From the Beginning of the Universe to Quantum Gravity: Theoretical Physicist Yasunori Nomura on the Frontiers of Cosmology

What runs throughout is a habit of distinguishing established knowledge from theories still in progress. Nomura considers the multiverse "quite plausible" while acknowledging that it is not as certain as the hot Big Bang. On quantum gravity, too, he says that although something that looks like a key, holography, has come into view, the work is "still in progress." This article follows the flow of the discussion while distinguishing between the program's narrated explanations and Nomura's own remarks.

Nomura first looks back on how the very fact that the universe was born was a major discovery of the early 20th century. It is, he says, a fine example of theory and observation intertwining to uncover a truth about the universe.

Einstein created general relativity, a theory of gravity. Its equations took a form that could be applied to and solved for the universe as a whole, but when solved, a static universe that stays still was not among the answers. Space as a whole can only expand or contract. Einstein could not believe this and at one point even tried to modify the equations instead. Observations, however, revealed that all galaxies are moving away from us.

Tracing time backward, the early universe must have been extremely dense and therefore also extremely hot. Since the equations already exist, one can calculate how far back one must go for the temperature to become extremely large. The result showed that about 13.8 billion years ago the universe was in an extremely hot state and has been cooling ever since. In other words, the universe did not exist from an infinite past but began about 13.8 billion years ago.

The narration adds that this hot, dense state is precisely what has been called the Big Bang. Humanity observes light from about 380,000 years after the birth of the universe in the form of radio waves; this is the cosmic microwave background. Before that, the universe was too dense for light to travel in a straight line, so there is a limit to how far back we can see the universe directly with light.

It was once thought that the hot, dense Big Bang was the beginning of the universe. According to Nomura, however, recent research suggests that before it there was a cold period with a temperature of almost zero. That period was so short that it would take 20 to 30 zeros after the decimal point to express it in seconds. In that extremely brief interval, the universe expanded violently: something about the size of an atomic nucleus, for example, grew to roughly the size of the entire visible universe today, about 13.8 billion light-years. This rapid expansion is called inflation.

According to the narration, when inflation ended, the energy that had driven the rapid expansion turned into heat, elementary particles were created, and the universe became hot all at once.

Here Nomura explains why some books say "the Big Bang came after inflation" while others say it came "before." This is not a matter of competing theories. If the word Big Bang is used to mean "the state in which the universe became hot after inflation," then the Big Bang comes after inflation. If it is used to mean "the true beginning of the universe," then inflation happened after the Big Bang. The word Big Bang, he says, has come to carry a double meaning that easily causes confusion.

How, then, did galaxies and stars arise from a universe that was almost perfectly uniform? Nomura first emphasizes the difference between today's universe and the early universe. In today's universe, matter is concentrated where there are galaxies, and there is almost nothing where there are none. Stars are extremely dense, and the space between stars is nearly empty. But when the universe was 380,000 years old, there was no such structure; like a "featureless" soup, it had almost the same density everywhere. There were merely regions slightly denser or sparser by just one part in 100,000.

Nomura illustrates how extreme this uniformity is using the air in the room where the program was being filmed. Even the air in a room is not uniform in density, since the upper part is a little warmer and the lower part a little cooler. It easily deviates by about 0.1%. By comparison, the early universe was uniform to a tremendous degree of precision.

Even so, regions with slightly higher density have slightly stronger gravity than their surroundings. They therefore pull in more and more matter, while matter is drained from sparser regions. In this way, small differences grew.

The question is where those fluctuations of one part in 100,000 came from. According to Nomura, if inflation theory is correct, the seeds are fluctuations produced by quantum mechanics when space expanded violently. Nomura and his colleagues think this theory is probably correct. The statistical properties of those fluctuations and of the pattern of fluctuations actually seen in the universe 380,000 years later "match perfectly," Nomura says. The fluctuations that seeded the galaxies were created by quantum mechanical effects during the inflationary period. They became galaxies, then stars, and probably led to life—that, he says, is the story.

