A photon certainly appears to travel in spacetime, relative to an observer. But could it also be completely stationary (relative to the observer and the entire universe), and that its the medium that causes the relative motion?
A piece of flotsam in the middle of the Pacific Ocean has no velocity in and of itself. Over time, its path of movement may exhibit wave-like properties, but this behaviour is also NOT a property of the flotsam.
Precisely. Light is part of the electromagnetic spectrum. A photon is simply a particle with zero mass at rest.
To say the wave-like property belongs to light is essentially describing a property of the electromagnetic field.
The photon is the particle. The field is the wave. Where is the duality, other than photon being bound to the field?