What is it then? If you say it’s a wave, well, that wave is in Hilbert space which is infinitely dimensional, not in spacetime which is four dimensional, so what does it mean to say the wave is “going through” the slit if it doesn’t exist in spacetime? Personally, I think all the confusion around QM stems from trying to objectify a probability distribution, which is what people do when they claim it turns into a literal wave.
To be honest, I think it’s cheating. People are used to physics being continuous, but in quantum mechanics it is discrete. Schrodinger showed that if you take any operator and compute a derivative, you can “fill in the gaps” in between interactions, but this is just purely metaphysical. You never see these “in between” gaps. It’s just a nice little mathematical trick and nothing more. Even Schrodinger later abandoned this idea and admitted that trying to fill in the gaps between interactions just leads to confusion in his book Nature and the Greeks and Science and Humanism.
What’s even more problematic about this viewpoint is that Schrodinger’s wave equation is a result of a very particular mathematical formalism. It is not actually needed to make correct predictions. Heisenberg had developed what is known as matrix mechanics whereby you evolve the observables themselves rather than the state vector. Every time there is an interaction, you apply a discrete change to the observables. You always get the right statistical predictions and yet you don’t need the wave function at all.
The wave function is purely a result of a particular mathematical formalism and there is no reason to assign it ontological reality. Even then, if you have ever worked with quantum mechanics, it is quite apparent that the wave function is just a function for picking probability amplitudes from a state vector, and the state vector is merely a list of, well, probability amplitudes. Quantum mechanics is probabilistic so we assign things a list of probabilities. Treating a list of probabilities as if it has ontological existence doesn’t even make any sense, and it baffles me that it is so popular for people to do so.
This is why Hilbert space is infinitely dimensional. If I have a single qubit, there are two possible outcomes, 0 and 1. If I have two qubits, there are four possible outcomes, 00, 01, 10, and 11. If I have three qubits, there are eight possible outcomes, 000, 001, 010, 011, 100, 101, 110, and 111. If I assigned a probability amplitude to each event occurring, then the degrees of freedom would grow exponentially as I include more qubits into my system. The number of degrees of freedom are unbounded.
This is exactly how Hilbert space works. Interpreting this as a physical infinitely dimensional space where waves really propagate through it just makes absolutely no sense!
Schrödinger was not “rejecting” quantum mechanics, he was rejecting people treating things described in a superposition of states as literally existing in “two places at once.” And Schrödinger’s argument still holds up perfectly. What you are doing is equating a very dubious philosophical take on quantum mechanics with quantum mechanics itself, as if anyone who does not adhere to this dubious philosophical take is “denying quantum mechanics.” But this was not what Schrödinger was doing at all.
What you say here is a popular opinion, but it just doesn’t make any sense if you apply any scrutiny to it, which is what Schrödinger was trying to show. Quantum mechanics is a statistical theory where probability amplitudes are complex-valued, so things can have a -100% chance of occurring, or even a 100i% chance of occurring. This gives rise to interference effects which are unique to quantum mechanics. You interpret what these probabilities mean in physical reality based on how far they are away from zero (the further from zero, the more probable), but the negative signs allow for things to cancel out in ways that would not occur in normal probability theory, known as interference effects. Interference effects are the hallmark of quantum mechanics.
Because quantum probabilities have this difference, some people have wondered if maybe they are not probabilities at all but describe some sort of physical entity. If you believe this, then when you describe a particle as having a 50% probability of being here and a 50% probability of being there, then this is not just a statistical prediction but there must be some sort of “smeared out” entity that is both here and there simultaneously. Schrödinger showed that believing this leads to nonsense as you could trivially set up a chain reaction that scales up the effect of a single particle in a superposition of states to eventually affect a big system, forcing you to describe the big system, like a cat, in a superposition of states. If you believe particles really are “smeared out” here and there simultaneously, then you have to believe cats can be both “smeared out” here and there simultaneously.
Ironically, it was Schrödinger himself that spawned this way of thinking. Quantum mechanics was originally formulated without superposition in what is known as matrix mechanics. Matrix mechanics is complete, meaning, it fully makes all the same predictions as traditional quantum mechanics. It is a mathematically equivalent theory. Yet, what is different about it is that it does not include any sort of continuous evolution of a quantum state. It only describes discrete observables and how they change when they undergo discrete interactions.
Schrödinger did not like this on philosophical grounds due to the lack of continuity. There were discrete “gaps” between interactions. He criticized it saying that “I do not believe that the electron hops about like a flea” and came up with his famous wave equation as a replacement. This wave equation describes a list of probability amplitudes evolving like a wave in between interactions, and makes the same predictions as matrix mechanics. People then use the wave equation to argue that the particle literally becomes smeared out like a wave in between interactions.
However, Schrödinger later abandoned this point of view because it leads to nonsense. He pointed in one of his books that while his wave equation gets rid of the gaps in between interactions, it introduces a new gap in between the wave and the particle, as the moment you measure the wave it “jumps” into being a particle randomly, which is sometimes called the “collapse of the wave function.” This made even less sense because suddenly there is a special role for measurement. Take the cat example. Why doesn’t the cat’s observation of this wave not cause it to “collapse” but the person’s observation does? There is no special role for “measurement” in quantum mechanics, so it is unclear how to even answer this in the framework of quantum mechanics.
Schrödinger was thus arguing to go back to the position of treating quantum mechanics as a theory of discrete interactions. There are just “gaps” between interactions we cannot fill. The probability distribution does not represent a literal physical entity, it is just a predictive tool, a list of probabilities assigned to predict the outcome of an experiment. If we say a particle has a 50% chance of being here or a 50% chance of being there, it is just a prediction of where it will be if we were to measure it and shouldn’t be interpreted as the particle being literally smeared out between here and there at the same time.
There is no reason you have to actually believe particles can be smeared out between here and there at the same time. This is a philosophical interpretation which, if you believe it, it has an enormous amount of problems with it, such as what Schrödinger pointed out which ultimately gets to the heart of the measurement problem, but there are even larger problems. Wigner had also pointed out a paradox whereby two observers would assign different probability distributions to the same system. If it is merely probabilities, this isn’t a problem. If I flip a coin and look at the outcome and it’s heads, I would say it has a 100% chance of being heads because I saw it as heads, but if I asked you and covered it up so you did not see it, you would assign a 50% probability of it being heads or tails. If you believe the wave function represents a physical entity, then you could setup something similar in quantum mechanics whereby two different observers would describe two different waves, and so the physical shape of the wave would have to differ based on the observer.
There are a lot more problems as well. A probability distribution scales up in terms of its dimensions exponentially. With a single bit, there are two possible outcomes, 0 and 1. With two bits, there’s four possible outcomes, 00, 01, 10, and 11. With three bits, eight outcomes. With four bits, sixteen outcomes. If we assign a probability amplitude to each possible outcome, then the number of degrees of freedom grows exponentially the more bits we have under consideration.
This is also true in quantum mechanics for the wave function, since it is again basically a list of probability amplitudes. If we treat the wave function as representing a physical wave, then this wave would not exist in our four-dimensional spacetime, but instead in an infinitely dimensional space known as a Hilbert space. If you want to believe the universe actually physically made up of infinitely dimensional waves, have at ya. But personally, I find it much easier to just treat a probability distribution as, well, a probability distribution.