Chapter Content
Okay, so, like, if you've actually stuck with me this far, you've pretty much got all the pieces you need to understand the basic physics picture of the world we have today. You know, the good, the bad, and the, uh, kinda limited parts.
So, like, fourteen billion years ago, warped spacetime just, poof, showed up. Nobody really knows how, you know? And it's still expanding. This space, it's, like, a real thing. A physical field. Einstein's equations? They're how it works. Gravity from stuff bends space, and if there's too much stuff, it just, like, falls into a black hole.
And, uh, all that stuff is spread across a zillion galaxies, each with, like, another zillion stars. And it's all made of these, these quantum fields. Sometimes they pop up as particles, like electrons or light, you know, photons. Other times they're, like, waves, you know, like the radio waves that give us TV or, like, the light from the sun and the stars.
So, these quantum fields, they make up everything. Atoms, light, the whole shebang. And they're kinda weird, right? Their quanta, these particles, only show up when they, like, bump into stuff. When they're not interacting, they spread out into this, like, "probability cloud." So, the world's basically a bunch of events, all, like, swimming in this huge, dynamic ocean of space, kinda like waves in the sea.
With this picture, and a few little tweaks, we can, like, describe pretty much everything we see.
"Pretty much," though, right? So, there's gotta be something missing. And, that's what we're after. The rest of this book? It's about that missing piece.
Turning this page, for better or for worse, you're stepping out of the world we know for sure, and heading into the world we're trying to, like, glimpse.
It's kinda like stepping out of a cozy little spaceship into the unknown.
So, like, spacetime, it's quantum.
There's this, like, big problem at the heart of how we understand physics. The two best things the 20th century gave us, general relativity and quantum mechanics, they’re both super useful for understanding the world and for all our tech. General relativity gave us, you know, cosmology, astrophysics, the study of gravitational waves and black holes, that kind of stuff. And quantum mechanics, well, it's the foundation for atomic physics, nuclear physics, particle physics, condensed matter physics, and tons of other things.
But, like, these two theories, there's something kinda, you know, annoying about them. They can't both be right. At least not the way they are now, because they seem to, like, contradict each other. The description of gravity doesn't take quantum mechanics into account, like, it doesn't acknowledge that a field is a quantum field. And quantum mechanics? It doesn't consider the curving of spacetime that Einstein’s equations describe.
So, some college student, right? They go to a general relativity class in the morning, then quantum mechanics in the afternoon. You could forgive them if they thought their professors were, like, total idiots, or if they at least suspected they hadn't talked to each other in a hundred years. Why else would the world be curved spacetime in the morning, where everything's continuous? And then in the afternoon, it’s, like, discontinuous jumps of energy and flat space?
The crazy thing is, both theories work, like, really, really well.
Every experiment, every test, nature keeps telling general relativity, “Yep, you're right!” And it keeps telling quantum mechanics, “Yep, you're right too!” Even though they're based on, like, totally opposite assumptions. So, clearly, we're missing something.
Most of the time, we can just ignore either quantum mechanics or general relativity, or even both. Like, the moon's too big to be affected by tiny quantum stuff, so we can forget about that when we're figuring out how it moves. And atoms, well, they’re too light to bend space enough to matter, so we can forget about space bending when we're studying atoms. But, in some cases, space bending and quantum stuff both matter. And for those cases, we just don’t have a solid theory yet.
The inside of a black hole, that's one example. What happened during the Big Bang, that's another. Basically, we don’t know how space and time work at really, really small scales. When we try to use our current theories in those situations, they just break down and give us nonsense. Quantum mechanics can't deal with curved spacetime, and general relativity can't deal with quantum stuff. That's the problem of quantum gravity.
It kinda goes deeper than that. Einstein knew that space and time are a way that a physical field, gravity, shows itself. And Bohr, Heisenberg, and Dirac knew that physical fields are quantum: discrete, probabilistic, and they only pop up when they interact with stuff. So, it's pretty clear that space and time themselves must be, like, quantum things too.
So, what is quantum space? What is quantum time? That's what we call the problem of quantum gravity. Physicists all over the world are working on this. They're trying to find a theory, a set of equations, that solves this incompatibility between quantum mechanics and gravity.
