INDUCTIVE LOGICAL CONSTRUCTIONS - CHAPTER THREE PHYSICS, Specialized Part

Specialized part

6. I want to begin this part by admitting that some of the ideas at which we will arrive have already been expressed, be it in this or another form, by other people, but there will be others which I believe will be new to the reader, for at least I have not come across them before. However, I can firmly state that no one has interpreted the concept of matter, its laws and the basic principles behind it (its organization) in the same way I have. I also presume that the reader is familiar with concepts such as ‘time’, ‘spatial dimensions’ and ‘time as the fourth dimension of space’ (space-time), since they have been alluded to in section 2 of the current chapter.

So far in our study of physics we have arrived at the idea of synthesizing a physical concept as a way of clarifying it. If in the previous section we were forced to base the synthesis of our model of the atom on electromagnetism only, then the synthesis of the model of matter should be based on nothing at all. If the model is expanded to the utmost, it is logical to assume that the initial conditions are minimized to the utmost. In the construction of this model we will synthesize a more complex scheme of inductive logic than the ones we have dealt with so far. We will arrange the model of matter along the scheme’s first line of effects, and the test data about matter along the scheme’s second line. However, the second line will only be used when an impediment to the development of the first one presents itself.

Before we start I would like to provide the following definitions to facilitate the perception of the exposition:

‘Dimension’ denotes a characteristic feature of an object or a process which describes a state different from the rest.

‘Space’ denotes the full set of an object’s or a process’s characteristics describing its state.

These two definitions show that dimensions describe entirely different states. This in turn means that something cannot be a dimension if it can be described by another dimension. Which dimension is real and which is not could be determined with the help of the criterion of applicability.

A single-value or a single-state dimension cannot be considered one, and the object or the process does not exist in it. In order to exist, a dimension should have at least two different values. The reader can draw an analogy with a single line which is defined by two points. A set of dimensions which does not include every characteristic feature of the examined object or process cannot be called ‘space’. What I mean is that such an object cannot exist in that space; it can only be related to it. The full set of dimensions which constitutes ‘space’ is pertinent only to the examined object and nothing else.

If two spaces do not share any dimensions, they do not exist for each other.

There is no subspace (i.e. a space which is formed after some dimensions from another space have been removed). The grounding of this argument can be found in the first note, and it can be proved by redefining space as a dimension.

These complicated laws, which matter has to obey, will be reduced in the future, but until that time comes we must use them.

The point of departure our study should be the basic physical concepts such as ‘space’ and ‘time in space’.

7. Let us imagine nothingness – the absence of matter, space to accommodate it and time to describe its motion.

Let us now place a unit of matter (i.e. something) inside nothingness. According to the arguments presented in section 6, this thing should be spherical in shape. If we want to synthesize a complete (i.e. real) model of matter, this object must be tree-dimensional (i.e. its completely symmetrical shape should be spherical). If it were two-dimensional, it would be a circle. However, a circle does not possess all the characteristics of real matter, and therefore it is not a space. Thus the object which we place inside nothingness, automatically defines three-dimensional coordinate system. The conclusion is that matter is not accommodated by the object’s linear dimensions (or space), but is the thing which defines them.

Let us now set the object in motion. This motion defines the dimension of time which describes the changes in the object’s state. At this point we should determine the relationship between the object’s motion and the object’s space, which is defined by the same object. In other words, what should we relate the object’s motion to, if it is accompanied by a corresponding motion of a coordinate system which it itself defines, and furthermore its motion determines the dimension of time? First I would like to point out that the placing of a second object within the same space would solve this problem entirely, but I’d rather postpone this a little. Second time and space are fiction, and that is why I can define them as immobile, despite the object’s motion. It is a paradox that the immobility of the dimension of time lies in its irreversible and uniform flow. Third if we refrain from using a second object, I can define a fluctuating coordinate system and the military will win this round. If we imagine a space which changes its basis (i.e. its zero point, standard quantities and positive direction) indiscriminately and unpredictably, there cannot be a motion, related to these dimensions, which cannot be registered during the period of the slowest change in the basic quantities. However, as the change of the basic quantities is arbitrary, the slowest change is a prognosis, and therefore the time it takes approximates zero. For the time being I will call such a model of space an absolute coordinate system.

I assume that the reader might have already noticed the discrepancy between the definitions of space and dimension we agreed on, and the way I deduced the dimension of time. In view of the fact that I do not mean for the same definitions to become postulates, but to clarify the concepts we use, I offer the following explanations: if the object’s motion in relation to the absolute coordinate system defines the dimension of time, the flow of time should stop with the cease of the motion. But where does this paradox rise from? It does not come from the secondary position of the dimension of time in relation to the motion nor from the possibility that time can stop under certain circumstances, but from time’s relation to the object’s linear dimensions. It is true that motion determines this dimension, but it is not the motion related to the space mentioned above. If it were, it would be possible to describe time in relation to a three-dimensional coordinate system. However, this would contradict the corollaries of the definitions of space and dimension. Therefore, in the object that we are examining there is motion which cannot be described in relation to linear dimensions, and it is precisely for this reason that it defines a new dimension of space – the so called fourth dimension. I have to admit that it is this conclusion that lies at the core of my study of physics. Perhaps there are people who cannot imagine a motion which cannot be described or related to the three-dimensional coordinate system, especially after we introduction of the fluctuating coordinate system. In other words, how is it possible that something moves and remains at the same place at the same time? This is not a contradiction in terms but a conflict between a possibility and a too narrow understanding of motion. As a temporary solution to this problem we could assume that the object changes its color. This makes things clearer.

