Теория бесконечности
и время

© Godarev-Lozovsky M.G., 2012

Saint-Petersburg Philosophical Society

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Godarev-Lozovsky M.G.Determined infinity as the metaphysical base of science. This paper is intended for philosophers and physicists. A positive definition of infinity is suggested and a theorem of absolute cause of infinity is stated and proved. Absolutisation of relative reality in modern science is analyzed from the point of view of the determined infinity theory. Metaphysical base for physics and science in general is suggested. In the most general way we establish agreement between: a) scientific and religious knowledge; b) quantum mechanics and common sense; c) transportation of objects in classical and quantum mechanics.

Key words: infinity, teleportation, absolutisation, determinism, causality, materialization.


Why cannot science be a ground for itself? The Tarsky’s theorem states that the predicate of truthfulness for formalized systems cannot be expressed by the means which are contained in these systems and because of that it is possible to say that such systems are not self-sufficient. The system of knowledge called “science” is one of them. [1].

Why does the real (that is quantitative and qualitative) infinity of relation of measure can just be such a ground? This is because the real infinity incorporates in itself everything which exists, and on top of that the determined real infinity explains existence from the point of view of causality.

It is also suggested to start from the idea that absolute nothingness and absolute emptiness do exist exclusively in people’s fantasies, which means that outside of these fantasies there exist infinity of motion of matter and the absolute cause of this motion.


An infinite set of all events – is the only set, equivalent to the most general composite phenomenon including in itself all particular things which have the Absolute as their cause (complete or partial).

Proof of the theorem

Step 1. An infinite set of all events – is the only set, which incorporates all events in the past and in the present time (Axiom).

Step 2. An element of any infinite set is understood as a subset – a composite phenomenon (Axiom).

Step 3. An infinite set of all events is understood as the most general composite phenomenon (MGCP) [2]*.

Step 4. Any composite phenomenon is not self-caused, which means that it is not the cause of itself.

Step 5. The most general composite phenomenon, which is equivalent to the infinite set of all events, is also not self-caused.

Step 6. Only a non-composite phenomenon can cause the MGCP.

Step 7. The Absolute is a non-composite phenomenon, causing the MGCP.

Step 8. Since the Absolute causes the MGCP, which is an infinite set of all events, it also causes existence of all elements of this set.

Step 9. The Absolute is a complete (necessary) cause of natural systems and a partial cause of artificial systems.

The following part of this paper can be considered as a scientific-philosophical interpretation and development of the idea, imbedded in this theorem (of cause one should bear in mind the famous commandment: “Don’t create an idol for yourself”).


In the context of this paper it is suggested to understand the term “absolutisation” as:

1. treatment of the reality only from the point of view of some single theoretical reasoning without consideration of its own restrictions and competing reasonings;

2. extension of the property of self-causing to substances which are not self-caused.

Appearance of the quantum mechanics faced philosophy of science with the following question: why is it not possible the make an arbitrarily exact description of dynamics of a micro-object in space and time? Unfortunately, the assumption of transportation of a micro-object in space within the limits of its wave package was not accepted by physics!

The theory of determined infinity (TDI) has suggested its own metaphysical answer to this “painful” question [3]. The formal logic of this theory is as following. Continuity (including metric infinity, infinity of world time, which has no beginning, potential infinite divisibility of space and time) is in agreement with causality, because it does not admit existence of absolute emptiness as a media which has no cause. The fundamental character of the micro-world indicates that its principle of objects transportation, implemented in continuous space, is also fundamental.

Transportation in the micro-world takes place along a discreet trajectory by means of multiple quantum extra-temporal teleportation of the micro-object’s mass. Atemporal character of transportation of a micro-object mass between points of the trajectory is explained by impossibility to cover the way, consisting of infinite sequence of segments of the infinitely divisible space.

Fig 1. Diagram of a discreet trajectory of a single quantum micro-particle in the state of superposition (the arrow indicates the direction of its travelling in space).

In this case the following three conditions are observed:

1. a micro-object is ideally travelling in an ideal space (logic of the process);

2. a micro-object does not disappear in space while travelling (demand of the energy preservation law);

3. in accordance with the von Neuman’s theorem, hidden parameters of a micro-object are excluded.

