Quantum theory of the primal alternatives

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The quantum theory of the original alternatives (or original theory ) is a theory devised in the second half of the twentieth century by the physicist and philosopher Carl Friedrich von Weizsäcker . It aims to provide a uniform description of nature based solely on quantum theory , which in this context is understood as a theory of information in time . It thus represents a description of nature formulated purely in quantum-theoretical terms. Due to the abstract nature of the concept formation within the theory and the resulting mathematical difficulties, it has not yet been able to be developed into a full physical theory. However, it is precisely the high degree of abstraction, which is associated in particular with “overcoming” field-theoretical concepts, that is viewed by some authors as necessary for a uniform description of nature.

Basic idea

The quantum theory of the original alternatives emerged from Carl Friedrich von Weizsäcker's attempt to understand the reason for the universal validity of quantum theory and its resistance to any attempt at change. Here he tried to derive quantum theory as a fundamental theory of nature from epistemological postulates. In this context he wanted to realize in a new way the Kantian idea of ​​justifying the fundamental laws of nature from the conditions of the possibility of experience. From his point of view, he largely succeeded in justifying this, and essentially based on a temporal logic and the concept of the alternative. In this approach, only time with its structure of past, present and future and the logical concept of an alternative is assumed as an ontological entity . In this context, quantum theory refers to what Carl Friedrich von Weizsäcker called abstract quantum theory. It is about the general Hilbert space formulation from Paul Dirac and Johann von Neumann of the form of quantum theory, originally going back to Werner Heisenberg and Erwin Schrödinger , which initially manifested itself specifically as quantum mechanics . After the abstract quantum theory has been reconstructed, the next task is to justify concrete physics based on it. What is decisive is von Weizsäcker's assumption that for this purpose no further statements about the concrete nature of nature, such as the existence of a local area or special objects, are necessary. This is all supposed to result from the outflow of abstract quantum theory, which thus has a much more decisive role in characterizing the physical concept of reality than is the case in ordinary physics. In order to achieve the goal of deriving concrete physics from abstract quantum theory, von Weizsäcker now made use of the logical possibility of representing any state in a finite-dimensional abstract Hilbert space, to which a quantum-theoretical alternative corresponds, as the tensor product of two-dimensional states . Such two-dimensional states correspond to the quantum-theoretical formulation of the simplest possible logical alternative, namely a binary alternative, i.e. a yes-no decision. Such a binary alternative formulated in quantum theory should now be the fundamental term on which a fundamental description of physical reality is based, and in this role Weizsäcker calls it the original alternative. With the use of a purely logical term on the fundamental level, abstract information becomes the fundamental entity of nature. And that in turn has the consequence that nature seems to dissolve on a basic level into something purely spiritual in the sense of objective spirit.

Von Weizsäcker was convinced by Werner Heisenberg, on the grounds that he was studying physics, that one had to process the most important philosophical event of the twentieth century, the emergence of the theory of relativity and quantum theory, intellectually if one wanted to produce significant philosophy. From later remarks by Heisenberg on von Weizsäcker's approach of the original alternatives, it becomes clear how much physics and philosophy are linked in von Weizsäcker's thinking:

“So you want (...) to build the elementary particles, and ultimately the world, from alternatives in the same way that Plato wanted to build his regular bodies and thus the world from triangles. The alternatives are no more matter than the triangles in Plato's 'Timaeus'. But if one takes the logic of quantum theory as a basis, the alternative is a basic form from which more complicated basic forms arise through repetition. The way should therefore (...) lead from the alternative to a symmetry group (...); the performers (...) are the mathematical forms that represent the elementary particles; they are, so to speak, the ideas of the elementary particles, to which the object elementary particle ultimately corresponds. (…) The alternative is certainly a much more fundamental structure of our thinking than the triangle. But I imagine the exact implementation of your program to be extremely difficult. Because it will require a way of thinking of such a high degree of abstraction as it has never happened before, at least in physics. (...) "

- Werner Heisenberg : The part and the whole . Conversations in the area of ​​atomic physics.

Von Weizsäcker himself writes about his theory:

“We are dealing with an unfinished but, it seems to me, promising theory. Your progress would have been faster if I had succeeded in getting more of today's theoretical physicists interested in your question. It does not try, as was often the case before a Kuhnian revolution and in elementary particle physics today, to solve the unsolved problems within the framework of the old concepts by means of models of increasing complexity. Nor does it try to guess a new paradigm through imagination. Rather, it tries to treat the fundamental problems of quantum theory as consistently as possible and to derive the solution approaches for special problems from this. "

- Carl Friedrich von Weizsäcker : time and knowledge.

