Physicists talk about wave-particle duality because it is a fundamental concept in quantum mechanics, which describes the behavior of particles at the microscopic level. Wave-particle duality refers to the fact that particles, such as electrons and photons, can exhibit both wave-like and particle-like properties under certain circumstances.
In classical physics, such as Newtonian mechanics, particles are described as having definite positions and velocities. Newton's law of gravity, for example, provides a deterministic description of the gravitational force between objects based on their masses and distances.
However, at the quantum level, the behavior of particles is fundamentally different. Quantum mechanics introduced the concept that particles, such as electrons and photons, can also exhibit wave-like properties. This means that they can exhibit characteristics such as interference, diffraction, and superposition, which are typical of waves.
The wave-particle duality is often illustrated by the famous double-slit experiment, where particles like electrons or photons are shown to exhibit interference patterns similar to waves when passed through two slits. This experiment highlights the dual nature of particles, suggesting that they can behave as both particles and waves.
The mathematical formulation of quantum mechanics, which utilizes complex numbers and wave functions, provides a powerful framework to describe and predict the behavior of particles at the quantum level. It allows for the calculation of probabilities and predictions of particle behavior in terms of wave-like properties.
While Newton's gravitational law is a classical description of gravity and is based on real numbers, it does not fully capture the behavior of particles at the quantum level. The differences you mentioned, involving complex numbers and the wave-particle duality, arise because quantum mechanics provides a more accurate and comprehensive description of the behavior of particles at the microscopic scale.
Einstein's theory of general relativity, on the other hand, provides a framework for understanding gravity at the macroscopic scale, where the effects of gravity are significant, such as the behavior of massive objects and the curvature of spacetime. It is a theory that unifies gravity with the geometry of spacetime and is distinct from the quantum mechanical description of particles.