Chapter Content
Okay, so, here's the deal, this whole thing, right? It's about going beyond space and time. Like, really thinking about what's actually out there. You know, I've been talking a lot about the basics of quantum gravity, and kind of the picture of the universe it paints. Now, I want to dive a bit into some of the crazy stuff this theory suggests, like, what does it tell us about the Big Bang, or black holes? And, uh, also, where are we with actually, like, testing this stuff? And what is nature trying to tell us, especially about, like, those supersymmetric particles that we haven't, you know, totally seen yet.
Because, listen, our understanding of the world is still, like, missing pieces, big time. I want to wrap things up by thinking about those gaps, especially when it comes to thermodynamics. What's the deal with information in a theory that doesn't even have time and space as fundamental things? And how, like, does time even, you know, reappear?
So, all this basically brings us to the edge of what we even know. And from there, we can kinda peek into the, you know, the great unknown, and like, really look at the mysteries around us.
So, let's talk about going *beyond* the Big Bang.
Back in, uh, 1927, this young Belgian scientist, also a Jesuit priest, mind you, he was studying Einstein's equations. And he realized, just like Einstein did, that they were saying that the universe had to be, like, either expanding or contracting. But, unlike Einstein, who, you know, kinda stubbornly tried to avoid this, this Belgian dude, he believed it. And he went looking for data to, you know, back it up.
Now, back then, "galaxies" weren't even called "galaxies." They were just "nebulas," because through telescopes, they just looked like, you know, kinda milky clouds around space stuff. People didn't even know they were massive groups of stars like our own galaxy. But this priest, he saw that the data that *did* exist, actually hinted that the universe *was* expanding. Like, the nearby galaxies were zooming away super fast. And the far-off ones were zooming away *even faster*. You know, it was like, the universe was a balloon being blown up.
So, a couple years later, two American astronomers, Henrietta Leavitt and Edwin Hubble, they kind of confirmed this idea. Leavitt found this cool way to measure the distance to nebulas, and showed that they were *really* far away, way beyond our galaxy. And Hubble, using her method and this giant telescope, he got some super precise data, showing that the galaxies were, like, receding at a speed that was, you know, proportional to their distance.
But this Belgian guy, back in 1927, he'd already figured out the key thing. You know, it's like, if you see a rock flying upwards, it means it was down low before, and something threw it up. So, if we see galaxies zooming away, the universe expanding, that means they were all closer together before, the universe was smaller, and something made it start expanding. So, he suggested that the universe started out, like, super tiny and compressed, and then, you know, *boom*, big explosion, it started expanding. He called that initial state the "primeval atom." We call it the Big Bang now.
This guy's name? Georges LemaƮtre. And in French, that sounds kind of like "The Master," which is pretty fitting for the guy who first thought of the Big Bang, right? He wasn't one for arguing, though. He never really, like, claimed he was the first to figure it out, so Hubble kinda got all the credit, you know? But LemaƮtre was smart. He, like, stood up to Einstein, and even the Pope.
Einstein, you know, like I said, he was skeptical about the universe expanding. He wanted it to be static. Even the smartest people get stuff wrong, right? LemaƮtre met with him, tried to convince him to, like, ditch his biases. But Einstein, he was like, "Your calculations are correct, but your physics are bad." He eventually had to admit LemaƮtre was right. Not everyone would have argued with Einstein.
Einstein also introduced the cosmological constant to kind of force his equations to fit with a static universe. When he had to admit the universe *wasn't* static, he blamed the cosmological constant. LemaƮtre had to convince him *again*. He said, "No, the cosmological constant, it's right. You need it." And he was right again. The cosmological constant makes the universe expand faster, and that's been measured. So, Einstein was wrong *twice*.
So, when the Big Bang idea started catching on, Pope Pius XII said in a speech that it, you know, confirmed the creation story in Genesis. LemaƮtre was worried about this. He contacted the Pope's science advisors, and did everything he could to get the Pope to avoid connecting creationism to the Big Bang. He thought mixing science and religion like that was dumb, you know? The Bible doesn't know anything about physics, and physics doesn't know anything about God. And the Pope, he listened! The Catholic Church hasn't talked about it publicly since. Not everyone argues with the Pope.
