The Geometrized Vacuum Physics based on the Algebra of Signature

The aim of the article is to develop geometrized physics of a vacuum on the basis of two basic postulates: 1) the constancy of the speed of light (more precisely, the speed of propagation of electromagnetic waves) in the vacuum; 2) the ‘vacuum balance condition’ associated with the statement that only mutually opposite formations are born from the vacuum, so that, on average, they completely compensate of the manifestations of each other. The Algebra of signatures is proposed as a mathematical basis for geometrized physics of a vacuum.

The light beams in a perfect vacuum are not visible, but they can be visualized using a finely dispersed sol with a low density (i.e., using small particles with a size of several microns, evenly distributed throughout the entire investigated volume of the "vacuum", so that the distance between the particles much larger than their size).
Of course, a "vacuum" filled with a transparent sol is not a perfect vacuum.
Nevertheless, the rays propagate in the "vacuum" itself (i.e., between the particles of a low-density sol), while the influence of the sol on the metric-dynamic properties of the macroscopic volume of the "vacuum" in this case can be neglected.
A laser light beam is a narrowly directed propagation of mono-chromatic electromagnetic waves with a wavelength of -4,-5, taken from the range of lengths Δ =10 -4 10 -5 cm. Therefore, a 3-dimensional lattice consisting of the mutually intersecting laser beams with an edge length of one cubic cell ε -4,-5 ~ 100⸳-4,-5 (see  However, if the investigated area of the vacuum turns out to be curved, then all m,n-vacuums will slightly differ from each other due to the fact that light rays with different wavelengths have different thicknesses. This circumstance is theoretically substantiated in the sections of geometrical optics related to the resolving power of optical devices [17,18], and is confirmed by experimental data (see Fig.   2.3). In this case, each a m,n-vacuum (i.e., a 3Dm,n-landscape) will be unique (see   According to the "vacuum balance condition", any movement in a vacuum must be accompanied by a similar anti-movement. Therefore, if one 3-basis (together with a cubic cell) rotates clockwise, then this is possible only if an adjacent cubic cell (together with a 3-antibasis) rotates counterclockwise in the same way, since there is no fulcrum in vacuum.

The stignature of an affine 4-dimensional space
Each of the sixteen 4-bases shown in Fig. 2.7 sets the direction of the axes of the 4-dimensional affine space.
In order to introduce the characteristic "stignature" of these spaces, we first define the concept of "base".

The two-row stignatures and the Hadamard matrices
If we return the original units to the two-row stignatures (3.6), then we obtain the two-row matrices 1 1 1 1 1 1 (3.11) are the Hadamard matrices, since they satisfy the condition . (3.12) When raising to Kronecker powers of any of the matrices (3.11), the Hadamard matrices H (n) are again obtained, satisfying the condition: The Algebra of signature 15 ____________________________________________________________________________________________ , ) ( ) ( nI n Н n Н Т =  (3.13) where I is a diagonal unit matrix of dimension n×n: (3.14) For example, 16) and so on according to the algorithm (3.17) Recall that Hadamard matrices are used to construct the noise-proof protected error-correcting codes. In particular, it is believed that DNA molecules are built on the basis of the Hadamard matrices [10,11].
If in the matrix (3.15) we again use the signs {+} and {-} instead of 1 and -1, then we obtain the rule for raising to the Kronecker power of the two-row stignatures. For example, The two-row stignatures corresponding to matrices (3.11) will be called the two-row Hadamard stignatures.
It is easy to verify by direct calculation that the sum of all 16 types of "colored" quaternions (3.20) is equal to zero , 0 that is, the superposition (i.e., the sum) of all types of "colored" quaternions is balanced with respect to the zero and satisfies the "vacuum balance condition".

