Physicists believe that at the smallest scales, space emerges from quantum phenomena. So, what do these constructs look like?
People often take space for granted. It is empty, the backdrop for everything else. Time, similarly, is simply an unceasing ticking. However, if physicists discover anything after a long process of research to unify their theories, it is that space and time form a complex system so astonishing that it can challenge our most intense efforts just to understand it clearly.
In early November 1916, Albert Einstein foresaw what was about to happen. A year earlier, he had developed the theory of general relativity, proposing that gravity is not a force acting through space but a characteristic of spacetime itself. When you throw a ball upward into the air, it returns to the ground because Earth distorts the space around it, causing the ball’s path and the ground to intersect once again. In a letter to a friend, Einstein reflected on the challenge of integrating general relativity with another of his intellectual offspring, the early theory of quantum mechanics. This would not only distort space but also destroy it. Mathematically, he hardly knew where to begin. “I have made things difficult for myself more times than I can count in this way!”, Einstein wrote.
Einstein never got too far. Even today, there are many competing ideas for a quantum theory of gravity as scientists explore this topic. Debates obscure an important truth: all competing approaches assume that space originates from something deeper—a groundbreaking idea that challenges 2,500 years of scientific and philosophical understanding.
Falling into a Black Hole
A typical magnet can clearly illustrate the problem that physicists face. It can attract a paperclip that would otherwise fall due to Earth’s gravity. The gravitational force is weaker than magnetic, electric, or nuclear forces. Despite quantum effects, it remains weaker. The only tangible evidence of these processes’ presence is the speckled matter model in the early universe (before the Big Bang)—believed to be caused by quantum fluctuations in the gravitational field.
Black holes are the best testing ground for quantum gravity. “That is the closest thing we have to a laboratory experiment,” says Ted Jacobson from the University of Maryland, College Park. He and other theorists study black holes as a theoretical anchor. What happens when you formulate an equation that works perfectly in the lab and extrapolate it into a completely imaginable situation? Could certain small holes manifest themselves?
Black holes are the best testing ground for quantum gravity.
The theory of relativity predicts that matter falling into a black hole will be infinitely compressed as it approaches the center—the point known mathematically as a singularity. Theorists cannot extrapolate the trajectory of an object beyond the singularity; its timeline ends there. Even saying “there” is problematic because spacetime itself defines the endpoint of the singularity’s existence. Researchers hope that quantum theory can thoroughly analyze this singularity and trace what happens to objects falling into the black hole.
Outside the black hole’s boundary, matter is not compressed, and the gravitational force is weaker. In short, the known laws of physics should be preserved. Therefore, it becomes even more complex than it inherently is. Black holes are delineated by the event horizon, a point of no return: matter that falls in cannot return. The fall is irreversible. This is an issue because all known fundamental laws of physics, including general quantum mechanics, can be reversed. At least in principle, you should be able to reverse the motion of all particles and restore what you had.
A puzzling question is very similar to the inquiries of physicists in the late 1800s when they envisioned the mathematics of a “black body”, idealized as a cavity full of electromagnetic radiation. James Clerk Maxwell’s theory of electromagnetism predicted that such an object would absorb all radiation impacting it and could never reach thermal equilibrium with its surrounding matter. Rafael Sorkin from the Perimeter Institute for Theoretical Physics in Ontario explains: “It would absorb an infinite amount of heat from a reservoir maintained at a fixed temperature.” In thermodynamic terms, it is possible for the object to have an absolute zero temperature. This conclusion contradicts observations of real black bodies (like ovens). Following Max Planck’s research, Einstein demonstrated that a black body can reach thermal equilibrium if the energy radiation comes from discrete units, or from quantum phenomena.
Theoretical physicists have struggled for nearly half a century to provide an appropriate explanation for black holes. Ultimately, Stephen Hawking from the University of Cambridge made a significant breakthrough in the mid-1970s when he applied quantum theory to the radiation field around black holes and showed that they have a non-zero temperature. Thus, they not only absorb but also emit energy. Although his analysis placed black holes within the realm of thermodynamics, it delved deeper into the irreversibility issue. Radiation emanates from outside the black hole’s boundary, and there is no information about the inside of the hole. It is random thermal energy. If you reverse the process and send energy back, the things that fell in will not bounce out; you will receive more heat. And you cannot conceive that the original things are still there, merely trapped inside the hole, because as the black hole emits radiation, it shrinks and, according to Hawking’s analysis, ultimately vanishes.
