Why such a strange name? Why is this concept important?

Long time submission by physicists, and together with them and the general public about emptiness was very simple. And now, for the most part, people continue to think the same way., as before. What is there to imagine — emptiness is the absence of anything. When looking at the world, which was laid by the works of Newton, the whole world is in empty space. If you take something away, for example out of the box, what remains? Emptiness, this is the most empty space. so what, what is there for example, air. Let's make the box airtight and pump out the air from it. Let's get a vacuum there, emptiness. With the discovery of the electromagnetic field, with the creation of its theoretical description and the beginning of its practical use for physicists, it became clear, that the emptiness created in this way may well be not empty at all. Area of ​​space, seemingly containing nothing, may actually contain this very field. An example of the implementation of such a non-empty void is ordinary radio tubes. The notion of emptiness has become a little less clear. It turns out, even when there seems to be nothing in an empty container, there may still be something. And everywhere, in the entire volume of this container. Say, let's make the container metal, so that the electromagnetic field does not penetrate there, there will be a real vacuum. To her. And how will you screen the gravitational field? Whether it stays there or not? Remains. Perhaps, the highest purity vacuum we can find in interstellar space, not in our laboratories. And that, that the stars are attracted to each other despite the fact, that separated by this very emptiness proves, what something (gravitational field, at least), in this vacuum there is. It turns out, emptiness in its most literal sense does not exist at all. In the process of realizing this fact, the worldview of physicists began to change.. Newton painting, describing the world as a collection of massive bodies, located in a space independent of these bodies and evolving in a time independent of them and of space, acting on each other at a distance is no longer satisfactory. The first thing we decided, that all space is filled with a kind of continuous environment, ether. But this design also faced unsolvable problems., it turned out that its consequences contradict experience. After all, if massive bodies are not in empty space, and in a certain environment, their movement through this environment should have quite definite manifestations. And these manifestations are not observed in nature.. As is commonly believed, these problems led to the formulation of a special, and then general theories of relativity. The ether was expelled from the theory and the emphasis shifted to the properties of space and time.. These entities have ceased to be those simple containers for physical bodies and processes., not influencing them and not being influenced by them, which space and time were considered earlier. Moreover, G. Minkovsky convincingly showed, that the understanding of nature achieved by that time is necessary to stop considering space and time as separate entities, they can only be used together, as a single space-time. It was possible to identify the gravitational field with the field of a certain geometric structure, curvature, which, in turn, was linked to the properties of another geometric field, metric tensor fields. However, this whole reform of the worldview of physics was not completed.. Massive bodies and an electromagnetic field remained alien entities for the resulting structure.. They are still considered placed, the truth is now in space-time, and not just into space. Although I must say, what is the concept of the enclosing space, and not space-time still dominates minds, even over the minds of those, who declares adherence to the ideas of the general theory of relativity and is considered the luminaries of this science. What is so popular today idea of evolution of the universe, her “emergence” as a result “Big bang“.

Further development of physics went in a direction generally poorly compatible with the concept of the integrity of the world., which were the source of the revision of the properties of space-time. For quantum mechanics and the theory of quantized fields that grew out of it, space-time remains a repository, and a receptacle in the style of Newton's views, not Einstein. And the emptiness? What's wrong with this concept?

In the special theory of relativity, emptiness as a concept is present, however, it should not be applied to a region of space, and to the region of space-time. In the real world, this emptiness is at its purest, when in some region of space-time there are no massive bodies,  still remains full as before, margins, electromagnetic and / or gravitational. General relativity is largely the same., only the gravitational field is no longer assumed to be something external, and already a property of this space-time itself. In this sense, empty space-time should cease to exist altogether.. But, since everything else is still foreign to space-time, then the concept of emptiness is preserved, as the concept of the absence of such alien entities in a certain area of ​​space-time.

But in quantum theory, an impressive metamorphosis occurred with the concept of emptiness.. It turned out, that for a correct description of the observed phenomena in the vacuum, “emptiness”, it is necessary to assign a bunch of very different properties. There you are, eg, one of the terms of quantum theory: “vacuum polarization”.  And it's not about an electromagnetic field, which could be in a certain area. Not, we are talking about, what in “emptiness” electron-positron pairs appear by themselves, then disappearing, and this gives the observable corrections to the theoretical calculations. Moreover, for each quantized field, each of the sacred cows of modern theory, vacuum needs its own. One for electrons, another for protons, third for muons, etc.. Something is wrong in the Danish kingdom… Of course, when describing the Standard Model, all these absurdities are carefully swept under the carpet. Used to them, they have become a commonplace of the current worldview. There are a bunch of rules, how to calculate certain effects. So there is nothing to philosophize, it is necessary to count. We cannot count everything? Let's come up with a new rule, add a bunch of new dimensions, symmetries and ways to break them. Our fantasy is rich. so what, that our methods cannot cope with the theory of gravity. We will come up with this, such… Great unification. Not? Strings! Not? Super strings! We can't calculate anything ourselves? Yes, OK, we continue to count, and there are so many options, how many of them, there we will definitely count everything we need! More 40 years of crisis in fundamental physics due to this approach…

