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arXiv:1707.08640

Raum, Zeit und Wechselwirkung in der Quantentheorie der Ur-Alternativen

Martin Kober

Published Jul 25, 2017• 0 citations
arXivHTMLPDF

Abstract

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 $G_2$ 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.

DOI
10.48550/arxiv.1707.08640

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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.
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 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.
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-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.
It is made the attempt to explain why there exists a division between internal symmetries referring to quantum numbers and external symmetries referring to space-time within the description of relativistic quantum field theories. It is hold the attitude that the symmetries of quantum theory are the origin of both sorts of symmetries in nature. Since all quantum states can be represented as a tensor product of two dimensional quantum objects, called ur objects, which can be interpreted as quantum bits of information, described by spinors reflecting already the symmetry properties of space-time, it seems to be possible to justify such an attitude. According to this, space-time symmetries can be considered as a consequence of a representation of quantum states by quantum bits. Internal symmetries are assumed to refer to relations of such fundamental objects, which are contained within the state of one single particle, with respect to each other. In this sense the existence of space-time symmetries, the existence of internal symmetries and their division could obtain a derivation from quantum theory interpreted as a theory of information.
Abstract Difficulties in meshing general relativity with quantum theory have prompted a widespread conviction that space-time is not fundamental but emergent. This raises a difficult ontological question: What is there more fundamental than space-time from which it might emerge? Rather than try to answer this question, this essay suggests that one reject its presupposition that emergence demands a precisely characterized ontological basis. Instead, it explores the possibility that space-time emerges in the domain of a quantum theory of gravity in a way that does not depend on objects, properties, or processes represented by that theory. How can a quantum theory of gravity help itself to talk of physical systems or situations without representing them in space-time? This essay shows how it can in a pragmatist view of quantum theory.