Let us consider this ‘strange’ motion. The first question we have to answer is: are there any conditions or laws which govern it? I other words, since all known matter is governed by laws, this synthesized object should be governed by laws too. That is to say we are indeed trying to construct a real model of matter. Consider the following logical scheme. Since there is an object, apart from which there is nothing else in this space, we can consider it as a closed system. It is for this reason that I was unwilling to use another object. Whatever the system of the object is, if it comprises everything, it can be considered as a closed system, and it will be subject to the same laws governing all other closed systems. Unification though, which the reader might have already thought of, is not among the processes flowing in this closed system. What unification? The processes we are considering now have an entirely different form. If the processes flowing in a system tend to recur, it can be considered a closed system, be it a complete or a partial one. Every closed dynamic system (of a real type) exhausts the number of its possible states. In other words, the permutations of its elements are a limited number, which suggests that the elements themselves are a limited number. The system’s dynamics, on the other hand, which is characterized by a limited number of strictly defined laws, entails the recurrence of this limited number of permutations. This principle is no longer valid if the system cannot be considered a closed one, or the number of its elements varies (this is closely related to the previous condition), or there is no regularity in its motion. As regards the first condition, we already know why we consider the object a closed system. The other two conditions are not relevant to real objects – even the universe is made up of a limited number of elements (it is an entirely different question whether we make a difference between infinite and numberless) which are governed by certain objective laws (regardless of whether or not we have discovered them). That is why I see no reason why the object we are examining should not be governed by the same principle. In case the reader has not gathered the essence of the above mentioned principle, I will provide a simple explanation: imagine that we arrange a pack of cards in a certain pattern then we select the cards on the right and shuffle them perfectly. After we repeat this action a fixed number of times will be restore the initial arrangement of the pack. If we continue to shuffle the cards, we will notice that each time we restore the initial arrangement we have shuffled the cards as many times as before. I could give other examples but this one is particularly pertinent because the length of interval (i.e. its period) between two identical arrangements is determined by the number of times we shuffle the cards. But how can we apply this variable to our object? What determines its period? The answer is rather simple. Since the change of the object’s state defines the dimension of time, it is logical to assume that its period is an interval of this time. In other words, it is a period of the kind typical of. The two basic quantities characterizing a harmonious oscillation are its period and its amplitude. Undoubtedly, the period is a standard unit of measurement similar to the meter as regards space. The question is whether the period is divisible or not. In order to find the answer to this question, I suggest we analyze a single vibration in a single period from the endless number of periods. If we examine the last but one phase in the period, we will see that vibration’s amplitude’s quantity cannot be related to anything. If we project the initial phase in the period on the last but one, we will also see that, in fact, there is nothing to observe. We could as well try to find the beginning of a circle. All this shows that any division imposed on the period is of artificial nature. From the point of view of space the period of the examined object is indivisible; it is a point in the timeline and there are no other time constants that can divide it without a residue, i.e. there are only multiple periods, existing as time quantities. From the point of view of the examined object the period is minimal and maximal at the same time. In other words, it is unique. Figuratively speaking, the object comes into being and dies every other period. What we have just done is establishing the dimension of time – there cannot be a quantity of time smaller than any quantity stipulated by matter. From now on we will refer to this period as an elementary period of time. In fact it is a point in time. As regards the dimension of time, the geometrical interpretation of the term ‘point’ is irrelevant. We are not dealing with a circle which has a vanishing radius, but, according to the definition of a closed system, with the smallest precisely determined and unalterable period of time. The infinite recurrence of one and the same period, which could be represented by the model of the harmonious oscillation, not only determines the dimension of time as one of the points in the infinite recurrence, but also endows the model(as a model adopted by us) with every characteristic of real time - its mono-directional and monotonous flow. For the sake of precision I must explain that I introduced (rather artificially) the finite number of a system’s elements to achieve clarity. From the point of view of philosophy this resulted in the emergence of the problem of the possibility of division of the whole. On these grounds to claim that there cannot be anything smaller than the whole would be a supportable contention. The whole could be divided if two whole units, which differ in a characteristic they share, are compared. This would lead to a difference which will be smaller than one of the compared items at least. If we refer back to the harmonious vibration we will see that there is nothing finite, be it the amplitude or the period that is not related to something else. For this reason, if we have to compare something to something else, the second object should be of the same kind. I mean that we will realize that we should correct our arguments if we apply the underlying principle of a closed system to this thread of thoughts. We could still define the elementary period’s capacity for division, but it would still be an artificial affair. Let us analyze a phase (a state) in the object’s motion. Its dynamics presupposes a change of the phase. If you remember the departure point for our analysis of the underlying principle of closed systems was nothing else but dynamics, and the principle itself meant that the body returns to its initial state. In other words we deal with the same circular motion on which we based the analogy with the harmonious vibration. However, such an analogy cannot be used as the basis for a model and for this reason I have carefully avoided it. The infinite number of the object’s elements and of the phases in its motion is caused by object’s the strictly defined, and therefore limited laws which govern its motion.

I can already state that the entire model of matter could be deduced from the philosophical principles we have formulated. This is the second time philosophy has turned out to be very helpful in our understanding of physical matters, and as we are about to see, this is not the last time. Physicists should not think that I am trying to pull the rug from under their feet, for I am giving them a serious and successful logical approach to their study of matter.

8. This section is a real firework display. What we will do in it is consider the different laws of preservation alongside our object of study.

The lowest quantity of the time interval, we have registered, can be partially applied to other characteristics/properties of the examined object. What could those properties be then? In order to answer this question we must remember the fact that time is one of motion’s characteristics/properties and restricting time would mean restricting the object’s motion. It is obvious that motion cannot be restricted because it is what determines the restrictions – the restriction of restrictions is a very complicated logical configuration to use in such a simple example as this one. Then, what we are left with is only the restriction of the linear coordinate system (i.e. of speed).

