To me, it seems that the interference pattern is the evidence that the wave function is a physical aspect of reality, but people still seem to be trying to decide whether or not it's ontological or just a mathematical construct.
Why is the double slit experiment not considered proof that the wave function is ontological?
In general, we can never prove anything is ontology because systems can always be simulated in multiple ways. We only have access to perceptions, sensory experiences. We build a mental model of some external reality (the 'ontology') that explains how those perceptions arise, but the behind-the-scenes reality can look quite different to the perception. Appearances can be deceiving.
In the case of the measurement problem, we have a conflict between two different ontologies that seem to arise naturally from our perceptions. There is the 'wave' picture, where the wave passes through both slits at once, and the 'particle' picture, where the particle can be in only one place at a time. Our perceptions appear to 'prove' both of them at once. If the wave collapses to a particle flash at one end of the screen, somehow it knows not to do so at the other end of the screen, even if there is no time for any lightspeed signal to get there, and which in general leads to all sorts of weird backwards-in-time causal paradoxes in the ontology. We can just as easily say that the only-ever-observed-in-one-place-at-a-time behaviour 'proves' a particle ontology.
At least one of these appearances is deceptive. Either the ontology is a wave which somehow gives the appearance of only ever being in one place at a time, or the ontology is a particle which somehow gives the appearance of being in several places at once. We can't take either argument for granted.
Some people say that the particle picture is the deception, that is caused when the wave of the photon interacts with the wave of the observer, correlating them, so the observer becomes a superposition of orthogonal mutually-non-interacting states, in each of which the photon is only seen in one place. Some people say that both proposed ontologies lead to intuitively unacceptable conclusions, both proposed ontologies could be deceptive appearances of some other ontology we haven't yet thought of, we can't possibly find out by any conceivable experiment, and so there's no point in wasting time speculating. It's not a scientific question.
To believe we have answered the question of ontology, we need an explanation that explains everything about what we have observed. If it's a wave, how and why do we only ever see a single flash in a single location? By what mechanism does one part of the screen know not to flash because another part is about to? You can't say this part proves it's a wave, and then just wave away the parts that 'prove' it's a particle. Nobody has yet managed to produce an explanation that fills in all the details to everybody's satisfaction, so the debate goes on.
The wave function is a projection of the more abstract state vector onto position space. If you want to say that the wave function is a "physical aspect of reality", then naturally you have to say that any other space one can project the state onto (momentum, energy, angular momentum, etc.) is also a "physical aspect of reality". Sometimes these spaces can even be discrete. What makes this even more interesting is that you can project state vectors onto spaces that don't represent physical observables as well.
I like to give the analogy of vectors in classical mechanics. We use vectors to describe many things in classical mechanics (position, velocity, force, etc.). We can use formalism that relies on vectors to make very nice predictions and verifications about how the world works. Does this mean that vectors are "a physical aspect of reality"? I think most people would relegate vectors to be "mathematical tools" rather than things that physically "exist".
In any case, not everyone even agrees on what "a physical aspect of reality" is. Even if we did, at best ask we can say is that Quantum Mechanics is a successful model that gives correct results. It doesn't give us a "physicality rating" of what is used, and the fact that we have many interpretations of Quantum Mechanics that model things differently yet give the same result indicates that maybe there is more we have yet to (or may never) learn and understand.
Even classical physics predicts a wave pattern on the screen when you do the double-slit experiment with light. Not all waves are wave functions. In fact, any wave that you can see isn't a wave function. The wave function encodes the probabilities of various measurement outcomes before measurement happens. To say that it's real amounts to saying that the measurement outcomes that don't happen, and that you don't see, have some sort of reality as well.
The wave function is a way of representing a pure quantum state of a system. Quantum states are the key mathematical objects in quantum mechanics but there is still some debate concerning what a quantum state represents.
The Pusey-Barrett-Rudolph no-go theorem is a (debated) result proposed in 2012. It is of significance for how one may interpret the nature of a quantum state: it rules that pure states must be "ontic" (they correspond directly to states of reality), rather than "epistemic" (they represent probabilistic, or incomplete, states of knowledge about reality), see also:
The original paper is On the Reality of the Quantum State (journal: Nature Physics, arxiv version here). There are claims that the theorem is supported experimentally: Experimental test of the no-go theorem for continuous ψ-epistemic models.
Among the many attempts to show the reality of the quantum state, the Pusey-Barrett-Rudolph theorem seems to get recognition. However, some of its assumptions are criticized, and it's still not considered to be entirely free of loopholes: Is the Quantum State Real in the Hilbert Space Formulation?
The review Is the quantum state real? An extended review of ψ-ontology theorems contains some consideration on the double-slit experiment. In a realist picture, something "wavelike" needs to exist in order to explain the interference fringes (the obvious candidate is the wave function!). However, interference phenomena occur also in some of the ψ-epistemic models (like the Spekkens toy model). Therefore, the inference from "there is interference" to "the wave function is real" is incorrect (i.e. interference is not enough).
Moreover, regarding the double-slit, there is also some discussion in Double slit experiment and single particles. Is the wave function just a mathematical model?
Galileo's experiments established that falling objects (outside the celestial domain) had a universal downward acceleration. Did that make the universal acceleration "ontological"?
But then, Newton found a different theory of gravitational force, and that very precisely included celestial motions. So, was the universal force of gravity "ontological"?
And then, Einstein came up with his force-free geometric theory, and experiments and observations demonstrated that it's more accurate than Newton's.
History suggests that no theory of physics is ever the final word. Nature doesn't give us axioms, it gives us phenomena. Only a small part of reality is accessible to our experiments and observations, so who can say that any theory encompasses all phenomena?
The double-slit experiment is a famous experiment in quantum mechanics that demonstrates the wave-particle duality of matter and the fundamental role of the wave function in determining the behavior of quantum systems.
In the double-slit experiment, a beam of particles, such as electrons or photons, is directed at a barrier with two slits. The particles pass through the slits and interfere with each other, creating an interference pattern on a detector behind the barrier. The interference pattern is characteristic of a wave-like phenomenon and can only be explained by the wave nature of the particles.
The wave function, which describes the probability distribution of the particles, plays a crucial role in determining the interference pattern observed in the experiment. The wave function is a mathematical object that is not directly observable, but its square modulus gives the probability density of finding the particle at a particular location.
However, the fact that the wave function determines the probability distribution of the particles does not necessarily mean that the wave function is ontological, meaning that it represents a real physical property of the system. There are different interpretations of quantum mechanics, and some of them interpret the wave function as an epistemic or subjective concept rather than an ontological one.
In summary, the double-slit experiment demonstrates the wave-particle duality of matter and the fundamental role of the wave function in determining the behavior of quantum systems. However, it does not necessarily prove that the wave function is ontological, as there are different interpretations of quantum mechanics that view the wave function as an epistemic or subjective concept rather than a physical property of the system.