And, of course, LemaƮtre was right about that, too. Now, there's talk that the Big Bang wasn't the true beginning, that there might have been another universe before it. Imagine how awkward the Catholic Church would be if LemaƮtre hadn't talked the Pope down.
So, to challenge Einstein *and* the Pope, and convince them both that they were wrong, *twice*, is a pretty big deal. He deserved the name "The Master."
Now, there's so much evidence it's basically impossible to ignore. In the very, very distant past, the universe was super hot and dense, and it's been expanding ever since. We can, like, trace back the universe's history in detail from that initial, super-hot state. We know how atoms, elements, galaxies, all that stuff formed, and how they developed into the universe we see today. Tons of observations from, mostly, the Planck satellite, which measured all the radiation spread through the universe, have completely confirmed the Big Bang theory. We're pretty certain about what happened on a grand scale after the universe started as a fireball, fourteen billion years ago.
It's funny, the name "Big Bang theory" was actually coined by opponents of the idea, who thought it was ridiculous. But in the end, we all bought it, you know?
But, what happened *before* that initial hot, dense state?
If you rewind time, the temperature goes up, and the density and energy of everything get bigger. At some point, about fourteen billion years ago, you hit the Planck scale. At that point, Einstein's theory, general relativity, it breaks down, because quantum mechanics can't be ignored anymore. You're in the world of quantum gravity.
So, quantum cosmology. To understand what happened before the Big Bang, we need quantum gravity. And what does loop theory tell us?
Think about something similar, but simpler. According to classical mechanics, an electron falling into an atomic nucleus would be swallowed and disappear. But it doesn't. Classical mechanics is wrong. You need to consider quantum effects. The real electron is a quantum object, it doesn't have a fixed path, and you can't confine it to a tiny space. The closer it gets to the center, the faster it flies away. If you try to keep it close to the nucleus, the best you can do is put it in the smallest orbit. Quantum mechanics prevents real electrons from falling into the nucleus. Quantum repulsion pushes it away if it gets too close. Thanks to quantum mechanics, matter is stable.
It's the same with the universe. Imagine a dense universe, compressed to be tiny by its own weight. According to Einstein, it would be compressed infinitely, and disappear. If you ignore quantum mechanics, that's the Big Bang predicted by Einstein.
But if you bring quantum mechanics into it, the universe doesn't get compressed infinitely. Quantum repulsion makes it *bounce*. A shrinking universe doesn't collapse to a point. It bounces and starts expanding, like it was caused by an explosion.
Our universe's past might be the result of a bounce. A "Big Bounce," not a "Big Bang." That's what you get when you apply loop quantum gravity to the universe's expansion.
Don't take the bounce idea too literally. Think about the electron example. If you try to put it close to the atom, it stops being a particle. You can imagine it spread out as a probability cloud. The location doesn't matter anymore. Same for the universe. In the Big Bounce, you can't imagine it as just a single, separate space and time. It's a scattered probability cloud, where space and time are fluctuating wildly. The world dissolves into a cloud of probabilities.
So, our universe was probably born from a bounce, from a compressed state that went through a quantum phase where space and time dissolve into probabilities.
The word "universe" gets tricky here. If you mean "everything that exists," then, by definition, there can't be a second one. But in cosmology, "universe" means the continuous spacetime that we can directly see around us, filled with the geometry and history of the galaxies we observe. So, in that sense, there's no reason to think this is the *only* universe. You can trace it back to where spacetime breaks down, like ocean foam breaking into pieces, becoming a quantum probability cloud. And there's no reason to rule out that beyond that hot foam, there's another spacetime continuum, similar to what we see around us.
The probability of a universe going from shrinking to expanding, through the Big Bounce, can be calculated with the spacetime box method.
All this is still being explored. But the important thing is, we have equations we can use to try to describe these events. It's theoretical so far, but we're starting to carefully look beyond the Big Bang.
Okay, so, experimental evidence, right?
These cool, theoretical explorations of quantum cosmology, it's not just about what might have existed beyond the Big Bang. There's another reason to study how this theory applies to the universe. It might be a chance to see if it's actually *correct*.
See, the good thing about science is that after all the guessing, the reasoning, the gut feelings, and the equations, you can check if you did a good job. A theory makes predictions about stuff you haven't seen yet, and you can test if those predictions are true. *That's* the power of science. It's grounded, reliable. You can actually trust it, because you can see if a theory is right or wrong.