The proof is more than simple: if the object manages to travel a distance greater than its own diameter during a single elementary period of time (i.e. a moment in time) it will be at two different places at one and the same time, which is impossible. Therefore, during an elementary period the object can travel a distance no greater than its own diameter, whereby, from the point of view of geometry, it will have a point of contact with its initial position from the beginning of the elementary period. This shows that the object’s maximal speed is limited. This is, in fact, the very essence of the third postulate of Einstein’s general theory of relativity (Was it that hard, Albert?). Being satisfied that we have proved something a great physicist such as Einstein failed to do, we could dangerously neglect another discovery whose scientific importance is much greater than that of the preceding one, and which is much more difficult to prove. Such an absolute restriction on the object’s motions in relation to linear dimensions apodictically defines a real and absolute coordinate system. This means that the maximal speed of the examined object is not a sum of its speed and the speed of the linear nor is it deduced by means of subtraction. In other words, we do not deal with the relative effect of an object on a mobile coordinate system, for the object’s motion is irrelevant to it. At first the proposition that the object’s speed (i.e. its motion within linear dimensions) is of no importance to linear dimensions seems to be a contradiction in terms. The problem does not arise from the fact that somewhere or everywhere unalterable points of departure exist, but rather from the relations of two ‘things’ which cannot be relative, for they cannot be related to anything else but themselves – the object’s diameter, which encompasses the object’s volume, is related to the object’s elementary period. The coordinate system is unalterable in the sense that either the object’s spatial parameters are invariable because the object’s elementary period is invariable, or that they are variable, due to the fact that the period is variable. The latter successfully matches the fictitious nature of space and time, leaving only motion to matter, for the dimension of time encompasses the linear dimensions and makes them dependable on it. Such is, in fact, the real model of matter. However, for the sake of clarity I prefer to leave linear dimensions and time in the model of space; if I choose to do otherwise, what is still to be said will border on the completely unintelligible. The model of matter, when devoid of space, encompasses Einstein’s theory of relativity, but in a more universal and logical form. However, since this theory has to be analyzed from the point of view of our synthetic model, I will refrain from using the above mentioned modeling strategies; what is more - they can completely distort this treatise. Therefore, if we want to construct a lucid spatial model of matter, which can be easily interpreted with inductive logic, we have to assume that the object’s time interval (i.e. its elementary period) is completely unequivocal and indivisible. Consequently its spatial characteristics are also absolutely unequivocal. In other words, the object has only one elementary period and only one diameter, both of which are invariable. Since the object’s basic parameters are absolute in character, the object’s motion and the motion within the object will be the same as regards any other coordinate system or space. The last conclusion is, in fact, a logical summary of the first and the second principles of the General theory, despite the seeming contradiction. We have announced that we have deduced the underlying principles of the dimensions of time and space on the basis of the absolute character of these two dimensions. In time the reader will reach the same conclusion by themselves. Let them for the time being think that Einstein simply had a good start. The conclusions we will reach surpass the theory, its underlying idea and even its centenary unification.

It is time we placed another and different object in ‘our’ space. It will be defined as different from the first one because of its different elementary period and diameter. Its different characteristics should signify that its maximal speed is different too. This means that different types of objects within matter have different maximal speed. Unfortunately, this is untrue. The maximal speed of real objects is one and the same – it is the speed of light. If we refer back to the two objects now (considering the fact that their maximal speed is the speed of light), we will see that should their speed be different, the change of the elementary period would entail a change of the linear characteristics, which is impossible within the spatial model because time would swallow the linear dimensions. The only solution to this problem is to assume that the two objects have one and the same elementary period. We seem to have discovered something very important: matter is mono-corpuscular. The objects around us are made up of one and the same type of particles.

The reader might be under the impression that we have abandoned the synthetic nature of our model by introducing an experimental find such as the maximal speed of light to it. The situation is, in fact, entirely different. This contact with experimentation (as we have already stated above) serves the function of a corrective in the deadlocks one inevitably reaches when the conditions in the initial phases of the application of the scheme of inductive logic are rather limiting. We have already established the top speed of an arbitrary object. The analogy with the speed of light is a fact but it is not sufficient enough to serve as a basis for a conclusion. When we consider the different maximal speeds, whereby the spatial model becomes irrelevant, the speed of light fits perfectly well into this model for a second time. Let us not delude ourselves that we have entered Ali Baba’s cave with our decision not to develop the spatial model of matter, for we are about to make a step backwards and see that even if had examined different objects, we would have arrived at the idea of the corpuscular character of matter and consequently at the unalterable character of the speed of light when related to all material objects. In fact, the logical thread of the model cannot be of straightforward nature at all. In order t support a thesis or to refute it, one has to develop it first.

Let us now cease making fundamental discoveries, for otherwise they will be of no importance to science whatsoever. If we do not clarify the conclusions we have arrived at so far in the specialized part, all we do will become nothing but an interesting model of matter. For this reason the conclusion we have apodictically made during our logical synthesis will be used to refer back to real mater. This reference will not serve as a corrective (because our model will lose its synthetic character) but as an interpretation.

The idea of the mono-corpuscular character of matter is not new to us. One of the corollaries of the law of the unity of matter reads that there is only one thing in the world. However, if we had tried to develop this idea at that point in the exposition, it would have seemed rather artificial. Then we did not have a physical concept of matter, nor were we aware of the historical development of physics the way we were of philosophy. Even at this stage we are yet to discover what lies behind the term ‘mono-corpuscular character’. On the other hand, in view of the fact that I had promised to be as lucid as possible, I had no right to include as voluminous a chapter as this in a part of the treatise which follows a different thread of logic. The mono-corpuscular character of matter, as we have deduced it, is a proof of the law of the unity of matter but in another logical line. We will see later that the particle which constitutes matter is divisible, and we will find out why it could only be an artificial process. This mono-corpuscular character is a form of the unity of matter from a philosophical point of view, and a fundamental characteristic of its essence from a physical point of view. However, let us end this parenthetical remark and go back to physics.

If we trace the development of logic in the specialized part, and more precisely our basing of the analysis on nothing and the filling of a certain logical volume, created by the object of study in linear dimensions, we will see that we could consider our synthetic model as a closed system of logic as well. We will do that to demonstrate that it contains no danger provided that it is understood and carefully monitored. We will subject the interpretation of the concepts within this closed logical system to unification with the help of physical terminology. The reader is yet to find out with amazement that the discoveries in the realm of matter are not over yet.