It's not the first time physics has run into two super successful but totally contradictory theories. And in the past, when we’ve figured out how to bring theories together, we've made huge leaps in how we understand the world. Newton brought together Galileo's physics for things on Earth and Kepler's physics for things in space, and he figured out gravity. Maxwell and Faraday put electricity and magnetism together and came up with the equations for electromagnetism. Einstein created special relativity to solve a big contradiction between Newtonian mechanics and Maxwell’s electromagnetism, and he created general relativity to solve a conflict between Newtonian mechanics and special relativity.
So, when theorists find these kinds of contradictions, they get excited. It's, like, a great opportunity! The question is, can we come up with a way to think about things that can handle both of these theories at the same time?
To understand what quantum space and quantum time are, we're going to have to change the way we see things again, like, really rethink the basic stuff. Like how Anaximander figured out that the Earth is floating in space and that "up" and "down" don't really exist in the universe. Or how Copernicus realized we're all moving through space super fast. Or like how Einstein understood that spacetime is kinda like a squishy animal and that time moves differently in different places. To find a way to understand the world that fits with what we already know, we're going to have to change our ideas about what reality actually is, again.
The first person to realize that we needed to change our basic ideas to understand quantum gravity was this romantic, kinda legendary dude: Matvei Bronstein. A young Russian guy who lived during Stalin's time and, you know, died tragically.
Matvei was friends with Lev Landau, who was a bit older and became the Soviet Union's best theoretical physicist. People who knew both of them said that Matvei was actually the smarter of the two. When Heisenberg and Dirac were laying the groundwork for quantum mechanics, Landau thought that quantum stuff meant that fields couldn't be properly defined. He thought quantum fluctuations would stop us from measuring the size of a field in a tiny little area. Bohr figured out pretty quickly that Landau was wrong. He looked into it more deeply and wrote this long paper showing that fields, like the electric field, can still be defined even when you consider quantum effects. Landau gave up on the problem pretty quickly.
But Matvei, Landau's young friend, was really interested in it. He realized that Landau's intuition wasn't quite right, but it had something important in it. Bohr had shown that a quantum electric field could be defined at a point in space. Matvei did the same reasoning, but he applied it to the gravitational field, which Einstein had only just written down equations for a few years earlier. And that's where, like, boom! Landau was right! When you consider quantum stuff, the gravitational field can't be properly defined at a point.
There's a kinda simple way to see why. Imagine we want to look at a really, really tiny area of space. To do that, we need to put something there, something to mark the spot we want to study. So, let's say we put a particle there. Heisenberg said that you can't keep a particle at a point for long. It'll take off pretty fast. The smaller the area we put the particle in, the faster it'll take off. And if the particle's moving super fast, it'll have a lot of energy. Now, we bring in Einstein's theory. Energy bends space, and a lot of energy means a lot of bending. A huge amount of energy in a tiny area will bend space so much that it'll collapse into a black hole, like a star collapsing. But if the particle falls into a black hole, we can't see it anymore. We can't use it to mark our little area of space. We can't measure an arbitrarily small area of space, because if we try, that area will just disappear into a black hole.
If you add a little math to this argument, it becomes even clearer. The result is that when you bring quantum mechanics and general relativity together, you find that there's a limit to how finely you can divide space. Below a certain scale, nothing can exist. Or, more precisely, there's just nothing there.
How small is that smallest area of space? The calculation's pretty simple: you just figure out the smallest size a particle can be before it turns into its own black hole. The smallest length is, roughly, the square root of something with three natural constants. There's Newton's constant G, which we talked about in Chapter Two, which tells you how strong gravity is. There's the speed of light c, which we talked about in Chapter Three, which shows that the present isn’t just a single moment. And then there’s Planck’s constant h, from Chapter Four, which tells you how big quantum chunks are. So, all these three numbers prove that we are definitely studying gravity (G), relativity (c), and quantum mechanics (h).
The length you get this way, it's called the Planck length. Should have been called the Bronstein length, but, you know. It’s about 10 to the -33 centimeters. So...super tiny.
Quantum gravity only shows up at that scale. To get a sense of how small that is, imagine you blew up a walnut until it was as big as the whole observable universe. Even then, the Planck length would still be a millionth of the size of the original walnut. At that scale, space and time change. They become something different. They become “quantum space and time.” And figuring out what that means is the problem.
