Abstract
According to the standard probability interpretation, the wave function is a probability amplitude, and its modulus square gives the probability density of finding particles in certain positions in space. In this essay, we show that this central assumption of quantum mechanics may have an ontological extension. It is argued that microscopic particles such as electrons are indeed particles, but their motion is not continuous but discontinuous and random. On this view, the modulus square of the wave function not only gives the probability density of the particles being found in certain locations, but also gives the probability density of the particles being there. In other words, the wave function can be regarded as a representation of the state of random discontinuous motion of particles, and at a deeper level, it may represent the dispositional property of the particles that determines their random discontinuous motion.
Shan Gao