The spectral-stignature analysis
Let's point out a possible application of the Algebra of stignatures to expand the possibilities of the Fourier spectral analysis.
We recall the procedure known in quantum physics for the transition from a coordinate representation to a momentum representation.
These requirements are satisfied, for example, by a set of the 8×8 matrices The Algebra of signature 19 ____________________________________________________________________________________________ Let's perform the eight "color" Fourier transforms: where the objects ζm (3.29) perform the function of Clifford imaginary units.
We also find the eight complex conjugate "color" Fourier transforms: (3.32) In this case, there are the 16 types of "colored" spirals with the corresponding stignatures The Algebra of signature 21 ____________________________________________________________________________________________ Definition 3.5.1 "Stignature" is an ordered set of signs in front of the corresponding terms of a linear form.
The Expression (3.34) will be called a "rank", since in its numerator, actions on the signs (+) and (-) are performed by columns and/or by rows.
The result of adding signs in one column is written to the denominator under this column, and the result of adding signs in one line is written to the side of the  (3.36) show that the "color" (i.e., spectralstignature) Fourier analysis is balanced with respect to zero, and can be applied in the physics of the "vacuum".
In particular, color (or spectral-stignature) Fourier analysis can be useful for the development of "zero" (i.e., a vacuum) technologies, such as the compression of the vacuum communication channels.

The metric spaces with different signatures
Let's pass from affine geometries to metric ones.
In this case, Expression (4.3) becomes a quadratic form (i.e., a 4-interval) with signature (+ + + -). the result of such a multiplication is written in the denominator (under the line) of the same column. Performing actions according to these rules will be called rank multiplication. Similarly to how it was done with the vectors ds (5) and ds (7) {see Expressions    The Algebra of signature approach largely coincides with the localreference (tetrad) formalism, which was developed by E. Cartan, R. Weizenbek, T. Levi-Civita, G. Shipov [5] and was often used by A. Einstein in the framework of differential geometry with absolute parallelism.
The difference between the Algebra of signature and the tetrad method in General Relativity is as follows. In geometry with absolute parallelism, at each point of a 4-manifold there are two 4-frames (i.e., two tetrads), which define one metric with an interval ds (аb)2 = ei (а) ej (b) dx i(а) dx j(b) and signature (+ ---), while in the Algebra of signature at each point of a 3-manifold (i.e., m,n-vacuum) there are sixteen 4-bases (or 4-frames, or tetrad) (see Fig. 2.7), the scalar products of which form 256 metrics (4.8) having the corresponding signature from the collection of signatures (4.9).

Four kinds of the rank multiplication and the rank division rules
Within the framework of the Algebra of signature, the multiplication and division of signs in the numerators of the ranks can be performed according to the following four types of the arithmetic rules: As an example, we write down the rank (4.6) for the four types of the m,n-vacuums (4.11) -(4.18) The sum of the signs in the denominators of these ranks is zero In this paper, we will only use the rule of rank multiplication and rank division of the signs (4.11) for the commutative m,n-vacuum.
However, it should be borne in mind that in a more consistent theory, all four types of the m,n-vacuums with the rules of multiplication and division

The first stage of compactification of the extra dimensions
One of the main tasks of any multidimensional theory is to determine the method of compactification (i.e., folding) of the additional mathematical dimensions to the observable three spatial dimensions and one time dimension.
A similar problem is faced by the Algebra of signature. However, we note in advance that the compactification of extra dimensions in the Algebra of signature leads to a nontrivial (i.e., to an unexpected) result.
Note that, for example, the 16 types of scalar products of the 4-bases shown in Fig. 4.2, lead to sixteen quadratic forms (metrics) of the form (4.8) with the same signature (-+ -+). Therefore, these metrics can be averaged. Thus, it is possible to distinguish only 256/16 = 16 types of the metric 4-spaces with intervals (i.e., metrics) with appropriate signatures

The relationship between a signature and a 4-space topology
According to the classification of Felix Klein [2], metric spaces with intervals (4.21) can be divided into three topological classes: 1st class: is a 4-spaces, the signatures of which consist of four identical signs [2]: are zero metric 4-spaces. These "spaces" have only one valid point, located at the beginning of the light cone. All other points of these 4-spaces are imaginary. In fact, the first of the Expressions (4.23) describes not the space, but a single point (or the "white" point), and the second one is a single antipoint (or the "black" point).
2nd class: is a 4-spaces, the signatures of which consist of two positive and two negative signs [2]: are various options for 4-dimensional tori.
A simplified illustration of the relationship between the signature of a 2-dimensional space and its topology is shown in Fig. 4.3. It can be seen from this 3. An illustration of the relationship between the signature of a 2-dimensional space and its topology [12] The sixteen types of signatures (4.22), corresponding to the 16 types of topologies metric spaces, form the matrix The properties of the signature matrix (4.26) partly coincide with the properties of the stignature matrix (3.2).