In view of the fact that we deduced the principles of the General theory on the basis of the absolute quantities of the particle’s linear dimensions and elementary period, now we have to clarify the meaning of those principles. So far we have come across three absolute ‘things’ – the ones mentioned above and the particle’s maximal speed, which is determined by them. Let us now establish a standard segment within the fictitious coordinate system and draw an axis line through the centre of the sphere of the examined object. Let us now set the object in motion and try to figure out the result from comparing the object’s dimensions at the beginning and end of its elementary period to the segment’s own measurements. At the beginning of the period the sphere’s rear end has a particular position in relation to the object’s motion, whereas at the end of the period the front end is displaced forwards at a particular distance. In other words, the object’s size has increased in relation to its linear dimensions. This means that from the point of view of the moving object the dimensions of space decrease with the increase of the object’s own dimensions in the direction of the displacement. Thus, and not in a projection within a spherical coordinate system, in our conclusion regarding the relative values of linear dimensions and time we can conclude that the projections along other axes do not change their values. At this point we have to note that the examination of a process should be carried out in relation to all dimensions of space. In this case we have examined an object at a particular moment in time, as defined by its elementary period and we have concluded that the linear measurements are shortened along the axis of movement at this particular moment (a point in the dimension of time or time’s axis). The object’s measurements, as well as those of time, remain the same. We have been able to reach the conclusions of the general theory only because of our scrutiny of the dimension of time. Therefore, the relative values of time and space could be related only to a spatial model of matter. However, as regards the fictitious nature of space, this is a very treacherous theoretical trap. If we are trying to construct a spatial model of matter, we are only doing it to provide the brain’s scheme of inductive logic with an opportunity to do some work. However, we should not think that the model excluding space is impossible to synthesize; it is but in it we will not be able to use experimental data. If we refer back to the general theory, we will see that it has accepted the object’s maximal speed as an absolute value, and has defined as relative the dimensions of time and space (i.e. the linear dimensions and the elementary period), which determine the object’s maximal speed. It is for this reason that I claim that this theory confuses absolute and relative concepts; if the object’s dimensions and time interval change with motion the object’s speed should change too. The speed could remain unaltered but linear dimensions would take over the dimension of time. This is obviously in contradiction with everything we have deduced so far. Physicists though, do not see a flaw in this kind of logic and define an interesting concept, namely, a space-time continuum – something I would agree with if they did not consider space (which is essentially the same as our term linear dimensions) to be the dominant dimension. We have deduced a much more logical, successful and most importantly – synthetic model of matter (in which there is nothing relative and everything is as absolutely defined as matter) in which the dimension of time can swallow the continuous dimensions from the model excluding space. When I said that Einstein had had a good start, I meant that he had defined matter’s dynamics as absolute at speeds lower than the speed of light. Space and time are directly dependant on it and it is these grounds that the space-time continuum is defined. On a second thought, what could we possibly define as absolute after Michaelson’s experiment? I’d rather leave the question open for further consideration.

At the time we were considering the absolute nature of linear dimensions and the elementary period in relation Einstein’s theory, we tried to find out what the distance between the object’s rear end at the beginning of its period and the object’s front end at the end of its period would be. In other words we summed up the object’s volumes during the entire period. Thus we reached the conclusion that the continuous (linear) interval of the three-dimensional coordinate system becomes shorter in the direction of the movement. However, there is logic contrary to this one. If we analyze anew the distance between the object’s rear end at the beginning of its period and the object’s front end at the end of its period, we will find out that the same interval is longer because this distance becomes shorter. Physicists cannot escape from this vicious circle (I remember it only now) because the General theory does not take into consideration the alteration of the interval of the linear dimensions in relation to the direction of the movement. If the reader remembers, I claim that the interval lengthens in the reverse direction. You can consider this a curtsy to Einstein. He reason we are dealing with such reverse logic is entirely different. It is quite obvious that in this case we are examining the single reverse vector of the linear dimensions. From the standpoint of modern physics it is rather interesting that the object does not perceive other objects within a three-dimensional coordinate system but within a four-dimensional one (in the simplest of cases) or within a six-dimensional one, excluding time, if (from the point of view of an object moving at the speed of light) the vectors of the spatial basis in the direction of the movement and in the reverse direction are different. However, since I am completely convinced that no physicist will take advantage of this idea, I will return to our arguments.

The analysis of the difference between the object’s volumes at the beginning and end of its elementary period, rather than the sum of the volumes the object fills during the period, makes us think that the object ceases to be a particle when its speed is maximal because the object’s volume equals zero. If we add the physical term corpuscular (which denotes a particle, i.e. a closed volume) to the above argument, we can come up with the following definition: ‘An object possesses corpuscular properties if it permanently encloses a volume.’ First we are examining not just a corpuscle, for the object is such a thing by nature, but properties possessing such characteristics. In other words we are examining the concept in the same way physics does. Second since we are dealing with properties, they should have more or less constant nature. This means that there should be a part of the body which cannot be at one and the same place in two succeeding moments in time. Third the closing of a minimal volume means that the section of the spheres which are, in fact, the object itself should be different from a geometrical point. In other words, the object should move at a speed lesser than its maximal speed. Following this thread of logic, the other object cannot have corpuscular properties if it does not enclose a volume in two succeeding elementary periods (i.e. when it moves at its maximal speed). From the continuous nature of the property it becomes clear that it is not appropriate to consider the sum of the volumes in an elementary period, even if the reverse case is added to it. If we did so, we would arrive at the conclusion that the object would only have corpuscular properties in the direction of the motion. In fact, it either has some properties or does not have any regardless of any relations. If we observe that the object cannot permanently enclose a volume at its maximal speed, the conclusion is that it does not possess any corpuscular properties in any directions. This is true for other bodies with which the object can interact, and in relation to which we can consider any changes in the object’s shape. The object cannot possibly interact with itself because it is indifferent to itself and there is no indication of any changes in the object’s parameters.

The evaluation of the object’s corpuscular properties excluded the addition of the sum of volumes and their subtraction in the object’s period can provide us with a visual interpretation of the object’s form at maximal speed. When we add volumes in the direction of the motion, on the one hand we deal with length which is greater than the object’s length at peace, and on the other we deal with a geometrical point which is, in fact, a section in a plane perpendicular to the direction of the motion. In plain words, the object has a narrow long shape. Recalling the fact that the same object’s periodical change could be described by means of harmonious vibration, we can claim that from the point of view of all other objects the one which moves at its maximal speed resembles a string. It would be dangerous to assume that we are trying to use the theory of strings within our own scheme of inductive logic, for the points of contact between the two, although many are of a purely formal nature. This means that the laws, described by trigonometry functions and governing strings in physics and our synthetic dimension of time, only make the two models appear similar. However, the similarities between the two models are rather superficial and irrelevant to the evolution of the ideas in them. I had to make the above explanation because the logic behind the theory of strings is much closer to our own logic than all other theories in physics, the General theory of relativity included. It is probably for this reason that theoretical physics perceives strings as an exotic phenomenon and it is for the same reason that our own arguments will probably be rejected by physical circles until a new generation of scientists emerges, but let us not forget that history it the best judge of all. Contemporary physicists are not accustomed to working with logical schemes and they have not yet arrived at an understanding of the importance of the relation between reason and the subject of their study, namely matter. Anyway, it is time we came back from the future.

