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arXiv:quant-ph/0309183

C. F. von Weizsaecker's Reconstruction of Physics: Yesterday, Today, Tomorrow

Holger Lyre

Published Sep 24, 2003• 2 citations
arXivHTMLPDF

Abstract

Carl Friedrich von Weizsaecker's thinking has always crossed the borders between physics and philosophy. Being a physicist by training he still feels at home in the physics community, as a philosopher by passion, however, his mind cannot stop thinking at the limits of physics. His physical ideas are based on the general conceptual and methodological preconditions of physical theories. Such a line of reasoning about the foundations of physics has brought Weizsaecker into an abstract program of a possible reconstruction of physics in terms of yes-no-alternatives, which he called "ur-theory." I shall start this paper with a review of the basic ideas of ur-theory: the definition of an ur and the connection between ur-spinors and spacetime. I then go over to some of ur-theory's present borders: the construction of quantized spacetime tetrads and the difficulties to incorporate gravity and gauge theories. Finally, I shall discuss the possible prospects of ur-theory -- partly with a view to modern quantum gravity approaches, but mainly in connection with its philosophical implications. Here, one of the crucial questions is, whether form, or, modern, information is an entity per se and what particular consequences this may have.

DOI
10.48550/arxiv.quant-ph/0309183

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Carl Friedrich von Weizsaecker's thinking has always crossed the borders between physics and philosophy. Being a physicist by training he still feels at home in the physics community, as a philosopher by passion, however, his mind cannot stop thinking at the limits of physics. His physical ideas are based on the general conceptual and methodological preconditions of physical theories. Such a line of reasoning about the foundations of physics has brought Weizsaecker into an abstract program of a possible reconstruction of physics in terms of yes-no-alternatives, which he called "ur-theory." I shall start this paper with a review of the basic ideas of ur-theory: the definition of an ur and the connection between ur-spinors and spacetime. I then go over to some of ur-theory's present borders: the construction of quantized spacetime tetrads and the difficulties to incorporate gravity and gauge theories. Finally, I shall discuss the possible prospects of ur-theory -- partly with a view to modern quantum gravity approaches, but mainly in connection with its philosophical implications. Here, one of the crucial questions is, whether form, or, modern, information is an entity per se and what particular consequences this may have.
The quantum theory of Ur-alternatives of Carl Friedrich von Weizsaecker tries to constitute general quantum theory based on the concept of logical alternatives in time. Based on this interpretation of quantum theory the existence of free objects in space, their symmetry properties and their interactions shall be inferred. The alternatives are represented by binary alternatives, which are called Ur-alternatives because of their logically fundamental character. Through Ur-alternatives as elementary quantum theoretical units of information the Copernican revolution with respect to the question of space is realized in a consequent way. This means that not the objects of nature are in a given space, but the existence of space arises as a kind of indirect representation of relations between abstract quantum theoretical objects. The Ur-alternatives do not exist in a given physical reality, but the existence of space is constituted by Ur-alternatives at all. Such a concept of reality is implicitly contained within the uncertainty relation and can be seen especially in the EPR-paradoxon. It is shown in this thesis in a mathematical consistent way that a state in the tensor space of many Ur-alternatives can directly be mapped into a real three dimensional space which means that together with the dynamics a representation in a (3+1)-dimensional space-time becomes possible. By considering the G2G_2G2​ an approach for the incorporation of the internal symmetries can be suggested. Furthermore the Ur-alternatives enable the constitution of a concept of interaction, which is based on quantum theoretical entanglement. By using this concept it is tried to obtain a purely quantum theoretical description of electromagnetism and gravity. This corresponds to a much more principle and in a radical sense background independent way of quantization.
The quantum theory of ur-objects proposed by C. F. von Weizsaecker has to be interpreted as a quantum theory of information. Ur-objects, or urs, are thought to be the simplest objects in quantum theory. Thus an ur is represented by a two-dimensional Hilbert space with the universal symmetry group SU(2), and can only be characterized as ''one bit of potential information''. In this sense it is not a spatial but an ''information atom''. The physical structure of the ur theory is reviewed, and the philosophical consequences of its interpretation as an information theory are demonstrated by means of some important concepts of physics such as time, space, entropy, energy, and matter, which in ur theory appear to be directly connected with information as ''the'' fundamental substance. This hopefully will help to provide a new understanding of the concept of information.
The quantum theory of ur objects postulates that all existing physical objects and their properties are constructed from fundamental objects called ur objects being described by an element of a two dimensional complex Hilbert space. This approach is based on the assumption that quantum theory represents a theory being constitutive for human knowledge. Physical objects are characterized by the information one can gain from them being contained in the quantum state they are described by. Since every Hilbert space can be represented as a tensor product of two dimensional Hilbert spaces, one is led to the ur objects. According to this approach relativistic quantum fields and thus the existence of a Minkowski space-time are the consequence of an iteration of a quantization of binary alternatives. In the original formulation there was only obtained a description of quantum fields on a flat Minkowski space-time. In this work there is made the attempt to incorporate general relativity and to describe the gravitational field within this approach. Thus the existence of a (3+1)-dimensional space-time in the sense of general relativity is assumed to be a consequence of quantum theory interpreted in an abstract sense.