Operations with metric ranks
Ranked Expression (4.28) allows to perform some operations in the vicinity of the investigated point O (see Fig. 2.5) without violating the "m,n-vacuum balance condition". Such operations include, for example, a symmetric transfer of the first columns to the other side of the equality with the inverted signs: ) or the transfer of any of the lines from the numerators of the ranks (4.28) to their the denominators, also with the inversion of a signs, for example: Such ranked operations correspond to certain symmetric vacuum manifestations, which will be considered below and investigated in [14,15].

Definition 4.7.1
The concepts of a «subcont» and an «antisubcont» are mental constructions, which are intended only to create the illusion of "visibility" of two adjacent mutually opposite sides of one m,n-vacuum. These concepts are introduced only to facilitate the visualization of intra-vacuum processes, but they have nothing to do with reality. However, in terms of these mental concepts, real vacuum effects can be inspired.
In expanded form, the ranks (4.32) have the following form (4.37) The operation described by the ranked Expression (4.32) makes it possible to "reveal" the two-sided of the m,n-vacuum with the number of the mathematical dimensions 4 + 4 = 8 = 2 3 . Therefore, we propose to call such a two-sided 8 -di- Let's recall that in the general theory of relativity (GR) of A. Einstein there is only one metric 4-space with one signature, for example, (+ ---). Whereas in the light-geometry of vacuum developed here, the any m,n-vacuum can have at least two sides (i.e., mutually opposite metric 4-spaces): the outer side (i.e., subcont) and the inner side (i.e., antisubcont), with the corresponding mutually opposite signatures (+ ---) and (-+ + +).
The ranked binary triads presented below lead to this dyad too Similarly, out of 256 metrics with signatures (4.9), 128 conjugate pairs of metrics can be distinguished, each of which can be expressed in terms of a superposition of a 7 + 7 = 14 metric 4-spaces. As a result of mathematical dimensions, it become 128  14  4 = 3584.
In turn, the conjugate pairs of a 4-spaces can be similarly decomposed into the sums of a 7 + 7 = 14 subspaces, and this can continue indefinitely.
The result is a vacuum light-geometry balanced with respect to the "split zero", in which the "vacuum" is first represented in the form of an infinite number of m,n-vacuums nested into each other (see § 2.1). This representation is called the longitudinal stratification "vacuum" (Definition № 2.1.5).

The spin-tensor representation of metrics with different signatures
Let's go back to considering the interval For brevity, we omit the differentials in this Expression and write the quadratic form (5.1) in the form As is known, the quadratic form (5.2) is the determinant of the Hermitian 22-matrix ).
The fact that this matrix is Hermitian can be easily verified by direct calcu- In the spinor theory, matrices of the form (5.4) are called the mixed Hermitian spin-tensors of the second rank [9]. 39 ____________________________________________________________________________________________ We represent the 22-matrix (5.4) in the expanded form In the spinor theory an A4-matrices of the form (5.5) are uniquely associated with quaternions of the type Similarly, each quadratic form with the corresponding signature: : (5.8) can be represented as a spin-tensors or as an A4-matrix, which are shown in the Table 5.1:   . 0 Each an А4-matrix from the Table 5 where σij are the Pauli-Cayley spin-matrices, which are generators of the Clifford algebra satisfying the conditions Table 5.1 shows only a special cases of the spin-tensor representations of quadratic forms. For example, the determinants of all thirty-five 22 matrices (Hermitian spin-tensors): (5.11) In a number of cases, the discrete degeneracy (i.e., latent multivaluedness) of the initial ideal state of the m,n-vacuum when deviating from ideality, can lead to splitting (quantization) into a discrete set of dissimilar states of its transverse layers.
For clarity, all types of "colored" A4-matrices are summarized in Table 5 The Algebra of signature associates a zero-balanced superposition of the affine spaces with the 16 possible signatures: with one of the variants of an additive superposition of a 16-and A4-matrices: The Algebra of signature The Expression (5.13) is equal to the zero 22-matrix corresponding to the m,n-vacuum balance condition.
The mathematical apparatus presented here is convenient for solving a number of a problems associated with the multilayer intravacuum rotational processes.