When LemaƮtre was arguing that the universe was expanding, Einstein didn't believe him. One of them had to be wrong. Einstein's reputation, his influence, didn't matter. The observations showed he was wrong. Game over. This nobody Belgian priest was right.
Sociology of science shows the complexity of the knowledge process. Just like any human endeavor, it's irrational and messy. But that doesn't mean science is useless, unlike what some postmodernists or cultural relativists like to say. Because, in the end, you can usually figure out who's right and who's wrong. Even the great Einstein would say, "Ah, I made a mistake!" If you want something reliable, science is the best bet.
But that doesn't mean science is just about making observable predictions. Some philosophers say that science is *only* about predictions, but that's too narrow. Quantifiable predictions are just a way to test a hypothesis. The goal of science is to understand the world, to build and develop a picture of it, to give us a framework for thinking. Science is visionary *before* it gets technical.
Testable predictions are a strong tool to see if you're wrong. A theory without experimental evidence hasn't been tested yet. The testing never stops. A theory isn't proven right after one or two experiments. But as its predictions are proven true, the theory becomes more believable. Theories like general relativity and quantum mechanics, they were confusing at first. But as every single one of their predictions was confirmed by experiment, they gained trust.
But experimental evidence isn't *everything*. You can still make progress without it. People always say that science only makes progress when there's new experimental data. If that was true, we'd have no hope of finding quantum gravity before we actually see something new. But that's clearly not the case. What new data did Copernicus have? Nothing. His data was the same as Ptolemy's. Did Newton have new data? Barely. His data was Kepler's laws and Galileo's results. What new data did Einstein have? None. It was special relativity and Newton's theory. The idea that physics only makes progress with new data is clearly wrong.
Copernicus, Newton, Einstein, they found a way to combine and rethink pre-existing theories and experiences from different fields.
That's how the best quantum gravity research works. Experiments are the source of knowledge, in the end. But the data we're using to build quantum gravity doesn't come from new experiments. It comes from the existing theories that already make up our picture of the world. Quantum gravity's "experimental data" is general relativity and quantum mechanics.
We're encouraged by the success of the giants who came before us, like Newton, Einstein, Dirac. We don't presume to be as great as them, but we have the advantage of standing on their shoulders. We just have to try our best.
So, we need to tell the difference between hints and actual solid proof. Hints are just clues that lead you to the right theory. But you need real proof before you can convict someone. The hints are good and specific. The theory hasn't been tested yet.
In the research I'm talking about in this book, the other main theory is string theory. Most physicists working on string theory expected supersymmetric particles to appear as soon as the Large Hadron Collider (LHC) in Geneva turned on. String theory needs those particles to work. But loop quantum gravity is defined well even without them. Loop theorists tended to think those particles might not exist.
The lack of supersymmetric particles has disappointed a lot of people. In 2013, those who celebrated the discovery of the Higgs boson also hid the same disappointment. The fact that supersymmetric particles didn't show up at the energy levels that many string theorists expected doesn't definitively prove anything. But nature has given a small hint that might favor loop theory.
There have been three important experimental results in basic physics. First, the LHC found the Higgs boson. Second, the Planck satellite's observations, released in 2013, confirmed the standard cosmological model. And third, the first detection of gravitational waves was announced in early 2016. Those are the three latest signals from nature.
All three have something in common: no surprises. That doesn't make them less important, quite the opposite. The discovery of the Higgs boson strongly proved that the standard model of particles is correct. The Planck satellite results are a solid sign that the standard cosmological model is right. Detecting gravitational waves proves that general relativity is still accurate, even after a hundred years. These three achievements, which took hard work and scientists from all over the world collaborating, just reinforced our current understanding of the universe. No real surprises.
That lack of surprise is a surprise in itself. Many people were hoping for big surprises. They were expecting to find supersymmetric particles, not the Higgs boson. Many hoped that the Planck satellite would observe deviations from the standard cosmological model, supporting other theories of the universe outside of general relativity.
But nothing. Nature just said yes. General relativity, quantum mechanics, and the standard model inside quantum mechanics, they're all correct.
