In quantum mechanics, are the position and trajectory of a particle special?

In the last century, figures such as David Bohm, who attempted to interpret quantum mechanics as a form of realism, treated the position and trajectory of particles as superior to other physical quantities. They seemed to unconsciously assume that position, which appears visually in particle detectors like bubble chambers, occupies a special place in observation theory compared to momentum, which is obtained by Fourier transforming the wave function. Consequently, they sought to construct a theory centered on particle trajectories.

However, in modern quantum mechanics, the position of a particle is not treated as a special physical quantity. In relativistic quantum field theory in particular, it is known that the very concept of the "position of a single particle" cannot be properly defined.

Position is merely a physical quantity that emerges in non-relativistic approximations. In other words, there is currently no reason to treat "position" as sacred.

Humans possess senses other than vision for perceiving the location of objects, such as hearing. In the cochlea, the spiral organ within the ear, sound is converted into electrical signals by utilizing the fact that the natural frequency of sound waves changes at different parts of the cochlea. In terms of function, this is essentially performing a Fourier transform on sound waves.

It is also well known that spatial cognition can be formed from sound waves using this sense of hearing. By Fourier transforming the sound that reaches the ears after reflecting off objects placed in space, one can perceive spatial extent. The position of an object obtained through this sense of hearing is merely secondary derived information.

An intelligence that thinks with its ears rather than its eyes would likely not consider particle positions or their trajectories to be special physical quantities. Rather, the momentum obtained through Fourier transformation, or the frequency proportional to it, would be physically fundamental.

The Bohmian approach, which attempts to understand quantum effects through realism based on particle trajectories, has become outdated due to experimental results on the violation of Bell's inequalities and the emergence of the formulation of quantum mechanics as information theory. Today, the wave function is a concept defined experimentally through quantum state tomography, and from the framework of "wave function = probability distribution," it is understood that the measurement problem did not exist to begin with.

In the current century of quantum natives, an information-theoretic and epistemological understanding of quantum mechanics is spreading. New technologies such as quantum computers will likely continue to advance significantly under such an understanding.