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It is well known, in the bases of the modern unificated theories of matter lies the theory of the gauge fields by Hermann Weyl. The Weyl’s theory is not only an effective mathematical model, but also it contains some ontological statements, which are non-trivial and very interesting for our analysis.
G. Leibniz stated the idea of global gauge invariability of our world. He proposed that if the God changed scales of all things in the world, we could not reveal this transformation. H. Weyl gave the physical interpretation of local gauge invariability4. The next example shows essence of that interpretation. Let’s imagine a spaceship that is moving in space far from gravitational mass. The astronaut is in the state of imponderability. There is such gauge transformation of the flight path, that the spaceship begins moving on the circle. To provide physical processes to occur identically both in the first and in the second case gravitational field must to exist, which compensates the effects of the spaceship path curvature. The general idea of our example consists in assumption that physical laws may be invariant with respect to local gauge transformations if some physical field exists for compensation of changes from point to point. Thus the theory of local gauge transformations gives the geometric description of physical forces and fields.
The fundamental idea of the Weyl’s theory is the assumption that the absolute ideal measures of physical values exist. These measures are distributed through all Weyl’s space, or space of gauge transformations. This space has a wonderful property. Transference of a real physical value in the Weyl’s space results in changing of its scale. This fact is obtained by means of comparing the real value with the ideal scale. The knowledge about change of real scale is a posteriori. Such comparison corresponds to the principle of near-action according to which one cannot speak about equality and inequality of two values situated in different areas of the space. Along with this the fact of gauge transformation existence requires that there is the principle of far-action in nature. Due to this principle we can speak about existence of two identical absolute scales in the Weyl’s space without procedure of comparison of these scales. Such knowledge is a priori.
Ideal measures are strange, absurd objects. They cannot be defined as physical objects because one cannot conduct physical experiences, based on the principle of near-action, which discover existence of such objects. The scale of ideal measures would change during of transfer along Weyl’s space, if they were real physical objects. However this fact would conflict with the gnoseological status of the ideal scales as the means of measurement. At the same time if the ontological status of the above-mentioned ideal scales as identical to each other is not proposed it is impossible to speak about existence of gauge transformation of real physical values. So one speaks about ideal scales as metaphysical essences, which are non-physical essences of the physical world. The existence and functions of such essences are based on accept of unity of the far- and near-action principles. It is impossible to substantiate existence of the gauge invariability of the physical laws and therefore to give a sense of the physical forces as a reality which compensate of infringement of the fixed invariability without recognizing of the above-mentioned unity.So ideal scales of Weyl’s space are impossible objects in the physical world. They can be understood as non-being of the physical world. The relation to this non-being determines the being of the measured physical reality. Thus it must to recognize the non-being as an existence. We thought this existence as that has not of predicates of the being in the physical world.
So the ideal scales give a physical sense a gauge transformation and one give possibility to substantiate gauge invariability of the physical laws. The impossible existence may be interpreted both ways – ontologically and semantically. On the one hand this is subject’s transcendental being, on the other hand this is sense “dimension” of being of nature. The first statement means that the impossible existence is a transcendental being concerning to nature. Thus we can say, for instance, that calibration of ideal scales can be changed arbitrarily, but these changes cannot be found in real the experience. Japanese physicist R. Utiyama expresses this fact so: “However God gives the measured relation (calibration) in each point, we do not able found it. And if He decides to change calibration we cannot found it too”5. In this citation God is understood as the transcendental subject, which knows and notices that does not see and known an empirical subject, or “internal” observer. The transcendental subject has a priori knowledge because this knowledge is given to him not from the experience. A priori knowledge gives “vision” and understanding of the world. This knowledge expresses such relation between the subject and the object, which based on the principle of action at a distance. This knowledge denotes about the simultaneous change of the calibration of all ideal scales in the gauge space.
The second statement says that the impossible existence can be understood as a sense “dimension” of the physical being. The sense of the being is closed for the being. The being “does not know” itself. So, in our example, a physical force “does not know” that it compensates a scale changing of a physical value in case of its transfer in a gauge space. According to H. Weyl in nature the action of the physical force does not distinguish from the gauge changing. The changing of calibration, which is not found in experience, is the sense of the compensating act of the physical force. Thus the impossible comparatively “internal” observer gives a sense to the physically observed existence. So in the theory of relativity for the observer, connected with the local system of coordinate, relativity of simultaneity has a sense as far as there are not signals which move with the infinite velocity.
In order to illustrate these statements I’d like to remind of the example given by Albert Einstein while explaining his general theory of relativity. Let us imagine two-dimensional creatures, living on a spherical object. Their local experience gives evidence of two-dimensional character of the world, described in Euclid's geometry. To find out a non-Euclidean character of their distorted two-dimensional space it is necessary to enter the «third» dimension. Thus, the truthful knowledge of one's own world requires transcendenting into the impossible for this world «third» dimension. The sense of distortion of two-dimensional space is explicated in its idea as surface in three-dimensional space. The world loses its «flatness» and acquires its «volume» due to transcendenting of the subject and an origin of sense dimension of the world. In this example the three-dimensional sphere is a symbolic being due to that the subject is thought outside of two-dimensional space. Due to symbolic being of the subject it can be interpreted as the distortion of two-dimensional space. In according to considerations in the previous part of article the transition from the being with smaller dimension (the being of a man into the world) to the being with greater dimension (the being of a man outside of the world) may be understood as a timeless act of transcendenting, which is connected with the genesis of the subject of knowledge. The inverse transition is an act conscious «inserting» of a man in the being of the world. This is connected with the process of transition from the knowledge of the world to the being in the world on laws of this world. In this case that world forfeits «semantic coordinate» and becomes «its», that is inhere a man, but a man becomes «property» of the world.
On my opinion, modern theory of cognition must be based on the accepted of unity or complementarity of the principles of action at a distance and short-range. Subject of cognition is an unity of immanentness and transcendentness. In order to know the world, it is necessary something already be aware of the world. But in order to person can know that it actually knows him necessary experience. Therefor knowledge of nature and its laws is possible when the subject exists both outside of the world and inwardly this world. Man a subject of cognition is really present in the cognitive world, but due to the knowledge about the world man is absents in the world. Man finds own presence in the semantic structures of the world.
In conclusion I’d like to notice that idea of a dialogue of man with nature certainly it is important for modern understanding of the scientific cognition. But herewith we must not forget that than enter in a dialogue, man must be. Human being is not defined only by that possibility, which he affords nature. In order to be, man needs for own bases, different from natural. Man as surplus essence for nature, holds in the world of nature by the symbolic impossible and absurd (for nature) existences. They ensure a possibility of monologue of man in nature. And without the ability to monologue a dialogue is impossible.
1 Prigogine I., Stengers I. Order out of chaos. Man’s new dialogue with nature.– Moscow: Progress, 1986.-. P.371.
2 See Neuman von I. Mathematical foundations of quantum mechanics. - Moscow: Nauka, 1964. - Ch. 6.
3 Gaidenko P. Evolution of notion of science. Becoming and development of first scientific programs. - Moscow: Nauka, 1980. - P.221-222.
4 See Utiyama R. A Physics соме то that? The theory of gauge fields. - Moscow: Nauka, 1986.
5 Ibid. P.162.
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