No, individual photons do not travel in straight lines along the amplitude of a traveling wave. Photons are quantum particles that exhibit wave-particle duality, meaning they possess characteristics of both particles and waves. While electromagnetic waves, such as light, can be described by a wave-like behavior, the behavior of individual photons is distinct.
Photons, as quantized packets of energy, can be thought of as discrete particles. When they propagate through space, they do so in a probabilistic manner, following a wave-like probability distribution. This distribution describes the likelihood of finding a photon at a particular location.
The direction of travel of a photon is not determined by the amplitude of the wave. Instead, the direction of propagation is given by the direction of the wave vector, which is perpendicular to the wavefronts of the electromagnetic wave. Photons can travel in any direction within the constraints of this wavefront.
Furthermore, photons can undergo various interactions and scattering events as they interact with matter or other particles. These interactions can cause photons to change their direction or be absorbed and re-emitted by atoms or molecules. These behaviors are not determined solely by the amplitude of the wave but depend on the specific properties of the particles involved and the nature of the interaction.