Using a spin-tensors with different stignatures
Let's look at two examples using spin-tensors.

The Dirac stratification of a m,n-vacuum
Consider the Dirac's stratification of a quadratic form using for example the metric (6.1) Let's represent this metric as a product of the two affine (linear) forms There are at least two options for determining the quantities  that satisfy the equality condition of the Expressions (6.1) and (6.3): 1) the method of the Clifford aggregates (for example, quaternions); 2) Dirac's method.
In the first case, the linear forms included in the Expression (6.2) are represented as a pair of the affine aggregates: In the second case, the Dirac method assumes instead of the Crohneker symbols (6.7) to use the unit matrix   The Algebra of signature 55 ____________________________________________________________________________________________ The Dirac method, in contrast to the method of the affine aggregates, allows one to simultaneously "stratify" metric 4-spaces with four metrics that are components of the matrix (6.11).
In the Algebra of signatures, we consider quadratic forms (5.8) with a sixteen possible signatures: (6.16) Each of them can also be "stratified" by the Dirac method The signs in front of the ones in the diagonal b (ab) -matrices correspond to the sets of signs in the components of the signature matrix (4.26) In this paragraph, for brevity, we will temporarily omit the superscripts and instead of the "b (ab) -matrix" we will write the "b-matrix".
Let's return to the Dirac stratification of the quadratic form (6.10) ( ) The entire collection of vc nk γ lm ij -matrices will be called generalized Dirac matrices, and the m,n-vacuum prepared by means of these matrices, will be called the Dirac stratification of the m,n-vacuum.

The curved area of a m,n-vacuum
Let's consider a curved 3D area of a vacuum. If the wavelength m,n of the test monochromatic light beams is much less than the dimensions of the vacuum irregularities, then in this area the cubic cell of the m,n-vacuum (i.e., the cubic cell of 3Dm,n-landscape, limited by these rays) will be curved (see Fig. 7.1). Fig. 7.1 a) The deformed cubic cell of the m,n-vacuum; b) One of a corners of the curved cube

_______________________________________________________________________________
The distortions of the angle of the considered cube of a m,n-vacuum can be decomposed into two components: 1) the change in the lengths (compression or expansion) of the axes x 0(а) , x 1(а) , x 2(а) , x 3  (а) while maintaining right angles between these axes; 2) the deviations of the angles between the axes x 0(а) , x 1(а) , x 2(а) , x 3(а) from straight lines while maintaining their lengths.
Let's consider these affine distortions separately.
1) Suppose that only the lengths of the axes x 0(а) , x 1(а) , x 2(а) , x 3  (а) have changed during the curvature. Then these axes can be expressed in terms of the axes of the original ideal cube x 0(а) , x 1(а) , x 2(а) , x 3(а) using the corresponding transformations of coordinates: where αij (a) =dx i(a) /dx j(a) (7.2) is the Jacobian of the transformation, or the components of the elongation tensor.

