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Deformation of physical space


olencki

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The existence of three-dimensional space is obvious. Accepting more dimensions of space requires justification. In three-dimensional space, the length does not need to be justified. All other physical quantities need to be defined. In the language of mathematics, general relativity describes the gravitational interaction as the curvature of space-time caused by the presence of matter. Since physical quantities other than length have not been defined, further analysis concerns the curvature of space, not space-time. The physical interpretation of the curvature of space is the bending of one, two, or all three axes of space. The curvature of the space implies the springiness deformability of the space. The springiness of the space causes the space to return to its pre-deformation state after the cause of the deformation ceases to work. The cause of the return to the pre-deformation state is the tension induced by deformation. There are two possible interpretations of the bend:

1.      bending

2.      compression (buckling).

The amount of bending is limited both in bending and in compression.

After the maximum amount of bend is reached, further bending or compression causes the bending or compression element to move without changing the amount of bend. Bending requires three factors to act on the bending element. For this reason, we interpret the curvature of space as compression that requires only two factors.

In the model of elementary structures, we use length and physical quantities related to length: surface area and volume determining the size of the space. A space deformation is described by a difference, relative difference, or relative change in length, area, or volume. Two physical quantities are sufficient to describe the deformation of space:

1.      relative space deformation

2.      tension

The relative deformation of the space (p) is equal to the relative change in volume due to the deformation.

The value of the relative space deformation can be determined for each point in the space. Physical quantities other than length and derivatives are functions of relative space deformation. A non-deformed space with a unit relative deformation (p = 1) is defined as a flat space. For a compressed space, the relative deformation of the space is less than unity (p <1). For a tensile space, the relative deformation of the space is greater than unity (p> 1). The tension (f) is equal to the relative length difference due to the deformation.

Tension is a vector quantity, has value, direction and sense (sign).

Unbalanced tension is the cause of movement.

A second physical space is necessary to cause a deformation of the physical space. Overlaying a given place of physical space with another physical space does not change the volume and length of the place of overlap. Changing the length and volume requires displacement of one physical space from a given place in the geometric space by another physical space. We define the displaced space as the surrounding space. We define displacing space as a fragment of space. The volume of a fragment of space is very small in relation to the volume of the surrounding space.

To describe the displacement of the surrounding space by a fragment of space, we use the analogy to a gas bubble (a fragment of space) located in a very large liquid reservoir (ambient space). After the liquid is displaced from a given place in the tank, a limited amount of gas forms a bubble. Displacement of the liquid from a given place in the tank locally changes the shape of the liquid. The locally deformed liquid forms a surface film on the contact surface with the gas bubble. Circumferential tension stretching and radial tension 

compressive appear in the surface membrane of the liquid. The circumferential tension balances itself. Radial tension compresses the gas bubble. Compression deforms the gas bubble. The tension compressive in the deformed gas bubble balance the tension compressive in the liquid surface membrane. During its movement, the surface of the liquid moves along with the gas bubble.

The locally displaced ambient space creates a locally deformed layer with a closed surface around a fragment of space. In the circumferential directions, the deformed layer of the ambient space is stretched, and in the radial direction it is compressed.

Circumferential tension stretching is balance. A fragment of the space is compressed by radial tension compressive. Due to the size of the space fragment, local compression is compression of the entire space fragment. The tensile compressive in a fragment of space balance tension compressive in a deformed layer of environmental space. The equilibrium of tension compressive connects a fragment of the space with the deformed layer of the surrounding space, creating an elementary space. With the spherical shape of the elementary space, the tension stretching in the deformed layer of the ambient space are the lowest.

The deformation and associated tension may be in one direction (axis), two directions perpendicular to each other, or three mutually perpendicular directions. The surrounding space may be locally displaced by a fragment of space in one direction in two perpendicular directions or in three mutually perpendicular directions. It is impossible to analyse in terms of physics why a fragment of space displaces the surrounding space in one way and no other way.

Depending on the direction of displacement of the surrounding space, the elementary space is compressed in one axis, in two axes or in three axes. The deformation of an elementary space can be:

1.      uniaxial - space is deformed in one axis, undeformed in two axes - uniaxial space

2.      biaxial - the space is deformed in two axes, undeformed in one axis - biaxial space

3.      three-axis space - the space is deformed in three axes - three-axis space.

The change in the volume of the ambient space resulting from local deformation is negligible. The relative deformation of the surrounding space is equal to one. Compression through the space of the surroundings reduces the volume of the elementary space. The relative deformation of the elementary space is clearly less than one.

