In the 1930s, John von Neumann consolidated ideas from Bohr, Heisenberg and Schrodinger and placed the new quantum theory in Hilbert space. In Hilbert space, a vector represents the Schrodinger wave function. I know they are equivalent.. But can we say it is more natural and intuitive to say a particle has wave function (waves of probability) and this is better when conveying to layman as it is easier to visualize waves than a vector? Also can't we say the probability wave really exist in some higher space. When describing more than one particle.. the wave no longer occur in 3D space, but in higher dimensional mathematical space. Is it more logical to think this higher dimensional space really exist in actual. Notice that vector space is just for convenient arrangement of information. So we can't say our bank account database have objective existence in reality. But in the case of wave function. Perhaps we can say the waves have factual existence (like in MWI or BM)? There is no version of MWI or BM of the vectors because they are obviously for arrangement of information only. But waves are different and more real, is this correct way to think of it? I'm asking because when conveying to laymen. I plan to use pure wave function only or the language of waves without complicating it with state vectors and so on. But then I wonder if there is possibility waves are really more factual than vectors (which has no possibility of being factual or actual existing physically). Lastly. How do you describe quantum field theory using the language of pure waves. What is the equivalent of Fock space using the language of waves only? Can you do QFT without using any concept of vector but waves (or wave function) only?