The Wave Function as Matter Density: Ontological Assumptions and Experimental Consequences

SHAN GAO

Shan Gao

The wave function 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 . John S. Bell (1990) Introduction The physical meaning of the wave function is an important interpretative problem of quantum mechanics. Notwithstanding nearly ninety years of development of the theory, it is still an unsolved issue. During recent years, more and more research has been done on the ontological status and meaning of the wave function (see, e.g. Monton, 2002; Lewis, 2004; Gao, 2011a, 2011b; Pusey, Barrett and Rudolph, 2012; Ney and Albert, 2013). In particular, Pusey, Barrett and Rudolph (2012) demonstrated that under certain non-trivial assumptions such as the preparation independence assumption, the wave function of a quantum system is a representation of the physical state of the system. This poses a further question, namely whether the reality of the wave function can be argued without resorting to non-trivial assumptions. Moreover, a harder problem is to determine the ontological meaning of the wave function, which is still a hot topic of debate in the realistic alternatives to quantum mechanics such as the de Broglie–Bohm theory or Bohmian mechanics (Belot, 2012). In this chapter, we will first give a clearer argument for the reality of the wave function in terms of protective measurements, which does not depend on non-trivial assumptions and can also overcome existing objections. Next, based on an analysis of the mass and charge properties of a quantum system, we will propose a new ontological interpretation of the wave function. According to this interpretation, the wave function of an N -body system represents the state of ergodic motion of N particles.

Daniel Bedingham, Detlef Dürr, G. C. Ghirardi +3 more

Guoqiu Zhao

Micro-object is both particle and wave, so the traditional Particle Model (mass point model) is actually not applicable for it. Here to describe its motion, we expand the definition of time and space and pick up the spatial degrees of freedom hidden by particle model. We say that micro-object is like a rolling field-matter-ball, which has four degrees of freedom including one surface curvature degree and three mapping degrees in the three-dimensional phenomenal space. All the degrees are described by four curvature coordinate components, namely “k1, k2, k3, k4”, which form the imaginary part of a complex phase space, respectively. While as to the real part, we use “x1, x2, x3, x4” to describe the micro object’s position in our real space. Consequently, we build a Dual 4-dimensional complex phase space whose imaginary part is 4-dimension k space and real part is 4-dimension x space to describe the micro-object’s motion. Furthermore, we say that wave function can describe the information of a field-matter-ball’s rotation & motion and also matter-wave can spread the information of micro-object’s spatial structure & density distribution. Matter-wave and probability-wave can transform to each other though matter-wave is a physical wave. The non-point property is the foundational source of the probability in Quantum Mechanics.

Quentin Ruyant

Primitive ontology is a program which seeks to make explicit the ontological commitments of physical theories in terms of a distribution of matter in ordinary space-time. This program targets wave-function realism, which interprets the high-dimensional configuration space on which wave-functions are defined as our fundamental physical space. Wave-function realism allegedly fails to account for a correspondence between the ontology it postulates and the ‘manifest image’ of the world in which experimental tests of the theory are performed, and therefore the wave-function must be completed with an additional structure which describes what fundamentally exists in ordinary space-time: the ‘primitive ontol- ogy’. However primitive ontologies face some difficulties, in particular concerning the ontological status of the wave-function. In this paper, I defend a realist inter- pretation of the wave-function as describing objects in ordinary space-time, which does not require supplementing the theory with additional structure. The main dif- ference between this proposal and other primitive ontology proposals is that the fundamental constituents of reality are not conceived of as localised objects, but as primitive relations. This interpretation purports to share the advantages of both wave-function realism and primitive ontologies without facing the same difficulties. I argue that the need for an additional structure stems from a commitment to the locality of the fundamental constituents of reality, and that such commitment is unnecessary for recovering the manifest image of the world.

大庆 李