The geometrical interpretation of the non-corpuscular form of matter, namely the string, could help us understand the interaction of the string with another form of matter. If this other from is solid (i.e. made up of corpuscles) and provided that the section of the string which has to interact with the corpuscle is a geometrical point (i.e. its diameter equals zero or approximates zero), the string does not exist, no matter whether it is observed from a point facing the direction of the motion or the reverse direction. Therefore, it should be able to pass unhindered and without any interaction through solid matter. However, we will put aside this conclusion only adding the thought that the lack of interaction is a result of the very small dimensions of the string’s section. When the diameter equals zero everything is alright, but if the diameter approximates zero (i.e. although it is small it exists) the string should interact with the matter possessing corpuscular properties. This makes it clear that the analogy we have just made cannot be interpreted in geometrical terms. In addition to that the geometrical interpretation treats space as an initial cause. However, this does not mean that this interpretation is wrong or simply unnecessary. With the help of this logical connection we define a more general problem such as the relation between corpuscular and non-corpuscular matter in the context of our arguments. We should note that within the content of the examined phenomena the term ‘matter’s mono-corpuscular character’ already encompasses strings (or just the string for the time being).

We have to make the conclusion that the geometrical interpretation of a ‘string’, as well as the spatial model of matter, treats the interactions within matter in rather different logical ways, which lead to ineffective conclusions. Therefore we should go back to the model of mater which excludes space. It also follows that the issue of the interactions should be considered before the issue of diversity, for otherwise it would represent the effects of unification.

10. Before we start developing the spaceless model (which as regards matter is real, whereas it is fictitious to reason) let us find an answer to the question ‘Why are we juxtaposing those fictitious concepts in a pretentious logical scheme?’ The answer is that we are doing this research because immediately before the presentation of the essential part of ‘our’ model we took a very important logical decision from a structural point of view.

10a. The fact that we are doing the right thing (which can be logically explained) at a time when we can make a serious mistake does not allow us to regard the stars with different eyes. The spatial model of matter or the graphic interpretation of inductive logic deduced another form of mono-corpuscular matter, namely the string, on the basis of its maximal speed. It is the artificial character of the graphic interpretation of the string, rather than the natural character of this division which posed the problem of the relation between the ‘string’ matter and corpuscular matter. Inductive logic immediately established the fact that it was a question of one and the same thing and that the solution to problem lies outside the spatial model. Formal logic would have considered the corpuscle within a two-dimensional figure such as a circle, and the string as an expanded circumference (i.e. a segment whose length equals half of the circles’ circumference. The dangerous thing here is not the visualization but the quantitative characteristic, which would have been immediately processed with the help of mathematics even without an attempt at grounding such an action, all the more it derives from one interpretation of the concepts of a corpuscle and a string. The fact that inductive logic has led us to believe that the relation of the interactions and the spatial model is not of utmost importance does not mean that the conclusion made is not valid (as we will see later) but that it is incomplete. Inductive logic has narrowed down the circle of the existing arguments and consequently found that they and all other arguments could originate only from a spaceless model of matter, or in other words, from real matter which exists as a solid vision within our synthetic model. It is this internal corrective (which is, in fact, a return to the source) that makes this kind of logic a successful scientific method.

10b. Generally speaking, an interaction between one and the same kind of things is impossible. If it is a question of the interaction between a corpuscle and a string as forms of the mono-corpuscle from the point of view of the qualitative differences in their motion, then we should be looking for an interaction between an object possessing properties of a corpuscle and an object which does not possess any such properties. Those properties were defined within the structure of the spatial model with the purpose of harmonizing our terminology with that of physics. It is clear that even if there were an interaction in this case, it would decrease the string’s speed, for the opposite is impossible, and increase the corpuscle’s speed. But here we come upon the law of the preservation of impulse, which governs corpuscular matter and cannot be applied to the string, and besides it requires an understanding of the concept of mass. In other words, this thread of logic is unacceptable. In order to discuss interactions within matter which are in harmony with every philosophical law, we should select such an interaction which causes the emergence of diverse forms of matter. Therefore, it’s a question of the diversity of matter.

10c. If we recall how we dealt with problem of diversity when we were constructing the model of the atom, we will realize that our conclusions have not changed, due to the simple reason that both the model of the atom and the model of matter, which is being constructed now, are apodictic, whereas the current problem has a thoroughly synthetic nature. From this it follows that the model cannot be changed; if something has to be changed, it must be something unrelated to it. Within the spatial model the maximal linear distance (i.e. the diameter) and the minimal time interval (i.e. the elementary period) of the corpuscle cannot be changed under any circumstances. This refers to their relationship and anything else which can be related to them somehow. This is so, for a change can destroy the model. It is at this point that we must refer to the spacelss model of matter, for the above parameters belong to the spatial model. The primary cause of time and linear dimensions, as well as the spatial model based on them is nothing else but motion itself (according to dialectical materialism the world is moving matter). This motion has already been defined and its periodic character determined. However, the diversity of nature presupposes poli-harmonious, rather than mono-harmonious character. In other words this motion is made up of numerous other motions which are, in accordance with what has been said about motion as such, harmonious vibrations. On the other hand all these motions must have a common period identical to the corpuscle’s elementary period. If we refer back to the spatial model, we will notice that we have divided the dimension of time to sub-dimensions whereby the dimension of time, being the sum of its sub-dimensions, is, in fact, a sub-element of its sub-dimensions in the same way the sub-dimensions of time are elements of the dimension of time. This is a trap into which formal logic can easily find itself in its attempts to describe the model in mathematical terms. On the other hand inductive logic cannot fail to take into consideration the dual character of the dimension of time, for the common period encompasses the shorter ones (i.e. the dimension of time encompasses its sub-dimensions) and the sub-dimensions, whose basic characteristic is time, determine the diversity of matter in the real world, as well as the further construction of the model in the world of logic. Referring to our previous arguments we will find out that the subdivision within the dimension of time does not change the model at all. We are again dealing with a particle whose diameter and period are precisely defined, but the latter is made up by other periods. Figuratively speaking, we are dealing with a set of strings (whose individual vibrations are characterized by periods of their own) whose harmonious sounds form the character of matter as we know it. From now on we will discuss different dimensions of time, but whether we perceive them as a set or a single unit, they will be an already fictitious dimension of space. This diversity does not spoil the model’s synthetic nature at all, for it has been copied from real matter. It is easy to prove that a universe which contains only one thing does not exist. Why our own universe contains more than one thing we are about to find out presently.

