Quantum physics applies to those realms of our existence for which we have no classical anology, no mechanical model to explain the observations of classical experiments. In one respect, Quantum physics begins with a contradiction, in that the phenomenon that it attempts to describe are built upon a classical framework, the experiment itself. The problem is the discontinuity between classical notions of what a particle should be and the results of the experiment itself. Perhaps, in that respect, particle-wave duality is an important cause of the discontinuity. Quantum theory attempts to project the nature of particles away from any concept of what they might be in a classical sense, since no model or inherent understanding of their internal nature yet exists, into a projection of what that entity as a whole accomplishes. While it begins in one sense with an uncertainty, it ends with a probability that something will occur, that a particle will follow a certain path of uncertainty to a position that we know as a fact, within uncertainty...
The necessity of quantum theory arose from the blackbody radiation, wherein the constant h was described by Planck. This is the first place where our classical ideas, mechanical models, failed to describe the nature of the observation. The work of Einstein in the photoelectric effect, showed that light was packaged, again, an idea with no classical foundation. Bohr and others attempted to use these concepts to explain the nature of the spectrum of light emitted by atoms, but every attempt that they made to use classical constructs led to failure. Eventually, it was realized that a successful approach might be reached if we disconnect ourselves from the need for classical analogy, interpretations of what is occurring in a modular sense, and just accept the mathematical treatment of quantum physics and the results it is able to reproduce.
From a classical perspective quantum physics is a mathematical projection of a realm of our existence that we cannot describe with a rational classical model.