An Axiom of Chirality as the Basic Principle of Physics E-Book

Hans Wehrli

• Herausgeber: wbg Academic
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Deutsch
• Veröffentlichungsjahr: 2020

Seitenzahl: 99

Beschreibung

Warum sind die Naturgesetze so, wie sie sind? Der Autor entwickelt eine Strategie, nach welcher eine Theorie gefunden werden kann, welche Relativitäts- und Quantentheorie, die Naturkonstanten, die vier Wechselwirkungen und alle Elementarteilchen einheitlich beschreibt. Die Naturgesetze sind so, wie sie sein müssen, damit Wahrnehmung möglich ist. Unendlichkeit, eine Zeit, in der nichts passiert und ein Raum ohne Objekte sind nicht per se empirisch wahrnehmbar, weshalb auf diese metaphysischen Begriffe verzichtet wird. Das Axiom A=A widerspricht sich selbst, weshalb es durch ein neues «Chiralitätsaxiom» ersetzt wird. Erst dieses Axiom ermöglicht es, Wahrnehmungen in unserem Bewusstsein zu ordnen. Der Begriff des Schwarzen Loches wird erweitert. Raum, Zeit, Substanz und Wechselwirkung sind nur noch verschiedene Aspekte der mathematisch neu definierten Wesenheit Ereignis. Ereignisse sind empirisch zählbar.

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Hans Wehrli

An Axiom of Chirality as the Basic Principle of Physics

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Contents

1 Philosophy of Physics

2 Contradictions between Physics and Mathematical Models of Physics

3 The Model of Chirality Theory

4 Physical Interpretation

5 Comparison of Chirality Theory with Other Theories

6 Open Questions

References

1 Philosophy of Physics

The century-long, vain search for a comprehensive physical theory which makes the theory of relativity compatible with quantum theory and is able to describe all known interactions compels us to look for fundamentally new ideas. Fundamentally new ideas in a science always call for changes in the corresponding metascience. In the case of physics, that is metaphysics in its narrower sense, i.e. the science of language and methods of physics. In an on-going work, therefore, the basic metaphysical conditions – which are to comply with a physical theory – are examined, so that nature can be described as close to reality as possible. To do this, a dialogue between physics and philosophy is required. Most physicists underestimate the effect of their own epistemological prejudices on their research [Weinberg (1999); Rovelli (2010), 415]. Today natural laws are usually found by looking for experimental regularities with empirical perceptions of nature, whereas the metaphysical preconditions for the perceptions are ignored. With chirality theory, the laws of nature are as they must be for perception to be possible. The laws are not derived from nature, but as with Immanuel Kant [Kant (1783/2001)] and C.F. von Weizsäcker [Weizsäcker (1999)] from the way nature can be perceived, that is, from metaphysics in a narrower sense. This is the first paradigm shift of the new chirality theory.

It cannot be a task of this article to construct an axiomatic system for chirality theory. A mathematician once told me that for this goal 200 mathematicians and physicists would have to work for 20 years. But in a rather philosophical article like this it is necessary to list the contradictions between the usual axioms and physical perception. This concerns mainly the axioms of infinity and identity. The first is the main cause of the incompatibility of relativity theory with quantum theory, the latter for the neglecting of chirality as the basic principle of order in physics. However, there is no need to build up a complete axiomatic for chirality theory to understand the main ideas of its strategy.

In order to avoid misunderstandings, a few linguistic questions should be clarified from the outset. Languages have their limitations, which cannot in principle be overcome. Among other things, the meaning of the words or symbols is always vague, because for their definition one needs further words, which for their part, need to be defined in turn. If, for example, one defines space as the sum of all points and the point as an infinitely small place in space, then the definition turns in a circle. Such cycles are fundamentally inevitable, even if every child has a certain conception of what a point is and what space is. Nevertheless, there are a few important terms, as they are to be understood in this work, which should be defined.

Physics describes observed nature and formulates by means of mathematical methods laws of nature, which permit predictions (about the future). Nature is the entirety of all those things which can, in principle, be empirically – directly or indirectly – perceived [Whitehead (1939)]. In this sense, nature is real or material. Existence in chirality theory is an ontological property of anything that is either real or – if not real – must have a Be-ing in nature. For example, a point or a natural number is not real but it exists. A boson is directly, a fermion indirectly perceivable; therefore, both are real. Also black holes can be indirectly observed and are real. Space and time per se, all numbers except the natural numbers, and infinity are neither existing nor real but only ideas or mathematical models. The examples mentioned for this definition of reality and existence will be discussed later in the article. I am aware that depending on the philosophical and epistemological point of view there might be other definitions. Mathematics studies patterns in abstraction of the individual things which are patterned [Hampe (1998)]. Empirical perception is a flow of information from the outside into the conscious mind of a subject. The subject is an entity, which can take up, store and consciously process information. If the observer is transcendental, he is called a presumed observer and he is not part of reality. It is left open as to whether a subject can itself be part of nature. For the considerations in the present work it is sufficient to proceed from only one subject, the ego [Descartes (1641/1960)]. Possible further subjects and intersubjective communication are not brought up for discussion, because such further subjects can never be unequivocally differentiated from objects. An object is a summary of mathematical quantities or patterns, whose current values permit predictions about these very values (in the future) [Drieschner (1981)]. Information can be defined as answers to potential questions which can be reduced to a countable number of so-called binary choices, i.e. to alternatives which can be decided with a simple yes/no answer. The binary choices are computable as bits or qubits [Weizsäcker (1985), 163–173].

