The concept of "evolution relative to the <PERSON> equation" is an insightful means of considering your questions via a holistic interpretation of the reality to which most of modern physics seems to point. One should recognize that interacting with a measurement device is another aspect of interacting with "the world". This concept of the photon as a wave "interacting with the world" over "many paths" simultaneously is a much more significant element of determining the final outcome of all the interactions in which what we are taught to think of as a photon is involved than a semi-classical interpretation of the photon as a particle some of the time and a wave some of the time might suggest. (What we call a photon is, fundamentally, no more than our perception of the localization of a collection of properties associated with specific, quantum fields via a mode of "bundling" that interact in a pre-defined manner with particles with specific properties.)
"The world" exists in a multi-dimensional framework that includes time. "The world" evolves in time, as must all experiments performed in "the world" that we detect as beings made of matter. The perception of a wave function as being uniquely linked to one photon that is somehow in one position in some temporal interval associated with measurement in a detector may be one cause of the questions that have been posed. Stop thinking of photons as highly localized in space and time in the same manner that one might think of a little ball as being highly localized in space and time when what is called a photon is, in fact, better conceived as a disperse, wave-like field that interacts with localized objects called atoms that we have learned to use to make what we call "particle detectors" (using a concept based on classical thinking).
The stuff that we use to interact with the photon in a detector is in a complex form that we call "an atom". 800
Because it is in this complex, atomic system, it is bound by rules that are defined by quantum physics relative to energy states and other particle properties. The photon in free space (in the classic, quantum description of what physics calls a "photon") is a free agent until it "gets mixed up" with the particle "crowd" that comprises the atom. The atom has a great deal of mass relative to the "photon", and it has a great deal of power to produce what we perceive as localized phenomenon in time and space, because the atom is, due to its mass (and, formally, momentum), a relatively localized phenomenon.
Re-think the photon crudely as electro-magnetic energy in the environment (manifested in quantum fields) that is bundled by an atom due to the atom's relatively high momentum, which forces its probability wave to be relatively localized. Think of the electro-magnetic energy of what we call a "photon" as being highly interactive with "the world" until it has sufficiently interacted with the particle detector's energy "bundling" atoms to produce a result. At that point, we get some output data from the machine.
Because of the highly interactive nature of the photon with the world around it given its "many paths" aspect, we may find the results a bit surprising if we are too used to digging a rut in the same logical path by forming what one author described as "cog-webs" that define the photon as a particle some of the time. If we think of detection of a photon by a measurement device as a means of localizing ("bundling") electro-magnetic energy that is disperse in the environment (that follows "many paths" that overlap with other photons' "many paths"), and think of the speed of light as the rate at which electro-magnetic energy can be localized by atoms (with mass) to produce quantized changes in energy in things called atoms that we can use to detect the electro-magnetic energy in the environment, then it might come as no surprise that we begin to gather data about the environment that exceeds our expectations in some three-dimensional, directional sense in a given, laboratory experiment.
If we use an electro-magnetic energy source in a particular position sending energy in a more or less directional manner to provide most of that electro-magnetic energy being put into a given environment in which an experiment is occurring, it should come as no surprise that we detect information that is biased relative to a specific directional thumb-print in space and time, because most of the energy we gather carries a certain amount of information due to its point of origin, and objects in the related path. Because we are gathering electro-magnetic energy from the environment, should we expect all of the information reflected in what we call "a signal" to originate from one direction? 800