Many theoretical physicists look for new theories by making random assumptions: "Let's imagine..." I don't think that's a good way to do science. Our imaginations are too limited to guess what the world is like unless we can find inspiration in what we already know. Our clues are successful theories and new data. That's how Copernicus, Newton, Maxwell, Einstein moved forward. They never just "guessed" a new theory.
The three experimental results are nature telling us, "Don't imagine new fields or strange particles. The puzzle is simple, just general relativity, quantum mechanics, and the standard model. The next step might 'just' be putting them together the right way." That's encouraging to the quantum gravity community, because that's what the theory already assumes: general relativity, quantum mechanics, and the standard model.
Those might not be proof, either. Supersymmetric particles might eventually show up.
To find better proof, we need to look elsewhere.
If we have equations to describe the universe's evolution in the quantum phase, we can calculate how quantum phenomena affect what we see today. The universe is full of radiation: photons left over from the early hot phase.
The electromagnetic field in the vast spaces between galaxies is vibrating. Those vibrations are called the cosmic background radiation, and they've been studied in recent years. The details of that radiation can tell us the history of the universe.
One of the most active parts of quantum gravity research is studying how the quantum dynamics of the early universe are reflected in that data. It's promising so far. More calculations and accurate measurements should allow us to test the theory.
In 2013, Abhay Ashtekar, Ivan Agullo, and William Nelson published a paper where they calculated that the statistical distribution of the fluctuations in those cosmic radiation should reveal the effects of the initial bounce.
There's also the traces of heat in the gravitational field. The gravitational field, which is space itself, is vibrating. So, there must be a cosmic gravitational background radiation, even older than the microwave radiation, because gravitational waves are less affected by matter.
We can now directly observe gravitational waves using LIGO, which has two long arms at right angles. When a gravitational wave passes, it stretches and shrinks space.
Those gravitational waves were produced by astrophysical events that are described by general relativity. But a more ambitious experiment, called LISA, is being considered. It would put three satellites in orbit, around the sun. The satellites would be connected by lasers, and would measure the distance between them. If LISA launches, it should be able to see the background radiation of primordial gravitational waves. Those waves would tell us about the quantum bounce.
We should be able to find traces of what happened when the universe began, and confirm our assumptions about space and time.
Okay, so quantum black holes, right?
There are tons of black holes in the universe. They're regions where space is extremely curved, collapsing in on itself, and where time stops. Like, I mentioned before, when a star burns up all its hydrogen, it collapses into a black hole.
Those collapsing stars are often paired with other stars, so the black hole and its partner orbit each other. The black hole sucks matter from the other star.
Astronomers have found tons of black holes as big as the sun. But there are also giant black holes. Almost every galaxy, including our own, has a giant black hole at its center.
The black hole at the center of our galaxy is being studied. It's a million times bigger than the sun. Sometimes a star gets too close to that monster and is crushed.
There's a cool project underway to build a network of radio antennas around the world. That would give astronomers enough resolution to "see" those giant black holes. We're expecting to see a small black disk, surrounded by light from the matter that's falling into it.
Anything that goes into a black hole can't come back out. The surface of a black hole is like the present. You can only pass it from one direction, from the past, not from the future. A rocket can stay a fixed distance from that sphere, called the black hole's "horizon." It would have to burn its engines constantly to counteract the black hole's gravity. Time would slow down for the rocket. If the rocket stayed near the horizon for an hour, it would find that centuries had passed outside. The closer the rocket is to the horizon, the slower time goes. So, traveling to the past is hard, but traveling to the future is easy. Just get close to a black hole for a while.
At the horizon, time stops. If we get super close and leave after a few minutes, millions of years might have passed in the rest of the universe.
It's amazing that these strange objects, which we can now observe, were predicted by Einstein's theory. It wasn't long ago that black holes were considered a strange result of a weird theory. I remember my professors introducing them as solutions to Einstein's equations, saying that "it's unlikely that real objects correspond to them." That's the amazing ability of theoretical physicists, they can find things before they can be observed.
The black holes we see can be described by Einstein's equations. But there are two black hole mysteries that need quantum mechanics to solve. Loop theory offers possible answers to both.
The first application of quantum gravity to black holes involves a strange fact found by Stephen Hawking. In the early 1970s, he theoretically derived that black holes are "hot." They act like hot objects: they emit heat. They lose energy and mass, and get smaller. They "evaporate." That "black hole evaporation" is Hawking's most important discovery.