The 4-strain tensor
In the classical theory of elasticity and in the general theory of relativity, the actual state of the local volume of an elastic-plastic medium (in particular, the Einstein vacuum) is described by only one "frozen in" reference system with the corresponding 4-basis. This results in the analysis of the only one quadratic form ds 2 = gij dx j dx j with signature (+ ---), (7.21) where gij are the components of the metric tensor of the local area of the curved metric space (there are 16 of these components, but due to the symmetry gji = gij, only 10 are significant).
The quadratic form (7.21) is compared with the quadratic form of the initial ideal state of the same local area of the elastic-plastic medium [6] ds0 2 = gij 0 dx i dx j with the same signature (+ ---). (7.22) Subtracting the metric of the initial state (7.22) from the metric of the actual state (7.21), we obtain [6] j i ij is tensor of the 4-strains, which is the subject of the classical theory of elasticity.
The light-geometry of the m,n-vacuum developed here, based on the Algebra of signatures, differs from the classical theory of an elasticity in that the investigated local volume of an elastic-plastic medium (in this case the m,n-vacuum) is described by more than one 4-basis associated with one of the eight corners of the investigated cube (see Fig. 7.1a,b), but with the all sixteen curved 4-bases (see the same Fig. 7.1 a), the beginning of which is at the investigated point O (see This circumstance leads to the fact that instead of one metric of the type (7.21) in the light-geometry of a m,n-vacuum, there are 256 metrics (7.18) ds (a,b)2 = сij (a,b) dx i dx j (7.25) with the corresponding signatures (4.9) or (4.20), which describe the same volume of the studied space (in particular, a m,n-vacuum) from different sides.
In this case, the metric-dynamic state of the investigated volume of the elastic-plastic medium (in particular, a m,n-vacuum) is described not by 16 numbers (i.e., by the components of the metric tensor gji), but by the 25616 = 4096 components of the 256 tensors сji (a,b) (7.19).
This not only achieves a much more accurate description of the curved volume of an elastic-plastic medium (in particular, a m,n-vacuum) in the vicinity of point O (see Fig. 2.5), but also prepares of the logical basis for identifying a number of vacuum effects that were previously not considered due to the lack of a proper mathematical apparatus.
We note once again that the mathematical apparatus of the light-geometry of a m,n-vacuum based on the Algebra of signatures developed here is suitable for studying the properties of not only objective and/or subjective emptiness, but also any other 3-dimensional continuous media in which wave disturbances (light, sound, phonons) propagate at a constant speed.

The first stage of the compactification of a curved dimensions
Just as it was done in § 4.3, at the first stage of compactification of the additional curved mathematical dimensions in the Algebra of signature, the averaging of metric 4-spaces with the same signature is performed.
For example, for the metrics with signature (-+ -+) (see Fig. 4  where p corresponds to the 14-th signature (-+ -+), according to the following conditional numbering of signatures: <ds (-+ -+) 2 > = сij (14) dx i dx j .  (7.30) then this Expression can be used in stochastic light-geometry for an averaged flat m,n-vacuum, since it is a condition for observing of the m,n-vacuum balance.
In this case, the all 16×16 = 256 components of the 16 averaged metric tensors сij (p) can be random functions of time. But, according to the m,n-vacuum condition, these metric-dynamic fluctuations should overflow into each other in such a way that the total metric (7.30), on average, remains equal to the zero.
On the basis of the total interval (i.e., metric) (7.30) the m,n-vacuum thermodynamics can be developed, considering the most complex, near-zero "overflows" of the local m,n-vacuum curvatures. The concept of the m,n-vacuum entropy and temperature (as the essence of the chaos and intensity of a local m,nvacuum fluctuations) can be introduced.
We can talk about: cooling of the m,n-vacuum to "freezing": heating of the m,n-vacuum to "evaporation"; and many other effects similar to the processes occurring in ordinary (atomistic) continuous media.
The features of the m,n-vacuum thermodynamics are associated with processes when the gradients of the m,n-vacuum fluctuations approach the speed of light (dсij (p) /dxa ~ c), or to zero (dсij (p) /dxa ~ 0).
More detailed consideration of the m,n-vacuum thermodynamics is beyond the scope of this article. However, some aspects of this direction of the research are considered in [15].