The narration continues that it was not only visible matter that built the structure of today's universe. How much mass the universe contains can be determined from the motions of galaxies and galaxy clusters. Because gravity affects the motion of surrounding celestial bodies, the presence of mass can be inferred even if it cannot be seen with light. Yet known matter such as stars and gas alone cannot explain either the motions of galaxies or the large-scale structure of the universe. Even when simulating the process from the early fluctuations to today's galaxies and galaxy clusters, ordinary matter alone does not reproduce the present universe. Only by adding dark matter can today's structure be reproduced well.

Nomura says there is "a mountain" of evidence for dark matter. Almost no physicist or astronomer doubts its existence, but its detailed nature is unknown. It is fairly well established, he says, that roughly five-sixths of matter is unknown dark matter and one-sixth is ordinary matter included in the Standard Model of particle physics.

Everything discussed so far concerned "matter." According to Nomura, there is an energy that is not matter yet fills the entire universe, and it accounts for about 70% of the universe's total energy. Matter—including dark matter, electrons, and neutrinos—amounts to only about 30% of the energy density all together. This became more or less established at the end of the 20th century, around 1998. Because it is energy but not even matter, something poorly understood, it is called dark energy.

The narration explains that the clue to its discovery was cosmic expansion. If the universe contained only matter, the mutual attraction of gravity would act as a brake, and the expansion should gradually slow down. Observations showed, however, that far from decelerating, the expansion was accelerating.

Nomura cites vacuum energy as one candidate, saying it is easier to understand if called "the energy of space." Even if you remove all matter—pencils, glasses, yourself—space remains. That space itself can carry energy, he says. This energy can be either positive or negative. Which one is called positive is merely a human convention, but if it is positive in the current convention, it acts like a repulsive force and expands space; if negative, it causes space to contract. It is known that such a thing can exist, and it has probably been found, Nomura says.

The program then moves on to the question of why galaxies, stars, and life can exist in this universe at all. Nomura considers the theory of the multiverse, which holds that there are multiple universes, to be "quite plausible." That is because there are quite a few phenomena that cannot be understood otherwise. Put simply, he says, the issue is that "the universe is too good to be true."

Our universe has fixed rules. There are electrons, and their mass takes a specific value. Because the same equations work on Earth and in Andromeda, we can understand what is happening there by analyzing the light that reaches us, without having to go there. But those rules themselves are "incredibly well made." Theoretically, there is no reason whatsoever why the electron's mass must have that value. The theory merely lets us calculate things if we plug in the experimentally measured value. Even the existence of electrons is not theoretically necessary. There are electrons, there are atomic nuclei made of protons and neutrons, which in turn are made of quarks. Change this structure even slightly, and you get an empty universe with not only no stars, forests, lakes, or humans, but not even galaxies. It is so well made, Nomura says, that "you'd think you couldn't understand it without bringing in God."

If, however, there are many kinds of universes, this is no longer mysterious. It becomes something science can understand without invoking God. Nomura compares this to Earth. Earth's distance from the Sun is just right; a little closer and liquid water would evaporate, and farther away it would probably be a world of liquid methane. At first glance this seems miraculous. In reality, though, most planets are scorching hot or frigid. Within our galaxy alone there are countless planets at various distances from their stars, and including other galaxies there are trillions. With that many, some places will happen to have favorable conditions. Since advanced life arises only in such places, looking around from there makes things appear miraculous. Nomura sees the universe as a whole as structured in a way that leaves no choice but to think about it the same way. The more quantities are measured through observation, the more values turn up one after another that have no known reason and are, moreover, far too convenient.

Nomura also touches on theoretical support. When superstring theory and other theories, which had been developed in the 1980s for motivations entirely different from the multiverse, were reexamined, they turned out to automatically include the existence of many kinds of universes. Nomura calls this fact, discovered later, "extremely suggestive."

Nomura further says the same thing has happened repeatedly throughout history. In the time of Copernicus, Kepler, and Newton, the solar system was thought to be almost the entire universe, and other stars were regarded as something like wallpaper. Yet the solar system turned out to be just one of many systems within the galaxy. In the early 20th century, that galaxy was still being called "the universe." Each time, humans have thought that wherever they had reached was everything. Since this keeps repeating, the multiverse is not unnatural; from both theory and observation, Nomura says, "whichever direction you think about it from, that seems more natural."