Okay. I will not criticize, back to understanding the concept of vacuum. Precisely vacuum, not emptiness. Because as I tried to show above, nowhere in nature do we find an example of emptiness as such, “lack of everything and everyone”. However, emptiness in a limited sense, even in two senses, as a concept for us is very useful. These two meanings are interconnected., but not identical.

• The first meaning is very simple. We will consider that area of ​​space-time empty, in which there is no massive tel. Fields, any, maybe. But there are no massive bodies. This idea grows out of our experience in the most natural way.. Besides, such a non-empty void does not contradict the idea of ​​the unity of the world, its connectivity, continuity. Although massive bodies find themselves separated, out of the field, this separation is not yet final, rather, it can be seen as a method of dividing the whole into parts. This separation is partly present in the General Theory of Relativity.. The gravitational field as a geometric structure is determined by the position and mass of the body, and the position of the body is determined by this field, the line of its existence is the geodesic of this field. What's missing for completeness, real unity? There is not enough definition of body mass through geometric structures of space-time. Body mass in general relativity can be any. It's free, external parameter. On that, that the concept of the mass of any body cannot be defined without taking into account the participation of all other bodies in the Universe, probably for the first time Mach. This idea became known as the Mach principle.. Einstein wanted in his constructions to achieve compliance with this principle. Failed.
• What is the problem? The problem is precisely in the artificial separation of massive bodies from space-time itself.. It is in a hypothetical empty space that we can move bodies from one place to another.. In real space-time, nothing like this can be done in principle.. Any existing body at every moment of its existence takes some place in relation to other bodies. Take it out, to separate it from the fabric of space-time we can only mentally, conditionally. Here is that, which remains in the same places at the same moments of time, and I call it a vacuum in the second sense of this concept. This vacuum is not empty either. It contains that field, then the manifestation of the rest of the universe, which is consistent with the existence of exactly here and right now of that body, which I mentally removed from her. The rest of the Universe determines all the properties of the mentally removed body. He has nothing of his own. it “his” there is only the result of its conditional separation from the rest of the world. This second meaning is also linked with the removal of the body from the tissue of space-time.. But the withdrawal is conditional, implying the immutability of that, what's left. The selection of a part as a whole is made symbolically, by recording — these properties are assigned only to a part, but these are attributed to the rest of the world, and everything together describes the whole.

Due to the limitations of these two meanings, I prefer to use for such “emptiness”  a word derived from an already dead Latin language “vacuum”. The relevance of the same word for seemingly two different situations is justified by the fact, that these situations are just two cases of a single state of an arbitrarily chosen region in the Universe, in space-time representing it. In one case, there is no one in the area, what do we associate with a massive body. The other has. But the description of both cases will be the same. Then, what the rest of the world creates in the selected area or its part of a smaller dimension, we call the vacuum.

From the point of view of physics, the most interesting is the second meaning, second situation in considering vacuum. Indeed, it is with this approach that one can try to understand, as a mass (and not only mass, and all the characteristics) this particular selected particle can be associated with the properties of the rest of the universe.

Let's see first, what can be done in classic approaching. Naturally, I spend all consideration in my belief system, described in the book “Measurement and properties of space-time“.  We guess, what the particle is described by a point in space and continuous line in space-time. Every point this line, particle trajectory is an event. The trajectory has a single scale, associated with this particular particle. It is depicted by the contravariant vector, tangent to the trajectory at each point. Since all points — events, then this vector is necessarily like. The vector exists and is constant along the trajectory. Out of trajectory, it does not exist. This can be described using a special (generalized) functions, equal to one on the trajectory, and outside it equal to zero. If we choose a special coordinate system, attached to the selected particle, then unit of time (on the trajectory) we have the ability to match any vector, proportional to the above tangent to the trajectory vector. Spatial scales can be chosen arbitrarily, to concretize them, one reference particle of reference is not enough, bonds with other particles are required. Let's leave these scales in general position., any possible. I want to focus on the fact, what functions will we have to describe the coefficients affine connection for a unit of time. Quite obvious, that due to the concentration of the selected time scale on and only on the trajectory of a given particle, the rates of relative changes of this scale will be equal to zero along the trajectory. Out of trajectory, when approaching her, they will rush to infinity. The trajectory is the pole of the connected object. All these infinities are just the result of the definition of a particle, separating it from the outside world, compactification to point, in vacuum. For a long time, physicists viewed infinities as a flaw in the theory., tried in every possible way to expel them from her. Is it productive? After all, this infinity can be expelled only by refusing to recognize the difference between the object and the rest of the world.. Refusing altogether the possibility of separating an object from the rest of the world. Is this approach consistent with our experience? Not, does not match. There is a very tangible difference between, eg, stone and surrounding space. Who denies it has the opportunity to kick a stone well. Perhaps, the impressions received will reason with him. “No movement, said the sage bradaty. The other was silent and began to walk before him.” I do not remember, who said that, but said ok.

