by Lee Smolin
Laws, then, are not imposed on the universe from outside it. No external entity, whether divine or mathematical, specifies in advance what the laws of nature are to be. Nor do the laws of nature wait, mute, outside of time for the universe to begin. Rather the laws of nature emerge from inside the universe and evolve in time with the universe they describe. It is even possible that, just as in biology, novel laws of physics may arise as regularities of new phenomena that emerge during the universe’s history.
Some might see the disavowal of eternal laws as a retreat from the goals of science. But I see it as the jettisoning of excess metaphysical baggage that weighs down our search for truth. In the coming chapters, I will provide examples illustrating how the idea of laws evolving in time leads to a more scientific cosmology—by which I mean one more generative of predictions subject to experimental test.
To my knowledge, the first scientist since the dawn of the Scientific Revolution to think really hard about how to make a theory of a whole universe was Gottfried Wilhelm Leibniz, who, among other things, was Newton’s rival, famously in the matter of which of them was the first to invent the calculus. He also anticipated modern logic, developed a system of binary numbers, and much else. He has been called the smartest person who ever lived. Leibniz formulated a principle to frame cosmological theories called the principle of sufficient reason, which states that there must be a rational reason for every apparent choice made in the construction of the universe. Every query of the form, “Why is the universe like X rather than Y?” must have an answer. So if a God made the world, He could not have had any choice in the blueprint. Leibniz’s principle has had a profound effect on the development of physics so far, and, as we will see, it continues to be reliable as a guide in our efforts to devise a cosmological theory.
Leibniz had a vision of a world in which everything lives not in space but immersed in a network of relationships. These relationships define space, not the reverse. Today the idea of a universe of connected, networked entities pervades modern physics, as well as biology and computer science.
In a relational world (which is what we call a world where relationships precede space), there are no spaces without things. Newton’s concept of space was the opposite, for he understood space to be absolute. This means atoms are defined by where they are in space but space is in no way affected by the motion of atoms. In a relational world, there are no such asymmetries. Things are defined by their relationships. Individuals exist, and they may be partly autonomous, but their possibilities are determined by the network of relationships. Individuals encounter and perceive one another through the links that connect them within the network, and the networks are dynamic and ever evolving.
As I will explain in chapter 3, it follows from Leibniz’s great principle that there can be no absolute time that ticks on blindly whatever happens in the world. Time must be a consequence of change; without alteration in the world, there can be no time. Philosophers say that time is relational—it is an aspect of relations, such as causality, that govern change. Similarly, space must be relational; indeed, every property of an object in nature must be a reflection of dynamical relations between it and other things in the world.
Leibniz’s principles contradicted the basic ideas of Newtonian physics, so it took some time for them to be fully appreciated by working scientists. It was Einstein who embraced Leibniz’s legacy and used his principles as major motivation for his overthrow of Newtonian physics and its replacement by general relativity, a theory of space, time, and gravity that goes far to instantiate Leibniz’s relational view of space and time. Leibniz’s principles are also realized in a different way in the parallel quantum revolution. I call the 20th-century revolution in physics the relational revolution.
The problem of unifying physics and, in particular, bringing together quantum theory with general relativity into one framework is largely the task of completing the relational revolution in physics. The main message of this book is that this requires embracing the ideas that time is real and laws evolve.
The relational revolution is already in full swing in the rest of science. Darwin’s revolution in biology is one front, manifested both in the notion of a species being defined by its relation to all the other organisms in its environment and in the concept that a gene’s action is defined only in the context of the network of genes regulating its action. As we are quickly coming to realize, biology is about information, and there is no more relational concept than information, relying as it does on a relationship between the sender and receiver at each end of a communications channel.
In the social sphere, the liberal concept of a world of autonomous individuals (conceived by the philosopher John Locke as analogous to the physics of his friend Isaac Newton) is being challenged by a view of society as composed of interdependent individuals, only partly autonomous, whose lives are meaningful only within a skein of relationships. The new informational halo within which we are so recently enmeshed expresses the relational idea through the metaphor of the network. As social beings, we see ourselves as nodes in a network whose connections define us. Today the idea of a social system made up of connected, networked entities increasingly crops up in social theories formulated by everyone from feminist political philosophers to management gurus. How many users of Facebook are aware that their social lives are now organized by a potent scientific idea?
The relational revolution is already far along. At the same time, it is clearly in crisis. On some fronts, it’s stuck. Wherever it is in crisis, we find three kinds of questions under hot debate. What is an individual? How do novel kinds of systems and entities emerge? How are we to usefully understand the universe as a whole?
The key to these puzzles is that neither individuals, systems, nor the universe as a whole can be thought of as things that simply are. They are all compounded by processes that take place in time. The missing element, without which we cannot answer these questions, is to see them as processes developing in time. I will argue that to succeed, the relational revolution must embrace the notion of time and the present moment as a fundamental aspect of reality.