Justification of the concrete physics from original alternatives

Justification of the existence of a real three-dimensional physical spatial space and the topology of the cosmos

In the context of the quantum theory of the primordial alternatives , the difficult task now arises, starting from the fundamental concept of the primordial alternative as an elementary quantum-theoretical information unit in time, to derive the concrete way in which nature is to us in the concrete Represents physics. This includes in particular the existence of a physical spatial space, which is by far not as fundamental in character as time, which is assumed in this approach in contrast to physical space. The more fundamental character of time compared to space, which exists in the sense of the theory despite the theory of relativity, is in accordance with the view of Immanuel Kant, in whose epistemology the time underlies all inner and outer perception and thus also the soul, while space itself relates only to external perception and thus to the perception of nature. Regarding the role of the spatial space in the quantum theory of the original alternatives , a mathematical property is of decisive importance, namely that the fundamental symmetry group of a two-dimensional complex Hilbert space , which leaves the inner product of two elements of this space and thus the norm of such an element, constant , i.e. the symmetry group SU (2) , the symmetry group of the rotations in a three-dimensional real space is isomorphic , i.e. the symmetry group SO (3) . Since a primal alternative represents an element of such a two-dimensional complex Hilbert space according to its mathematical form ( i.e. it is described by a Weyl spinor ), all physical relationships remain the same if all the primal alternatives that make up the world are included transformed to any element of SU (2). Due to the isomorphism of the SU (2) to the SO (3), this corresponds mathematically to an invariance under rotations in a real three-dimensional space and this in turn leads to the assumption that the possibility of representing physical relationships in a three-dimensional space, in which we are can be traced back to the fact that its mathematical properties are contained in the structure of an original alternative in a certain sense. Related to this is the mathematical fact that the mathematical space of a primordial alternative topologically corresponds to one, i.e. a three-dimensional sphere , the three-dimensional analogue of a two-dimensional spherical surface. This means that a point on a can be assigned to a state of a primal alternative . In this sense, the topology of the cosmos would result directly from quantum theory. In principle, time must already be included, since it already appears in the reconstruction of the abstract quantum theory. With regard to the original alternatives, time is linked to the symmetry group U (1) , i.e. a phase transformation that is fundamentally possible in every complex Hilbert space. ${\displaystyle \mathbb {S} ^{3}}$ ${\displaystyle \mathbb {S} ^{3}}$

The tensor space of the primordial alternatives, the conformal group, particle states and their dynamic equations

A concrete physical object can only be described by a combination of many original alternatives. This leads to a tensor space related to the mathematical space of an original alternative , whose base states correspond to the number of original alternatives that are in the various base states of a single original alternative. There are four basic states, because the two components of the original alternative are each complex-valued. The mathematical structure of this tensor space results directly from the quantization of a primal alternative, whereby the real components of the primal alternative become creation and annihilation operators of primal alternatives in the corresponding base states and thus act in the tensor space of the primal alternatives. The concept of multiple quantization plays an important role here. The quantization of a binary alternative assigns complex numbers to the two states , which makes it a quantum-theoretical original alternative. A further quantization of this original alternative then leads in the above sense to operators that act on a state in the tensor space of the original alternatives. The state of an elementary particle can be interpreted as a state in the tensor space of many primordial alternatives. The original alternatives must first obey a Bose statistic. As the largest possible symmetry group that can be represented in this tensor space of the original alternatives, and whose generators are represented accordingly by the creation and annihilation operators with regard to the base states of the original alternative, the result is SO (4,2), i.e. the conformal group the special theory of relativity . This consists of the three spatial translations and the time translation, the three spatial rotations, the three actual Lorentz transformations , the four special conformal transformations and the dilation transformation. Thus, the space-time structure of the theory of relativity is implicitly contained in the tensor space of the original alternatives. That the full conformal group results here and not just the Poincare group is very plausible in the sense of the theory insofar as no metric structure of space-time has yet been defined at this level of construction. Because the gravitational field and with it the metric structure of space-time must also be constructed from original alternatives. The fact that the conforming group of the special theory of relativity results as a symmetry group is connected with the possibility that one can map any state in the tensor space of many primordial alternatives directly into space-time. In addition, one can derive the dynamic equations (which are represented as wave equations in spatial space ) for elementary particles without interaction. Because it is possible to map the original alternatives to four-pulse vectors which, after further quantization, become operators and act on a state in the tensor space. This is of course directly related to the fact that the generators of the conformal group can be represented in the tensor space of the original alternatives, since the operators of the four-momentum components correspond to the generators of the space and time translations. The dynamic equations then result from the definition of the corresponding scalar product of these four-momentum vectors in a pseudo-Euclidean sense and their application to a state in the tensor space of the original alternatives, in the simplest case the Klein-Gordon equation for a massless elementary particle. By forming the tensor product from a (with respect to the permutation symmetry of Bose statistics) symmetrical state in the tensor space of the primary alternatives with a single primary alternative that describes the spin, one can also derive equations for fermions. Doubling the state space results in equations for particles with mass . This corresponds to the introduction of the parabosis statistics for original alternatives, which will be discussed in the next section.

