A physical theory, in the narrow sense of the word, is a logical structure based on assumptions and definitions which permits one to predict the outcome of a maximum number of different experiments on the basis of a minimum number of postulates. One usually desires the postulates to be as self-evident as possible; one demands simplicity, beauty, and even elegance. A physical theory seems to have only a finite lifetime. Newtonian mechanics was replaced by relativistic mechanics, thermodynamics by statistical mechanics, classical by quantum mechanics. There is a logical order in theoretical physics. Indeed, such an order is necessary if the endeavor of theoretical physics is to be meaningful and is to succeed in the direction of more and more general axiomatic deductive systems. The relationship between classical and quantum mechanics is especially interesting. The chapter also presents an overview of the key concepts discussed in this book.
A physical theory, in the narrow sense of the word, is a logical structure based on assumptions and definitions which permits one to predict the outcome of a maximum number of different experiments on the basis of a minimum number of postulates. One usually desires the postulates to be as self-evident as possible; one demands simplicity, beauty, and even elegance. A physical theory seems to have only a finite lifetime. Newtonian mechanics was replaced by relativistic mechanics, thermodynamics by statistical mechanics, classical by quantum mechanics. There is a logical order in theoretical physics. Indeed, such an order is necessary if the endeavor of theoretical physics is to be meaningful and is to succeed in the direction of more and more general axiomatic deductive systems. The relationship between classical and quantum mechanics is especially interesting. The chapter also presents an overview of the key concepts discussed in this book.
Although, the main objective of this book has been to expose the facts that underpin formal description of quantum mechanics and to make quantum mechanics seem natural, in going about this process we have tried to provide the young student with a guideline on how to approach learning a new theory. Thus, somewhat unconventionally, we start the discourse with a discussion on the meaning of theory and its formal description. This allows us to demonstrate, in concrete terms, how quantum mechanics is just another theoretical framework that conforms to the standard definition of a theory in the natural sciences. In this first chapter, we start with a nontechnical discussion of what one means by a theoretical framework and its formal description. We clarify what qualifies as a theory, and list the questions whose answers one must seek in trying to learn it. A notion of what amounts to understanding a theory is thus conveyed. The meaning of law, axiom, postulate, theorem, falsifiability etc., are thus discussed. We try to draw out the purpose of constructing a formal description of a theory. We also outline the role of abstraction and generalization in its construction. Finally, we discuss the sense in which the terms “philosophy” and “fundamental theorem” are used in the construction of a theoretical framework.
A deductive physical theory should in principle be a pure mathematical theory together with an identification of certain quantities/concepts (“observables”) in the theory and corresponding observable entities in the real world. This identification – the “interpretation” of the theory – should be unproblematic, both for the theoretician and the experimentalist. A general basis for a deductive physical theory, comprising both classical and quantum physics in a unified way, is proposed. The theory is based on successive confidence estimates on quantum-mechanical wave functions corresponding to space-localizations of particles. This allows a direct and simple way of describing both macroscopic and microscopic phenomena by means of the same basic concepts. Central in the axiomatics of the outlined theory is a concept called equiangular sequences of projection operators. It describes a successive sequence of “collapses of the wave function”. The proposed theory gives a basis for a general theory of irreversible processes based directly on quantum mechanics. It gives an alternative definition of entropy and an alternative derivation of entropy increase in irreversible processes.
The book investigates the ontology and logic of quantum physics. The first part discusses the relationship of theory and observation and different views on the ontological status of scientific theories. It introduces the fundamentals of quantum mechanics and some of its interpretations and their compatibility with various ontological positions. In the second part, implications of quantum mechanics on classical logic, especially on the distributive law and bivalence, as discussed by Garrett Birkhoff & John von Neumann (1936) and Hilary Putnam (1968), and their counterarguments are reconstructed and discussed. It is concluded that classical logic is sufficient for dealing with quantum mechanical propositions.