In the old way of thinking, individuals were just the smallest units in a system, and if you wanted to understand how a system worked you took it apart and studied how its parts behaved. But how are we to understand the properties of the most fundamental entities? They have no parts, so reductionism (as this method is called) gets us no further. The atomic viewpoint has no place to go here; it, too, is truly stuck. This is a great opportunity for the nascent relational program, for it can—and indeed must—seek the explanation for properties of elementary particles in the network of their relations.
This is already happening in the unified theories we have so far. In the Standard Model of Particle Physics, which is the best theory we have so far of the elementary particles, the properties of an electron, such as its mass, are dynamically determined by the interactions in which it participates. The most basic property a particle can have is its mass, which determines how much force is needed to change its motion. In the Standard Model, all the particles’ masses arise from their interactions with other particles and are determined primarily by one—the Higgs particle. No longer are there absolutely “elementary” particles; everything that behaves like a particle is, to some extent, an emergent consequence of a network of interactions.
Emergence is an important term in a relational world. A property of something made of parts is emergent if it would not make sense when attributed to any of the parts. Rocks are hard, and water flows, but the atoms they’re made of are neither solid nor wet. An emergent property will often hold approximately, because it denotes an averaged or high-level description that leaves out much detail.
As science progresses, aspects of nature once considered fundamental are revealed as emergent and approximate. We once thought that solids, liquids, and gases were fundamental states; now we know that these are emergent properties, which can be understood as different
ways to arrange the atoms that make up everything. Most of the laws of nature once thought of as fundamental are now understood as emergent and approximate. Temperature is just the average energy of atoms in random motion, so the laws of thermodynamics that refer to temperature are emergent and approximate.
I’m inclined to believe that just about everything we now think is fundamental will also eventually be understood as approximate and emergent: gravity and the laws of Newton and Einstein that govern it, the laws of quantum mechanics, even space itself.
The fundamental physical theory we seek will not be about things moving in space. It will not have gravity or electricity or magnetism as fundamental forces. It will not be quantum mechanics. All these will emerge as approximate notions when our universe grows large enough.
If space is emergent, does that mean that time is also emergent? If we go deep enough into the fundamentals of nature, does time disappear? In the last century, we have progressed to the point where many of my colleagues consider time to be emergent from a more fundamental description of nature in which time does not appear.
I believe—as strongly as one can believe anything in science—that they’re wrong. Time will turn out to be the only aspect of our everyday experience that is fundamental. The fact that it is always some moment in our perception, and that we experience that moment as one of a flow of moments, is not an illusion. It is the best clue we have to fundamental reality.
Falling
BEFORE STARTING THIS or any other journey of discovery, we should heed the advice of the Greek philosopher Heraclitus, who, barely a few steps into the epic story that is science, had the wisdom to warn us that “Nature loves to hide.” And indeed she does; consider that most of the forces and particles that science now considers fundamental lay hidden within the atom until the last century. Some of Heraclitus’s contemporaries spoke of atoms, but without really knowing whether or not they existed. And their concept was wrong, for they imagined atoms as indivisible. It took until Einstein’s papers of 1905 for science to catch up and form the consensus that matter is made of atoms. And six years later the atom itself was broken into pieces. Thus began the unraveling of the interior of atoms and the discoveries of the worlds hidden within.
The largest exception to the modesty of nature is gravity. It is the only one of the fundamental forces whose effects everyone observes with no need for special instruments. Our very first experiences of struggle and failure are against gravity. Consequently, gravity must have been among the first natural phenomena to be named by our species.
Nonetheless, key aspects of the common experience of falling remained hidden in plain sight until the dawn of science, and much remains hidden still. As we shall see in later chapters, one thing that remains hidden about gravity is its relation to time. So we start our journey toward the discovery of time with falling.
…
“Why can’t I fly, Daddy?”
We were on the top deck, looking down three floors to the back garden.
“I’ll just jump off and fly down to Mommy in the garden, like those birds.”
“Bird” had been his first word, uttered at the sparrows fluttering in the tree outside his nursery window. Here is the elemental conflict of parenthood: We want our children to feel free to soar beyond us, but we also fear for their safety in an uncertain world.
I told him sternly that people can’t fly and he was absolutely never to try, and he burst into tears. To distract him, I took the opportunity to tell him about gravity. Gravity is what holds us down to Earth. It is why we fall, and why everything else falls.
The next word out of his mouth was, unsurprisingly, “Why?” Even a three-year-old knows that to name a phenomenon is not to explain it.
But we could play a game to see how things fall. Soon we were throwing all kinds of toys down into the garden, doing “speriments” to see whether they all fell the same way or not. I quickly found myself thinking of a question that transcends the powers of a three-year-old mind. When we throw an object and it falls as it moves away from us, it traces a curve in space. What sort of curve is it?