10d. If we consider the dimensions of time as a separate space in time, which cannot be real, for it does not possess every characteristic of the object, we will observe a number of identical movements which differ only in their basic characteristic, namely their periods. Every one of these periods can be represented by any other period or by their common period as a constant within their own period or the respective one. In the first case it will be a fractional number, whereas in the second case it will be a whole number. The conclusion is the every dimension can take over the rest. However, since the whole cannot be divided, the above action is impossible, for it will entail the use of fractional coefficients in the description. Therefore, it is only the fictitious common dimension of time that can encompass the rest. Following this logic about ‘our’ space, within the real model of matter time dimensions can only exist together and as a whole. Without this space, not only as a theoretical possibility, some of these dimensions can indeed exist, but they cannot be relevant to our space, due to the simple reason that they are a part of its basis. The possibility that other sub-dimensions exist without this space is unreal because their elementary periods will differ from the elementary period of this space, which in turn will lead to interactions with the other time dimensions. This can be easily proved. If there existed matter in a space other than ours, the dimensions from its spatial basis should not be related to our space, which in turn means that those dimensions should be identical to the ones from our space, ergo our space and the other space must be one and the same. If there is another space, other than ours, it can only be examined as a part of it, regardless of the fact that this part is not related to the common basis.

The conclusion is that it is not possible that a dimension can encompass the rest or parts of them as the fictitious common dimension of time can. All dimensions have an equal share in the mono-corpuscle’s structure. Therefore the uniformity and diversity of the time dimensions’ periods do not affect the model’s character, and are significant only when they are related to the relationships within the dimension of time. This last thing means that the uniformity of time dimensions forms a common time dimension which is characterized by the elementary period of the mono-corpuscle, and the differences between the elementary periods of the sub-dimensions is a precondition for their interaction. This is how they form the varieties of the structurally more complex matter.

We can immediately unravel the secret of the interaction between the string and the corpuscle, as well as the one between strings or corpuscles. First the form of the particle does not make any difference. Second, on the whole particles are indifferent to one another, and therefore the result from the lack of interaction equals the state of the initial conditions – from an onlookers point of view of they do not interact. Third the differences between time sub-dimensions presuppose an interaction. There is a binary system or a system of two objects and a third one which interacts with them. Therefore, under certain conditions there is an interaction. In my opinion this could easily expand to a real theory of relativity which explains the relativity of interaction, rather than the processes flowing within fictitious spatial dimensions. The heretical idea that one and the same interaction could seem different from different points of view could amend many mistakes in experimental physics as we are about to find out later. That is why I claim that the physics of elementary particles cannot evaluate the character of an interaction on the basis of an indirect manifestation, for it is only circumstantially related to the interaction. When we elaborate on the definitions of mass and energy later on, the particulars of this position will become sufficiently clear.

We have arrived at the conclusion that the interaction between the mono-corpuscles is determined by time’s sub-dimensions. If time’s sub-dimensions did not exist, no interaction could be registered regardless of the point of view, which means that there would not be any dynamics within the system of material particles. Such a lack would mean that matter were absolutely static, i.e. that it were a substance ungoverned by laws, for the very concept of a law entails an interaction between its elements, which is impossible due to the lack of differences between the particles. Therefore, we can state that such type of matter, which is made up of a single constituent, be it a type of things or a single thing, is absolutely static, i.e. unreal and non-existent. This entails the conclusion that the matter’s dynamics is determined by the differences among the dimensions of time. This cannot prove anything unless it is closely related to the reverse logic. In their desire to discover what was the thing that first set time in motion, theologians, physicists and watchmakers have neglected the lack of motion in matter, and thus they have failed to find out that a universe or matter is nothing when it is motionless. The same goes for finances: money which is not in circulation is not money at all. Some people might accuse me of swapping the places of the cause (i.e. matter) and effect (i.e. motion). I will say, in defense of my actions, that there cannot exist a type of matter which is dynamic at first, but at a certain moment requires (What an amazing property would that be?) sub-elements of the dimension of time. It is the other way round. At first there is a set of periodic movements and only then there can be a model of any sorts. Following this line of logic I will allow myself the liberty to correct the fundamental postulate of dialectical materialism quoted above. Matter is, in fact, the dynamic interactions within time. First comes the dynamics of time’s sub-dimensions, followed by their interactions. After them the set of corpuscle matter, enhanced by its non-corpuscle variant (an unconscious step towards the spaceless model) emerges in its relation to the linear dimensions (which denotes the character of interaction).

Before we start discussing the interactions within matter, I would like to dwell a bit more on the General theory’s principle that all the processes in nature look the same from all possible points of view. At the time we agreed with it, but at the present moment we understand that what the principle says is not like that at all. The problem is that the processes within matter have always been considered from the point of view of their relation to other objects. We have to admit that the above-mentioned postulate is valid in such an approach. However, our model regards matter from the inside, i.e. from the point of view of the relations between the different dimensions. This is its most important contribution to physics, and the same time the point of contradiction with physics as we know it – a clash between the analytical and the synthetic approach to research.

So far we have found out what types of interactions exist between the dimensions of time. The dual analysis we have adopted contains an obvious risk of confusion as regards our point of departure. For this reason the reader should carefully discriminate between the external analysis of an interaction (i.e. an analysis which is made from the point of view of other objects) and internal analysis, which is made from the point of view of time dimensions. It is obvious that there will be a close connection between internal and external interactions, but it should be noted that the elementary period’s indifference to itself or a particle’s indifference to itself does not allow the internal interaction to manifest itself in relation to other objects.

Before we start our analysis of the different types of interactions between time dimensions, we should define their character. In other words, we should find out what laws they are governed by. Since we cannot deduce a law without having considered the matter that would be governed by that law, we have to deduce the law on the basis of the existing concept of matter. The set of the time dimensions which determines the mono-corpuscle’s elementary period is, in fact, a type of interaction between time dimensions. Therefore, the laws which govern it must be the same laws which govern more complicated interactions. Thus we are dealing with some harmonious or simply periodical movements. What is the cause of their coexistence within their common period? (The reader should note that we are not following the logic we used to synthesize the mono-corpuscle. What we are doing is conducting an experiment in our minds) Let us consider a vibration’s characteristics. The most important of them all is its period. Its values directly determine the vibration’s energy. The greater the period is (i.e. the smaller the frequency of the periodical motion is), the smaller the vibration’s energy is. When an object spins faster (i.e. with greater frequency), the energy of the rotation is bigger. The various dimensions with their periods form the common elementary period, i.e. their least common multiple. As a rule, the separate values of these periods are primal numbers. This means that no period or a group of periods can be a whole number which is several times bigger than the rest. The necessity to include a group of periods in the equation makes the general requirement that the periods should be separate and primal numbers. In other words, in theory it is not possible that a time dimension can encompass another time dimension. In reality the opposite is not unreal. However, this does not mean that we are considering one and the same thing. According to the above theory, the common period of the dimensions of time will always be greater than any one of them, which means that their energy is lower when they are together than when they are on their own. In this way we deduced that the principle of minimal energy is at the heart of the interactions between the dimensions of time, and therefore of matter as well. On this premise we can affirm one of our previous conclusions: even if there is a dimension of time which is not related to the rest, it will join them and thus change the mono-corpuscle’s elementary period.