Extra-temporal teleportation of system’s state also takes place in the micro-world.

Every physical object being a phenomenon, the quality of its interactions is infinitely diverse. These interactions of a quantum micro-object, which is in instant state of rest, determines its next (after the previous teleportation) coordinate. In the same way, the infinite diversity of interactions of an atom (for example, of radioactive uranium) determines the specific moment (in the range from seconds to millennia) of its decay.

However, physical interactions cannot be the cause of quantum extra-temporal teleportation because they take place in space-time.

In accordance with the TDI, transportation of quantum micro-objects is accomplished by the Universal Non-physical Force (UNF), that is – by the Absolute.

The TDI gives the following predictions:

1) further experiments on quantum teleportation of mass (including experiments on quantum tunneling of sets of micro-objects) together with experiments on teleportation of states would confirm extra-temporal character of these processes;

2) any physical theory which rejects continuity of space and/or time would face logically unsolvable problem of divergence.

There is a question to be answered by the TDI: how could the extra-temporal character of a quantum micro-object be explained? TDI gives the following answer: by potential infinity of segments of a path in a continuous space.

There is another question to be answered by the TDI: what is the process of quantum micro-object transportation? The TDI gives the following answer: this is a metaphysical, ideal, extra-temporal process.

The next question is absolutely inappropriate from the point of view of the atheistic paradigm, which still prevails in philosophy and science, although it has already exhausted its potential.

Here is this question: what is the logic of choice of the next coordinate after transportation of a micro-object and who would make this choice? The TDI gives the following answer: the choice of interactions, which determine the next coordinate of the micro-object and its life-time is made by the UNF (the Absolute) out of the infinite diversity of all possible interactions of the micro-object. The logic of choice is the following one: this is an intelligent dynamic system. More rough influence on the micro-world is made by the human being – observer.

Thus the main idea of the TDI is the idea of real existence of infinity and of the extra-temporal transportation where this infinity is taken into account.

Usually the following objection is set forth against explanation of motion in the micro-world by extra-temporal transportation of a micro-object along a discrete trajectory under the influence of the non-physical force: “You are trying to explain a thing, which is easy to understand (namely, transportation), by a more complicated thing, namely by extra-temporal teleportation of a micro-object’s mass along a discrete trajectory, which is extremely tangled, and besides that you use a supernatural force. But an explanation, as a rule, has a more abstract character in comparison with the reality to be explained. It is exactly the transportation of quantum micro-object which is the most paradoxical thing and which needs to be explained. As for the special force, which is responsible for the transportation and for the laws of nature, it is fair to say that without action of this Force the very intellect of a human being becomes a fruit of an evolution without reason.


Infinity is quantitative perfection of a set and qualitative perfection of diversity.

Determined infinity is a real quantitative-qualitative infinity, which is causally conditioned and connected into a single whole [4].**

Infinity unites logically such substances as continuous space, continuous time, transportation of a quantum micro-object and general interconnection of phenomena (GIP). Let us substantiate this statement.

1. Continuous space – that is a space which is completely filled, non-limited, potentially infinitely divisible and speculative, that is – ideal. The same considerations refer also to continuous time.

2. Transportation of a quantum object in an ideal and potentially infinitely divisible space presumes ideal (extra-temporal) character of this process.

3. GIP connects infinitely diverse infinite sets of phenomena.

Thus, in all three mentioned above cases the notion of infinity plays the key role.


Let us substantiate this statement.

Modern physics operates with a notion of practical infinity, which means “hypertrophied” finiteness. It is well known that the notion of “absolute” in physics has different content than the notion of “absoluteness” or “absolute” in philosophy. An absolutely black body is a body which completely absorbs an incident flow of radiation, and absolute zero of temperature is the beginning of measurement of thermodynamic temperature.

In philosophy the notion of “absolute” means something that exists by itself, having no need in external cause for its existence.

Let us consider the main versions of absolutisation of “absolute” in science.

5.1. Absolutisation of motion of matter and physical interactions

The general theory of relativity, electrodynamics, quantum theory of field, and modern cosmology, when including physical fields (gravitational, electromagnetic, quantum, scalar) into the space of material substances, in a non-obvious way presumes that field is a self-caused material substance [5].