Nomura does add a caveat, however. Since this is science, what ultimately matters is how much evidence accumulates. The multiverse is not as certain as the Big Bang theory, which holds that the universe was once hot.

Nomura also talked about what led to a career in research. In the third year of high school, Nomura had an interesting physics teacher who held an intensive summer course on relativity and quantum mechanics, topics that did not appear on entrance exams. That was when Nomura felt, "So there's a world like this." Looking back, though, Nomura recalls already reading Blue Backs, a series of popular science books, in junior high school, so the interest seems to have taken root even earlier. Whether or not becoming a physicist was the goal, Nomura wanted to study this field and enrolled in the physics department at the University of Tokyo.

During graduate school, Nomura had an encounter that changed their standards as a researcher. A postdoctoral researcher from the United States was going to spend a day or two in Tokyo on the way to a workshop in Kumamoto. When someone suggested a student show the visitor around, no one raised a hand, so Nomura ended up taking the visitor around. They even went up Tokyo Tower, but while looking at the view and occasionally reacting, the visitor talked about physics the entire time. The amount and depth of that knowledge was on a completely different level, with words pouring down "like a shower," Nomura says. When Nomura raised a topic, the visitor not only answered but pointed out one after another how it connected to other problems and how it was merely a special case of something else. Nomura recalls the feeling of tossing out a topic casually and having it hit back "about 100 times bigger."

Nomura had been a bit "happy-go-lucky" as an undergraduate but believed they had been focused in graduate school. Even so, Nomura felt a sense of crisis, thinking it would be impossible to survive if thrown into a world full of people like this, and studied even harder. That person was an exceptional case who would go on to become an associate professor at Harvard around age 30. But since that was the only sample Nomura knew, Nomura assumed everyone was at that level. On actually going abroad, Nomura found that there were hardly any people "like monsters" of that sort. Even so, Nomura says, this misconception turned out to be a major plus for their career.

Physical laws are indispensable for studying the universe. According to Nomura, in the 20th century Newtonian mechanics was found to be incomplete and was extended in two directions. That is precisely what made cosmology, which deals with the universe as a whole, possible. One of these was relativity.

It started with the speed of light. Using Maxwell's equations, one can calculate the speed of electromagnetic waves: about seven and a half times around the Earth per second, or 300 million meters per second. Nomura explains that in Newtonian mechanics this was "something that shouldn't happen."

Even if you say a car is traveling at 50 kilometers per hour, the Earth is rotating, and faster than that. Its orbit around the Sun is faster still, and the solar system itself orbits the center of the galaxy. So what is the "true speed"? Under Galilean relativity, the foundation of Newtonian mechanics, there is no concept of a true speed; only speed relative to something has meaning. Fifty kilometers per hour means moving 50 kilometers in an hour relative to the ground. Yet the speed of electromagnetic waves comes out of the equations as a value without any information about who is observing it. Einstein reasoned that since the equations say this is the speed of light, it must be that speed for everyone.

The narration adds the following. For the speed of light to be the same for everyone, time can no longer be absolute, and the faster something moves, the slower time passes for it. This is the special theory of relativity of 1905. According to Nomura, even just riding a train slows down the passage of time. We are simply unaware of it because the train is so slow compared with the speed of light, and if this tiny effect is ignored, the result agrees with Newtonian mechanics. Special relativity is a theory that contains Newtonian mechanics.

Special relativity, however, could only be used for uniform motion. Einstein next realized that accelerating and being in a gravitational field are the same thing. When a car accelerates and your body gets pressed back, it is as if gravity were acting sideways. Ordinary people merely think the two are similar, but "a genius at that level" wonders whether they might be the same thing, Nomura says. If a box floating in weightless space is pulled by a spaceship with a rope and accelerated, apples and people inside are pressed against one wall. From the inside, this is indistinguishable from a state with gravity.

The result was the general theory of relativity. Since it can also handle cases without acceleration, it fully contains special relativity. Special relativity continues to be used anyway because the mathematics of general relativity is "heavy-duty." If gravity and acceleration are not involved, there is no need to bring it in. The narration sums up that general relativity made it possible to understand gravity as a curvature of spacetime and to treat cosmic expansion and black holes using physical laws.

