From Quantum Cryptography to Intuitionism and beyond: relativity, many-worlds and non-locality

Science has long wrestled with the nature of reality, particularly the strange behavior of the smallest particles in the universe. For decades, physicists have debated whether the world is fundamentally determined, like a clockwork machine where every future event is fixed by the past, or if it is truly open, with new possibilities emerging as time moves forward. This question touches on the very fabric of how we understand time, space, and information. If the future is already written, then the universe is a static block where nothing new ever happens. If, however, the future is unwritten, then the universe is a place where new things are genuinely created moment by moment. This distinction is not just philosophical; it changes how we interpret the laws of physics, especially when dealing with the bizarre correlations between particles that seem to influence each other instantly across vast distances.

In a paper written for the seventieth birthday of his colleague and friend Gilles Brassard, physicist Nicolas Gisin explores these deep questions by proposing a new way to think about how information is created in the universe. Gisin suggests that nature might have a limit on how fast it can generate new information. He argues that while the universe can create new facts, it cannot do so infinitely fast. This idea, which he develops alongside a mathematical approach called intuitionism, offers a fresh perspective on why the world does not become a chaotic mess of infinite possibilities and how the strange rules of quantum mechanics might fit together with Einstein's theory of relativity.

The paper begins by challenging the standard view that the numbers we use to describe the world are complete and fixed. In traditional mathematics, a number like the temperature of a room is assumed to have a precise value at every moment, even if we do not know it. Gisin, drawing on a branch of mathematics where numbers are built up over time, suggests that for many physical quantities, the precise value does not exist until time passes and the value is determined. In this view, the future is not a hidden script waiting to be read; it is genuinely open. A temperature in ten years, for instance, has no value right now. It is not merely unknown to us; it is ontologically indeterminate, meaning that nature itself has not decided what it will be yet. As time flows, new bits of information are created, and the universe makes choices that were not predetermined.

This concept of an open future leads to a specific proposal about the limits of nature. Gisin imagines a scenario where a system, such as a gas of molecules, evolves in a way that is highly sensitive to its starting conditions. In a standard deterministic view, the system follows a single, precise path. But if the starting conditions are not infinitely precise—if they contain only a finite amount of information—then the system's path will eventually split. The different possibilities will spread out, and nature will eventually have to choose which path to take. Gisin suggests that nature can only create new information at a limited rate. If a system tries to evolve into a state that requires an enormous amount of new information to describe it all at once, nature might not be able to keep up.

To illustrate this, Gisin looks at a system of twenty tiny magnetic particles, known as spins. If these particles are arranged in a way that is classically chaotic, their quantum version becomes highly entangled very quickly. Entanglement is a state where the particles are linked so deeply that they must be described as a single group rather than as individuals. To describe this group, nature would need to generate a massive amount of new information in a tiny fraction of a second. Gisin proposes that if nature is limited in how fast it can produce this information, it might be forced to split the system into smaller, manageable parts. Instead of creating a single, massive entangled state for all twenty particles, nature might create two smaller groups of ten. This limitation could prevent the universe from evolving into a single, infinitely complex block of entangled matter. If this idea holds, it would mean that the "many-worlds" interpretation of quantum mechanics, which suggests that every possibility happens in a separate branch of reality, is incorrect because nature cannot generate the information required to sustain all those branches simultaneously.

The paper then turns to the relationship between this open future and the theory of relativity. A major puzzle in physics has been how to reconcile the idea of random, unpredictable events with Einstein's rule that nothing can travel faster than light. Some physicists have argued that if the future is truly random, it must violate relativity. Gisin disagrees. He proposes that facts are not absolute; they are relative to their location in space and time. When a random event happens, such as a particle being measured, the result becomes a fact only within a specific region of space-time called the future light cone. Outside of this region, the event has not happened yet, and the result does not exist.

This means that two events happening at different places can be correlated without one causing the other instantly. Imagine two random number generators placed far apart. If they produce matching numbers, it is not because one sent a signal to the other. Instead, the correlation is a single, non-local event that manifests at both locations. The fact that they match is true only where the two future light cones overlap. Before they overlap, the results are indeterminate. This view, which Gisin calls the "relativity of indeterminacy," allows for the strange connections seen in quantum experiments without requiring any "spooky action at a distance." It suggests that the universe is not a collection of separate objects influencing each other, but a single process where new information is created locally and spreads out at the speed of light.

Gisin acknowledges that this is a bold idea and that he does not have a complete solution to the measurement problem, which is the question of exactly when and how these indeterminate quantities become definite. He suggests that nature might have a mechanism for deciding when to make a choice, perhaps when the amount of information required to describe a system exceeds what can be created in a given time. This is not a proven fact, but a hypothesis that could lead to new predictions and technologies. If nature is indeed limited in its ability to create information, it could have serious implications for quantum computers, which rely on creating massive amounts of entanglement. If the universe cannot generate that entanglement fast enough, quantum computers might face fundamental limits that are more severe than currently thought.

The paper concludes by emphasizing that this new perspective does not require observers or conscious agents to make the universe real. The creation of new information is a physical process that happens regardless of whether anyone is watching. Gisin writes this in honor of his friend Gilles Brassard, a pioneer in quantum cryptography, to celebrate a lifetime of exploring the boundaries of information and reality. By combining the mathematical idea that numbers are built over time with the physical idea that information creation is limited, Gisin offers a vision of a universe that is dynamic, open, and fundamentally creative. It is a world where the future is not a fixed destination but a landscape that is being drawn, one new fact at a time.