The principle of superposition in wave mechanics states that when multiple waves are present in a system, the resulting wave is the algebraic sum of the individual waves. This means that waves can indeed pass through each other without directly disturbing each other.
However, when it comes to the creation of a new particle, it is important to distinguish between the behavior of waves and the behavior of particles in the context of quantum mechanics.
In quantum mechanics, particles are described by wave functions, which are mathematical representations that contain information about the particle's properties, including its position, momentum, and other observable quantities. The wave function evolves over time according to the Schrödinger equation.
When two or more particles combine or interact, their respective wave functions can indeed overlap and interfere with each other. This interference can result in the creation of a new particle or a change in the properties of the existing particles involved.
For example, in certain particle physics experiments, high-energy collisions can occur between subatomic particles. These collisions can lead to the creation of new particles as a result of the interaction between the initial particles' wave functions. The wave functions of the incoming particles overlap, and through quantum processes, such as particle decays or annihilation, new particles can be produced.
However, it's important to note that in these cases, the creation of a new particle is not simply the result of the combination of classical waves like water waves or sound waves. The behavior of particles and the creation of new particles involve quantum processes and are described by quantum field theory, which goes beyond the classical wave behavior described by the principle of superposition.
In summary, while the principle of superposition applies to waves and their interference, the creation of a new particle involves quantum processes that go beyond the classical wave behavior and are described by the principles of quantum mechanics and quantum field theory.