a very long time. And not just ordinary people, but also great physicists and mathematicians. This is the view of time of classical physics, also referred to as Newtonian physics, so named after the father of the famous three laws of motion, at the base of classical mechanics. In Newtonian physics, time is exactly as we perceive it in our daily life: a sort of fixed theatre stage where things happen; it appears in the equations just as an evolution parameter, but doesn’t do much more; it flows forward in a regular fashion, and it’s the same everywhere, equal for everybody, homogeneous and isotropic, in all parts of the universe. A rather reassuring picture, one might say. As with all reassuring pictures, however, there was something fundamentally wrong with that view, and soon the evidence of this couldn’t be ignored anymore.
This evidence came from another central theory of classical physics: electromagnetism, the theory of electricity, of magnetism, and of light. I don’t want to bother you with the details, but the fact that some of the conclusions of electromagnetism held true (as, for example, the fact that light has a constant speed no matter how you are moving with respect to its source) meant that the Newtonian view of time — and of space — couldn’t be right. It had to change. And changed it has: in one of his famous 1905 papers, a certain Albert Einstein collected all the dangling threads and knotted them in what became known as the special theory of relativity, which, in essence, contained a completely new view of space and time, which were no longer separate and independent absolute entities, but two faces of the same object: the spacetime.
In the world of special relativity, space and time became tightly connected and could even transform into each other, in a sense. But, most importantly, time was no longer a fixed and absolute construct flowing the same everywhere. No, in this world time was relative: my time was different than your time, if we were moving with respect to each other. You watch, for example, could be ticking twice as fast as mine, or half as fast. Two events that are simultaneous for me might no longer be so for you. In other words, time could contract, or dilate, depending on the relative motion of the observed systems. And so could space.
Visualizing the time contractions and dilations described by special relativity is particularly tricky, as the theory is only concerned with systems of reference moving at constant velocity with respect to each other, whereas in many of the classical examples out there, one is very much tempted to bring the two reference systems together, to make comparisons. In the twins paradox, for example, at the end of the story the two twins meet again, one of the two still being in its youth, the other one old and wrinkly. For the two to meet, however, it means that one of the two twins must have, at some point, reversed its velocity, in order to move towards the sibling, and then decelerated, until the two could shake hands in the same frame of reference.
Fortunately, Einstein didn’t stop at special relativity, and after years of hard work with manifolds and tensors, he presented the world his general theory of relativity (GR), which is, essentially, a theory of gravitation. Newton’s apple 2.0, one could say.
Wait a second, what has gravitation to do with time?! Good question! It turns out that gravity — at least at the macroscopic scale — is nothing else than an effect of spacetime curvature, which is caused by mass and energy. How do you have to imagine gravity as an effect of a curved spacetime? Another very good question, and not an easy one to answer. There are many resources (including YouTube videos) that try to do that, and since I’m already exceeding a reasonable word count, I won’t go into much more detail. In a nutshell, every object, if not subjected to any force, to go from spacetime point A to spacetime point B moves along the shortest possible spacetime path that connects A with B. In a curved spacetime, the shortest path may not be the one one would expect; instead it is one that, for us, appears as an accelerated trajectory, as though there was a force — gravity — influencing the motion of that object.
So, with his general theory of relativity, Einstein gifted the world with a complete new theory and understanding of space and time. In this new framework, phenomena that could not be explained before became clear, and many more incredible things became possible. Black holes, for example — another great mystery of the cosmos — and time travel (at least in one direction — those of you who have watched Interstellar may know what I’m talking about). Since its inception, GR has led to incredible scientific advances, has enabled space exploration, and has made some of today’s most used technologies possible — did you know, for example, that without corrections from GR, the GPS in your phone would quickly become off of kilometres? But, as powerful and complicated as it is, GR is a beautiful and self contained theory, and if it were the definitive theory, the end of the story, then it would be correct to say that time is way more complex and tricky than we might have thought, but it wouldn’t be so mysterious anymore. But GR is not the end of the story. Not even close to it. Dear reader, meet quantum physics.
Long story short, if GR is the theory of the cosmically big, of stars and galaxies, quantum physics is the theory of the infinitesimally small, of the atom and its components. And if you thought that relativity painted a funny version of reality, your common sense will be brutalized and left dying in agony by the weirdness of quantum mechanics. But, again, why should that be surprising? The scales at which we live and sense are many orders of magnitude larger than those described by quantum mechanics. All good, then, more or less. So, what does quantum mechanics tells us about time? Well, not much actually, and that’s the problem.
In the classical version of the quantum theory, time is once again merely a parameter along which a system evolves. And when we try to construct a quantum theory of gravity (which would be, as GR teaches us, also a quantum theory of time), we are lost. Currently there is no consensus on any one theory that could help us here. And since it was quantum physics that, until this point, was able to tell us how the universe works at the fundamental level, a missing quantum theory of gravity means that we lack a fundamental understanding of time. We know how it behaves at a macroscopic level, we know that it’s relative, that it’s tightly connected with space, and that it can be bent and curved, but we still don’t know what it is at its core, how it originates. Worse than that, we don’t even know if and in what sense we can say that it exists.
From order to chaos: the arrow of time
I opened the last section with the somewhat silly sounding question ‘What is time?’, and then I tried to explain that it’s not a silly question at all, and that, although we now know much more about time than we did two centuries ago, there’s still a lot about time that we ignore, with a quantum theory of gravity being one of the holy grails of modern physics.