In this introductory chapter, which actually is the core of the entire book, we make a serious effort to bring together a variety of ideas from philosophy and physics. We first lay the epistemological foundations for our approach to particle physics. These philosophical foundations, combined with tools borrowed from the amazingly sophisticated, but still not entirely satisfactory, mathematical apparatus of present-day quantum field theory and augmented by some new ideas, are then employed to develop a mathematical representation of fundamental particles and their interactions. In this process, also the relation between “fundamental particle physics” and “quantum field theory” is going to be clarified. This first chapter consists of two voluminous sections: a number of philosophical contemplations followed by a discussion of mathematical and physical elements . The reader might wonder why these massive sections are not presented as two separate chapters. The reason for keeping them together is the desire to emphasize the intimate relation between these two sections: the selection and construction of the mathematical and physical elements is directly based on our philosophical contemplations. The beauty of the entire approach is a fruit of this intimate relationship. The presentation of the material in this chapter is based on the assumption that the reader has a basic working knowledge of linear algebra and quantum mechanics. If that is not the case, the reader might want to consult the equally entertaining and serious introduction Quantum Mechanics: The Theoretical Minimum by Susskind and Friedman [4]. The book Quantum Mechanics and Experience by Albert [5] offers a fascinating introduction with a strong focus on the measurement problem. An almost equation-free discussion of the history and foundations of quantum mechanics can be found in the book Einstein, Bohr and the Quantum Dilemma: From Quantum Theory to Quantum Information by Whitaker [6]. Complex vector spaces, Hilbert space vectors and density matrices for describing states of quantum systems, bosons and fermions, canonical commutation relations, Heisenberg's uncertainty relation, the Schrodinger and Heisenberg pictures for the time evolution of quantum systems, as well as a basic idea of the measurement process are all referred or alluded to in Section 1.1; these basics of quantum mechanics are recapped only very briefly in Section 1.2. The crucial construct of Fock spaces is explained in a loose way in Section 1.1.3 and later elaborated in full detail in Section 1.2.1.
The mind of man is central to the structure and functioning of the physical world. Modern physical theory indicates that the mind stands in a relationship of equals to the physical world. Both are fundamental, neither can be reduced to the other, and both require each other for their full understanding. This thesis is at odds with the view of the universe found in Newtonian mechanics as well as the generally held view among contemporary physicists of modern physical theory. Since the Renaissance, people have come to understand a great deal about the physical world, and they have gained significant control over it. This increased power over the physical world has occurred hand in hand with the assumption that the structure and functioning of the physical world is essentially independent from human cognition. According to this assumption, if a person’s cognitive capacity did not exist, the functioning of the physical world would not be fundamentally altered. This last statement is not in fact correct, and modern physical theory, and even fundamentals underlying Newtonian mechanics, provide evidence to attest to this. Nonetheless, contemporary physicists for the most part do not see that the relationship of human cognition to the physical world is radically altered in their own modern theory, theory that is supported by a great deal of empirical data. Instead, attempting to preserve the thesis that the structure and functioning of the physical world is independent of the mind while on a practical level relying on modern theory that contradicts this thesis, physicists have placed themselves in the position of wondering at times exactly what is the nature of the physical world at the same time they obtain experimental results concerning the physical world that can only be labeled astonishing in their precision and the scope of their implications. Modern physical theory consists of three main components: 1) the special and general theories of relativity; 2) quantum mechanics; and 3) statistical mechanics. There are very successful theories that have been developed on the basis of these three bedrock areas. An example is quantum electrodynamics. But these theories owe their conceptual foundation to the three components mentioned. The basic issues at the core of these three components also are expressed in these later theories. In addition, there are new unresolved issues of a fundamental nature concerning the conceptual integrity of these later theories that do not apply to quantum mechanics, relativity theory, and statistical mechanics. Quantum mechanics and relativity theory are areas I have written about for over twelve years. The nature of statistical mechanics has also been of interest to me during this time. But when I took a serious look in 1993 at Tolman’s (1938) The Principles of Statistical Mechanics, it became clear that the mind is linked to the physical world in statistical mechanics, a relationship I had found earlier in both relativity theory and quantum mechanics. It was after reading Tolman’s justification of the method of statistical mechanics in the original that I decided to write this book. When I found that the three components of modern physical theory all pointed to the same relationship between mind and the physical world, it became clear that the fundamental isolation of the mind from the physical world that has characterized our experience since the development of Newtonian mechanics is unfounded. Based on empirically supported principles of modern physical theory, I determined that the appropriate assumption for one’s experience, that the mind is linked to the physical world, could be stated with confidence. The impact of this change in assumption concerning the relationship of man to the cosmos in modern physical theory will find its way into our everyday experience. It will perhaps have no greater effect than in reducing the sense of isolation of man from the world that has characterized modern existence.
First Published in 1982 Philosophy and the New Physics is a compact and yet remarkably rich excursion through the history of physics from Newtonian mechanics to quantum physics. The theory of relativity, quantum mechanics and ideas about the ‘fundamental constituents’ of matter have attracted a great deal of philosophical comment. Indeed, the originators of some of these theories thought they were solving philosophical problems as well as scientific ones. Classical physics is often portrayed as epitomizing ‘mechanistic materialism’, and the revolution in modern physics is variously claimed to vindicate ‘logical positivism’, ‘operationalism’, ‘organicism’, ‘dialectical materialism’ and ‘Buddhist metaphysics’. In this book Jonathan Powers criticizes all of these claims and argues that such varied and conflicting interpretations are possible because of ineradicable elements of conventionality in scientific theories. This is a must read for scholars and researchers of philosophy of science and philosophy in general.