The call to supplement the wave function with local beables is almost as old as quantum mechanics. But what exactly is the problem with the wave function as the representation of a quantum system? I canvass three potential problems with the wave function: the well-known problems of incompleteness and dimensionality, and the lesser known problem of non-locality introduced recently by Myrvold. Building on Myrvold’s insight, I show that the standard ways of introducing local beables into quantum mechanics are unsuccessful. I consider whether we really need local beables, and assess the prospects for a new theory of local beables. Full text
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What strikes me as odd in the paper on What’s wrong with the wave function? is the absence of the term `ensemble’ in it. Probability distributions calculated by means of the wave function are experimentally compared with measurement results obtained from measurements carried out on ensembles of identically prepared objects. It does not make sense to attribute a wave function to a single
object (as was done by the Copenhagen interpretation). That Bohr won the 1935 (in)completeness contest from Einstein is a result of an improductive empiricist fear of metaphysics: if physicists had followed Mach in his denial of the existence of atoms, much of present-day physics could not have been developed.
In my view it is a waste of time and energy to try to interpret the Schroedinger equation as describing a single object, in the same way we do not require such an interpretation from the classical diffusion equation. These equations yield only the statistical descriptions of measurement results obtained from ensembles.
I am aware that this is a bit disappointing if it is intended to manipulate single microscopic objects (rather than ensembles), but we can probably learn from the analogy with statistical thermodynamics what can be done about it. It should incidentally be noted that there is a large difference between classical and quantum statistics as a result of the complication of the interaction of object and measuring instrument inducing the notion of complementarity being important in the latter theory.
Willem M. de Muynck
I agree completely with You. the basic concept of the probability distribution is the attribute of the ensemble but not the attribute of the individual system. The probability distribution is the synonym of the concept of the state. But the quantum theory is time reversible contraty to the classical evolution. This creates the important differences between classical and quantum case. There exists individual phenomena in quantum physics, e.g. the result of the measurement. Thus the quantujm physics is defined by the interplay between collective (ensemble) phenomena and individual phenomena. The results of the measuring systems are individual, while measured systems are collective. This is exactly described in my paper (http://www.ijqf.org/wps/wp-content/uploads/2015/06/201503.pdf. I think that your appeal on the ensembles is completely OK !!
Your Jiri Soucek
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