Derivation of the Meaning of the Wave Function

We show that the physical meaning of the wave function can be derived based on the established parts of quantum mechanics. It turns out that the wave function represents the state of random discontinuous motion of particles, and its modulus square determines the probability density of the particles appearing in certain positions in space. The wavefunction gives not the density of stuff, but gives rather (on squaring its modulus) the density of probability. Probability of what exactly? Not of the electron being there, but of the electron being found there, if its position is ‘measured’. Why this aversion to ‘being’ and insistence on ‘finding’? The founding fathers were unable to form a clear picture of things on the remote atomic scale. (Bell 1990) The meaning of the wave function in quantum mechanics is often analyzed in the context of conventional impulse measurements. Although the wave function of a quantum system is in general extended over space, an ideal position measurement will inevitably collapse the wave function and can only detect the system in a random position in space. Thus it seems natural to assume the wave function is only related to the probabilities of these random measurement results as in the standard probability interpretation. However, it has been widely argued that the probability interpretation is not wholly satisfactory because of resorting to the vague concept of measurement (Bell 1990). On the other hand, although the wave function is regarded as a physical entity in some alternative formulations of quantum mechanics such as the de Broglie-Bohm theory and the many-worlds interpretation (de Broglie 1928; Bohm 1952; Everett 1957; De Witt and Graham 1973), it remains unclear what physical entity the wave function really represents. One of the main reasons, as we think, is that conventional impulse measurements ∗Unit for HPS and Centre for Time, University of Sydney, NSW 2006, Australia. Email: [email protected].