The law of large numbers and decoherence are important concepts in understanding the emergence of classical behavior from quantum processes, but they do not provide a complete explanation on their own. Physicists are still actively exploring and investigating the nature of this transition, known as the quantum-classical boundary or the measurement problem.
The law of large numbers is a statistical principle that describes the convergence of the average of a large number of independent and identically distributed random variables to a predictable value. It ensures that macroscopic objects, composed of an enormous number of particles, exhibit behavior that appears deterministic and classical. However, the law of large numbers alone does not fully explain why classical behavior emerges from quantum mechanics on a macroscopic scale.
Decoherence, on the other hand, refers to the process by which a quantum system interacts with its environment, leading to the loss of coherence and the emergence of classical-like behavior. When a quantum system interacts with its surrounding environment, the entanglement between the system and the environment grows, causing the quantum superposition to break down and become effectively classical. Decoherence plays a crucial role in understanding why macroscopic objects appear classical in our everyday experience.
While the law of large numbers and decoherence provide important insights into the classical limit of quantum mechanics, they do not address some fundamental questions associated with the measurement problem. The measurement problem refers to the challenge of understanding how a definite measurement outcome arises from the superposition of multiple possibilities in quantum mechanics.
Many interpretations and theories have been proposed to address the measurement problem, such as the Copenhagen interpretation, the many-worlds interpretation, and various forms of quantum interpretations involving objective collapse or hidden variables. However, there is still ongoing debate and active research in this area, as no single interpretation has been universally accepted or definitively proven.
In summary, while the law of large numbers and decoherence offer valuable explanations for the emergence of classical behavior, physicists are still searching for a complete understanding of how the classical world arises from quantum processes. The measurement problem remains an open and active area of research in quantum foundations.