Matvei Bronstein figured all this out back in the 1930s and wrote a couple of short, but really insightful papers. He pointed out that our normal way of thinking about space as a continuous thing that you can divide as much as you want just doesn't work with quantum mechanics and general relativity.
There's just one problem. Matvei and Lev were dedicated communists. They believed that the revolution was going to set humanity free and create a better society, with no injustice, none of the increasing inequality we still see all over the world. They were true believers in Lenin. When Stalin took power, they started to feel lost, then to criticize. They wrote some openly critical articles, nothing crazy, but, you know… It wasn't the communism they wanted...
It was a bad time. Landau managed to survive, though it wasn't easy. But Matvei, the year after he first realized that our ideas about space and time needed a big change, was arrested by Stalin's police and sentenced to death. He was executed on the same day he was tried, February 18, 1938. He was only thirty years old.
After Matvei Bronstein died, a bunch of brilliant physicists tried to tackle the problem of quantum gravity. Dirac spent the last years of his life working on it, opening up new paths and introducing ideas and techniques that are still used in quantum gravity today. Thanks to those techniques, we now know how to describe a world without time, which I’ll explain later. Feynman tried to adapt the techniques he developed for electrons and photons and apply them to quantum gravity, but he didn't get anywhere. Electrons and photons are quantum things in space, but quantum gravity is something else. It's not enough to describe “gravitons,” particles moving in space. It's space itself that needs to be quantized.
Some physicists, while trying to solve the problem of quantum gravity, accidentally solved other problems and won Nobel Prizes for it. Two Dutch physicists, Gerard 't Hooft and Martinus Veltman, won the 1999 Nobel Prize for proving the consistency of the theories we now use to describe nuclear forces, which are also part of the Standard Model. But they were actually trying to prove the consistency of a quantum gravity theory. They thought the work on other forces was just preparation, "preparatory work" that won them the Nobel Prize, but it didn't give them the proof they were looking for for their own quantum gravity theory.
The list goes on and on. It reads like a who's who of brilliant theoretical physicists, but also like a list of failures. Slowly, over decades, things got clearer. People stopped going down dead ends, the techniques and general ideas got stronger, and results started to come one by one. It would take way too long to name all the scientists who contributed to this slow process of building up knowledge.
I only want to mention one person, someone who brought together the threads of all this research. That's Chris Isham, this amazing, forever young British guy, a philosopher and a physicist. I got hooked on quantum gravity after reading one of his papers. The paper explained why the problem was so hard, how our ideas about space and time needed to be changed, and gave a clear overview of all the approaches, results, and difficulties people were running into at the time. I was a junior in college, and the possibility of rethinking space and time from scratch just blew my mind. And that hasn't changed. As Petrarch said, “Though the bow is broken, my wound will not heal."
The scientist who contributed the most to quantum gravity was John Wheeler, a legend in 20th-century physics. He was a student and collaborator of Niels Bohr in Copenhagen. He was a collaborator of Einstein after Einstein moved to the United States. He taught people like Richard Feynman. Wheeler was always right in the middle of 20th-century physics. He was incredibly imaginative, and he's the one who came up with the term "black hole" and made it popular. His name is associated with some of the earliest deep thinking about how to imagine quantum spacetime, often in ways that were more intuitive than mathematical. He took Bronstein's insight to heart, realizing that the quantum nature of the gravitational field meant that we needed to change our ideas about space at tiny scales. Wheeler looked for new ways to imagine this quantum space. He imagined quantum space as a bunch of overlapping geometric things, like how we think of an electron as a cloud of possibilities.
Imagine you're looking at the sea from really high up. You see this huge, flat blue ocean. Now, you get closer and you can start to see the waves being made by the wind. You get closer still, and you see the waves breaking, the surface is a frothy mess of foam. That's how Wheeler imagined space.
At scales much bigger than the Planck length, space is smooth. If we go down to the Planck scale, space breaks down and becomes foamy.