Objects have heat because their microscopic parts are moving. A hot iron vibrates rapidly. The molecules in hot air move faster than the molecules in cold air.
What are the vibrating "atoms" that make black holes hot? Hawking didn't answer that. Loop theory offers an answer. The vibrating atoms that give a black hole its temperature are the individual quanta of space on its surface.
Those vibrations happen because everything is vibrating in the quantum world. Nothing stays still.
There's another way to understand the source of black hole heat. Quantum fluctuations create a link between the inside and outside of a black hole. The quantum uncertainty through the black hole's horizon creates fluctuations in the horizon's geometry. Those fluctuations mean probability. Probability means thermodynamics, which is temperature. Black holes hide a part of the universe from us, but let its quantum fluctuations be detected in the form of heat.
A young Italian scientist, Eugenio Bianchi, completed a precise calculation that shows how to get the formula for black hole heat from these ideas and the equations of loop quantum gravity.
The second application of loop quantum gravity to black hole physics is even more amazing. Once a star collapses, it disappears from external view. What happens inside the black hole? What would you see if you fell into one?
At first, nothing special. You'd pass through the black hole's surface, not too badly hurt. Then you'd fall faster and faster toward the center. General relativity says that everything would be crushed into a point with no volume and infinite density. But that's what happens when you ignore quantum theory.
If you consider quantum gravity, that prediction isn't true. We expect that quantum pressure will slow down the falling matter as it gets close to the center. The density would be very high, but finite. Matter would be compressed, but it wouldn't get to a point, because there's a lower limit to the size of matter.
If you looked from there, the collapsing star's bounce would be very fast. But remember, time goes slower inside than outside. From the outside, the bounce could take billions of years. After a long time, we'd see the black hole explode. Black holes end up being a shortcut to the distant future.
So, quantum gravity might imply that black holes aren't eternally stable objects. Fundamentally, they're unstable.
It would be amazing if those black hole explosions were discovered. Some calculations suggest that those signals might be within reach of radio telescopes. Some point out that radio astronomers have already observed mysterious radio pulses, called "fast radio bursts."
Alright, so the end of infinity, right?
When we consider quantum gravity, the infinite point the universe is compressed to at the Big Bang disappears. Quantum gravity finds that there is no infinitely small point.
If we ignore quantum mechanics, we ignore the minimum size. In the weird situations predicted by general relativity, the theory gives infinite quantities, called "singularities." Quantum gravity sets a limit on infinity, and "cures" the singularities in general relativity.
The same thing happens at the center of black holes. The singularity goes away as soon as you include quantum gravity.
There's another situation where quantum gravity sets a limit on infinity. It involves forces, like electromagnetism. Quantum field theory, which was created by Dirac and completed by Feynman and his colleagues, describes those forces well. But it's full of mathematical absurdities. You often get meaningless infinite results, called "divergence difficulties." Those are then eliminated through a complicated technical process, eventually getting finite numbers. It works in practice. But why does the theory have to go through infinity to get the right number?
In his last years, Dirac was very unhappy with the infinities in his theory. He felt he didn't truly understand how things worked. He loved conceptual clarity, which others might not have considered obvious. But infinity wasn't clear.
The infinities in quantum field theory are caused by the assumption that space is infinitely divisible. When you calculate the probability of a process, you add up all the ways it can happen. But that's infinite, because they can happen at any of the infinite points in the space.
Those infinities go away when you consider quantum gravity. There's no infinite number of points. The discrete structure of space resolves the difficulties of quantum field theory.
It's amazing: quantum mechanics resolves the problems caused by Einstein's theory of gravity, and gravity resolves the problems caused by quantum field theory. They provide solutions to the problems the other theory presents.
Setting limits on infinity is a recurring theme in modern physics.
The existence of minimum and maximum values for length, speed, and action determines a natural system of units.
The determination of these three fundamental constants sets limits on the seemingly infinite possibilities of nature. It suggests that what we call infinity is just something we haven't calculated or understood yet.