Many-particle theory, mass and interaction

In order to arrive at a many-particle theory , a further quantization of a state in the tensor space of the original alternatives is necessary. This then leads to a state space whose basic elements correspond to the number of particles in a certain state, which in turn corresponds to a certain number of original alternatives in their various basic states. Such a many-particle state corresponds to the (in the sense of permutation symmetry) symmetrized product of single-particle states. However, since a symmetrized product of symmetrical states in the sense of Bose statistics does not necessarily lead to such a symmetrical state again, it is necessary to introduce a so-called Parabose statistic for the original alternatives, which is characterized by a certain algebra . Such then also allows the construction of elementary particles with mass. The interaction between different quantum objects must ultimately be based on this. The various interactions in nature must then result from this original interaction. This of course also includes the universality of gravity . However, so far only basic ideas exist regarding the derivation of the interaction. In this context, the idea is essential that the consideration of an object existing independently of the rest of the cosmos, which is decisive for the description of nature within physics, is only an approximation, and the occurrence of the interaction of different objects is the consequence from this results. Regardless of this, it can be assumed that symmetry transformations with regard to internal spaces of quantum numbers represent a transformation of certain primary alternatives of an elementary particle to other primary alternatives of the same elementary particle, while the spatial transformations correspond to transformations that either relate to all primary alternatives Alternatives of an elementary particle, to all original alternatives of several elementary particles or to all original alternatives in general, which corresponds to a symmetry transformation of the whole cosmos. Ultimately, of course, the quantum theory of the original alternatives would have to show why the specific concrete objects (elementary particles) and their interactions exist that are found in nature. However, this has not yet been achieved.

reception

Holger Lyre states about von Weizsäcker's approach: "It should be emphasized again that the original theory is at best a speculative approach up to the present time, but it may refer to deeper connections that are still not understood."

Important publications in scientific journals (selection)

• CF von Weizsäcker: Complementarity and logic. Die Naturwissenschaften 42, 521-529, 545-555, 1955.
• CF von Weizsäcker: Complementarity and logic. II. The quantum theory of the simple alternative. Zeitschrift für Naturforschung 13a, 245-253, 1958.
• CF von Weizsäcker, E. Scheibe, G. Süssmann: Complementarity and logic. III. Multiple quantization. Zeitschrift für Naturforschung 13a, 705–721, 1958.
• T. Görnitz, CF von Weizsäcker: Quantum Interpretations. Int. J. Theor. Phys. 26: 921-937, 1987.
• M. Drieschner, T. Görnitz, CF von Weizsäcker: Reconstruction of Abstract Quantum Theory. Int. J. Theor. Phys. 27, 289-306, 1988.
• T. Görnitz, D. Graudenz, CF von Weizsäcker: Quantum Field Theory of Binary Alternatives. Int. J. Theor. Phys. 31, 1929-1959, 1992.
• H. Lyre: The Quantum Theory of Ur-Objects as a Theory of Information. Int. J. Theor. Phys. 34: 1541-1552, 1995 (on-line).
• H. Lyre: Multiple Quantization and the Concept of Information. Int. J. Theor. Phys. 35: 2263-2269, 1996 (online).
• H. Lyre: Quantum Space-Time and Tetrads. Int. J. Theor. Phys. 37, 393-400, 1998 (online).
• T. Görnitz: Deriving General Relativity from Considerations on Quantum Information. Advanced Science Letters Vol. 4, 577-585, 2011 (online). .
• M. Kober: Representation of Quantum Field Theory by Elementary Quantum Information. Int. J. Theor. Phys. 51, 2476-2487, 2012 (online).