The other incompleteness of Newtonian mechanics appeared in the microscopic world. According to the narration, if one thinks only in terms of Newtonian mechanics and electromagnetism, the electrons around an atomic nucleus should lose energy and fall into the center, and atoms should collapse in an instant. Explaining why atoms are in fact stable required new rules: states take discrete values, and multiple possibilities overlap and interfere with one another. This is quantum mechanics.

The problem is the relationship between the two theories. Nomura points out that quantum mechanics as ordinarily used does not include gravity, and general relativity does not include quantum effects. They are separate theories. But the real world runs on quantum mechanics and at the same time has gravity. You cannot discard either just because you don't like it, yet there is no theory that includes both.

Cosmology is still possible because there are almost no situations where both become important at the same time. The reason, Nomura says, is that gravity is "pathetically weak." But in extreme places such as the center of a black hole or the very first moment when time and space began, matter is tightly concentrated so that gravity becomes important, and at the same time the scales are so small that quantum mechanics is decisive. If nature has rules, there should be a unified theory that includes both quantum mechanics and gravity, reducing to quantum mechanics where gravity is weak and to general relativity where quantum effects are small.

A theory combining special relativity and quantum mechanics has already been completed in the form of quantum field theory. Elementary particles move at very high speeds, so particle physics would be impossible without it. When dealing with elementary particles, gravity can be ignored. But to include gravity, a quantum theory that goes as far as including general relativity is needed, and that has not been achieved in complete form. This is the problem of quantum gravity.

According to Nomura, when one tries to combine quantum mechanics and gravity, "not even a single" method that works has been found. Combining them in the ordinary way leads to contradictions at the mathematical level, producing a theory that cannot even be calculated, where 3 + 5 doesn't equal 8 but "8 plus some weird garbage." Only when something very special is done does all this garbage become zero. That is the case where, zooming in on elementary particles, they turn out to be not points but strings, and those strings move in a nine-dimensional space where a single point is specified by nine numbers. This is superstring theory, one of the candidates for quantum gravity.

Nomura explains why strings appear using the example of scattering. Ordinarily, gravity is too weak to matter. But when particles collide at very high energies, energy also becomes a source of gravity, so gravitational effects can no longer be ignored. The scattering probability then grows larger and larger and diverges to infinity. A probability of "infinity percent" is meaningless; the theory has broken down.

In quantum mechanics, gravity can be regarded as the exchange of gravitons. That alone produces infinities, but if one assumes there is also another particle A with a specific mass, the infinities can be canceled. Another kind of garbage appears, however. Adding a somewhat heavier particle B cancels that garbage too, but yet another kind appears. By adding particles of specific masses one after another in this way, one can ultimately build a theory that eliminates the infinities completely, in which 1 + 1 equals 2 and 3 + 5 equals 8.

Here Nomura brings up the example of a guitar string. When you pluck a string, specific modes of vibration follow in sequence: one crest, two crests, three crests. Having discrete energies means, by E = mc², that there can be regarded as being many particles with specific masses. On close examination, the sequence of particles that had to be added to combine gravity and quantum mechanics matched the vibration patterns of a string perfectly. That is why the idea arises that the foundation of nature might be strings rather than points.

Superstring theory includes gravity, has no infinities, and is a fully quantum mechanical theory. You might think, "So it's done, then," but that is not the case, Nomura says. The situations in which superstring theory can be used are limited.

Nomura likens this to special relativity. Special relativity is a completely correct, consistent theory in situations of uniform motion, but it cannot be used once there is acceleration. Present-day superstring theory is the same: in limited situations, quantum mechanics and gravity are unified, but outside them it cannot be used. And our universe happens to fall precisely into the situations where it cannot be used.

As an example, Nomura cites the evaporation of black holes. When a black hole evaporates, the particles that come out number not one or two but 100 million or 10 billion. The current ways of handling superstring theory cannot deal with such situations. Researchers therefore recognize the need for a formulation with a broader range of applicability. The clue to that, he says, is black holes.

A black hole forms when so much mass gathers or density becomes so extremely high that nuclear fusion and the like can no longer halt gravitational contraction, and matter collapses to a single point. Once inside the event horizon, not even light can escape, and no information can be obtained from outside. That is why it is completely dark and called a "black hole."

