One of the more interesting challenges photon behavior poses to common sense is revealed in the Elitzur-Vaidman bomb tester thought experiment. It is well described on the Internet (for example, here) but a simpler version follows without the bomb. Some of the concepts below assume you have read pages "Wave Particle Duality" or Nonlocality.
A single photon encounters a half-silvered mirror (beam splitter) and divides ("quantum superposition") into two beams along separate paths at right angles to each other, one transmitted and one reflected. Fully reflective mirrors then redirect both paths (beams) so that they intersect out of phase and interfere at a second (half-silvered) beam splitter. The transmitted and reflected paths from this second beam splitter are at right angles to each other and separately lead to two detectors, C and D.
Assuming both paths between the first and second beam splitters are unobstructed then the single photon interferes with itself at the second beam splitter. In this case detector C benefits from constructive interference and receives the photon while the path of detector D suffers from destructive interference and can never receive the photon. However, if one path between the first and second beam splitters is obstructed without your knowledge, then the photon either registers on the obstruction (probability ½) and all paths (beams) collapse, or the photon proceeds to the second beam splitter, encounters no interference, and has an equal chance of registering on either detector C or detector D. Hence for 25 percent of the cases (detections at D) you know a path was obstructed without actually having the photon interact with (terminate upon) the obstruction. In effect you have discovered a fact (obstruction present) without directly ascertaining that fact. This is called "counterfactual" knowledge or interaction-free measurement.
Now the conventional "explanation" for this is that the first beam splitter puts the photon into a state of quantum superposition such that the single-entity photon follows two separate paths without ceasing to be singular and whole. But once the photon is received and superposition ends ("decoherence") we know (actually we assume we know) which path the actual photon took (i.e., the path without the obstruction). Simultaneous with this we have made (25% of the time) a measurement (i.e., obstruction present or not) along the path not taken. "Quantum superposition" obviously doesn’t really explain what is happening to the photon here. Rather quantum superposition is simply an assertion that what was discrete (the photon) is now continuous and quantum decoherence asserts that what was continuous is now once again discrete. This is really Bohr’s complementarity concept "enhanced" by an attempt to pinpoint when transitions occur between particle (field) and wave, between discrete and continuous. Postulating a mathematical "probability wave" for the photon doesn’t help either as it eliminates the distinction between what is physical and what is not.
In fact, there is no such thing as interaction-free measurement. That is unphysical. The photon is an occurring wave of potential mass that can subdivide and rarefy over space without limit while its oscillation (occurrence) in time remains unitary. The fact that the photon crosses over "on one path" does NOT mean that other paths were not taken; in fact all paths were taken by something real, namely waveform potential mass. In the interferometer experiment the obstruction blocks the potential mass wave on one path preventing interference at the second beam splitter.
This thought experiment offers perhaps the best indirect evidence we have of the reality of photon potential mass as a wave. This wave has a physical presence but is inherently probabilistic because of the discontinuous nature of the transition of mass or energy from stored to unstored, from potential/continuous/progressing to kinetic/discrete/extending. As the book details, having a physically real potential mass waveform as the source of probability seems preferable to having a descriptive mathematical wave function in multi–dimensional phase space as the source of probability.