On the wave function collapse

A photon interacts with the environment when it hits an atom and is absorbed. Some aspects of this are not obvious. It does not always cause decoherence. For example in reflection, incoming photons are absorbed and new photons are emitted. In this case, the new photons the phase and wavelengths are related to the original (E.G. $180^o$ phase shift on reflection.)

This kind of interaction is not always with a single atom. A wave is reflected at the same angle to a surface as an incoming wave. It takes many atoms to define a surface. In a metal, conduction electrons are spread out across many atoms. It is the interaction with these electrons that cause the reflection. In a dielectric mirror, electrons are bound to atoms. It is the interaction with many atoms in multiple layers of the mirror that generate the reflection.

Transparent mediums also interact with the photons that pass through them. But they come out the other side with the same wavelength and a phase that can be calculated from the original. So the the double slit experiment can be carried out in air or have a window in it.

Photons are described by wave functions. They are spread out. When they pass though the slits, there is a chance they will be absorbed and a chance they will pass through. If they do pass through, the wave function on the other side is consistent with them having passed through. So even though they are not absorbed, they are affected.

reduces to a single eigenstate due to interaction with the external world.[emphasis mine]

Here is the problem - the wave function reduction (collapse) is invoked not due to just interaction with the external world. Some interaction is necessary to create/find new facts about the system, which then imply collapse, but mere interaction itself is not sufficient.

Interaction can and often happens in time without any creating or learning new facts about physical quantities (shortly, without any measurement going on), and thus with no reason to invoke collapse. For example, we may calculate how external EM field interacts with electrons in an atom, derive oscillation of populations and coherences (non-dissipative Rabi oscillations) - all continuous, deterministic evolution, no collapse required.

We invoke collapse only in some situations when we are forced to do so, either due to 1) learning value of a quantity that is not compatible with our idea of a quantum state, obtained either by state preparation or by calculating future state from Schroedinger's equation; or 2) a belief that such values are being created, even if we do not know their values.

For example, the first case: when we learn that an atom, which enters a Stern-Gerlach (SG) magnet with initial spin state $|x+\rangle$, exits in direction corresponding to spin state $|z+\rangle$ and continues to another part of the experiment, we change the spin state to $|z+\rangle$ right when we learn that fact. We do this at this time not because this is when some objective state of the atom spin changes (the natural assumption is that it changes some time before we detect the change), but because we want to keep the quantum state in our real-time description compatible with the new fact, and predictive for next experiments. If we want to think of the quantum state as property of the atom itself (orthodox quantum theory), as opposed to as just a mathematical and probabilistic description of the experiment, we have to assume objective collapse happened some time before we learned about it, probably at some point when the atom is near the SG magnet.

Thus the failure of Schroedinger's equation for the spin state and the need for collapse of the spin state are forced on us by the behaviour of quantum systems with spin when measuring the spin projection value.

Again, this is not just due to interaction with magnetic field; as long as we do not learn the direction of the atom motion after leaving the SG magnet (and thus we do not know the spin projection value), we have no reason to use collapse.

For example, if the atom moves slowly, and the field gradient is weak enough, there won't be any detectable splitting of the atoms into two directions. Then, we describe the spin state evolution in time, taking into account the interaction with magnetic field of the SG magnet, by Schroedinger's equation(Pauli's variant). We obtain a prediction that the spin state performs precession, in agreement with the classical idea of the Larmor precession of a magnetic moment - the tip of the vector representing the spin state orbits around the external magnetic field, the stronger the field, the faster the orbiting. No reason to invoke collapse then.

Take the good old Double Slit experiment for instance. Even in this simple case, there are a few unclear behaviours I can't explain to myself rationally. Usually, such an experiment is performed in a dark environment. The reason for this, I believe, is just to see more clearly the interference pattern on the screen. But of course, the environment is not shielded completely, there is still some kind of radiation floating around, as long as the temperature is above absolute zero. The particle involved doesn't seem to care about it though. It's as if somehow it manages to distinguish, say, a photon of the background noise from that of a measuring device, and chooses to interact with the latter and not with the former.

Quantum theory has specific equations of motion such as the Schrodinger equation that aren't compatible with collapse.

There are alternatives to quantum theory that feature collapse:

https://arxiv.org/abs/2310.14969

but those theories don't currently reproduce the predictions of relativistic quantum theories and so don't account for the vast bulk of experimental results predicted using quantum theory:

https://arxiv.org/abs/2205.00568

In unmodified quantum theory when information about a measured system is copied out of the system that interaction suppresses interference: this effect is called decoherence. If an interaction with a system is weak enough then it acts a bit like a small but non-zero probability of preventing interference. This tends to diminish the interference without completely eliminating it. This effect has been observed in real experiments: see section 6 of Schlosshauer's review on decoherence:

https://arxiv.org/abs/1911.06282

So in both theory and practice a particle will care about the environment to the extent that the environment copies information out of the particle.

We first have to note that:

1. Our current best theory for quantum behavior is quantum field theory (QFT). In that theory the state of a system sometimes acts like a wave, but never like a classical point particle.
2. In addition, the collapse of the quantum state is not incorporated in QFT, it is just a postulate that some people believe in. There never has been a widely accepted theory in which it actually happens, all such ["objective collapse theories"] are plagued by inconsistencies, like violating energy conservation or relativistic invariance.
3. There is no compelling reason to insist that there has to be a collapse (as it once was), since nowadays we know that [einselection] can describe an apparent collapse, where in reality the superposition of many states simply remains in existence.

Still your questions about the double-slit experiment can then be translated to: Why does the EM quantum field act like a wave when light passes through a double slitted screen? And why does einselection lead to the observed result, i.e. the dots on the photographic plate with the pattern of dark and light fringes?

These questions are difficult to answer since QFT is a difficult theory as soon as more than a few particles are involved. If you look at the links I gave, you'll quickly find out that you have to delve into a lot of mathematics an fundamental physics to find out more.

And strangely, questions like this are always downvoted and quickly closed on physics SE. I do not understand why, but anyhow I'll quickly post this (admittedly incomplete) answer before closing occurs!