We shall now examine the extent to which today’s usual methods and terms of physics contradict the definitions above. Subsequently, those basic metaphysical conditions for a physics which conforms better to these definitions are to be described.

2 Contradictions between Physics and Mathematical Models of Physics

2.1 Theory and Reality

Both the observing physicist and the thinking mathematician are real. Their observations and thoughts obey natural laws. Today most physicists are aware of that fact but in classical mechanics this has not yet been the case. The mathematicians even today seldom think about the natural limits of their thinking although there is no thinking without order, no order without chirality and no infinity of thinking. The question to the extent the subject influences the object by his thinking and observing is a very difficult one. Kant [Kant (1786/1957)] was convinced that even the thinking subject alters the object of his thinking by his thoughts. Thus, Kant might be considered the first quantum theorist. In quantum physics the interaction between observer and object is the topic of innumerable discussions and philosophical interpretations such as the Copenhagen interpretation.

The relation between observer and observed object is fundamental to any metaphysical strategy. It must be decided whether one wants to start with a transcendental subject or with a real observer. At first sight the real observer seems to be preferable. But in that case one has to describe a system consisting of both the observer as well as the observed object and of the relation between both. This system must be observed by another subject. If this also has to be real, then the system of the second observer who observes the observing first observer and the observed object has to be described and so on. In any case a presumed transcendental observer will have to be part of the metaphysical model. Therefore, I prefer to start with the simplest metaphysical strategy: That is a presumed transcendental observer who observes the real world and describes it by a mathematical model.

Later, in a second step, the presumed observer might be replaced by a real one. That should not require much adaption because the real observer has to obey the same natural laws that have been described with the presumed observer. The only new aspect will be the consciousness of the real observer, what might be philosophically rather pretentious [Blackmore (2003); Hofstadter (1985)]. Also the event counting presumed observer is “built into the model” but he is transcendental and therefore does not require an ambient space. He does not influence the observed object. I assume that mathematical models without such transcendental aspects are impossible for metaphysical reasons. This is often ignored by theoretical physicists who believe that they describe real nature as it is. As soon as they describe a real observer they introduce a presumed observer who observes the real one.

The physicist seeks to describe nature with the help of a set of mathematical tools. In so doing, he must always remain conscious of what in his science is mathematics and what is physics, because physics has the task of describing the reality of nature as authentically as possible, whereas mathematics, with its logic and axiomatic theory is actually a purely theoretical construct, which remains to a large extent independent of nature. In order to make by means of the laws of nature statements which are as reliable as possible, it is therefore important to be conscious of what in these laws is based on theory and what on reality. This consciousness has been increasingly lost in modern physics. Often there are ontological misunderstandings because it is not made clear whether a proposition concerns nature, the perception of nature or the mathematical model which describes that perception. E.g. the dimensionality might be 10 for nature, 4 for the perception of nature and infinite with the mathematical model that describes that perception (see Section 4.3). And possibly a new definition of the mathematical notion of dimensionality or of physical terms might be useful.

2.2 Simplicity as a Metaphysical Criterion

With respect to mathematics, the physicist is free to a large extent. There are, however, practical reasons to prefer one type of mathematics to another: First, mathematics should be simple, Dirac would say beautiful. I want a model that is mathematically as simple as possible. Simplicity is one of the metaphysical prerequisites of the model. This was emphasized by Aristotle, Kepler, Newton, Mach, Einstein, Heisenberg and Weizsäcker [Wehrli (2008), 34]. Therefore, the mathematical model of chirality theory uses as few elements as possible, namely points which have no other intrinsic property than their existence and no external properties except their relations to other points, i.e. to the structure of the model. Then I ask, whether the model can be physically interpreted. Second, the mathematics should not contradict empirical observation. Third, its logic should be convincing for the physicist and its axiomatic theory immediately evident. In mathematics an infinite number of logical and axiomatic systems is possible [Quine (1963)]. According to the above criteria the best mathematical model must be chosen. In quantum mechanics for example, the logical proposition AB = BA contradicts empirical observation and therefore it has been dropped [Finkelstein (1996), 3ff.].

2.3 A ≡ A?

Similarly, the identity axiom A ≡ A is questionable in physics: If the A on the left and the A on the right hand side of the identity sign were really identical, then one could not distinguish them. Since one can, however, always distinguish the two A’s, this important proposition of logic is to be dispensed with if possible. The meaning of the A may remain open in this argumentation because two separate things – be it particles, observations, relations or times – never can be physically identical. Two distinct A’s may have some equal properties which allow the physicist to define precisely the extent to which the A