While it is true that individual photons cannot interact with themselves, the interference pattern observed in the double-slit experiment arises due to the interaction of the photons with the overall probability distribution or wavefunction associated with the system.
In the double-slit experiment, when a beam of photons (or electrons) is directed towards the two slits, each photon passes through one of the slits and then interacts with the screen. The key point is that the overall probability distribution, or wavefunction, describing the behavior of the photons, can interfere with itself.
The wavefunction associated with each individual photon splits into two components as it passes through the two slits. These components then spread out and overlap, creating an interference pattern on the screen. This interference occurs because the wavefunctions associated with the photons can constructively or destructively interfere with each other.
The wave-like nature of the photons is represented by their wavefunctions, which can be thought of as spreading out from the slits and interfering with each other to produce the observed pattern. The interference pattern emerges as a result of the superposition and interference of these wavefunctions.
However, once the photons are detected on the screen, they are localized events, appearing as individual points of detection. This is the particle-like aspect of the photons' behavior. The interference pattern arises from the probabilistic distribution of detections resulting from the interference of the underlying wavefunctions.
It's important to note that the wave-particle duality exhibited by photons (and other quantum entities) can be challenging to reconcile with our classical intuitions. However, quantum mechanics provides a mathematical framework that successfully describes and predicts the behavior of such systems.
In summary, while individual photons do not directly interact with themselves, the interference pattern in the double-slit experiment arises from the interference of their associated wavefunctions, resulting in a probabilistic distribution of detections on the screen.