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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?

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    $\begingroup$ Seems you are splitting hairs at best. Why is an ontological construct necessarily distinct from a mathematical construct? Both are metaphysical in various ways. $\endgroup$
    – Jon Custer
    Feb 18, 2023 at 2:00
  • $\begingroup$ From what I understand, it depends on how you interpret quantum mechanics: en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics $\endgroup$
    – hermancain
    Feb 18, 2023 at 2:11
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    $\begingroup$ As I understand it, "ontological" means "physically real", as opposed to just being a mathematical construct we use to model the quantum state. $\endgroup$
    – hermancain
    Feb 18, 2023 at 2:40
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    $\begingroup$ What does "physically real" mean? $\endgroup$
    – WillO
    Feb 18, 2023 at 2:43
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    $\begingroup$ I don't think the question is meaningful. "The particle has wave nature" and "observations about the particle can be predicted using a wave function" mean the same thing. Obviously the wavefunction itself is only as real as any other idea - if you bite it, you'll taste a physicist, not a particle. $\endgroup$
    – g s
    Feb 18, 2023 at 4:34

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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.

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    $\begingroup$ There's also the possibility that both views are true simultaneously, i.e. the de-Broglie - Bohm interpretation. $\endgroup$
    – patstew
    Feb 18, 2023 at 10:27
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    $\begingroup$ "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" If each quantum creates one flash, I'd expect the number per unit time to fit a poisson distribution. If one quantum can create multiple flashes, then I'd expect a poisson distribution for the number of flashes during the time one quantum arrives. So how long does it take a single quantum to pass the detector? If it takes a second, then we should have one quantum arrive every 10 seconds and measure the number of flashes during each second. $\endgroup$
    – J Thomas
    Feb 18, 2023 at 15:10
  • $\begingroup$ @JThomas actually the quanta are not released in such nice intervals either. Which gives rise to a hypothesis: what if the timing of the flashes of energy on the screen is completely uncorrelated to the timing of the flashes of energy that go missing from the source, that is, what if there is simply a wave that randomly creates flashes proportional to its intensity, with no particle knowledge? Though, entanglement experiments probably disprove this idea, as two screens flash simultaneously. $\endgroup$
    – user253751
    Feb 19, 2023 at 20:51
  • $\begingroup$ I predict that if it's just a wave and the flashes come at random times when individual crystals on the film or photodetector cells are ready to go, then it should fit a poisson distribution. If it's individual photons that leave the source randomly, uncorrelated, and each of them triggers at most one detector, the same. But if each photon travels like a wave and can interact with multiple detector cells or crystals, then the distribution could be different. You could get multiple detections at the same time, and if detections happen rarely, it wouldn't be poisson. $\endgroup$
    – J Thomas
    Feb 21, 2023 at 0:07
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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.

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    $\begingroup$ >"I think most people would relegate vectors to be "mathematical tools" rather than things that physically "exist"." Okay I don't believe mathematical constructs exist, but If particles form an interference pattern when not observed, isn't that evidence that the system actually exists in a quantum state, that can be accurately described by the wave function? $\endgroup$
    – hermancain
    Feb 18, 2023 at 3:04
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    $\begingroup$ @hermancain What do you mean by that interference pattern forming when not observed? Detecting particles at the screen is a measurement. $\endgroup$ Feb 18, 2023 at 3:18
  • $\begingroup$ @hermancain In any case, what you describe means we have a successful model. It doesn't tell us what is "real". Indeed, even different interpretations of Quantum Mechanics can lead to different ideas of what is "real" $\endgroup$ Feb 18, 2023 at 3:38
  • $\begingroup$ @hermancain "isn't that evidence that the system actually exists in a quantum state, that can be accurately described by the wave function" - sure, there's quantum mechanics involved, but what BioPhysicist is trying to say (I think, please correct me if I'm wrong), is that you could also say "if a ball falls down to the ground when released, isn't that evidence that there is gravity, that can be accurately described by a force vector field?" Yes, there is gravity, but the question "Is the wavefunction real?" is in some sense equivalent to "Is a vector field real?" 1/2 $\endgroup$ Feb 18, 2023 at 23:01
  • $\begingroup$ @hermancain - It's a description of something real (or of an aspect of it) - but it's unlikely that there are invisible arrows scattered throughout space that affect acceleration on objects (and in fact, there's an entirely different picture afforded to us by general relativity, where you instead have objects following geodesics in curved spacetime). The point is, one should not be too attached to a particular description. 2/2 $\endgroup$ Feb 18, 2023 at 23:01
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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.

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  • $\begingroup$ +1 this is my take. But a large (sometimes I think majority) of people do think the outcomes that don't happen are real in the "many-worlds" interpretation. $\endgroup$ Feb 18, 2023 at 19:59
  • $\begingroup$ The fact that there are probabilities to encode means that the wavefunction encodes (or models) some aspect of reality that gives rise to these probabilities. So, saying that the wavefunction is in some sense real doesn't necessarily amount to saying that the measurement outcomes that didn't happen are real (e.g., you don't need to invoke many-worlds), it just means that there is some underlying mechanism that can be described by the wavefunction at our current level of understanding. It abstractly captures an aspect of reality (= has predictive power, and this is experimentally validated). $\endgroup$ Feb 18, 2023 at 22:46
  • $\begingroup$ 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 that's quite a common thought in QM $\endgroup$
    – TKoL
    Feb 21, 2023 at 16:47
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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:

What are the differences between a $\psi$-epistemic ontological model and a $\psi$-ontic model of quantum mechanics, exactly?

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?

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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?

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    $\begingroup$ I can agree that there are things to discover and our knowledge is, and will probably always be, incomplete, but I still think it's useful to ask, "Does this tell us anything about reality, at all?" The wave function itself may have some fundamental or emergent relationship to something "real", or perhaps it doesn't, but we have the double slit experiment, we have the mach-zender interferometer, we have Bell's Theorem and the experiments that surround it - surely all of these things tell us something about reality. Even if that something is hazy and hard to make out. The question is, what? $\endgroup$
    – TKoL
    Feb 21, 2023 at 16:51
  • $\begingroup$ Galileo's experiments told us something about reality, the experiments that verified Newton's approach did too, and the experiments that verified relativity did too. The didn't give us perfect information of 100% certainty about just about anything, but they seem to tell us something. $\endgroup$
    – TKoL
    Feb 21, 2023 at 16:52
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    $\begingroup$ @TKoL The experiments distinguish between models that work in the tested domain, and models that don't. When I go hiking, I take a map, and the map tells me things about the territory. Still, the map isn't the territory. A good model, like a good map, is a joy, but it isn't reality. $\endgroup$
    – John Doty
    Feb 21, 2023 at 17:59
  • $\begingroup$ the map tells me things about the territory sure, that's exactly what I mean when I say they tell us something about reality. They aren't reality itself (although it's not out of the question that some aspect of some model could be computationally identical to something truly real). $\endgroup$
    – TKoL
    Feb 22, 2023 at 9:12
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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.

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