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Philosophy of Science

An Examination of the Quantum Theories. IV

William Marias Malisoff

Published Jul 1, 1935• 0 citations
Publisher

Abstract

We pause in the process of exposition to note what continuity we may in the progress of the theories of discontinuity we have been discussing. The following trends are rather distinct: (1) the development of more and more general mathematical approaches, (2) a marked broadening of the field of experimental issues, and (3) an increasing attention to analysis of fundamental concepts, the philosophy of physics.

DOI
10.1086/286378

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We pause in the process of exposition to note what continuity we may in the progress of the theories of discontinuity we have been discussing. The following trends are rather distinct: (1) the development of more and more general mathematical approaches, (2) a marked broadening of the field of experimental issues, and (3) an increasing attention to analysis of fundamental concepts, the philosophy of physics.
Recent discussions in the physical literature, designed to clarify the logical position of modern physical theory, have brought to light an amazing divergence of fundamental attitudes which may well bewilder the careful student of physics as well as philosophy. Quantum mechanics, representing an abstract formalism, should be capable of having its logical structure analyzed with great precision like any other mathematical discipline. Its consequences in all problems to which its method can be applied are so unambiguous, consistent, and successful in predicting physical experience as to disperse immediately all thoughts of possible discrepancies in its fundamental texture. Yet it must be said that even the founders of quantum theory are not in harmony in their various expositions of the bases of that theory. However, while this situation seems disquieting on the face of it, there is no cause for serious brow raising, for it is a fact that there exists agreement with regard to the central axioms of the theory, and that the ambiguities affect only their philosophical interpretation, a field in which differences of opinion may at present be honestly entertained.
Reference to quantum theory has become quite the fashion, and to base an expectation on an already receding episode with relativity theory, a great philosophical assault of interpretation of quanta is brewing in many quarters. The author of this series of studies would be content if by a plain statement of “what is the case” at this stage he could stem the more quixotic efforts, or rather reveal their unreal character to the spectators who may be enmeshed in the spell cast over such adventures. It is constantly necessary to restate the physicists' claims plainly in their positive content—as Einstein himself did once for relativity theory—so that one may know what is no-man's land and what is everyman's land in the new territory. This in itself is largely but a hope since there is no unanimity as to all the facts, and, worse, unanimity is no guarantee of stability. Nevertheless, the painstaking revision that is constantly going on on the experimental front enables us to arrange at least the data on a well-ordered scale of reliability. It then becomes much easier to detect false props to otherwise attractive theories, to discriminate live matter from the débris of progress, and to speculate on future growth. For such reasons the present examination of the various quantum theories will proceed from a presentation of facts and theories to their appraisal and then to a proposal concerning the organization of the facts, concepts and theories. The subject is very complex: There are several quantum theories, some of which are already referred to as “classical” although these themselves were anti-classical (anti-Newtonian); all have claimed success in their time; all have serious hiatuses, including the present. The author has chosen to hark back to some of the older issues before appraising the latest claims.
The argument of this chapter is governed by the double meaning of its title: (a) the relationships between the concepts of discreteness and continuity in modern mathematics and physics; and (b) the relationships, both continuous and discontinuous, between mathematics and physics, as, from Galileo on, a mathematical-experimental science, with mathematics coming first in this conjunction. The project of modern physics was, thus, defined by an essential continuity between mathematics and physics, as a mathematical representation of nature, principally by means of continuous functions and then calculus, until the rise of quantum theory, specifically as quantum mechanics (QM) and quantum field theory (QFT). With QM, at least in certain interpretations, such as the one adopted in this chapter, quantum theory disconnected the ultimate constitution of nature from any mathematical representation, thus, making physics discontinuous with mathematics. As this chapter will argue, however, this new epistemological situation did not disconnect quantum physics from mathematics, but, on the contrary, led to relating abstract mathematics, such as that of Hilbert spaces over ℂ and operator algebra there, to discrete physical phenomena in terms of probabilities, thus reestablishing the connection, which was no longer representational, between mathematics and physics. This chapter will also argue that the development of the concepts of continuity and discontinuity, and the relationships between them, has acquired a great richness and complexity through the nineteenth and twentieth centuries in mathematics itself, richness and complexity that found their way into physics, in particular relativity and quantum theory. One of the intriguing aspects of this development is the idea, advanced by, among others, A. Grothendieck, following B. Riemann's comment on the subject, that the continuous may serve as an approximation of the discontinuous, rather than seeing, as is more common, the discontinuous as a mode of technical approach to the continuous. This chapter will discuss this idea, and the relationships between continuity and discontinuity in, and between, mathematics and physics in terms of two new concepts: reality without realism (RWR), applicable in both mathematics and physics, and the relationships between them, and ideality without idealism (IWI), the version of the concept of RWR, applicable specifically to mathematics.
There are a lot of factors determining our process of defining and describing the nature. Our concept of information is one of these factors. When we consider the nature we are within, the points we have discussed are the concepts like in quest of the universe, infinity, space and absoluteness. Mankind regards the nature as the object of his actions, acts and activities because of perceiving himself within the nature. He abides by the concept of nature and its laws. However, he sometimes mistakes his own laws for the order of nature and claims that his knowledge is absolute laws of nature. He realizes that the concept of nature varies in time when he questions his concept of knowledge. \nWhen the natural science was examined within the philosophy of science in the 20th century, some dilemmas emerged. Namely, as technology gradually improves, the opportunity to experiment and to observe micro and macro scales has arisen. \nThe thesis is based on the exposition of methods, used to improve quantum physics, and the expression of the conception of natural science through the emergent table. As philosophical basics of quantum physics are commented, the history of classical physics and its methods has been analyzed. These two paradigms have been scrutinized fields, such as experiment, observation, mathematics and logic. Similarities and differences have been found. So, one of questions of the philosophy of science, the question about what the method of scientific examination is, has been given a comparative answer. As a result of the comparison between the methods of two paradigms, it has been found out that the source of contradictions, such as continuity-discontinuity, certainty-uncertainty and causality-probability requires to examine the method, instead of examining the world, the interpretation of the world or its meaning.