The evidence that the probability interpretation is indispensable for the wave function has not been reasonably revealed since the early stages of quantum theory like the topic of Schrödinger’s cat has been discussed from various viewpoints. Recently the Schrödinger equation has reasonably derived from the diffusion equation in accordance with the causality for the Newton mechanics, regardless of the de Broglie’s hypothesis. In the derivation process, the problem of probability interpretation has been reasonably solved in relation to a wave function collapse, and moreover not only the evidence for a micro particle having a wave nature but also the evidence for validity of the de Broglie’s hypothesis itself has been theoretically revealed. Further, the other fundamental problems having been unsolved for a long time are also reasonably solved. For example, it is theoretically revealed that such a single composite particle as a cluster molecule has a wave nature when it is composed of atoms smaller than about 770 numbers.
The evidence that the probability interpretation is indispensable for the wave function has not been reasonably revealed since the early stages of quantum theory like the topic of Schrödinger’s cat has been discussed from various viewpoints. Recently the Schrödinger equation has reasonably derived from the diffusion equation in accordance with the causality for the Newton mechanics, regardless of the de Broglie’s hypothesis. In the derivation process, the problem of probability interpretation has been reasonably solved in relation to a wave function collapse, and moreover not only the evidence for a micro particle having a wave nature but also the evidence for validity of the de Broglie’s hypothesis itself has been theoretically revealed. Further, the other fundamental problems having been unsolved for a long time are also reasonably solved. For example, it is theoretically revealed that such a single composite particle as a cluster molecule has a wave nature when it is composed of atoms smaller than about 770 numbers.
The relation of matter wave, which is well-known as a hypothesis proposed by de Broglie in 1923, gave basis for establishing the quantum mechanics. After that, experimental results revealed that a micro particle has a wave nature. However, the theoretical validity of the relation itself has never been revealed since his proposal. Theoretical basis that a micro particle has a wave nature has been thus disregarded in the unsolved state. The diffusion equation having been accepted as Fick’s second law was derived from the theory of Markov process in mathematics. It was then revealed that the diffusivity D depends on an angular momentum of a micro particle in a local space. The fact being unable to discriminate between micro particles in a local space resulted in having to accept the existence of minimum time t0 (>0) in the quantum mechanics. Based on t0 and D obtained here, the theoretical validity of relation of matter wave was confirmed. Denying the density theorem in mathematics for time in physics indicates that the probabilistic interpretation is essentially indispensable for understanding the quantum mechanics. The logical necessity of quantum theory itself is thus understandable through introducing t0 into the Newton mechanics. It is remarkable that the value of t0 between 1.14×10-17 s ≤ t0 ≤1.76×10-14 s obtained here is extremely larger than that of the well-known Planck time tp=5.396×10-44 s.
Investigating the elementary process of diffusion revealed that the De Broglie hypothesis is really valid in a material and further that the Schrödinger equation is reasonably derived from the diffusion equation. The diffusion equation is thus one of the fundamental equations in physics. The problem between a moving coordinate system and a fixed coordinate system for the diffusion equation had never been discussed until recently in the history of diffusion theory. In that situation, it is revealed that investigating the problem between those coordinate systems is indispensable for understanding the diffusion phenomena. The new findings obtained here, which are revolutionary in the existing diffusion theory, will be not only dominant but also indispensable for further advance in the diffusion study.
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.
In 1905, Einstein established relativity under the condition of denying the absolute space-time valid in Newtonian mechanics. In those days, the quantum theory was also established by accepting De Broglie’s hypothesis of matter wave, regardless of the causality of Newtonian mechanics. It has thus caused some fundamental problems unsolved in the quantum theory, as the causality of quantum mechanics for Newtonian mechanics is unknown. In that situation, it was recently revealed that the quantum theory is reasonably established in accordance with the causality for Newtonian mechanics, and also that the hypothesis of De Broglie is theoretically valid. The fundamental problems unsolved for a long time were also reasonably elucidated then. Further, we then found that a micro particle has an imaginary mass in a local space, or its behavior depends on an imaginary time. In the present work, we thus review fundamental problems in quantum mechanics from a viewpoint of the theoretical structure of physics in accordance with the causality for Newtonian mechanics.
The problem of Schrödinger’s Cat has figured prominently in the debates about the bearing of quantum physics on our understanding of physical reality. On its basis, various theorists have maintained the quantum physical world exhibits a probabilistically indecisive physical reality. The analysis of the paper that this appeal to quantum reality is methodologically at odds with and disjoint from its underlying approach to quantum theory itself. If there is to be methodological uniformity at this juncture it will have to be along the lines that Einstein always focused—an incomplete hidden factor (perhaps better than “hidden variables”) approach.
Since a material is composed of micro particles, investigating behavior of those particles is essentially dominant for materials science. The diffusivity of diffusion equation is relevant to not only a collective motion of micro particles but also a motion of single particle. An elementary process of diffusion was thus theoretically investigated in a local space and time. As a result, the investigation concluded that the wave nature of micro particle results from denying the mathematical density theorem of a real time in the Newton mechanics. In other words, the basic theory of quantum mechanics is established in accordance with the cause-and-effect relationship in the Newton mechanics, for the first time, regardless of the de Broglie hypothesis. In relation to the collective motion of micro particles, the new diffusion theory was also reasonably established using the universal expression of diffusivity obtained here. In the present paper, the new findings indispensable for the fundamental knowledge in physics are thus systematically discussed in accordance with the theoretical frame in physics.