The second stage of the compactification of a curved dimensions
Just as it was done in § 4.7, Expression (7.30) can be reduced to two terms ‹ds (-)2 › + ‹ds (+)2 › = ‹gij (+) ›dx i dx j + ‹gij (-) is the quadratic form (i.e., metric), which is the result of averaging of the seven metrics (7.29) with signatures included in the numerator of the left-hand rank (4.32) or (7.34) is the quadratic form (i.e., metric), which is the result of averaging of the seven metrics (7.29) with signatures included in the numerator of the right-hand rank  -averaged "inner" side 2 3 -m,n-vacuum (i.e., averaged antisubcont) with the average metric ds (-+ + +)2 = ds (+)2 = gij (+) dx i dx j with signature (-+ + +), To shorten the notation, the averaging signs in the metrics (7.35) - (7.38) are omitted.

THE COMPONENTS OF THE METRIC TENSOR 8.1 The 4-strains tensor of a 2 3 -m,n-vacuum
Let the initial non-curved metric-dynamic state of the investigated area of the outer side of the 2 3 -m,n-vacuum (i.e., the averaged subcont) be characterized by the averaged metric ds0 (-)2 = gij0 (-) dx i dx j with signature (+ ---), (8.1) and the curved state of the same area of the subcont is given by the averaged metric ds (-)2 = gij (-) dx i dx j with the same signature (+ ---). (8.2) The difference between the curved state of the investigated area of the subcont and its non-curved state is determined by the Expression (7.23) whence it follows [6] .

72
M. Batanov-Gaukhman _______________________________________________________________________________ This means that the line segments ( 2 1 ) 1/2 ds (-) and ( 2 1 ) 1/2 ds (+) are always mutually perpendicular to each other, i.e. ds (-) ⊥ ds (+) (see Fig.8.1a). In this case, two lines directed in the same direction can always be mutually perpendicular only if they form a double helix (see Fig. 8.1b). Fig. 8.1 a) The ratio of the segments ds (-) and ds (+) ; b) If project the double helix onto a plane, then at the intersection the its segments ds (-) and ds (+) are always mutually perpendicular Thus, the averaged metric (8.22) corresponds to a segment of the "braid"
In this case, just like the averaged relative elongation (8.20), the segment of this "double helix" can be described by a complex number [15] ds (±) = 2 1 (ds (-) +ids (+) ), (8.23) the square of the modulus of this Expression is (8.22). In this case, we have sixteen of the 4-strains tensors of all kinds of the 4-spaces is the 4-strains tensor of the p-th metric 4-space; cij0 (p)the metric tensor of the uncurved local area of the p-th 4-space; cij (p)the metric tensor of the same, but a curved local area of the p-th 4-space.
In this case, the segment of the 16-braid consists of 16 "threads" [15]: can be represented in the spin-tensor form Within the framework of the Algebra of signature, it is possible much more deeper 2 n -sided levels of the consideration of the metric-dynamic properties of the curved region of a m,n-vacuum, with an increase in the number of a components of the metric tensors to infinity (see Fig. 8.2).

The kinematics of a m,n-vacuum layers
Under the kinematics of a vacuum layers is meant such a section of the lightgeometry of the vacuum, in which the displacements (or movements) of the different sides of the m,n-vacuum are considered independently of their deformations.
With a more consistent approach, performed in [15], it turns out that any displacements (or movements) of the local area of each layer of the m,n-vacuum 76 M. Batanov-Gaukhman _______________________________________________________________________________ are inevitably accompanied by its deformation, and vice versa, the deformation of the local area of the any layer of the m,n-vacuum necessarily accompanied by its displacement (or flow).
Interconnected flows and deformations (i.e., 4-deformations) of the local area of the m,n-vacuum are considered in the Section "Dynamics of the m,n -vacuum layers" in [15].
In this article, we consider only the kinematic models of the behavior of the m,n-vacuum layers. These models, despite the above disadvantages, allow theoretically predicting a number of the previously unknown vacuum effects that can be tested in practice.