In this section I want to shortly address another question, which may sound even sillier than the first one: why does time flow in one direction and one direction only?
The reason why this is not a silly question is that all fundamental laws of physics are invariant under time reversal (with very few exceptions in particle physics, but those don’t affect the validity of the arguments presented here). What does that mean? It means that if a particular trajectory of a particle is possible, then also the time reversed trajectory is perfectly legit according to the fundamental physical laws. More concretely, if you were to record a bunch of particles moving around on a table (think for examples of some perfectly elastic balls on a frictionless billiard table with no holes), and then were to play that recording to some people from beginning to end, and to some other people from end to beginning, there would be no way for the two groups of people to tell if they’ve just watched the recording played forwards or backwards. In other words, that particular sequence of event is perfectly symmetric with respect to time. However, if you repeated the same experiment adding friction to the billiard table, or adding back the holes, or if you recorded, instead, an egg being dropped and crashing on the kitchen floor, then it would be obvious to tell if you’re watching the recording backwards: balls don’t jump out of billiard holes by themselves, neither do they suddenly start moving, if left undisturbed, and certainly smashed eggs don’t get back together and spontaneously jump in one’s hand. So, what’s happening here?
You see, I’ve told you that all fundamental laws of physics are invariant under time reversal, but not that all laws are. In particular, there’s one law you might be familiar with that is not: the second law of thermodynamics. This law is not a fundamental one, though, in the sense that it is not concerned with fundamental behaviour of sigle bodies, but rather with the macroscopic behaviour of systems composed by an enormous number of bodies. Gases, for example. In one litre of gas you have many billions of billions of atoms, all interacting with each other. That’s what thermodynamics (or also statistical physics) deals with: the macroscopic properties of such enormous ensembles of particles. And in such scenario a new quantity emerges: entropy.
An intuitive way to think about entropy is as a measure of order: a given state of a system as a low entropy if that particular state can be achieved only in a few ways. It has a high entropy if, on the contrary, there are many configurations of the system that give rise to that state: there’s only one way for a room to be tidy and in perfect order, but, from there, there are a million ways in which you can mess with it and bring it to a disordered and chaotic state. To simplify further: think, for example, that your system is composed of a million blue balls and a million red balls in a box. Then the state where all blue balls are in one half of the box and all red balls in the other has very low entropy, as there’s only one possible configurations of the balls to achieve this state (modulo, of course, the specific position of the balls in their half). If now we take one blue ball and move it on the other side, then this state, although still pretty ordered, has already a bigger entropy than the previous one, since there are a million ways in which I could have created it, as I could have chosen any of the million blue balls to move to the other half.
Now, back to the second law of thermodynamics, this law tells us that the entropy of a closed system will always increase with time. Namely, that a closed system will become more and more disordered as time goes by. Obviously, this law in not symmetric with respect of time: it explicitly distinguishes between a low entropy past and a high entropy future. And this is the reason why one says that entropy defines the arrow of time: the direction of time is the one along which entropy increases. A state with an intact eggs has a lower entropy than one where the egg has been shattered on the floor. Going back to the balls example, if you start in a system with blue balls in one half and the red ones in the other, and then start shaking the box, the configurations of the balls will become more and more disordered as time passes, eventually with all balls being perfectly mixed with each other.
To summarize, then, somehow the direction of time is nothing fundamental to the world, rather it emerges at the macroscopic level, when we consider the interactions of millions of microscopic components. The complexity of the world seems, at some point, to break the symmetry.
‘Wait another second!’, I hear you saying, ’Let’s go back to the box of balls. If I keep shaking it, and if I’m lucky enough, then it might happen that there will be a point at which the blue and red balls are separated again, right?’. Well spotted! That’s indeed true, and another reason why the laws of thermodynamics are not considered fundamental laws, but rather statistical ones. In theory, it is not impossible for the billiard balls to jump out of the holes, or for the egg to get back together; it is just astronomically improbable, and that’s why it is something that you will almost certainly never witness, even if you were to live as long as many billion times the current age of the universe and do nothing else than drop a new egg every second.
Fascinating, isn’t it? And we haven’t even touched on the reasons why we, as self-conscious beings, experience the direction of time as we experience it. Can it all be explained with entropy? Or is there more to it? This article is a great starting point to try to understand this part of the story.
All in all, there is still al lot of work to do to uncover all the secrets of time. Fortunately, the brightest minds of our time are on it, and one day we may know more, and maybe we will discover that time is something yet completely different from what we thought so far. Who knows! In the meantime, I can tell you something that I know for a fact: ever since I learned all these things about time, I look at the timepiece on my wrist with an even greater sense of wonder, knowing that the regular oscillations of its delicate hairspring measure something as mysterious as time; and I sincerely hope that the same will now be true for you too.
Reading list
For those of you who are interested in learning more about time and the other secrets of the universe, there are many books out there which can be read, understood and enjoyed also without a degree in physics of mathematics. And, most importantly, they are written by great scientists with a knowledge and understanding of physics way greater than mine. Here’s a short list of titles perfect to start:
- “The Elegant Universe”, by Brian Greene
- “Quantum: Einstein, Bohr and the Great Debate About the Nature of Reality”, by Manjit Kumar
- “A Brief History of Time”, by Stephen Hawking
- “The Order of Time”, by Carlo Rovelli
- “Einstein’s Greatest Mistake”, by David Bodanis