Wheeler was trying to find a way to describe this foamy space, these waves of probability of different geometric shapes. In 1966, a young colleague of his in California, Bryce DeWitt, came up with a solution. Wheeler went all over the place, meeting with collaborators whenever he could. He met Bryce at the Raleigh-Durham airport in North Carolina, where he had a few hours wait between flights. Bryce showed him an equation for a "wave function of space." The equation, you know, can be derived using a simple mathematical trick. Wheeler was really interested. That conversation led to the birth of a kind of "orbital equation" for general relativity. This equation could determine the probabilities of curved spaces. For a long time, DeWitt called it the Wheeler equation, Wheeler called it the DeWitt equation, and other people called it the Wheeler-DeWitt equation.
It was a great idea, and it became the basis for trying to build a whole theory of quantum gravity. But the equation itself had some problems, and they were pretty big. First, the equation was just badly constructed from a mathematical point of view. If you tried to use it to calculate anything, you got meaningless results, like infinity. The equation needed to be fixed.
Also, it was hard to interpret the equation, or even to understand what it meant. And one of the annoying things about it was that it didn't have the variable for time in it. If it doesn't have time in it, how can you use it to calculate how things change over time? Equations for dynamics in physics, they usually have the time variable, t. What does a physical theory even mean if it doesn't have time in it? A lot of research in the years that followed focused on these equations, trying to fix them in different ways, improve their definition, and understand what they might mean.
Towards the end of the 1980s, the fog started to clear a little. Some surprising solutions to the Wheeler-DeWitt equation started to show up. During those years, I visited Abhay Ashtekar, an Indian physicist, at Syracuse University in New York, and then Lee Smolin, an American physicist, at Yale University in Connecticut. I remember a lot of excited discussions, a real sense of academic passion. Ashtekar had rewritten the Wheeler-DeWitt equation in a simpler form. Smolin, along with Ted Jacobson at the University of Maryland in Washington, had found some of these strange solutions.
These solutions had a weird feature: they depended on closed lines in space. A closed line is just a "loop." Smolin and Jacobson could write down a solution to the Wheeler-DeWitt equation for every loop, every closed line. What did that mean? The first results of what would later become known as loop quantum gravity came out of these discussions. The meaning of these solutions to the Wheeler-DeWitt equation gradually became clearer. Based on these solutions, a coherent theory slowly started to take shape. Because of the initial research results, the theory was called "loop theory."
Now, hundreds of scientists all over the world are working on this theory, from China to Argentina, from Indonesia to the United States. The theory that's being built up bit by bit is called loop theory or loop quantum gravity. I’m going to dedicate later chapters to this theory. It's not the only direction people are taking in the study of quantum gravity, but I think it's the most promising.
So, the last chapter ended with those solutions to the Wheeler-DeWitt equation that Jacobson and Smolin found. These solutions depended on lines that close on themselves, or loops. What does that mean?
Remember Faraday's lines of force, those lines that carry the electric force and that Faraday imagined filling space? Those lines that were the starting point for the idea of "field"? Well, the closed lines that show up in the solutions to the Wheeler-DeWitt equation are Faraday lines of force for the gravitational field.
But now, there are two new things to add to Faraday's idea.
The first is that we're dealing with a quantum theory. In quantum theory, everything is discontinuous. The infinitely continuous web of Faraday's lines of force now looks more like a real spider web: it has a finite number of individual lines. Every line that determines a solution to the Wheeler-DeWitt equation describes one of those lines in the web.
The second new thing, and the most important one, is that we're talking about gravity, so, as Einstein understood, we're not talking about a field that exists in space. We're talking about the structure of space itself. The Faraday lines of force of the quantum gravitational field are the lines that weave space.
At first, the research focused on these lines and how they "weave" our three-dimensional physical space. People tried to draw early, intuitive diagrams of the discrete structure of space, that kind of thing.
Pretty soon, thanks to the insights and mathematical talent of young scientists like Jorge Pullin from Argentina and Jurek Lewandowski from Poland, people realized that the key to understanding the physics of these solutions was the points where the lines cross. These points are called "nodes," and the lines between the nodes are called "links." A bunch of lines that cross each other forms a "graph," a bunch of nodes connected by links.
Calculations showed that without nodes, there's no volume in physical space. In other words, the volume of space exists in the nodes of the graph, not in the links. The links "connect" the individual volumes that are located at the nodes.
