I am currently studying the textbook The Quantum Theory of Light, third edition, by R. Loudon. In the introduction, the author says the following:
In the customary photon description of quantum-optical interference experiments, it is never the photons themselves that interfere, one with another, but rather the probability amplitudes that describe their propagation from the input to the output. The two paths of the standard interference experiments provide a sample illustration, but more sophisticated examples occur in higher-order measurements covered in the main text.
The first sentence is a bit unclear. Is the author saying that it is never the photons themselves that interfere with one another, but rather the probability amplitudes (of the photons) that interfere with each other (which sounds weird, since the photons themselves are probability amplitudes, right?)? Or is the author saying that the photons (in the form of probability amplitudes) never interfere with each other at all, and that the photon propagation from input to output is fully described by the probability amplitude (that is, photons do not affect each other at all)? Or is it saying both?
I would greatly appreciate it if people would please take the time to clarify this.