Thus, on the basis of a periodic motion such as the period, we have found the principle of minimum energy. However, apart from the period the vibration possesses another characteristic, namely its amplitude. At the time we were analyzing the mono-corpuscle with a mono-harmonious time period, we arrived at the conclusion that it is impossible to use this amplitude in juxtaposition because there is nothing, apart from itself, we can juxtapose it to. For this reason we did not take into consideration its influence. However, now when we are dealing with several vibrations, possibly having different amplitudes, this impossibility vanishes. Thus, without any further argumentation, due to the fact that such an analysis is related to the mathematical model of matter, which is not the subject of this, I will formulate another principle – that of the minimum amplitude variation. The energy of the dimensions of time will not be distributed evenly along the span of the mono-corpuscle’s elementary period. In other words there will be peaks which will affect the interaction’s stability, rather than its character. The optimum state of the minimum energy and the maximum amplitude variation will determine the most common forms of matter. If someone wants to deduce already existing physical theories such as the theory of quarks, using the method of mathematical modeling, the following analogy could be of particular interest: In music the most melodious string harmonies are comprised of three tones. Well, this can serve as an analogy with quarks’ interactions and triplicate kinds. Every addition of a new tone results in low-frequency but high-amplitude harmonic.

Let us go back to our study. If dimensions from two different mono-corpuscles interact, the mono-corpuscle’s minimal energy, which comprises all time dimensions in itself, could be further reduced. I will now offer to you the following definition: the reduction of energy on the basis of the interaction between different time dimensions from different corpuscles is called a hybridization of these dimensions. Following this logic, hybridization appears to be an energy manifestation of matter occurring between two or more than two particles. It is an internal interaction which can only be registered during an interaction with a third object which cannot hybridization. Via hybridization matter achieves energy states within sets of particles. This interaction’s peculiarity lies in its being different from the separate dimensions of time (though not from the common one) as well as from any other hybrid dimensions. In other words, this is the matter we will refer to when we consider or analyze nature. It is possible that hybridization can take place more than once, i.e. that there could be further hybridization between hybrid dimensions. This, in practice, already determines the great diversity of matter as we know it.

Since the interaction takes place between dimensions from different corpuscles, we can claim that hybridization’s character is the same as that of the basic time dimension, namely the elementary period. In other words, hybridization’s meaning or essence is a replica of the set of time dimensions, but the common period of the hybrid dimensions is a multiple of the mono-corpuscle’s elementary period. Now, taking into consideration the fact that the greater the number of hybrid dimensions is, the less their common energy is, we should try to establish the conclusion of this chain of interactions. As mentioned above, hybrids copy the mono-corpuscle’s set of time dimensions. Therefore, we can call the elementary period’s change to a multiple number (involving minimal changes in energy levels), unification. Since unification is an expression of the energy reduction of a group of particles in relation to the elementary period, i.e. in relation to matter as such, it follows that it is an external manifestation of the interaction. From this, in turn, it follows that the energy manifestations of unification are easy to spot and analyze. However, it is entirely possible that unification reaches a period close to a multiple of the elementary period, rather than a multiple period. It is obvious that the energy difference to this multiple cannot be further reduced by means of further hybridization. What is important in this case is that such an energy difference can be the cause of an interaction typical of its value (for instance, short-lasting unstable hybridization), which can create an illusion of law energy particles accompanying the hybrid mono-corpuscles. It should be noted that the term ‘low-energy’ is not entirely appropriate; from the point of view of that short-lasting and ‘unnecessary’ hybridization the correct term to use is ‘low-inertia’. As regards the illusion, inductive logic immediately concludes that there are no electrons. This assumption is not related to our model and for this reason I will support it only with the following arguments: whenever elementary particles are subjected to analysis, the outcome of the experiments is nothing else but graphic models of the energy interactions within matter. However, they represent the interactions within matter, rather than matter’s content. It would be the same to add the income realized from the increased prices of rare goods to the gross national product – obviously this would lead to a gross national impoverishment. Energy hunters would not delay to remark that in practice it is a question of energy from vacuum (or nothing). Generally speaking, it is indeed correct, only it is not energy from vacuum, but for it. My humble opinion is that such adventurers should abandon all hope that they could alter the fundamental laws of energy. However, those people might consider the following: the difference between the period of unified hybridizations and the elementary period provides a separate energy possibility, due to its isolation from other energy manifestations. The problem is that the realization of this potential energy is the outcome of an arbitrary and short-lasting hybridization, even if its reduction is utterly incomparable to the unification difference. From this it follows that the atom is not electro-neutral at all. Electro-neutrality is possible as an integral function of an arbitrary process in time or a set/assembly of atoms, but as regards a single atom at one moment in time, it is not possible, for the time for hybridization would be equal to the common period of the hybrid dimensions.

12. In this section we will examine a pending problem related to the concepts used by contemporary physics. We have mentioned earlier that the illusory particles which seem to accompany the hybrid mono-corpuscles are law-inertia, rather than law-energy ones. Their law energy is the result of a minimal difference as regards a multiple period of the elementary period. However, we have not yet defined the term ‘inertia’, and for this reason it is rather new for us. In the most general sense of the word it is a resistance against a changing influence. On the other hand physics identifies the concept of mass with that of inertia, which we will accept, for it makes no difference what the term is. Mass does not signify anything by itself, for the unbiased mind associates it with a quantitative evaluation referring to the presence of a particular substance. To physicists it is an innate characteristic of matter, which is directly related to energy and impulse, although the latter a derivative of energy, even from a mathematical point of view. What we are going to do is examine mass as inertia, and thus support a stance contrary to that of physics.