literature

• Carl Friedrich von Weizsäcker : The unity of nature. Carl Hanser Verlag, 1971.
• Carl Friedrich von Weizsäcker: Structure of the physics. Carl Hanser Verlag, 1985.
• Carl Friedrich von Weizsäcker: Time and Knowledge. Carl Hanser Verlag, 1992.
• Thomas Görnitz : Quanta are different, the hidden unity of the world. Spectrum Academic Publishing House, 1999.
• Thomas Görnitz, Brigitte Görnitz: The creative cosmos, spirit and matter from information. Spectrum Academic Publishing House, 2002.
• Thomas Görnitz, Brigitte Görnitz: The evolution of the spiritual. Quantum Physics - Consciousness - Religion. Vandenhoeck & Ruprecht Verlag, 2008.
• Michael Drieschner: Modern natural philosophy. An introduction. Mentis Verlag, 2002.
• Lutz Castell, Otfried Ischebeck (Ed.): Time, Quantum and Information. Springer Verlag, 2003. (collection of articles)
• Holger Lyre : quantum theory of information, to the natural philosophy of the theory of the original alternatives and an abstract theory of information. Mentis Verlag, 2004.
• Carl Friedrich von Weizsäcker, Thomas Görnitz, Holger Lyre: The Structure of Physics. Springer Verlag, 2006. (English, abridged translation of Structure of Physics , supplemented by a chapter "Cosmology and particle physics" by Thomas Görnitz)
• Martin Kober: The constitution of space-time in a unified natural theory, about the relationship between the conceptual bases of quantum theory and general relativity. Südwestdeutscher Verlag für Hochschulschriften, 2011.

Web links

• Reconstruction of the quantum theory and the theory of the original alternatives - Carl Friedrich von Weizsäcker discusses his theses with Manfred Eigen and Manfred R. Schroeder , doi : 10.3203 / IWF / G-221 . Video from 1986, length 56 min.

Individual evidence

1. ↑ Martin Kober: About the relationship between the conceptual foundations of quantum theory and general relativity. Dissertation, Frankfurt 2010.
2. ^ Carl Friedrich von Weizsäcker: Structure of Physics. Carl Hanser Verlag, 1985, p. 23 f. & P. 330 f.
3. ^ Carl Friedrich von Weizsäcker: Structure of Physics. Carl Hanser Verlag, 1985, Chapter Eight Reconstruction of the abstract quantum theory.
4. ↑ Carl Friedrich von Weizsäcker: The unity of nature. Carl Hanser Verlag, 1971, p. 222.
5. ^ Carl Friedrich von Weizsäcker: Structure of Physics. Carl Hanser Verlag, 1985, p. 390 f.
6. ^ Carl Friedrich von Weizsäcker: Great physicist. Carl Hanser Verlag, 1999. Chapter Heisenberg as a physicist and philosopher. P. 316.
7. ↑ Werner Heisenberg: The part and the whole . Conversations in the area of ​​atomic physics. Piper Verlag 1969, p. 286.
8. ^ Carl Friedrich von Weizsäcker: Time and knowledge. Carl Hanser Verlag 1992, p. 318.
9. ↑ Immanuel Kant: Critique of Pure Reason. I.  Transcendental Elementary Doctrine. First part. The transcendental aesthetic. 2nd section. From the time. § 6. Conclusions from these terms. Edition Felix Meiner, Hamburg 1998, p. 109 f.
10. ^ Carl Friedrich von Weizsäcker: Structure of Physics. Carl Hanser Verlag, 1985, page 399 f.
11. ^ Carl Friedrich von Weizsäcker: Structure of Physics. Carl Hanser Verlag 1985, page 350 f.
12. ^ Carl Friedrich von Weizsäcker: Structure of Physics. Carl Hanser Verlag, 1985, page 406 f.
13. ↑ CF von Weizsäcker, E. Scheibe, G. Süssmann: Complementarity and logic. III. Multiple quantization. Zeitschrift für Naturforschung 13a, 705-721, 1958. pp. 707-714.
14. ^ Carl Friedrich von Weizsäcker: Structure of Physics. Carl Hanser Verlag, 1985, page 424 f.
15. ^ Carl Friedrich von Weizsäcker: Structure of Physics. Carl Hanser Verlag, 1985, page 431 f.
16. ^ Holger Lyre: Information theory. A philosophical and scientific introduction . Wilhelm Fink, Munich 2002, ISBN 3-8252-2289-6 , p. 83 .
17. ↑ Entry at DNB, with table of contents
18. ↑ Entry at DNB, with table of contents