We cannot refuse to select an object, as a method of describing it. But it is also necessary to preserve its ties with the rest of the world.. How to do it? Quite simple. After all, our chosen coordinate system is significantly underdetermined.. What? Not so important, that the spatial scales are still in general position. The main thing, that we have determined the time scale only on the trajectory. And outside of it, time scales what? How are they implemented?? And nothing. There are no funds for this. We can only redefine their existence everywhere in the area under consideration.. How specifically? Many permissible ways. Description “acceptable ways”  very extensive and I do not want to dwell on this here. One of such methods in the classical approximation is the assumption of the existence in the considered region metrics and its introduction by solving the Einstein-Hilbert equations (Schwarzschild and Kerr solutions). but, for any such extension, we will have to keep the emphasis, the presence of a given particle on a given trajectory and nowhere else. This can be achieved very simply.. It suffices to ascribe to the vacuum the regular behavior affine connection coefficients, linking their polar sets precisely and only with the presence of massive particles on these sets. Due to the requirement for coordinate system transformations to be regular (non-infinite singularities, and others too) we naturally distinguish the singular parts of the connection on the trajectories as tensors, measurement results. Regular remainder of a connection is not a tensor, depends on the choice of the coordinate system and describes the rest of the world in a given place, ie. in our terminology describes a field in a vacuum. The vacuum is not empty, but filled with something. There are other massive objects somewhere else, the influence of which here and now manifests itself in the form of a distinguished regular (external) parts of connectivity. And in the language of physics it will be a field, created by the rest of the Universe. This influence is written as the equation for the existence of a given selected particle, reduced to its only characteristic, vector tangent to the trajectory. The vector along the trajectory is transferred without change, it is constant in the accompanying trajectory of the instantaneous frame of reference. It was this sense that was used to define connectivity and absolute (covariant) differentiation. therefore geodesicity (constancy of the tangent vector as a selected scale for each point of the trajectory) the trajectory of any massive body is essentially an axiom, tautology when using the terminology of spaces of affine connection to describe the real world. Geodesicity in full connectivity.

But what about the mass, how it relates here to the rest of the universe? I enter mass as the rate of occurrence of events on the trajectory in the selected unit of time. But how to calculate (or define) this speed, if events fill the trajectory continuously? But no way. This characteristic in the classical approximation remains a parameter external to the theory. It is impossible to define it in such an approximation., since it is generated by a purely discrete set of special events in the history of any particle. But something, allowing us not to lose the connection of this selected body with the world, we can introduce into the theory. And thus preserve, in a sense, the correspondence of the theory to the Mach principle. This something is formulated as the absence of self-action of the particle. As the requirement for the absence of the contribution of the singular part of the connection to the change in the tangent vector to the trajectory of any massive particle. This automatically means, what the trajectory must be geodesic, not only in full connectivity, but also in external. All changes to the selected scale, describing the particle, due only to the rest (external) the world. Vacuum, existing on the trajectory.

In the quantum approximation, events on the trajectory of the particle no longer merge into a continuous line. Therefore, the theory must now not only provide the possibility of determining the mass of an elementary particle. All particle characteristics, distinguishing it as an individual, a different object should appear as a result of theoretical consideration. And exact adherence to the Mach principle would mean, what are all these characteristics, including rest mass, should manifest themselves as a combination of the influence of the rest of the Universe. Certain hints, but there are only hints of the possibility of realizing such expectations in the modern theory of quantized fields.. but, even the most advanced Standard Model of fundamental fields and particles to date has nothing to say on this topic, besides the stupid postulation of the necessary (read demonstrated by experiment) properties have not yet been able. And it is also impossible to call this model a full-fledged theory.. It is rather a phenomenological model, collection of dissimilar techniques and tricks, bypassing the identified difficulties of these methods, based, moreover, on a fairly large number of free parameters, whose values ​​are selected by fitting the calculated values ​​to the experimental data. Whereas in the present theory the number of such parameters should be very small. Besides, the theory must explicitly state their meaning along with the rationale for why they exist. What can a belief system offer in this regard?, set out in the second part of the book “Measurement and properties of space-time“? So far, only the basics are presented in it., allowing to substantively discuss this issue here. Specific methods, which would help to conduct a detailed discussion of the entire set of fundamental particles discovered in nature have not yet been fully developed. However, even that, there is already enough, to see opportunities along the way.