For example the twistor program of N.Penrose absolutises particles and physical interactions [6], while ether-dynamics absolutises ether [7].

Absolutisation of matter’s motion is revealed also in materialization and relativization of Newtonian absolute space and absolute time in the Einstein’s relativity theory [8]. If one considers TDI then the presumption that transportation in micro-world is a result of a physical interaction, which is so obvious for ordinary people, becomes entirely arbitrary for a scientist.

5.2. Absolutisation of information

The following things could be considered as absolutisation of information: a) absolutisation of ideas, laws and principles, including, for example, ideas of self-organisation of systems in the synergy theory [9], ideas of indeterminism in quantum physics [10], global evolutionalism in cosmology [11], systems of connections in binary geometrical physics [6] and some others.

б) Absolutisation of space and time, including, for example, absolutisation of time in the N.A.Kozyrev causal mechanics [12], non-obvious absolutisation of space in the string theory [13], absolutisation of space-time in the geometrical dynamics of V. Klifford and J. Willer [6]. Hidden energy of the space dilatation process is also absolutised in cosmology [14].

в) absolutisation of emptiness following Democritus is revealed as a tendency to attribute fundamental meaning to primary fluctuations of cosmological vacuum[14], as well as a tendency to deny ether in the spirit of the special relativity theory.

5.3. Absolutisation of human mind

Absolutisation of incredible abilities of the extraterrestrial civilizations is common to K.Tsiolkovsky and his like-minded writers of science fiction. Conviction that quantum reality does not exist without a human observer, shared by majority of modern physicists who adhere to various interpretations of quantum mechanics, – isn’t it an impressive example of absolutisation of the observant’s role in science? [15].

Thus, absolutisation of information and human mind denies, to a certain extent, the Absolute, which has philosophical or religious meaning.

Absolutisation of finiteness in physics denies infinity, and absolutisation of matter’s motion in philosophical materialism denies metaphysical reality.


The Newton’s idea of existence of absolute space and absolute time is, in essence, an entirely modern idea of existence of a metaphysical base for science.

How did Newton understand absolute space and absolute time?

In his mind, they mean filled space and time, which are not given to human beings in physical senses, which are not influenced by physical forces, but which exist in the objective reality and which are not connected with a finite reference system [16].

It is obvious that, in Newton’s understanding, absolute space and absolute time are fundamental metaphysical substances [17].

What does the universal interconnection of phenomena comprise?

It comprises qualitative-infinite determinism (interconnection of states) and causality (genetic interconnection of phenomena), which are ultimately realized on infinity, representing fundamental metaphysical substances and their relations.

What does the process of transportation in the micro-world mean in conjunction with the TDI?

This is a fundamental metaphysical process of transportation through the potentially infinitely divisible space.

So, space, time, transportation, interconnections and relations, understood in their fundamental meaning, can be considered as a metaphysical base of physics.

While neither mind nor knowledge comprises the subject of interest in physics, and also neither biological nor social reality, there presumably should be no other metaphysical bases of physics at present.

As for science in general, it would be fair to add the Absolute to the metaphysical bases mentioned above. This is because of the fact that otherwise it is quite difficult to explain the biological evolution which has human mind as its result.

Thus, as it has been already mentioned it this paper, the real infinity unites all the listed above metaphysical bases for physics, and the determined real infinity includes the cause of the Universe into this list of bases.


Acceptance of the determined infinity conception as the metaphysical base for science will make it possible to obtain the following results:

a) through the idea of the UNF (the Absolute) it will be possible to establish agreement between scientific and religious knowledge;

b) through metabolic motion, related to the process in which some space points enter the system and other points leave it, it will be possible to establish agreement between transportations in micro- and macro-worlds [18];

c) through the experimentally confirmed idea of extra-temporal teleportation of quantum micro-object mass along a discreet trajectory it will be possible to establish agreement between the quantum mechanics, common sense and visual clearness [19]***.


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*The term MGCP as a global phenomenon was suggested in [2].

**The conception of real infinity was developed by these authors [4].

***It is interesting to mention, that this author has suggested the principle of visual non-clearness.