The framework for formulating the physical laws that govern the world at microscopic length-scales – the physics of the micro-world, for instance of atoms, atomic nuclei or elementary particles, but also the physics of ultra-precise measurements such as those made by gravitational wave detectors.
The laws of quantum theory are fundamentally different from our everyday experience and from those of classical physics.
The first unusual feature is that, in many cases, quantum theory merely allows statements about probabilities. For instance, in classical physics, one can assign to every particle, at every point in time, a location and a velocity. Whosoever can measure those quantities precisely can, in principle, predict where the particle in question can be found at every point in the future. In quantum theory, all one can assign to a system of particles is an abstract quantum state from which can be derived no precise predictions, but merely the probabilities for detecting a specific particle at a given time in a given place. Whether or not one will really find the particle at that location is governed by chance.
The second unusual feature is a fundamental restriction placed on the exactness of certain measurements (Heisenberg uncertainty relation). For instance, the more precise one measures a particle’s location, the less definite any statements one can make about its velocity.
The third feature is how quantum theory came by its name: A number of physical quantities in nature come in little packets, in quanta. For instance, according to quantum theory, electromagnetic radiation is made of tiny quanta of energy called photons.