The classical limit refers to the situation where the behavior of a quantum system becomes indistinguishable from classical physics when observed at macroscopic scales. In other words, quantum predictions converge to classical predictions as the size, complexity, and number of particles involved in a system increase.
The reason why quantum phenomena appear to vanish at the macroscopic scale is primarily due to a process known as decoherence. Decoherence refers to the interaction of a quantum system with its environment, leading to the loss of coherence and the emergence of classical-like behavior. When a quantum system interacts with its surroundings, the delicate superpositions and quantum entanglement that are characteristic of quantum behavior become more difficult to maintain.
Environmental factors such as temperature, electromagnetic fields, and interaction with other particles can cause the quantum state of a system to rapidly spread and become entangled with the environment. As a result, the system effectively behaves as a classical system, with distinct, well-defined states rather than exhibiting the wave-like behavior and superposition associated with quantum mechanics.
Additionally, macroscopic objects are composed of an enormous number of particles, each with their own quantum states. The interactions and entanglement among these particles can quickly become extremely complex and challenging to describe quantum mechanically. As the number of particles increases, the sheer complexity of quantum calculations required to describe the system becomes computationally intractable, leading to the use of classical approximations.
While the exact mechanisms and boundaries of the classical limit are still areas of ongoing research, the phenomenon of decoherence provides a fundamental understanding of why quantum phenomena tend to vanish at macroscopic scales. However, it's important to note that there are instances where quantum effects can still be observed at larger scales, such as in certain condensed matter systems or under specific experimental conditions.