This brings us to entropy. The narration explains entropy as a quantity representing how many possibilities a given state has. Just as ink dropped into water spreads out, things in nature proceed in the direction of increasing entropy.

According to Nomura, what is strange about black holes is that they do not have a surface like Earth does. Humans have merely drawn a boundary beyond which light cannot escape, and it is just "smooth" space. Since space cannot take on many different patterns, thinking in terms of classical general relativity, black holes appear to have no entropy. Then, if you dropped an object with entropy into a black hole, the entropy of the universe as a whole would decrease.

In response, Jacob Bekenstein made a bold proposal. It was already known as a property of black holes that if two black holes with horizon areas A and B merge, the area C of the resulting black hole is always larger than A + B. Area only ever increases and never decreases. This property is the same as that of entropy. Bekenstein therefore argued that black holes have entropy proportional to the area of their horizon. If pink water carrying entropy is dropped into a black hole, the black hole becomes slightly larger. It can be proven that the entropy corresponding to the increased area is always greater than the entropy of the water dropped in. In other words, entropy increases overall. Bekenstein argued that black holes, too, do not escape the three pillars of quantum mechanics, relativity, and statistical mechanics.

Stephen Hawking took issue with this. If there is entropy, there must be a temperature, and if there is a temperature, there must be some kind of radiation, just as heated iron glows. Since a black hole is an object that only absorbs, it breaks down even before the second law of thermodynamics comes into play—that was Hawking's rebuttal. Although there was no theory fully unifying quantum mechanics, Hawking was extremely good at calculations that incorporated quantum mechanics into general relativity like a "patchwork." According to Nomura, Hawking performed calculations intending to show that Bekenstein's idea was wrong, but instead discovered that black holes emit a tiny amount of radiation and evaporate. This is Hawking radiation. The temperature derived from that radiation corresponded exactly to the entropy Bekenstein had proposed.

That, however, gave rise to a new problem. Suppose Betelgeuse is crushed into a black hole. Even if a different star of the same mass but with different patterns and so on is crushed, once it becomes a black hole only the information about its mass remains on the surface, so it becomes the same black hole. The Hawking radiation is then exactly the same as well, and the information about what kind of star it originally was is completely erased.

Nomura anticipates the question: isn't information being erased all the time? If you burn a diary, nobody can know what was in it. But that is not what physics means by information. Even if burning a diary and a magazine makes them look the same, in principle, if you knew precisely all the positions and velocities of the molecules—that is, the full quantum mechanical state—you could solve the equations in reverse. Then one would turn back into the diary and the other into the magazine. Until then, physics held that information is never lost in principle.

If Hawking's calculation is correct, however, starting from different states would lead to exactly the same final state. Time evolution would no longer be one-to-one. Then the past could not be reconstructed, and physics would be robbed of its predictive power. It is an "even more baffling problem" than entropy or temperature, and this, Nomura explains, is the black hole information problem that Hawking put to physicists around the 1970s.

According to Nomura, this problem has recently been nearly settled in the direction that the original problem Hawking raised does not exist. What played a role there, he says, was the holographic principle.

The idea that a black hole's entropy is proportional to its area is, on reflection, odd, Nomura says. Normally, entropy is proportional to volume. Double the volume and it doubles; multiply by ten and it becomes ten times larger. If you make each side ten times longer, the volume becomes 1,000 times larger, so the maximum entropy should also become 1,000 times larger. Area grows only as the square, so it would be only 100 times larger.

Moreover, a black hole should be the state of maximum entropy that a region can take. You can crush chairs and desks into a black hole, but a black hole will not spontaneously turn back into chairs, desks, or Betelgeuse. A black hole is the final state that entropy increases toward. Yet that maximum corresponds only to area, not volume. Nomura says this is extremely puzzling.

From this comes the proposal that since the amount of information that fits in three-dimensional space (nine-dimensional, if the small dimensions of superstring theory are included) is only two dimensions' worth, it should be possible to rewrite it as a two-dimensional theory. This is the basic idea of the holographic principle. The narration likens it to a hologram, in which a three-dimensional image emerges from information on a flat surface.