If inertia is a resistance against a changing influence, then it is directly related to the stability of a concluded interaction, i.e. with a momentary state of matter. Since there are two types of interactions, namely hybridization and unification, we can talk about hybridization and unification stability. The former is artificial (i.e. unreal) to a certain extent, for the hybrid state of nature is a low-energy state, and therefore it is more stable. In this sense hybridization stability should mean the absence of low-energy hybridization, but this would be a question of something which has not taken place and might not happen. The latter is absolutely real and refers to the relation between the common period of the hybrid mono-corpuscles and the multiple periods standing closest to the elementary period. If the energy difference between the hybrid mono-corpuscles and this multiple period is big, the inertia is big as well, and vice versa. From all this it follows that, if unification stability is directly related to real inertia, inertia is an external characteristic of matter, which describes the interaction with other objects, but is dependant on the internal interactions between the mono-corpuscle’s time dimensions during hybridization. It is this last peculiarity, but not in this logical form, that has misled physics to define mass as an internal characteristic. The logic behind this conclusion is rather simple: An object’s mass becomes apparent only in the objects interaction with other objects. This makes it clear that inertia or mass are directly related to matter. The question is what type of energy are we talking about? The answer is not provided by energy itself, but by the logical connection between inertia and the interaction. In view of the fact that there could be external interactions of matter only after hybridization, we can conclude that what we are dealing with is a reduction of energy. First, any hybridization is inert. This means that mass is manifested only when at least two mono-corpuscles begin the process of hybridization (the connection between Einstein’s formula and the formula of kinetic energy becomes apparent); low levels of matter a have higher mass than the higher ones within the framework of a unification. From this arises the following illusion of a contradiction: on the one hand hybridization is a chain of energy reductions, but on the other hand the low states of matter have the highest mass, and therefore the greatest reduction. Second, any exact unification is not inert, which means that unification bears no relation to the mono-corpuscle when hybridizations reach a precise period, multiple of the elementary one. This excludes any interaction with other objects. Therefore, if inertia vanishes at the beginning and end of a process of unification, but between these two points has a value different from zero, the inertia has a maximum value. On the other hand, since we examine mass in close relation to stability, we should take into consideration the principle of minimal amplitude variation which becomes bigger with greater number of hybridizations, accompanied by a decrease of stability to conclude that the maximum of inertia is relocated towards the initial hybridizations. It does not a profound consideration to conclude that the above is logical. If we draw an analogy with chemical compounds, we will see that the simplest of them such as water, carbon dioxide, molecular oxygen, etc. are very stable. Furthermore, even complex chemical compounds have a higher mass than the simple ones, i.e. higher matter is more massive than lower matter. This is indeed true, but it is applicable to a chain of unifications, and not to a single one. If we consider their succession as a periodic process, we can state that, since the initial hybridizations of mono-corpuscles are characterized by the greatest energy reduction in relation to the elementary period, the initial hybridizations following the first unification will be characterized by even greater reduction of energy, for they will have been performed in relation to a period which is a multiple of the elementary (i.e. higher) period. This divergence of energy reduction determines the greater mass of higher matter. An finally, we must say that there cannot be any connection between the full energy of matter and its mass, for if there were one, it would only represent the energy, reduced to mass in the process of hybridization. It is true that the rare hypothesis, stipulating that every mono-corpuscle’s dimensions undergo hybridization, does not exclude such a mathematical correlation but the only theoretical model of such a phenomenon is that of the black hole, and still it does not describe mono-corpuscles which have not undergone the process of hybridization, which suggests that what we are dealing with, is not the black hole theoretical physics describes, but something similar to it.

It has already become clear that mass is an energy manifestation of the interactions within matter, i.e. matter’s external characteristics, dependent on the type of mono-corpuscles’ hybridization as related to the order of matter’s unification. However, if there is such a close connection between mass and matter’s interactions, it follows that mass varies with the type of interaction, i.e. being an external manifestation related to other objects, mass should have a different value depending on the other object involved in the interaction . Since this contention as it is, is completely true in its entirety, I fully support the thesis that inertia is relative. However, if we consider inertia as a variable, we will reach the conclusion that an object’s most probable interactions will be connected with matter’s mono-corpuscle and unification forms because they are more stable than the rest. The above suggests that mass will be a stable and constant value. To all merchants’ relief it should be made clear that we are discussing elementary matter and nothing else. However, inertia’s constant could be interpreted otherwise. The accidental nature of matter’s interactions does not entirely affect the types of those interactions, i.e. hybridization and unification. At the same time, usually during physical experiments, aiming to prove the presence or absence of a particular particle by precisely determined interactions, It is possible that the forceful use of numerous interactions will ‘distort’ inertia’s value. Furthermore, the object could even be forced undergo unification until its own hybridization period reaches values which are not multiple of the elementary period at all. In plain words, the object cannot possibly find out which is its elementary period unless it or the rest of particles of the same type are not reduced to mono-corpuscles, or undergo unification in relation to the elementary period, which is impossible by default.

I am convinced that the reader has already understood why, before the beginning of the specialized part, I repeated persistently that physics had not yet defined its concept with the necessary precision. An object’s mass, which is measured in kilograms, and which in the wake of the general theory has been referred to as something of supreme importance, related to energy as such (which, by the way, we have proved wrong, for it is related to the reduced energy), in fact combines every peculiarity of matter, we have considered until now, to form a complex interdependence. Thus it comprises the fictitious concepts of linear dimensions and time (i.e. the set of time dimensions); the two types of interactions mono-corpuscles are involved in, namely internal hybridization and external unification which are have complex connections with energy, which matter’s dynamics possesses by default; the relative nature of objects’ interaction as well as the strictly defined nature of these interactions. It is nothing else but a conglomeration of concepts, phenomena and processes whose lights and shades contemporary physics has rather unfortunately failed to notice. Contemporary physics has established mass relativity in connection with motion within the linear dimensions. Now that we have roved that matter’s maximal speed is limited, it has become crystal clear that the inertia will reach infinity with the maximal speed. However, it will be such only in connection with the type of interaction which we did not even bother to relate to mass.

In fact, this is the reasonable bulk of the specialized part. If we try to expand it, we will only abandon the synthetic nature of our conclusions and distort the synthesized concepts by linking them to experience which is liable to criticism. I beg your pardon if the specialized terms, which I have been forced to use, have hindered the reader’s understanding, but let us never forget that this part’s task is to deploy inductive logical constructions in the study of matter.

End of the Specialized Part


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