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In this paper, we propose a new ontological interpretation of the wave function in terms of random discontinuous motion of particles. According to this interpretation, the wave function of an N-body quantum system describes the state of random discontinuous motion of N particles, and in particular, the modulus squared of the wave function gives the probability density that the particles appear in every possible group of positions in space. We present two arguments supporting this new interpretation of the wave function. The arguments are mainly based on an analysis of the mass and charge properties of a quantum system. It is realized that the Schr\”{o}dinger equation, which governs the evolution of a quantum system, contains more information about the system than the wave function of the system, such as the mass and charge properties of the system, which might help understand the ontological meaning of the wave function. Finally, we briefly analyze possible implications of the suggested ontological interpretation of the wave function for the solutions to the measurement problem.
This is a very interesting idea. Here are a couple of questions about how it might work:
You write that “it seems natural to assume that the origin of the Born probabilities is the random discontinuous motion of particles”. Certainly some kind of reconciliation of your interpretation of the wave function with the Born rule is required. If a position measurement consisted of sampling the position of the particle at an instant in time, I can see how this might go. But measurements take place over finite intervals of time. How could that kind of process pick out one position (with the relevant probability)?
Second, how is interference handled in your approach. Presumably, in a two-slit context, the particle occupies the top-slit wave packet half the time and the bottom-slit wave packet half the time. But then how is interaction between the wave packets to be explained if the particle is always in either one or the other? The particle presumably can’t interact with itself (as you remark elsewhere). Any suggestions?
Hi Peter, thanks a lot for your very helpful comments. Your questions are closely related to the understanding of RDM (random discontinuous motion) of particles. RDM gives an ontological interpretation of the wave function, but the instantaneous picture cannot explain interference and measurement. To explain the former, we still need the law of motion, which is supposed to be the linear Schrodinger equation for the wave function (which describes the state of RDM during a time interval dt). For the latter, we still need a solution to the measurement problem. Here RDM may help. My idea is that RDM may be the source of the randomness of measurement results, and especially, if wavefunction collapse is real, RDM may be the random noise that collapses the wave function. I proposed a model here (http://rspa.royalsocietypublishing.org/content/469/2153/20120526). No doubt further study is needed for my idea of RDM. Best, Shan
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