There's another infinity that confuses us: the infinite spatial extent of the universe. But Einstein has found a way to think about a finite but unbounded universe. Current measurements suggest that the universe is definitely bigger than a hundred billion light years. That's a scale we can't directly touch. It's approximately 10 to the 120 times the Planck length.
The universe from tiny quanta of space, to quarks, protons, atoms, chemical structures, mountains, stars, galaxies, all the way to the visible universe. We only know a few aspects of this universe. It's vast, but finite.
The value of the cosmological constant in our theory's equations can reflect the scale of the universe.
What is really infinite is our ignorance.
So, information, right?
We're getting close to the end. I talked about concrete applications of quantum gravity: what happened in the universe, black holes, and eliminating infinity.
Before I wrap it up, I want to talk about information, a concept that's been stirring up interest and confusion in theoretical physics.
I'm going to talk about concepts and theories that are well defined, but haven't been tested yet. It's going to get weird.
Many scientists speculate that the concept of "information" might be the key to new progress in physics. It's mentioned in thermodynamics, quantum mechanics, and other fields.
What is information? The word "information" has many different meanings in common usage. That lack of precision is a source of confusion in science. In 1948, the American mathematician Claude Shannon gave a clear and simple definition: information is a measure of the number of options. For example, if you roll a die, it can land on one of six sides. When you see which side it lands on, you have information N=6, because there are six possible choices. If you don't know what day of the year someone's birthday is, there are 365 possible choices. If they tell you the date, you have information N=365.
Scientists measure information with a quantity S, instead of the number of possible choices N. S is defined as the log base 2 of N: S=log2 N. Using logs means that a unit of information S=1 corresponds to N=2. That makes the unit of information the smallest possible choice: choosing between two options. That unit is called a "bit." When you know that the roulette ball lands on a red number instead of a black number, you have one bit of information. When you know that a red even number won, you have two bits of information. Three bits of information corresponds to eight choices.
Information is being able to make a distinction between possible choices. Information measures a physical system's ability to communicate with another system.
Let's go back to Democritus' atoms. Imagine a world with only atoms, bouncing, attracting, and sticking together. Are we missing something?
Plato and Aristotle insisted that there was. They said that the *form* of things should be added. For Plato, the forms existed independently in an ideal world. The idea of a horse existed before and independently of any real horse. The atoms that make up a horse don't matter. The important thing is the form "horse." Aristotle was more practical, but even for him, the form couldn't be reduced to just matter. In a statue, there's more than just the stone that makes it up. That extra something is the form. That's the basis for the ancient critique of Democritus' materialism.
But did Democritus really claim that everything could be reduced to atoms? He said that when atoms combine, the important thing is their form, the way they're arranged, and how they combine. He gave the example of letters in the alphabet: there are only about twenty letters, but "they can be combined in different ways to create comedy or tragedy, absurd stories or epics."
There's more than just the atoms. The key is how they're combined. But in a world of only other atoms, what connects the ways they're combined?
If the atoms are also an alphabet, who can read the words written with that alphabet?
The atoms are connected to the ways other atoms are arranged. A group of atoms has information that is accurately perceived by another group of atoms.
Light carries information about objects. The color of the sea has information about the color of the sky. A cell has information about the viruses that are attacking it. New life has a lot of information. We're exchanging information.
The world isn't just a network of colliding atoms. It's a network of links between groups of atoms, a network of physical systems exchanging information.
There's no idealism here. It's just applying the idea that you can count the number of choices. It's a part of the world.
Once we realize that this network of exchanged information exists in the universe, it's natural to describe the world in terms of it. What is "heat?" Boltzmann was the first to figure it out.
Heat is the random microscopic motion of molecules. If the tea is hotter, the molecules are moving faster. Boltzmann made a bold assumption: the number of possible states of molecules in cold air and hot tea is less than the number of possible states in hot air and cold tea.
The total amount of entropy can only increase, because information can only decrease.
Physicists now accept that information can be used as a concept tool to clarify the properties of heat. The concept of information can also be used to understand the mysteries of quantum mechanics.
One of the important conclusions of quantum mechanics is that information is finite. Quantum mechanics can be understood as discovering that information in nature is always finite.
The entire structure of quantum mechanics can be read and understood according to information. A physical system only manifests itself when it interacts with another physical system. Any description of a system is a description of the information that one system has about another system. The mysteries of quantum mechanics aren't so deep if you explain them in terms of the information physical systems have about each other.
