1.1 Introduction

Despite the many successful applications of classical mechanics (based on Newton's famous laws of motion) to a wide range of physical phenomena, it was apparent at the beginning of the last century that many of the known phenomena could not be explained in terms of the concepts of classical mechanics. To meet the challenge of these classical inexplicable observations, a complete new theory, quantum mechanics, was developed. The basic underlying assumptions of quantum theory are quite different from those of classical mechanics, and they constitute a fundamentally different way of looking at nature.

Quantum mechanics provides precise answers to many problems, but it tells only the average value of many individual measurements made on a given dynamical system in a certain initial state. One of the fundamental differences between classical mechanics and quantum theory is that in quantum mechanics it is not possible to measure all variables with specific accuracy at the same time, while in classical mechanics it is. Another difference is that classically, the effects of the disturbances due to the measurements can be exactly allowed in predicting the future behavior of the system, whereas quantum mechanically the exact effects of the disturbances accompanying any measurements are inherently unknown. For example, in quantum mechanics the measurement of the position of a particle introduces an unpredictable uncertainty regarding its momentum.

Early examples of observations that required a revision of classical mechanics are numerous. We will discuss a few of them here.