Quantum nonlocality

Quantum nonlocality is a phenomenon in theoretical physics regarding multipartite quantum systems. It describes a situation where the measurement statistics of a system cannot be explained by local hidden variables. A local hidden variable is a theoretical set of internal instructions that determines measurement outcomes. In such a model, particles would carry pre-set information to guide their behavior locally. Quantum nonlocality suggests that these particles are linked in ways that defy such local explanations. This concept is central to debates about the fundamental nature of reality and quantum theory.

To understand the mechanism, consider two particles in an entangled state. We often name the two experimentalists performing measurements Alice and Bob. Before any measurement occurs, the two particles share a single quantum state. When Alice performs a measurement on her particle, the state of the entire system collapses. This collapse has an immediate effect on the state of Bob's particle. Erwin Schrödinger called this phenomenon "steering." For example, if Alice measures her particle's spin in the z-direction, Bob's particle is instantly left in a specific state. If she measures in the x-direction, Bob's system is left in a different specific state. This happens regardless of the distance between Alice and Bob.

This process is often discussed through different types of scientific interpretations. In the orthodox view, Alice's measurement choice directly affects Bob's state. However, if we assume the principle of locality, Alice's actions should not change the "ontic" or true state of Bob's system. Einstein, Podolsky, and Rosen argued that if Bob's state must be compatible with multiple possible outcomes from Alice, the quantum state is incomplete. They suggested that local hidden variables must exist to provide a complete description. One such model is Bohmian mechanics, which uses hidden variables. However, Bohmian mechanics is explicitly nonlocal, meaning it does not satisfy the principle of local action.

History shows that this debate began with the 1935 EPR paper. Albert Einstein, Boris Podolsky, and Nathan Rosen proposed a thought experiment involving spatially separated particles. They used particles with perfectly correlated positions and momenta to challenge quantum mechanics. They believed the theory was incomplete because it violated the classical principle of locality. Their work sparked decades of foundational discussions. Later, in 1964, John Bell provided a mathematical way to test these ideas. He developed Bell's theorem to show that local hidden variables cannot reproduce all quantum predictions. This moved the debate from philosophy to experimental science.

Bell's theorem relies on specific mathematical limits called Bell inequalities. If these inequalities are violated, then reality cannot be described by local hidden variables. Researchers Clauser, Horne, Shimony, and Holt later reformulated these into the CHSH inequality. This version was designed to be much easier to test in a real laboratory. In a CHSH scenario, two parties perform local polarization measurements on photons. Each party chooses between two different polarization directions. If the results match certain probabilistic patterns, the inequality is violated. Experimentalists like Alain Aspect have successfully verified these violations in real-world tests.

There are also stronger versions of nonlocality known as possibilistic nonlocality. While Bell's work is probabilistic, possibilistic nonlocality involves events that are strictly impossible under local theories. In 1993, Daniel Greenberger, Michael Horne, and Anton Zeilinger demonstrated this using the GHZ state. Lucien Hardy also provided a logical proof of this type of nonlocality. These proofs show that local theories cannot even agree on which outcomes are possible. This represents a much more radical departure from classical logic than simple probabilistic differences. It shows that the correlations are even more deeply embedded in the quantum structure.

It is important to note that quantum nonlocality does not allow for faster-than-light communication. This means the phenomenon is compatible with special relativity and its universal speed limit. Because no signal can be sent through these state updates, causality is preserved. Some scientists even argue that the term "quantum nonlocality" is a misnomer because of this compatibility. Despite this, the concept remains vital for understanding how different physical systems relate. It connects the study of individual particles to the broader structure of spacetime and information theory.