It took a long time to fully explain this picture of quantum spacetime. The fuzzy math in the Wheeler-DeWitt equation had to be turned into a complete enough structure that you could do calculations and get precise results. The key to explaining the physics of the graph was figuring out the possible values of volume and area.
Take any area of space, like the room you're reading this book in. How big is that room? The size of the room is measured by its volume. Volume is a geometric quantity that depends on the geometry of space. But the geometry of space, as Einstein understood, and as I described in Chapter Three, is the gravitational field. So, volume is a property of the gravitational field. It tells you how much gravitational field there is between the walls of the room. But the gravitational field is a physical quantity, and like all physical quantities, it follows the laws of quantum mechanics. Volume, like all physical quantities, can't take on just any value. It can only take on certain values, like I described in Chapter Four. If you remember, the set of all the possible values is called a "spectrum." So, there should be a "volume spectrum."
Dirac gave us a formula for calculating the spectrum of every physical quantity. Calculating the volume spectrum took a lot of time. First, it had to be written down, then calculated. It was a long and winding road. The calculation was finished in the mid-1990s, and the result was what people expected. As Feynman said, you shouldn't calculate something if you don't already know the answer. The volume spectrum is discrete. That is, volume can only be made up of discrete "packets." It's similar to the energy of the electromagnetic field, which is also made up of discrete photons.
The nodes in the graph represent discrete packets of volume. Each node n in the graph has its own volume, νn, a number from the volume spectrum. The nodes are the basic quanta that make up physical space. Every node in the graph is a "quantum particle of space." The emerging structure is like this.
A link is a single quantum of Faraday's lines of force. Now we can understand what that means: if you imagine two nodes as two small "areas of space," those areas are separated by a tiny surface. The size of that surface is its area. The second quantity, after volume, is the area associated with each link, which marks the features of the quantum network of space.
Area, like volume, is a physical quantity with its own spectrum that you can calculate with Dirac's equations. Area isn’t continuous. It's discrete. There's no such thing as an arbitrarily small area.
Space looks continuous to us only because we can't see the super tiny scale of these individual quanta of space. It's like when we look closely at the fabric of a t-shirt, we see that it's made of really thin threads woven together.
When we say that the volume of a room is, say, 100 cubic meters, what we're really doing is counting the particles of space, the quanta of the gravitational field, that the room contains. In a room, that number would have over 100 digits. When we say that a page of this book has an area of 200 square centimeters, we're really counting the number of links in the network, or the loops, that make up the page. That number would have around 70 digits for a page in this book.
The idea that measuring lengths, areas, and volumes is actually counting individual elements was already proposed back in the 19th century by Riemann himself. As the mathematician who developed the theory of continuous curved space, Riemann was already clear that discrete physical space made more sense than continuous space.
To sum up, loop quantum gravity, or loop theory, brings general relativity and quantum mechanics together in a pretty conservative way, because it doesn't introduce any new assumptions beyond those two theories. It just rewrites them to make them compatible. But the result is pretty wild.
General relativity tells us that space is a dynamic thing, like the electromagnetic field: a huge, active, bendy animal that we live inside. Quantum mechanics tells us that every field is made up of quanta, which means it has a fine, discrete structure. So, physical space, as a field, is also made up of quanta. The discrete structure that marks other quantum fields also marks the quantum gravitational field, so it also marks space. We predict that there are quanta of gravity, just like there are quanta of light, the quanta of the electromagnetic field, and quanta of other quantum fields, particles. But space is the gravitational field. So, the quanta of the gravitational field are the quanta of space: the discrete elements of space.
The key prediction of loop quantum gravity is that space isn't a continuum. It's not infinitely divisible. It's made up of "atoms of space" that are way smaller than the smallest nucleus.
Loop quantum gravity describes these atoms of space and the discrete quantum structure in a precise, mathematical way. It gets there by applying Dirac's general equations for quantum mechanics to Einstein's gravitational field.
Loop theory specifically says that volume, like the volume of a given cube, can't be arbitrarily small. There's a minimum volume. There's no space smaller than that minimum volume. There's a quantum of minimum volume, a basic atom of space.