This issue is referred to as the information paradox because black holes obliterate information about the fallen particles that would allow you to rewind their motion. If the physics of black holes can truly be reversed, something must carry the information back, and our conception of spacetime may need to change to allow for that.
Spacetime Atoms
Heat is the random motion of microscopic components, such as gas molecules. Because black holes can heat up and cool down, this explains why they have many parts; in other words, black holes have a microstructure. And because a black hole is just empty space (according to general relativity, matter falls through the horizon but cannot linger), the parts of a black hole must be parts of space.
Even theories proposed to preserve a conventional concept of the endpoint of spacetime conclude that there exists a secret behind the flat façade. For example, in the late 1970s, Steven Weinberg, now working at the University of Texas, sought to describe gravity similarly to other natural forces. He still obtained results fundamentally suggesting that spacetime changes at its smallest scale.
Early physicists imagined microscopic space as a mosaic of tiny spatial blocks. If you zoomed in on the Planck scale to an almost unimaginable size of (10^{-35}) meters, you would see something resembling a checkerboard. But that is not entirely accurate. Moreover, within the grid lines of the checkerboard space, there will be some directions that dominate over others, causing asymmetry. This contradicts special relativity. For instance, the light of different colors may travel at different speeds—like in a glass prism, causing the refraction of light into its constituent colors. These contradictions with relativity are quite evident.
The thermodynamics of black holes increases skepticism about envisioning space as a simple mosaic. By measuring the thermal behavior of any system, you can count its parts, at least in principle. Extract energy and check the thermometer. If it spikes, that energy certainly covers relatively few molecules.
If you experiment with a normal substance, the number of molecules increases relative to the mass of the material. This means: If you increase the radius of a beach ball by a factor of 10, you will obtain 1,000 times the number of molecules inside it. But if you increase the radius of a black hole by a factor of 10, the number of molecules retrieved only increases by 100 times. The number of “molecules” it forms must be proportional to its mass but inversely proportional to its surface area. A black hole appears as a three-dimensional object, but its behavior resembles that of a two-dimensional entity.
This strange effect is called the three-dimensional principle because it evokes the idea of a three-dimensional shape. However, upon closer examination, it becomes an image created by a two-dimensional film. If the three-dimensional principle accounts for the micro-components of space and its content, then the time required to constitute space will be longer than simply piecing together small fragments.
However, the relationship of a part to the whole is rarely as simple as that. A water molecule (H2O) is not simply a tiny water droplet. Consider what liquid water does: it flows, forms droplets, has ripples and waves, freezes, and boils. An individual H2O molecule cannot perform these actions: these are collective behaviors. The same applies to space. Daniele Oriti from the Max Planck Institute for Gravitational Physics in Potsdam, Germany, states: “The atoms of space are not the smallest parts of space. They are the building blocks of space. The geometric properties of space are new, collective, emergent properties of a system made up of many such atoms.”
The exact building blocks depend on various theories. In loop quantum gravity, they are quanta synthesized by applying quantum principles. In string theory, they are fields similar to electromagnetic fields existing on surfaces, probed by a moving string or energy loop—strings of characters. In M-theory, which relates to string theory and may underlie it, they are a special type of particle: from a membrane shrinking to a point. In causal set theory, they are events related to a causal network. In amplitude theory and some other approaches, there are no building blocks at all—at least not in the conventional sense.
Although the organizing principles of these theories differ, all attempt to maintain some version of the so-called relational theory proposed by the 17th and 18th-century German philosopher Gottfried Leibniz. Broadly understood, relational theory posits that space arises from a specific pattern of correlations between objects. From this perspective, space is a jigsaw puzzle. You start with a large pile of pieces, observe how they connect, and place them accordingly. If two pieces share similar properties, such as color, they may be placed close together; if they differ significantly, you temporarily place them far apart. Physicists often represent this relationship as a network with a certain connection pattern. The relationships are determined by quantum theory or other principles, and the arrangement of space follows.