The relation between Physics and Philosophy brings to mind the proverbial marriage of high drama; the parties do not approve of each other, but separated they cannot live. Philosophers find physicists shallow, and many physicists claim that they find philosophic speculations useless or worse. Mostly both display a lack of knowledge and understanding of the methods and goals of the other. A few researchers have tried to bridge this gap and explore the worlds of both parties. Michael Redhead has worked in this borderland, and when he retired from his chair in Cambridge, a symposium was arranged to honour him. The talks presented on this occasion are now published in a volume presenting much food for thought to both philosophers and physicists. The essays in this publication do not offer easy reading; not too many readers will have the preparation to penetrate the technical arguments offered. The authors are well acquainted with both philosophical argumentation and mathematical formalism, and, following the lead of Professor Redhead, they combine these in intricate and suggestive ways. Only a close reading can offer understanding of the points of view taken by the various authors. Browsing and mere reading defines the scenery, exploring it demands much more. Many of the nine essays included investigate the meaning of terms used loosely in physics contexts: locality, beables, symmetries and time in relativity. All essays utilize the mathematical structures of physics, but the approach is mainly philosophical; concepts like reality and metaphysics are applied. Some writings are more physical in their treatment of technical questions relating to modern quantum theory. Bohmian mechanics, localized quantum states and gauge symmetries are discussed in detail. It is, however, found that these present interpretational problems that are usually glossed over in purely physical treatments. For an old sceptic like myself, it is quite refreshing to find that many assertions, taken for granted in our textbooks, are indeed doubtful and offer conceptual or technical difficulties. This insight is what a philosophical analysis can offer the working physicist; future progress may well arise from such realizations. However, the results offered by philosophical analysis are usually found unsatisfactory; the hope that philosophy can suggest novel directions for the theory remains unfounded. Philosophers can learn that modern physics rests on a very shaky conceptual foundation. The theory has evolved by a combination of serendipity and opportunism. The beast that finally has emerged is neither well founded nor internally consistent. Its only merit is that it works. That offers the ultimate philosophical problem of modern physics. If the present book can help the philosopher to behold this challenging but overwhelming wilderness, then it serves a useful purpose indeed. But the prospective researcher has to learn to master the difficult language used by the natives, who are not always friendly. I enjoyed reading the book immensely, but the technical difficulty of the text made my understanding remain mostly superficial. I hope to have the time to return some of the essays, and look into the references and issues involved. The work is genuinely what it promises: a guide From Physics to Philosophy .
In this research work the quantum theory of Ur-alternatives of Carl Friedrich von Weizsäcker is considered. In This theory all objects and interactions in nature are constituted by abstract purely quantum logical relations in time. Such structures can be devided into binary alternatives, which are called Ur-Alternatives with respect to this principle meaning, and this leads to a tensor space of many Ur-alternatives. The indistinguishability of the Ur-alternatives yields two Hilbert spaces, the tensor space of symmetric and antisymmetric states under permutations of the Ur-alternatives. It is shown how the structures in the symmetric space can be represented in a three dimensional real position space connected to time according to special relativity. Accordingly this theory obtains ultimately a deep understanding of the EPR-paradox, since logic is independent of topological structures and causal relations in space. The antisymmetric space, which because of the Pauli principle contains much less degress of freedem, yields the additional quantum numbers of the elementary particles. Based on the demand for the highest possible symmetry in the tensor space, the Yang-Mills gauge theories of the standard model as well as a translational gauge formulation of general relativity in a purely quantum logical description are derived. The equations determine entanglements of states containing many Ur-alternatives and this concept is the analogue to classical pointwise interactions between separated objects. This means that the main structures of the SU(N)-interactions of the standard model of elementary particle physics as well as gravitation according to general relativiy are unified in a purely quantum theoretical conceptional framework. Finally it is derived an extended version of the E8-group, the biggest exceptional Lie-group.
THE conceptual problems raised by the discovery of quantum effects have not been fully resolved after half a century. Part of the reason for this is undoubtedly to be found in the mutual ignorance which prevails between physicists and philosophers. In his book Heisenberg brings together a philosophically inclined temperament with an unrivalled knowledge of physics. The result is a book of very great interest, however much one might disagree with his conclusions. The collection of essays of which the other book is made up is intended to bring crucial conceptual problems in physics especially to the notice of philosophers. The design and intention of the collection is admirable for this is the proper way to overcome the departmentalization of interest that has left the deep conceptual problems still unresolved. Men like Heisenberg who combine philosophical temperament with scientic knowledge of great distinction are rare, and yet the difficulties can only be cleared up by the application of philosophical techniques of analysis to problems which are an intimate and difficult part of physics. A great deal of the interest of Heisenberg's book lies in the very comprehensive account he gives of the origin and growth of the Copenhagen school, and the way the new phenomena forced a largely unwelcome picture of nature upon Bohr and his friends. The most important chapter from a philosophical point of view is that in which Heisenberg defends this interpretation against the attacks to which it has been subjected. The essence of his argument for the interpretation can be summed up in two propositions. (i) The Copenhagen interpretation of physical theory, which depends upon the acceptance of the so-called Principle of Complementarity, is an inevitable and final interpretation. The reason for this is that there are only two possible general models for understanding given physical phenomena; a particle model or a wave model. These are exhaustive and exclusive because the former depends upon discontinuous and the latter upon continuous (using substance here in the traditional philosophical sense). If we find, as we do, that the two fundamental constituents of the universe, matter and radiation, each exhibit two classes of phenomena, one explainable only on a particle model and one on a wave model, then we are compelled to adopt a complementarity hypothesis and give up the idea of finding a single and uniform model for the understanding of phenomena. There are only two kinds of models; they are mutually exclusive; both are required; hence we either despair before an insoluble problem or adopt the Copenhagen interpretation. (2) Any serious criticism of this interpretation must offer an alternative