Relational quantum mechanics

Relational quantum mechanics (RQM) is an interpretation of quantum mechanics that changes how we think about the state of tiny particles and systems. Instead of having one fixed state, RQM says the state is about the relationship between an observer and the system being observed. This idea was first explained by Carlo Rovelli in 1994 and has been developed by many other scientists since then.

RQM is inspired by special relativity, which tells us that what we see depends on where we are standing. It also builds on ideas from Wheeler about how information theory might help us understand quantum mechanics. In RQM, different people looking at the same system might describe it in different ways, and all of these descriptions can be correct. For example, one person might see a particle in a single state, while another person sees it in many states at once, called a superposition. RQM says both descriptions are valid because the "state" always depends on who is looking.

This approach helps solve some of the tricky problems in quantum mechanics, like the measurement problem and questions about whether things happen in a definite way everywhere at once, called local realism. RQM shows that reality is about relationships between things, not about one single, absolute description of everything.

History and development

Relational quantum mechanics began when Carlo Rovelli compared problems in understanding quantum mechanics with issues in Lorentz transformations before special relativity was developed. He suggested that, just like older ideas about time were wrong, assuming that a system's state is the same for all observers also causes confusion.

Later, other scientists like Lee Smolin and Louis Crane used these ideas to study the universe’s beginnings. In 2020, Rovelli wrote a book called Helgoland to explain these concepts. In 2023, he and Emily Adlam changed the theory further by introducing new rules about how different viewpoints connect.

The problem of the observer and the observed

When we study quantum mechanics, we often think about what happens when someone observes, or "measures," a tiny particle or system. This is a big question in a theory called Relational Quantum Mechanics.

Imagine one scientist, named O, looking at a tiny particle called S. Scientist O can describe what happens when they observe S. But there is another scientist, named O′, who is interested in what happens to both O and S together. Even though both scientists are describing the same event, they might tell the story in different ways. This shows us that in quantum mechanics, what we observe can depend on who is doing the observing. This idea connects to famous thought experiments like Wigner's Friend, which helps us understand different ways people can think about quantum theory.

Central principles

Relational quantum mechanics suggests that the state of a quantum system depends on who is observing it. This idea comes from the thought that, just like in special relativity where things look different depending on your viewpoint, quantum systems might appear different to different observers.

The theory has two main ideas: first, that all systems—big or small—are fundamentally quantum systems, and second, that quantum mechanics is complete as it is, without any hidden rules. Because of this, the description of a system is always tied to a specific observer. For example, one observer might see a system in one state, while another observer sees something different. This helps explain some tricky questions in quantum mechanics without changing the theory itself.

Consequences and implications

In relational quantum mechanics, the state of a quantum system depends on the relationship between the observer and the system. This means that different observers might describe the same system differently based on their own perspectives.

One key idea is that an observer can check whether their description of a system matches reality, but they cannot always say exactly what the system’s state is without interacting with it. This creates interesting situations where two observers might seem to have different results, but these differences can be explained by the fact that each observer’s description depends on their own interactions with the system.

The theory also suggests that interactions between systems are limited by the rules of special relativity, meaning that systems can only interact if they are close enough in space and time. This ties together the ideas of location and interaction, showing how they depend on each other.

Relationship with other interpretations

Relational quantum mechanics (RQM) works differently from some other ideas about quantum mechanics. It does not fit well with hidden variables theories, which suggest there are hidden factors that explain quantum behavior. RQM believes quantum mechanics gives a full picture of the world and does not need these extra ideas.

RQM is somewhat like the Copenhagen interpretation, but it says that any interaction — not just big ones with machines — changes how we see quantum systems. This is different from the Copenhagen idea that only big interactions cause changes.

RQM also has some similarities with the many-worlds idea, but it does not believe there is one big description of the entire universe. Instead, it says there are many smaller, related descriptions.

RQM fits well with the consistent histories approach, which looks at sequences of events instead of single moments. RQM helps explain how these sequences can still make sense even when they depend on the observer's view.

Main articles: Copenhagen interpretation, Bohm's interpretation, many-worlds, consistent histories

EPR and quantum non-locality

RQM provides a unique way to understand the EPR paradox. It solves the problem by showing that no faster-than-light communication happens during a Bell test experiment. The idea of locality stays intact for all observers.

In the EPR experiment, a source creates two electrons with linked spins. These electrons move far apart to two observers, Alice and Bob, who measure the spins. The spins are perfectly linked: if Alice finds her electron spinning up, Bob will find his spinning down, and vice versa. This link seems to happen instantly, even over large distances, which might look like faster-than-light communication.

In RQM, an observer needs to interact with a system to see its properties clearly. Since Alice and Bob are too far apart to measure both electrons at the same time, they can't know each other's results right away. Only later, when they meet and share information, do they see the links between their results. This way, RQM explains the links without breaking the rules of faster-than-light travel or locality. All observers still see results that match standard quantum mechanics predictions.

Derivation

Relational quantum mechanics (RQM) suggests that the state of a quantum system depends on the relationship between the observer and the system. This idea was first introduced by Carlo Rovelli in 1994. RQM is inspired by special relativity, which tells us that observations can differ depending on the observer’s viewpoint.

RQM can be built from a few basic ideas, or postulates, based on experiments. These postulates help explain how information about quantum systems works. One key idea is that there is a limit to how much information we can get from a quantum system. Another idea is that we can always find new information about a system. These simple starting points help build a deeper understanding of quantum mechanics.

Problems and discussion

Relational quantum mechanics suggests that what we know about an object depends on how we observe it, much like how things look different depending on where you stand. It focuses on how a system behaves under different conditions rather than on fixed properties like an electron's mass. Some thinkers argue that even properties such as mass can only be known through our interactions with the object.

Main article: phase space
Main article: state space