The wave-like behavior of an arrow and a photon in flight is fundamentally different, and they are governed by different physical principles.
When we talk about the wave-like behavior of a photon, it refers to the wave-particle duality of light, which is a fundamental concept in quantum mechanics. Light can exhibit both particle-like properties (photons) and wave-like properties. The wave behavior of light is described by its electromagnetic wave nature, which includes properties such as wavelength, frequency, and interference patterns. This wave behavior of light is captured by the mathematical description of its wavefunction.
On the other hand, the movement of an arrow through the air is a classical phenomenon and can be explained using classical mechanics, specifically the laws of motion described by Newton's laws. The trajectory of the arrow follows a predictable path determined by the forces acting upon it, such as gravity, air resistance, and the initial velocity imparted to the arrow.
While there may be superficial similarities in the motion of an arrow and a photon, such as their trajectory or propagation through a medium, the underlying physical principles responsible for their behavior are fundamentally distinct. The wave behavior of light arises due to the quantum nature of photons, while the motion of an arrow is described by classical mechanics.