The wave-like nature of particles, as described by the wave-particle duality, does not imply that there is a physical entity "doing the waving" in the classical sense. It's a mathematical description that captures the behavior and properties of particles at the quantum level.
In quantum mechanics, particles are described by wavefunctions, which are mathematical functions that represent the probability distribution of finding a particle in different states. The wavefunction evolves over time according to the Schrödinger equation, which describes the dynamics of quantum systems.
The wave-like behavior of particles can be understood in terms of interference and superposition. Just as waves can interfere constructively or destructively, particle waves can also interfere with each other, resulting in patterns of constructive and destructive interference. This phenomenon is observed, for example, in the double-slit experiment, where particles exhibit an interference pattern similar to that of waves.
However, it's important to note that the wave-like behavior of particles should not be interpreted as a physical wave propagating through space. The wavefunction represents the probability distribution of a particle's properties, such as position or momentum, rather than an actual physical wave in the classical sense.
The nature of wave-particle duality and the behavior of quantum systems is still a subject of ongoing scientific research and interpretation. While we can describe and predict the behavior of particles using mathematical formalism, the underlying nature of quantum phenomena is still a topic of exploration and debate in physics.