Remember Achilles and the tortoise? Zeno said that Achilles has to run through an infinite number of distances before he can catch up to the slow-moving creature. We have a hard time accepting that idea. Math has found a possible answer to this problem. It shows that an infinite number of ever-decreasing intervals can add up to a finite interval.
But is that really how it works in nature? Are there really arbitrarily small intervals between Achilles and the tortoise? Does it really make sense to talk about a billionth of a billionth of a millimeter, and then divide that an infinite number of times?
The calculations of the quantum spectrum of geometric quantities show that the answer is no: there's no such thing as arbitrarily small space. There's a lower limit to how finely you can divide space. It's super tiny, but it exists. That's what Matvei Bronstein realized intuitively back in the 1930s. The calculations of the volume spectrum and the area spectrum have confirmed Bronstein's idea and expressed it in a precise mathematical form.
Achilles doesn't need to run an infinite number of steps to catch up to the tortoise, because infinitely small steps don't exist in a space made up of particles of finite size. The hero gets closer and closer to the tortoise, and then finally catches it with a quantum leap.
But think about it. Isn't this basically the solution that Leucippus and Democritus proposed? They talked about the discrete structure of matter. We're not sure how they discussed space. Unfortunately, we don't have their texts, only a few little fragments from other people's quotes. It's like trying to rebuild Shakespeare's plays from quotes of Shakespeare.
Aristotle quoted Democritus as saying that the idea of the continuum as a collection of points just doesn't make sense. I imagine that if we had the chance to ask Democritus if it made sense to divide space infinitely, he would have to answer that there must be a limit to division. For the philosopher from Abdera, matter was made up of indivisible atoms. Once you understand that space is a lot like matter, that, as he himself said, it has its own properties and "specific physics," I suspect he would have no problem inferring that space can only be made up of indivisible basic units too. Maybe we're just following in Democritus' footsteps.
I'm not saying that two thousand years of physics has been useless, that experiments and math don't matter, or that Democritus is as convincing as modern science. Of course not. Without experiments and math, we couldn't understand what we understand. But when we're developing a conceptual way to understand the world, we need to explore new ideas and also draw on the powerful insights of the giants of the past. Democritus is one of those giants. We're standing on his shoulders to discover new things.
But let's get back to quantum gravity.
In the graph that describes a quantum state of space, every node is marked with a volume, v, and every link is marked with a half-integer number, j. A graph with this extra information is called a spin network. (Half-integer numbers are called "spin" in physics because they show up in the quantum mechanics of spinning objects.) The spin network represents a quantum state of the gravitational field: a quantum state of space. Area and volume are discrete. Space is made up of discrete elements. In other areas of physics, fine meshes are used to approximately describe continuous space. Here, there's no continuous space to approximately describe. Space is truly discrete.
The important difference between photons (the quanta of the electromagnetic field) and the nodes in the graph (the quanta of gravity) is that photons exist in space, while gravitons make up space itself. Photons are described by where they are.
The quanta of space don't exist in a location. They are the location. The only information that can describe their spatial characteristics is information about which other quanta of space they're next to. That information is carried by the links in the graph. Two nodes connected by a link are next to each other. They're two particles of space that are touching each other. That "touching" builds the structure of space.
The quanta of gravity aren't in space. They are space. Spin networks, which describe the quantum structure of the gravitational field, aren't in space. They don't occupy space. The location of each quantum of space is only defined by the links and the relationships they represent.
If I walk along the links from one point to another until I complete a loop and get back to where I started, I've completed a "loop." Those are the original loops in loop theory. I showed that you can measure the curvature of space by seeing if an arrow that you carry along a closed loop ends up pointing in the same direction or gets deflected. The math of the theory determines the curvature of every loop in the spin network. That makes it possible to calculate the value of the curvature of spacetime and to figure out the force of the gravitational field based on the structure of the spin network.
Now, besides the discreteness of quantum mechanics, there's also the fact that evolution is probabilistic. The evolution of spin networks is also random. I'll talk about that when I talk about time in the next chapter.
Also, things aren't what they are. They're how they interact. Spin networks aren't things. They describe how space acts on things. Just like an electron isn't in any one place, it's spread out in a cloud of possibilities. Space isn't really made up of individual spin networks either. It's made up of a cloud of probabilities covering all the possible spin networks.
