The distinction between quantum mechanics and classical mechanics arises from the fundamental differences in their underlying principles and mathematical descriptions.
Classical mechanics, also known as Newtonian mechanics, is the branch of physics that describes the motion of macroscopic objects such as planets, balls, and everyday objects. It is based on Newton's laws of motion and assumes that particles have definite positions and velocities. Classical mechanics is deterministic, meaning that if you know the initial conditions of a system, you can predict its future behavior with certainty.
On the other hand, quantum mechanics is the branch of physics that describes the behavior of microscopic particles, such as atoms, electrons, and photons. It was developed in the early 20th century to explain phenomena that classical mechanics couldn't account for, particularly in the realm of atomic and subatomic physics. Quantum mechanics introduces probabilistic behavior and wave-particle duality, meaning that particles can exhibit both wave-like and particle-like properties. Instead of definite positions and velocities, quantum mechanics uses wavefunctions to describe the probabilities of finding particles in different states.
The transition from classical mechanics to quantum mechanics occurs when the scales of the system become comparable to the scale of Planck's constant (h), which has a value of approximately 6.626 x 10^-34 joule-seconds. This scale is known as the "quantum realm" or the "quantum regime." In this realm, the behavior of particles is governed by quantum mechanical principles rather than classical laws.
For macroscopic objects, such as everyday objects, the effects of quantum mechanics are negligible, and classical mechanics provides accurate predictions. However, as the system size decreases to the atomic and subatomic scale, quantum effects become more pronounced, and classical mechanics breaks down as an accurate description of the system. At these scales, quantum mechanics becomes necessary to accurately describe and understand the behavior of particles and their interactions.