It’s not surprising that this question doesn’t occur to a three-year-old. It doesn’t seem to have occurred to anyone for thousands of years after we regarded ourselves as highly civilized. It seems that Plato, Aristotle, and the other great philosophers of the ancient world were content to watch things fall around them without wondering whether falling bodies travel along a specific kind of curve.
The first person to investigate the paths traced by falling bodies was the Italian Galileo Galilei, early in the 17th century. He presented his results in Dialogue Concerning Two New Sciences, which he wrote during his seventies, when he was under house arrest by the Inquisition. In this book, he reported that falling bodies always travel along the same sort of curve, which is a parabola.
Galileo not only discovered how objects fall but also explained his discovery. The fact that falling bodies trace parabolas is a direct consequence of another fact he was the first to observe, which is that all objects, whether thrown or dropped, fall with a constant acceleration.
Galileo’s observation that all falling objects trace a parabola is one of the most wonderful discoveries in all of science. Falling is universal, and so is the kind of curve that falling bodies trace. It doesn’t matter what the object is made of, how it is put together, or what its function is. Nor does it matter how many times, from what height, or with what forward speed we drop or throw the object. We can repeat the experiment over and over, and each time it’s a parabola. The parabola is one of the simplest curves to describe. It is the set of points equidistant from a point and a line. So one of the most universal phenomena is also one of the simplest.
Figure 1: Definition of a parabola: the points equidistant from a point and a line.
A parabola is a concept from mathematics—an example of what we call a mathematical object—that was known to mathematicians well before Galileo’s time. Galileo’s observation that bodies fall along parabolas is one of the first examples we have of a law of nature—that is, a regularity in the behavior of some small subsystem of the universe. In this case, the subsystem is an object falling near the surface of a planet. This has happened a great number of times and in a great number of places since the universe began; hence there are many instances to which the law applies.
Here’s a question children may ask when they’re a bit older: What does it say about the world that falling objects trace such a simple curve? Why should a mathematical concept like a parabola, an invention of pure thought, have anything to do with nature? And why should such a universal phenomenon as falling have a mathematical counterpart that is one of the simplest and most beautiful curves in all of geometry?
Since Galileo’s discovery, physicists have profitably used mathematics in the description of physical phenomena. It may seem obvious to us now that a law must be mathematical, but for almost 2,000 years after Euclid codified his axioms of geometry no one proposed a mathematical law applying to the motion of objects on Earth. From the time of the ancient Greeks to the 17th century, educated people knew what a parabola was, but not a single one of them seems to have wondered whether the balls, arrows, and other objects they dropped, flung, or shot fell along any particular sort of curve. Any one of them could have made Galileo’s discovery; the tools he used were available in the Athens of Plato and the Alexandria of Hypatia. But nobody did. What changed to make Galileo think that mathematics had a role in describing something as simple as how things fall?
This question takes us into the heart of some questions easy to state but hard to answer: What is mathematics about? Why does it come into science?
Mathematical objects are constituted out of pure thought. We don’t discover parabolas in the world, we invent them. A parabola or a circle or a straight line is an idea. It must be formulated and then captured in a definition. “A circle is a set of points equidistant from a single point. . . A parabola is a set of poi
nts equidistant from a point and a line.” Once we have the concept, we can reason directly from the definition of a curve to its properties. As we learned in high school geometry class, this reasoning can be formalized in a proof, each argument of which follows from earlier arguments by simple rules of reasoning. At no stage in this formal process of reasoning is there a role for observation or measurement.
A drawing can approximate the properties demonstrated by a proof, but always imperfectly. The same is true of curves we find in the world: the curve of a cat’s back when she stretches or the sweep of the cables of a suspension bridge. They will only approximately trace a mathematical curve; when we look closer, there’s always some imperfection in the realization. Thus the basic paradox of mathematics: The things it studies are unreal, yet they somehow illuminate reality. But how? The relationship between reality and mathematics is far from evident, even in this simple case.
You may wonder what an exploration of mathematics has to do with an exploration of gravity. But this is a necessary digression, because mathematics is as much at the heart of the mystery of time as gravity is, and we need to sort out how mathematics relates to nature in a simple case, such as bodies falling along curves. Otherwise when we get to the present era and encounter statements like “The universe is a four-dimensional spacetime manifold,” we will be rudderless. Without having navigated waters shallow enough for us to see bottom, we’ll be easy prey to mystifiers who want to sell us radical metaphysical fantasies in the guise of science.
Although perfect circles and parabolas are never to be found in nature, they share one feature with natural objects: a resistance to manipulation by our fantasy and our will. The number pi—the ratio of a circle’s circumference to its diameter—is an idea. But once the concept was invented, its value became an objective property, one that must be discovered by further reasoning. There have been attempts to legislate the value of pi, and they have revealed a profound misunderstanding. No amount of wishing will make the value of pi anything other than it is. The same is true for all the other properties of curves and other objects in mathematics; these objects are what they are, and we can be right or wrong about their properties but we can’t change them.
