Ehrenfest theorem is a fundamental principle in classical mechanics that states that the average values of the position and momentum of a particle in a quantum system will follow the same equations of motion as those in classical mechanics. This means that classical mechanics can be seen as a special case of quantum mechanics.
Ehrenfest theorem is related to big particles because it was originally developed by Paul Ehrenfest to explain the behavior of macroscopic systems, such as large particles, in quantum mechanics. It was proposed as a way to reconcile the differences between classical and quantum mechanics.
The Ehrenfest theorem is important in classical mechanics because it provides a link between classical and quantum mechanics, allowing for a better understanding of how classical mechanics emerges from the underlying quantum behavior of particles. It also helps to explain the behavior of large particles in quantum systems.
No, classical mechanics does not necessarily need big particles. The Ehrenfest theorem shows that classical mechanics can be derived from the underlying quantum behavior of particles, regardless of their size. However, classical mechanics is typically applied to macroscopic systems, which are made up of many particles, so in that sense, it does involve big particles.
The Ehrenfest theorem has had a significant impact on our understanding of the physical world by showing the connection between classical and quantum mechanics. It has also helped to explain the behavior of macroscopic systems and has allowed for the development of new theories and technologies based on quantum mechanics. It has opened up new avenues of research and continues to be a fundamental principle in modern physics.