Here's a rough outline of the path, which allows one to obtain a self-consistent description of the properties of the distinguished elementary (indivisible) particles (the entire set of possible such particles)  as the offspring of only and only the rest of the world, which on the trajectory of this particle is represented by vacuum, affine connection coefficients:

• Consider set of elementary (not divisible into smaller) events, united in a single and unique sequence of cause-and-effect relationships. Each of these events we portray point, located on continuous line, trajectories. These points are separated from each other by finite intervals and are ordered. The elementary nature of events is described by their image with minimal elements., dots, which by themselves, outside connections with others have only one property, existence (in a mathematical sense), being. Line continuity describes the causal relationship between events, does not allow, when changing the description of events, to separate them from each other or arbitrarily change their order in the sequence of the history of this object.
• On such a line with a selected set of points, if these points are at least three, you can enter natural for a given object (this sequence of events) scale. This the scale is by definition constant for a given object, equal to oneself on the whole trajectory, throughout the history of this object. This is achieved simply by defining the scale as linear. (on a straight line!) distances between extreme points in a sequence of any three consecutively adjacent, moreover, the point that is located between the other two, considered equidistant from them. And when shifting in the sequence of this set, the magnitude of this (single) distance by definition remains equal to itself. Clear, that this is the scale of proper time for a given object. The existence of this unit scale extends to all intermediate points between events and, in this way, the unit vector of scale tangent to the trajectory is determined.
• We also assume, that the sequence of events in question, the selected elementary particle is not the only one, but embedded in a single, continuous peace, in which there is some unknown set of such elementary particles, which as a whole, including this, makes up the universe, which we describe using the mathematical ideal construction space-time, multidimensional (for specifics 4). The trajectory is treated as a line, embedded in the region of the 4-dimensional continuum, space-time. In this area, a description of all its points has been introduced using coordinates, assigned to all points of the area. Coordinates are based on realizable time scales (such as described above) and on unrealizable, imaginary spatial scales. The entire set of such possible coordinates in itself also constitutes a continuum, continuous group. The trajectory in different coordinate systems looks like a completely different curve, only in those of them, which include the proper time of a given particle as a time scale, she will be straight.
• Because of, that any realizable scale is by definition the proper time scale of some elementary (or not elementary, which is closer to our reality) particles, among the complete group of coordinate systems, it turns out that Poincaré subgroup, associated with a given selected particle. This is an important point, from which the difference in descriptions comes (names and properties) certain sequences of events, which can be considered as different elementary particles.
• Since the only one available to our experience, the only valid elements of that description of the region of the world, which we are building, are only events and their connections, then the same set of events can be embedded in an infinitely large number of different continua. And as applied to a given isolated particle, this means, that even in her rest system the statement, that its trajectory is straight, if we capture the description of the rest of the world (choosing the coordinate system) will be excessive. An infinite number of continuous lines can be matched with a fixed sequence of events, through these events passing, and the order of events that do not violate. This fact is usually formulated in physics as the Heisenberg uncertainty relation. Indeed, event coordinates are fixed, which means they are known for sure. But a line, passing through it, can have at this point in a given coordinate system an infinitely large number of tangent vectors.
• This can also be reformulated differently.. for instance, if the given particle is fixed (a discrete set of events in its history), then the rest of the world in the description cannot be represented accurately, but only as a set of an infinite number of continua, united only by this set of events, as a common property. but, in any such approach, each such line (object trajectory) and the rest of the world must be in complete harmony with each other, in that sense, that the world on the trajectory is represented by a set of affine connection coefficients, which are always consistent with the trajectory itself, which is in this connection geodetic. Geodesicity is the equivalent of the statement about the existence of that very own scale., what we described above. This is the name of those properties, which we attributed to him by definition, only applied to a continuous line, located in the most general position in the continuum.

It could seem, that this is an infinite number of possible continua, in each of which the trajectory of the considered particle can be described only by integrating the essentially nonlinear equations, makes the task of describing the real world, even in such a small way, completely overwhelming. However, it is not. The concept of “vector” fortunes. Moreover, this “vector” state receives from us a completely clear physical (and math) meaning, not introduced, how is it done in standard quantum theory, purely axiomatic. At the same time, the structure is immediately fixed. “vector” fortunes, and methods of its possible classification, and together with them the methods of classification of elementary particles.

© Gavryusev V.G.
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