The nonzero components of the metric tensor
Let the metric-dynamic states of the two 4-dimensional sides of the 2 3 -m,nvacuum local area be given by the intervals (7.35) and (7.37) (see Fig. 7  The scalar curvature of a 3-dimensional m,n-vacuum cell in a two-sided consideration within the framework of the Algebra of signatures is determined by the averaged Expression [15] R (±) = 2 1 (R (-) +R (+) ) , (9.2) where the scalar curvature of each of the two sides is determined in the same way as in general relativity is the Ricci tensor of the outer (-), or inner (+) "side" of the m,n-vacuum local area; is the Christoffel symbols of the outer (-), or inner (+) side of the m,n-vacuum local area, where g αβ is, respectively, g (-)αβ or g (+)αβ .
The theory of the deformation of the m,n-vacuum local 3-dimensional region can be developed by analogy with the theory of elasticity of the conventional (atomistic) continuous elastic-plastic media [6], taking into account the two-sided (or 2 n -side) consideration.

The zero components of the metric tensor
To clarify the physical meaning of the zero components of the metric tensors  let's use the kinematics of two-sided of a 2 3 -m,n-vacuum.
It can be seen from the considered kinematic examples that the zero components of the metric tensor (9.9) are associated with the translational and/or rotational motion of various 2 3 -m,n-vacuum layers.
The state of motion of the local 3-dimensional area of a 2 3 -m,n-vacuum is characterized by averaged zero components of the metric tensor ( ).
In all four considered cases, the averaged zero components of the metric tensor (9.32) are equal to zero . This means that inside the local 3-dimensional area m,n-vacuum, mutually opposite intravacuum processes can occur, but, on the whole, this area remains motionless.
Nevertheless, there are cases when intravacuum processes due to phase shifts can compensate each other not locally, but globally. In this case, the local 3-dimensional area of the m,n-vacuum can participate (as a whole) in the some intricate closed motion. Let's consider such a case with a specific example.
Let's extract the root from the two sides of the resulting Expressions (9.51) and (9.52). As a result, according to the notation (9.11) -(9.14), we get where ax (-) is the actual acceleration of the area of the subcont mask, taking into account its inert properties; аx (-) ' is ideal acceleration of the same area of the subcont mask. We represent the Expression (9.65) in the following form or |ах|t = c, or |ах| = c /t, (9.77) the first and second terms in the averaged metric (9.76) turn to infinity. This singularity can be interpreted as a "rupture" of the investigated area of the subcont (i.e., the outer side of the 2 3 -m,n-vacuum). The "rupture" of a subcont is an incomplete action. For a complete "rupture" of the local area of the 2 3 -m,n-vacuum, it is necessary to "rupture" its inner side (i.e., antisubcont) described by the metric (9.50) with the signature (-+ + +).
To do this, it is necessary to create similar uniformly accelerated and equally slowed flows in the antisubcont of the same area of the 2 3 -m,n-vacuum, so that its average state is determined by the averaged metric [15] ( ) The Algebra of signature 91 ____________________________________________________________________________________________ That is, the process of "rupture" of the m,n-vacuum local area is similar to the rupture of an ordinary (atomistic) solid body, to which sufficiently large and equal forces, more precisely accelerations, are applied from both sides.
It is not excluded that the conditions described above for the "rupture" of the m,n-vacuum are formed in the collision of the accelerated elementary particles.
It is possible that a strong collision of particles leads to the emergence of a web of vacuum "cracks", while the closed cracks scatter in the form of a many new "particles" and "antiparticles".

CONCLUSION
The article proposes a method for studying the local volume of a perfect "vacuum" (i.e., an empty space in which there are no particles at all) by probing it with light rays directed from the three mutually perpendicular directions.
As a result of such probing, a 3-dimensional lattice (i.e., a 3D-landscape), consisting of the light rays, is formed in a "vacuum" (see Fig. 2.1). This 3-dimensional landscape is called m,n-vacuum, where m,n is the wavelength of the probing rays taken from the sub-range Δ = 10 m  10 n cm.
There are an infinite number of such m,n-vacuums in the investigated volume of the "vacuum" depending on the wavelength m,n of probing beams (see

TERMS AND DEFINITIONS
New terms and numbers of their definitions are presented in the