The formal structure of quantum mechanics can be expressed as two simple principles:
1. The relevant information in any physical system is finite.
2. You can always get new information about a physical system.
"Relevant information" is what you've learned from past interactions with a system. It allows you to predict the results of future interactions with that system. The first principle expresses the discrete nature of quantum mechanics: there are only a finite number of possibilities. The second expresses its uncertain nature: there's always something you can't predict. When you get new information about a system, the total amount of relevant information can't increase infinitely. The part of the information that was relevant before becomes irrelevant. In quantum mechanics, when you interact with a system, you learn things and delete relevant information.
It's amazing that the theory lets itself be expressed in terms of information.
John Wheeler coined the phrase "it from bit" to express this.
Any surface's area is determined by the spin of the loops that intersect it. Those spins are discrete quantities, each contributing to the area.
A surface with a fixed area can be formed in many different ways. If you know the area of the surface, but don't know how the quanta of area are distributed, you've lost information about the surface. You can calculate the heat of a black hole. Black holes are surrounded by a surface of a certain area. There are N different possible distributions of the area's quanta.
When information enters a black hole, it can't be recovered from the outside. But the information carries energy, so the black hole grows larger, increasing the area. From the outside, the information lost in the black hole now shows up as the entropy that's related to the black hole's surface area.
Black holes emit thermal radiation. They very slowly evaporate, shrink, and might eventually disappear. Where does the information that fell into the black hole go? Theoretical physicists are still arguing about that.
This all shows that to understand the basics of the world, you need to combine three basic elements: general relativity, quantum mechanics, and the theory of heat, which is thermodynamics, and information theory. But the thermodynamics of general relativity, the statistical mechanics of quanta of space, is still in its early stages.
I'm going to talk about one last concept: thermal time.
The concept of thermal time comes from a simple problem. I've proven that you don't need the concept of time to describe physics. It's best to forget about time completely. It plays no role at the most basic level of physics.
It's obvious to run into the next problem once you've accepted this idea. How do you get back the concepts from everyday experience?
The concepts of "up" and "down" don't appear in Newton's equations, but we know what they mean. Near a big object, like a planet, "up" and "down" make sense.
For "time," the concept might not play a role at the most basic level, but it plays an important role in our lives, just like "up" and "heat." What does the "flow of time" mean?
The origin of time might be similar to the origin of heat. It comes from averaging many microscopic variables.
The link between time and temperature is an old and recurring idea. Everything that shows the passage of time is related to temperature. Time moves forward, not backward. Mechanical phenomena that don't involve heat are reversible. If you film them, you can play the film backward and it will still make sense. A swinging pendulum, or a rock thrown up and falling back down.
But when the rock hits the ground and stops, its energy heats the ground. The process is irreversible at that moment: the past is distinguished from the future. Only heat distinguishes the past from the future.
Think about the solar system. At first glance, it seems like a giant machine that's always the same. It doesn't produce heat. But the sun is running out of hydrogen. The moon is slowly moving away from Earth, because it causes tides, which heat the ocean. Whenever you think about something that proves time passes, you'll find that it's proven through the production of heat. Without heat, time has no selected direction.
But through heat, we can name the average of many variables.
The concept of thermal time inverts that experience. Instead of asking how time produces heat, it asks how heat produces time.
We know that heat comes from our interactions with averages. The concept of thermal time is that the concept of time also comes from the fact that we only interact with the averages of many variables.
As long as we have a complete description of a system, all of the system's variables are equally important. But as soon as we describe the system with the average of many variables, we have a variable that we've given priority. It acts like the usual time. It's the time where heat is dissipated.
Time isn't a basic part of the world. But it seems to be, because the world is so vast. We're just tiny systems in the world, only interacting with macroscopic variables that are the average of countless microscopic variables. In everyday life, we never see a single particle, or a single quantum of space. We see rocks, mountains, and faces. We're always related to averages. That's how heat gets dissipated, and time gets created.
The hard thing is imagining a world without time, and imagining time appearing as an approximation. We're so used to thinking of reality as existing inside time. But we should still try to understand it better.
Time is the result of us ignoring the microscopic physical state of things. Time is the information we don't have.
Alright, so reality and information.