The transition from the quantum mechanical regime to the classical regime is known as quantum-classical crossover. It occurs when the behavior of particles or groups of particles becomes dominated by classical physics rather than quantum mechanics. The exact size or mass at which this crossover happens is not precisely defined and can vary depending on the specific system and experimental conditions.
Generally, quantum effects become less significant as the size and complexity of a system increase. This is because quantum mechanics describes the behavior of particles at the microscopic scale, where wave-particle duality, superposition, and entanglement are prominent. On the other hand, classical mechanics provides a good approximation for macroscopic objects where these quantum phenomena are negligible.
The boundary between the quantum and classical realms is not well-defined and is a subject of ongoing research. However, in certain cases, a rough estimate known as the "decoherence limit" is used to characterize the transition. Decoherence refers to the loss of quantum coherence and the suppression of quantum interference due to interactions with the environment.
For example, in experiments with isolated atoms or small molecules, quantum effects can be observed at the nanoscale or even larger. However, as the number of particles and interactions with the environment increase, the system becomes more difficult to describe purely in terms of quantum mechanics. Consequently, macroscopic objects consisting of a large number of particles, such as everyday objects, are typically well-described by classical physics and are not subject to quantum effects.
It's important to note that while quantum mechanics may not be the dominant factor in the behavior of macroscopic objects, it still underlies the fundamental laws of nature. Classical mechanics is, in fact, an approximation that emerges from the more fundamental quantum description at larger scales.
In summary, the precise boundary at which a particle or group of particles is no longer governed by quantum mechanics is not precisely defined. It depends on various factors such as the system's complexity, the level of isolation from the environment, and the specific quantum effects of interest.