At super tiny scales, space isn't continuous. It's woven from a finite number of interacting pieces.
At super tiny scales, space is a bunch of fluctuating gravitons that interact with each other and together act on things. They show themselves in these interactions as spin networks and interacting particles.
Physical space is woven from these networks of never-ending relationships. The lines themselves aren't anywhere. They're not in any location. They create location through their interactions. Space is created by the interactions between gravitons.
That's the first step in understanding quantum gravity. The second step involves time, and I'm going to dedicate the next chapter to that.
So, time, it doesn't exist.
"Time by itself does not exist; but from things themselves there results what was, what now is, what must next be."
—Lucretius, On the Nature of Things
The careful reader might have noticed that we hardly considered time in the last chapter. But Einstein showed over a century ago that we can't separate time and space. We have to think of them as one thing: spacetime. It's time to fix that and bring time back into the picture.
Quantum gravity has finally built up the courage to face the problem of time after a lot of years of studying equations for space. Over the last fifteen years, a new way of thinking about time has shown up. I'm going to try to explain it here.
In quantum gravity, space, the container with no fixed shape, disappears from physics. Things, quanta, don't occupy space. They depend on each other. Space is woven by the relationships between quanta. Just like we're giving up on the idea that space is a fixed container, we also have to give up on the idea that time is fixed, that reality unfolds over time. Just like continuous space where things exist has disappeared, now, flowing time, where phenomena happen, has to disappear too.
In a sense, space no longer exists in the basic theory. The quanta of the gravitational field aren't in space. And time no longer exists in the basic theory either. The quanta of gravity don't evolve in time. Time only counts their interactions. Just like the Wheeler-DeWitt equation showed, the time variable is no longer in the basic equations. Time, like space, shows up in the quantum gravitational field.
That's partly true in classical general relativity too, where time already shows up as an aspect of the gravitational field. But as long as we ignore quantum theory, we can still think of spacetime in the traditional way. The rest of reality unfolds like a tapestry, though it's a dynamic, changing tapestry. Once we bring quantum mechanics into the picture, we realize that time has all the same features that every reality has: probabilistic uncertainty, discreteness, and relationships.
The second conceptual result of quantum gravity is even more extreme than the disappearance of time.
Let's try to understand.
We've known for over a century that time isn't what we usually think it is. Special and general relativity made that clear. Our common-sense ideas about time just don't hold up in the lab.
For example, let's go back to the first conclusion of general relativity, which I explained in Chapter Three. Take two watches. Make sure they're showing the same time. Put one on the floor and the other on a piece of furniture. Wait half an hour and then put them together again. Will they still show the same time?
As I described in Chapter Three, the answer is no. The watches we normally wear on our wrists, or the clocks on our phones, aren't precise enough to let us check this. But there are clocks in physics labs all over the world that can show you the difference that will show up: the watch on the floor runs slower than the watch that's up higher.
Why? Because time doesn't flow in the same way everywhere. It goes faster in some places and slower in others. The closer you are to the Earth's surface, the stronger gravity is, the slower time goes. Remember the twins from Chapter Three? One lived by the sea and the other in the mountains, and they ended up at different ages. The difference is super tiny: living by the sea for a lifetime only gives you a tiny fraction of a second less time than living in the mountains. But that tiny quantity doesn't change the fact that the difference is there. Time doesn't work the way we usually imagine it does.
We can't think of time as a giant cosmic clock that records the life of the universe. We've known for over a century that we should think of time as a local phenomenon: every object in the universe has its own flow of time, and the speed of that flow is determined by the local gravitational field.
But once we bring the quantum properties of the gravitational field into the picture, even the idea of local time stops working. At the Planck scale, quantum events no longer happen one after another in a flow of time. In a sense, time no longer exists.
What does it mean to say that time doesn't exist?
First, the disappearance of the time variable from the basic equations doesn't mean that everything is still or that change doesn't happen. Just the opposite. It means that change is everywhere. It just means that the basic processes can no longer be described as "one moment following another." At the super tiny scale of quanta of space, the dance of nature no longer follows the same beat set by the baton of a single conductor. Every physical process