It’s not that it doesn’t make sense in words, it’s more that it isn’t something we can intuitively understand. Basic physics is intuitive. Advanced physics is much less intuitive but you can sort-of get it if you use analogies to things that are understandable. Truly advanced physics is so far removed from the world we experience that you just have to trust the math.
IMO, everything being a wave is not quite pure math territory. Things like constructive and destructive interference are ideas you can understand using water waves or sound, so when concepts are explained in those terms you can sort-of get it. But, things like electron spin or quark flavours are things you just have to accept.
bunchberry@lemmy.world 2 months ago
We can’t see wave functions. It is a tool used to predict observations but itself cannot be observed, and cannot be an observable object as it exists in an abstract Hilbert space and not even in spacetime. It is only “space” in the sense of a state space, kind of like how if I have a radio with 4 knobs, I can describe the settings with a single point in a 4 dimensional space. That doesn’t mean the radio actually is a 4 dimensional object existing in this state space, it only means that we can represent that way for convenience, and the dimensions here moreso represent degrees of freedom.
If you believe everything is a wave function then you believe the whole universe is made out of things that cannot be observed. So how does that explain what we observe? Just leads to confusion. Confusion not caused by the mathematics but self-imposed. Nothing about the mathematics says you literally have to think everything is made out of waves. In fact, Heisenberg’s original formulation of quantum mechanics made all the same predictions yet this was before the Schrodinger equation was even invented.
People take the wave formulation way too literally and ultimately it just produces much of this confusion. They are misleadingly taught that you can think of things turning into waves by starting with the double-slit experiment, except it is horribly misleading because they think the interference pattern they’re seeing is the wave function. Yet, (1) the wave function is associated with individual particles, not the interference pattern which is formed by thousands, millions of particles. There is nothing wave-like visible with just a single particle experiment. (2) Even the interference pattern formed by millions of particles does not contain the information of the wave function, only a projection of it, sort of like its “shadow” as the imaginary terms are lost when you apply the Born rule to it and square it. (3) They also like to depict a literal wave moving through two slits, but again there are imaginary components which don’t map to anything physically real, and so the depiction is a lie as information has to be removed in order to actually display a wave on the screen.
The moment you look at literally anything that isn’t the double-slit experiment, the intuitive notion of imagining waves moving through space breaks down. Consider a quantum computer where the qubits are electrons with up or down spin representing 0 or 1. You can also represent the state of the quantum computer with a wave function, yet what does it even mean to imagine the computer’s internal state is a wave when there is nothing moving at all and the state of the quantum computer doesn’t even have position as one of its values? You can’t point to that wave even existing anywhere, you get lost in confusion if you try.
It is more intuitive to not think of wave functions as entities at all. But people have this very specific mathematical notation so burned into their heads from the repeated uses of the double-slit experiment that it is very difficult to get it out of their heads. Not only did Heisenberg instead use matrix transformation rather than the Schrodinger equation to represent QM, but it is also possible to represent quantum mechanics in even a third mathematical formulation known as the ensemble in phase space formulation.
The point here is that the Schrodinger equation is just one mathematical formalism in which there are multiple mathematically equivalent ways to formulate quantum mechanics, and so treating these wave functions wave really existing waves moving through a Hilbert space which you try to imagine as something like our own spacetime seems to be putting too much weight on a very specific formalism and ultimately is the source of a lot of the confusion. Describing the whole universe as thus a giant wave in Hilbert space evolving according to the Schrodinger equation is thus rather dubious, especially since these are entirely metaphysical constructs without any observable properties.