Just like in relativity where the 4D postulate motivates many to believe it is the actual reality because of its success, in QM many believe the world of particles is not the prominent reality [1].
The argument however is not as simple. Here I try to present it. In summary, it is based on the 2 interpretations of configuration space, representations that were introduced in the nineteenth century*, although similar i.e. based on same "ancestry", of where the quantum state is based
Classic configuration space
This means configuration spaces used to represent a system of particles with apparent locations in three-dimensional space will be 3N-dimensional, where N is the number of particles. That is to say that each point in space will be labelled by 3N numbers. For a system with two particles, the configuration space is six-dimensional and a point in space (a configuration) can be provided by six numbers where the first three correspond to the x, y, and z coordinates for the first particle and the second correspond to the x, y, and z coordinates for the second.
Quantum configuration space
In a classical situation, one in which the locations of all particles is determinate, a system can be represented by one simple point in its configuration space. In quantum mechanics, however, particles have indeterminate positions, and so a quantum system must be represented as a field smeared out over this configuration space.
This is the quantum wave function [1]. The wave function field will have amplitudes at points in configuration space that correspond to locations in three-dimensional space where these particles may be found.
The Schrödinger equation is a deterministic equation [2]: if the quantum state is given at any particular instant of time, the solution follows for any other time value, both before and after that instant. The interpretation of quantum state is, however, drastically different from classical fields such as E or B, because it is defined not in spacetime, but on a high-dimensional configuration space.
(Its connection with classical quantities is described by the probability interpretation) **
Hilbert space
Another higher-dimensional framework for representing systems in quantum mechanics is Hilbert space. Each dimension in a Hilbert space corresponds to a determinate state of some observable (a position coordinate or spin along a given axis, for example) [1].
Here, total systems are represented as vectors or rays in Hilbert space. For example, to represent a system of two spin-1/2 particles, physicists will use a ray in a four-dimensional Hilbert space, with two dimensions corresponding to the spin of the first particle being up or down along some dimension, and two corresponding to the spin of the second particle being up or down along that or some other dimension. When we consider observables like position coordinates that can take an infinite number of possible values, the Hilbert spaces become infinite-dimensional
Novel predictions and ideas
Based on the above, on QM there is the idea that the wavefunction field excludes the prominence of a world of particles.
i.e. a field-like object that exists in some higher-dimensional quantum reality [1].
In such a world, as quantum mechanics predicts, our three-dimensional reality is nonlocal
References
1. https://iai.tv/articles/reality-is-just-a-quantum-wave-function-auid-2024
2. CLAUS KIEFER, Concept of Law in Physics On the Concept of Law in Physics
* to provide more rigorous and elegant formulations of classical mechanics
** In 1926, as is well known, Schrödinger reformulated quantum mechanics using his famous wave equation. This formulation lent the promise of allowing not only a simpler and more familiar mathematical statement of the theory, but also a formulation that would be more capable of providing a clear account of the nature of the world according to quantum mechanics, at least more capable than Heisenberg’s matrix formulation [1]. Schrödinger’s formulation allowed one to see quantum systems as waves or fields evolving smoothly and continuously over time in accordance with his wave equation [1].
There are 2 main differences, in my view, with classical physics
1) A quantum system is not only explicitly and singularly defined in a configuration system, it is also represented as a field smeared out over this configuration space, i.e not locally defined in configuration space
2) The wavefunction as a kind of field or a time-evolving qm characterization of a physical system, is not defined on physical space like Em field but on configuration space.
Higher-dimensional systems used in quantum mechanics, like Hilbert spaces, don't exclude or seriously undermine the concept of a particle-based world. Instead, they provide a more comprehensive framework to describe quantum states and phenomena. These mathematical representations extend our understanding of particles and their interactions, rather than contradicting the particle concept.
chapter{Introduction}
The question of the materialistic interpretation of the principle of least action and the question of the materialistic interpretation of quantum mechanics are studied. Going beyond the framework of classical mechanics, we have moved from representing a particle as a material point in physical space (i.e., a geometric point with its own mass) to representing a particle as a material circle (i.e. that is, a geometric circle having its own angular velocity) in a metaphysical 4-dimensional Euclidean space (in which 3-dimensional Euclidean space is only its observable part), which made it possible to interpret the principle of least action as a statement that a particle moves in metaphysical space along a path that delivers a minimum of the total (total) number of revolutions rings, and quantum mechanics is interpreted as the problem of a random walk of a ring in metaphysical space. In such a quantum world, Planck's constant is equal to one revolution of 3-dimensional Euclidean space in 4-dimensional Euclidean space. In this case, we mean that the 4-dimensional Euclidean space from the point of view of a 3-dimensional Euclidean observer is represented by a conical surface, since $\mathbb{R}^{4}=\mathbb{R}^{+}\ast S^{3}= \mathbb{R}^{3}\ast\mathbb{R}P^{1}=\mathbb{R}^{3}\ast S^{1}$, where the asterisk indicates the direct product with the singularity at the zero point of the space $\mathbb{R}^{+}$ and $\mathbb{R}^{3}$, in which $S^{3}$ and $S^{1}$ converge to a point. Next, as a metaphysical space, we consider the 8-dimensional Euclidean space in which our 3-dimensional Euclidean space rotates, formed by the lamination of a dynamic flow moving along the surface of a 7-dimensional sphere.
https://www.researchgate.net/publication/329252706_MATHEMATICAL_NOTES_ON_THE_NATURE_OF_THINGS?_sg%5B0%5D=WO2RvgLlfMZmdmIxyYJ7zlWb8gIbYBWNNUaMz8gzhOBoqCCvns42dj2whdNCgObpa5xUvfXilS2W-z_brUz7thdiQPAnj46jgCiNQZim.3pXOjSBSTUTEDGTK80CBwPsccFjC5Z2Q-JsJRTmXfLCSemWE2snXt1HOsBG0FtiOzD6B2TSK5HOI4GGjrlEieQ&_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6InByb2ZpbGUiLCJwYWdlIjoicHJvZmlsZSIsInByZXZpb3VzUGFnZSI6InByb2ZpbGUiLCJwb3NpdGlvbiI6InBhZ2VDb250ZW50In19