On the base of years of experience of working on the problem of the physical foundation of quantum mechanics the author offers principles of solving it. Under certain pressure of mathematical formalism there has raised a hypothesis of complexity of space and time by Minkovsky, being significant mainly for quantum objects. In this eight-dimensional space and time with six space and two time dimensions all the problems and peculiarities of quantum mechanical formalism disappear, the reasons of their appearance become clear, and there comes a clear and physically transparent picture of the foundations of quantum mechanics.
On the base of years of experience of working on the problem of the physical foundation of quantum mechanics the author offers principles of solving it. Under certain pressure of mathematical formalism there has raised a hypothesis of complexity of space and time by Minkovsky, being significant mainly for quantum objects. In this eight-dimensional space and time with six space and two time dimensions all the problems and peculiarities of quantum mechanical formalism disappear, the reasons of their appearance become clear, and there comes a clear and physically transparent picture of the foundations of quantum mechanics.
In this chapter we are going to address the famous ‘problem of time’ which has become the headline for all the physical interpretational problems of the mathematical formalism. Roughly speaking the problem of time is that there is none in GR: at least in the spatially compact case without boundaries the Hamiltonian vanishes on the physical, constraint surface. This is physically relevant because we seem to live in a universe with precisely that spatial topology. Since the Hamiltonian generates time translations in any canonical theory we arrive at the conclusion that ‘nothing moves’ in GR, which is in obvious contradiction to experiment. Since there is no time also the usual interpretation of quantum mechanical measurements at given moments of time breaks down. One can fill books about this issue and we will not even try to cover a substantial amount of the existing literature. A superb source of information on these conceptual problems is Carlo Rovelli's book [3]. Rather, what we will do in what follows is to collect various proposals for solutions to the problem of time taken from other authors, especially Rovelli's relational approach to classical and quantum physics and Hartle et al. 's consistent history interpretation, and combine them into a consistent picture. We do not want to suggest that the resulting picture is to be accepted, rather we want to draw attention to the problems involved and to develop a working hypothesis. The discussion on the interpretation of quantum mechanics is very alive and some authors such as Penrose [243] not only propose to alter the interpretational aspect of quantum mechanics but also the mathematical framework.
This chapter, based on the background information of the previous chapter, will review the formalism of quantum mechanics – its fundamental mathematical structure (the basic contents of Hilbert space representation and operator algebra representation) and physical assumptions (kinematics, dynamics, and measurement theory). These are the premise and foundation for discussing the quantum histories interpretation. Then, in combination with the viewpoints of some literature in recent years, we will explore what is the interpretation of quantum mechanics, analyze the relationship between the theory of quantum mechanics and its interpretation, and declare the author’s basic stance on these two issues. These two are the primary issues that all interpretive work in the philosophy of physics will face (not limited to the interpretation of quantum mechanics), and the necessary clarification here is also conducive to the subsequent discussion. Three common terms – theory, formalism, and interpretation – are explicated and differentiated by offering the necessary definitions of their meanings, based on the works of Acuña and Ruetsche. The clarification will help to make the subsequent related discussions more precise.
The argument of this article is threefold. First, the article argues that from its rise in the sixteenth century to our own time, the advancement of modern physics as mathematical-experimental science has been defined by the invention of new mathematical structures. Second, the article argues that quantum theory, especially following quantum mechanics, gives this thesis a radically new meaning by virtue of the following two features: on the one hand, quantum phenomena are defined as essentially different from those found in all previous physics by purely physical features; and on the other, quantum mechanics and quantum field theory are defined by purely mathematical postulates, which connect them to quantum phenomena strictly in terms of probabilities, without, as in all previous physics, representing or otherwise relating to how these phenomena physically come about. While these two features may appear discordant, if not inconsistent, I argue that they are in accord with each other, at least in certain interpretations (including the one adopted here), designated as “reality without realism”, RWR, interpretations. This argument also allows this article to offer a new perspective on a thorny problem of the relationships between continuity and discontinuity in quantum physics. In particular, rather than being concerned only with the discreteness and continuity of quantum objects or phenomena, quantum mechanics and quantum field theory relate their continuous mathematics to the irreducibly discrete quantum phenomena in terms of probabilistic predictions while, at least in RWR interpretations, precluding a representation or even conception of how these phenomena come about. This subject is rarely, if ever, discussed apart from previous work by the present author. It is, however, given a new dimension in this article which introduces, as one of its main contributions, a new principle: the mathematical complexity principle.
Some aspects of the interpretation of quantum theory are discussed. It is emphasized that quantum theory is formulated in the Cartesian coordinate system; in other coordinates the result obtained with the help of the Hamiltonian formalism and commutator relations between “canonically conjugated” coordinate and momentum operators leads to a wrong version of quantum mechanics. The origin of time is analyzed by the example of atomic collision theory in detail; it is shown that the time-dependent Schrödinger equation is meaningless since in the high-impact-energy limit it transforms into an equation with two time-like variables. Following the Einstein-Rozen-Podolsky experiment and Bell’s inequality, the wave function is interpreted as an actual field of information in the elementary form. The concept “measurement” is also discussed.
During the past two or three centuries western philosophy and science have confirmed each other in their ontological attitude towards external reality. The particular opinion that physical objects have an existence completely independent of observation was established as the necessary basis for all scientific investigation. The discovery in quantum physics that the phenomena ultimately constituting the stability of the material world cannot be separated from the instruments of observation was necessarily felt disastrous to the scientific world-picture, and many philosophers and scientists, including celebrated physicists, are still trying by all means to save ontology in quantum physics. The motive power behind this activity is the belief that the objectivity of science can be maintained only if the elementary particles of matter can be objectified in the usual way. The present chapter deals with the fundamental conditions in quantum physics which entail a complete breakdown of the conceptual frame of classical mechanics
The argument of this article is threefold. First, the article argues that, from its rise in the sixteenth century to our own time, the advancement of modern physics, as mathematical-experimental science, has been defined by the invention of new mathematical structures. Secondly, the article argues that quantum theory, specifically with quantum mechanics, gave this thesis a radically new meaning by virtue of the following two features: one the one hand, quantum phenomena themselves are defined by purely physical features, as essentially different from all previous physics; and on the other, quantum mechanics and quantum field theory are defined by purely mathematical postulates, which connect them to quantum phenomena strictly in terms of probabilities, without representing or otherwise relating to how these phenomena physically come about. While these two features may appear discordant, if not inconsistent, I argue that they are in accord with each other, at least in certain interpretations (including the one adopted here), designated as “reality without realism,” RWR, interpretations. This argument allows this article to offer a new perspective on a thorny problem of the relationships between continuity and discontinuity in quantum physics. In particular, rather than being concern only with the discreteness and continuity of quantum objects or phenomena, quantum mechanics and quantum field theory relate their continuous mathematics to the irreducibly discrete quantum phenomena, in terms of probabilistic predictions, while, at least in RWR interpretations, precluding a representation or even conception of how these phenomena come about. This subject is rarely, if ever discussed, apart from previous work by the present author. It will, however, be given a new dimension in this article which introduces, as one of its main contributions, a new principle: the mathematical complexity principle.