Phase transitions are another popular topic. If space can be assembled, it can also be disassembled; then the building blocks can rearrange into something resembling space. Thanu Padmanabhan from the Inter-University Centre for Astronomy and Astrophysics in India states: “Just as matter exists in many different states, such as ice, water, and steam, the atoms of space can also reconfigure themselves in different phases.” From this perspective, black holes could be places where space melts away. Known theories break down, but a more general theory would describe what happens in the new phase. Even if space ends, physics continues.
Entangled Networks
A significant discovery in recent years is the correlation relationships associated with quantum entanglement. An extraordinary type of correlation intrinsic to quantum mechanics, entanglement appears more primitive than space itself. For example, an experimenter can create two particles flying in opposite directions. If they are entangled, they remain correlated no matter how far apart they are.
Ordinarily, when people refer to quantum gravity, they mean quantum uncertainty, quantum fluctuations, and nearly every other quantum effect in the record—but no one has ever mentioned quantum entanglement. That changed thanks to black holes. Throughout a black hole’s lifetime, entangled particles fall in, but after the hole has completely evaporated, their external components become disentangled from anything. “Hawking should have called it the entanglement problem“, says Samir Mathur from Ohio State University.
Even in a vacuum, with no particles around, electromagnetic and other fields remain entangled within. If you measure a field at two different locations, the materials you read will become scrambled in a random yet resonant manner. And if you divide an area into two, the parts will be correlated, with the degree of correlation depending on the unique geometric quantity they share: their interface area. In 1995, Jacobson argued that entanglement provides a link between the presence of matter and the shape of spacetime. That is, it could explain the laws of gravity. “More entanglement implies weaker gravity—when that happens, spacetime is more severe,” he said.
Some quantum gravity approaches now find entanglement to be crucial. String theory applies the three-dimensional principle not only to black holes but also to the universe as a whole, providing a recipe for generating space—or at least a part of it. For instance, a two-dimensional space can be woven through fields, when structured correctly, to create an additional spatial dimension. The primordial two-dimensional space would be the boundary of a much larger realm, known as bulk space. And entanglement is what weaves the block of space into a whole.
In 2009, Mark Van Raamsdonk from the University of British Columbia put forth an argument for this process. Suppose the fields at the boundary are not entangled—they form a pair of uncorrelated systems. They correspond to two separate universes, with no way to traverse between them. As the systems become entangled, it resembles a tunnel, or a wormhole, opening between those universes, allowing a spacecraft to travel from one to the other. As the degree of entanglement increases, the wormhole shrinks in length, pushing the universes together until no one calls them two universes anymore. When we observe correlations in electromagnetic and other fields, they are a remnant of the entanglement linking space together.
Many other features of space, beyond its adjacency, may also reflect entanglement. Van Raamsdonk and Brian Swingle, currently working at the University of Maryland, argue that the omnipresence of entanglement explains the universality of gravity—it affects all objects and cannot be filtered out. For black holes, Leonard Susskind from Stanford University and Juan Maldacena from the Institute for Advanced Study in Princeton suggest that the entanglement between a black hole and the radiation it emits creates a wormhole. This could help preserve information and ensure that black hole physics can be reversible.
While string theory ideas only apply to specific geometries and reproduce only a single spatial dimension, some researchers have sought to explain how all spaces could emerge from scratch. For example, ChunJun Cao, Spyridon Michalakis, and Sean M. Carroll at the California Institute of Technology begin with a minimalist quantum description of a system, constituted without direct reference to spacetime or even matter. If it has the right correlation patterns, the system can be split into parts that can be identified as different regions of spacetime. In this model, the degree of entanglement defines a concept of spatial distance.
In physics and in the natural sciences, spacetime is the foundation of all theories. However, we never directly observe spacetime. Instead, we infer its existence from our daily experiences. We assume that the most economical aspect of the phenomena we observe is some mechanisms operating in spacetime. But the ultimate lesson of quantum gravity is that not all phenomena fit neatly within spacetime. Physicists will need to discover some new foundational structures, and as they do, they will complete the revolution that Einstein began over a century ago.
