TITLE: Is it possible for a wavefunction to partially collpase?
QUESTION [2 upvotes]: What would happen in this situation: You have an ideal empty space with only two objects: a photon emitter, and a small observer. The emitter emits a photon in a random direction, with every direction being equally likely.
Given that the probability of observing the photon travels at the speed of light, what happens at the point when the observer is able to observe the photon? I have come up with two possibilities:

The wavefunction is collapsed everywhere: the possibility of measuring the photon forces the photon to collapse to some random point in the spherical shell of probable locations
The wavefunction only collapses if it collapses onto the observer. Otherwise, the wavefunction will be modified to exclude passing through that point

Is one of these possibilities correct? Or are both wrong? I am completing an introductory quantum mechanics course, and trying to build intuition.
Here is a picture about how I am visualizing the setup:

REPLY [1 votes]: The wavefunction only collapses if it collapses onto the observer. Otherwise, the wavefunction will be modified to exclude passing through that point

That's correct, except that what you called "modified" is also a collapse. The case where the photon is not detected, but the wavefunction nonetheless is modified/is updated/collapses to a state reflecting its non-detection, is called interaction-free measurement.

The wavefunction is collapsed everywhere: the possibility of measuring the photon forces the photon to collapse to some random point in the spherical shell of probable locations

This would happen only if you had a detector everywhere on the sphere. "Complete" position measurements where there's a detector everywhere are the norm in introductory quantum mechanics courses, but they never happen in the real world.
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