Nomura stresses that gravity plays a decisive role in this argument. Without gravity, black holes would not form, and you could pack in as much as you liked. It is precisely because there is gravity that three-dimensional information is limited to two dimensions' worth. And if there were gravity on the two-dimensional side, it could be reduced by yet another dimension, eventually all the way down to zero dimensions. So, strictly speaking, an n-dimensional theory of gravity should be equivalent, in terms of degrees of freedom, to an (n−1)-dimensional theory that does not include gravity. If it can be formulated as a theory without gravity, the problem of quantum gravity does not arise in the first place—since there is no gravity, Nomura says.

This idea was considered interesting, but it had "a feeling of just being talk." Then, in 1997, Juan Maldacena found a concrete example. Consider a space called anti–de Sitter space, which has a boundary far away. Maldacena discovered that quantum gravity in that space corresponds to a specific theory one dimension lower that does not include gravity, a conformal field theory. This is the so-called AdS/CFT correspondence. It cannot be applied directly to our universe, but a concrete example was actually found in which an n-dimensional theory of gravity can be written equivalently as an (n−1)-dimensional theory without gravity.

Maldacena found this while studying superstring theory. Nomura therefore corrects the way the question "Is the theory of gravity superstring theory or holography?" is framed. Superstring theory is the name of a theory, while holography is the name of a property. Superstring theory is a holographic theory, and the two do not contradict each other.

Superstring theory, however, can only be used in limited situations. Meanwhile, the property of holography appears to hold even for black holes in our universe, where superstring theory cannot be used. So the property is thought to be more general. That is why research is now moving toward completing a theory that satisfies holography and that includes superstring theory rather than being superstring theory itself, Nomura explains.

Maldacena's example also has limits to its applicability. It requires a wall-like boundary on the gravity side of the space, beyond which "there is nothing more." Our universe, however, probably has no boundary. So the theory is not yet complete.

The narration summarizes the connection to the information problem as follows. If a gravitational world containing black holes can be rewritten as a different theory on the boundary, information is not lost within that theory. Information may not have disappeared; it may simply not have been visible without a complete theory. This correspondence, however, has been shown only for special spaces with boundaries and does not apply directly to our universe.

What is needed to complete quantum gravity? Nomura first cautions that if it were fully known what needs to be done, it would just be a matter of doing it, but that itself is not known. That said, Nomura says that at the very least the existence of the boundary needs to be eliminated, because AdS/CFT is a formulation that depends heavily on there being a boundary. Since our universe seems to have no boundary, a correspondence that satisfies holography in the absence of a boundary must be found.

That might be learned from superstring theory, but so far there is no formulation that cleanly extracts holography from superstring theory in the boundaryless case, as Maldacena did. There are many hints, however, Nomura says. Superstring theory captures certain correct aspects, and investigating it often reveals what should be done. Some researchers think the hints lie there, while others think it is necessary to go fundamentally beyond superstring theory.

What many researchers consider key is the property of holography. But Nomura adds that once complete, the theory might turn out to be described in different terms, and concludes that the work is "still in progress."

Finally, asked why people are drawn to the universe, Nomura answered as follows. As children, everyone had questions: what is the universe like, why am I here, how was the universe born? It is probably because those questions remain in everyone's heart, even if people are too busy and have forgotten them.

The solar system is a tiny thing within the galaxy, and that galaxy is like a dot among countless galaxies. Even our universe may be just one of many universes. Thinking that way, wouldn't Earth and one's own worries cease to matter? To this question, Nomura answers, "No, they don't." Earth is something the universe could do with or without, something that could be blown away with a puff. That is precisely why it is fragile and could be destroyed in no time if we do not take care of it. Life is the same: precisely because humans are beings that could be blown away with a puff, we live by cherishing it. Because research on the universe shows us how tiny we are, that tininess becomes precious. In that sense, Nomura said, research on the universe may have influenced their way of thinking to some extent.

The program ends by leaving open the question of whether the day will ever come when we know everything about the universe. In Nomura's remarks as well, the nature of dark matter, the properties of dark energy, evidence for the multiverse, and a holographic theory of quantum gravity that holds in a universe without boundaries were all presented as problems that have yet to be answered.