In a three-axis space, there is a state of three-axis compression. In a triaxial compression state, the tension is the same in any direction. In a three-axis space, there is no tension difference between any two directions. There is a biaxial compression state in the biaxial space. In the biaxial compression state, there is a tension difference between the deformed axes and the non-deformed axis. In the uniaxial space there is a uniaxial compression state. In the uniaxial compression state, there is a tension difference between the deformed axis and the non-deformed axes. The internal tension difference causes the elementary space to move:

1.      of the biaxial space in the direction perpendicular to the compression plane, the sense of motion is random

2.      uniaxial space in the plane perpendicular to the direction of compression, the uniaxial space has two degrees of freedom of movement: linear motion in the plane perpendicular to the direction of compression and rotational motion in the plane perpendicular to the direction of linear motion, the direction and sense of linear motion are random , the direction of rotation is random.

Time is a number that determines the number of changes in the position of a moving elementary space. The number of changes in the position of the moving elementary space depends on the relative deformation of the space. Reducing the value of the relative deformation of the space increases the number of changes. The number of changes in the non-deformed (flat) space is the smallest (the time is the shortest). The surrounding space is homogeneous and it is not possible to determine the change of the position of the elementary space in relation to the surrounding space. The position of an elementary space can be defined in relation to another elementary space. Time relative to another elementary space is relative time. Time allows you to define the speed of movement.

The following interpretations of the deformation of the elementary space are possible:

1.      compression; length is geometrically "compressed", space is compressed

2.      compaction; length is kinematically "compressed", space is compacted

3.      buckling; the length is "bent", the space is curved.

In a compressed space and a curved space, the change in travel time is associated with a change in length (road of traffic). In a dense space, the change in the travel time is related to the change in the speed of movement. For a compacted space, the value of the speed of movement is equal to the relative deformation of the space. The time of movement and the properties of elementary structures do not depend on the adopted interpretation of the deformation of space.

            During movement, elementary spaces can collide with each other. The collision of elementary spaces does not cause additional displacement of the surrounding spaces. The collision does not change the relative deformation of the elementary space. A collision may result in overlapping elementary spaces. The deformation of the space is the sum of the deformation of the spaces of the overlapping elementary spaces. Changing the shape of the elementary space does not cause additional displacement of the surrounding space and does not change the relative deformation of the elementary space. Changing the shape of the elementary space changes the length of the elementary space in certain directions and causes additional tension inside the elementary space. The tension difference inside the elementary space displaces the individual parts of the elementary space relative to each other in the direction of the tension difference.

 

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2 minutes ago, olencki said:

In the language of mathematics, general relativity describes the gravitational interaction as the curvature of space-time caused by the presence of matter. Since physical quantities other than length have not been defined, further analysis concerns the curvature of space, not space-time.

Observation and experimentation show that the curvature involves spacetime not just space.

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The elementary space is many times smaller than the Planck length. The problems with the Lorentz transformation and the concept of space-time for such distances are well illustrated by the quote by prof. Meissner:

“The Planck length, as a measure of such small distances (or so high energies) at which the effects of quantum gravity should begin to play a role, is indeed in contradiction with the Lorentz transformations, which in moving frames of reference could shorten such a length arbitrarily. It was noticed some time ago and attempts were made to modify these transformations (and the special theory of relativity, STR) in such a way that for large distances they would turn into ordinary Lorentz transformations, and for very small ones, of the order of Planck length, each observer would measure the same length - i.e. it was an algebra with two invariants, the speed of light and the Planck length. There have been several proposals, collectively known as DSR (Doubly or Deformed Special Relativity), but on the one hand, there are no experimental confirmations so far, and on the other, there is a relationship between ordinary special relativity and DSR (suggesting that DSR is simply STW written in other coordinates) did not result in wider adoption in the environment of elementary particles physicists, where the dominant belief is that this problem should be solved within the framework of the yet unknown quantum theory of gravity, where the Lorentz transformations are likely to be significantly modified anyway.”

The formation of structures composed of elementary spaces depends on the maximum possible deformation of the space. Structures composed of elementary spaces may arise when the maximum deformation of the space meets the following conditions:

1.      the three-axis deformation of the space (Z) is smaller than the maximum deformation of the space (Tmax) (the condition for the formation of a deformable three-axis space)

2.      the sum of the three-axis deformation of the space (Z) and the uniaxial deformation of the space (X) is greater than the maximum deformation of the space (Tmax) (the condition for the formation of a structure based on a three-axis space)

3.      Z <T_max <Z + X

No space can be superimposed on the triaxial space. The space colliding with the triaxial space must move along its outer surface. The time of movement depends on the relative deformation of the space with which the elementary space touches or overlaps. The deformation caused by the difference in movement time is called the kinematic deformation. The relative deformation of the space on which the elementary space is superimposed or in contact with for point A is smaller than for point B. The difference in the movement time of points A and B causes a kinematic deformation of the elementary space. Extending the time of point A's movement stretches the elementary space. Additional tensile stretches appear in the vicinity of point A. The difference in tensile between points A and B causes point B to move towards point A. After the change of the movement of point B, the directions of the movements of points A and B intersect. The compressive tension causes a change in the movement of point A proportional to the change in the movement of point B. The movement of elementary space is centripetal. To describe the kinematic interaction, we use the following general relationships:

1.      for a moving elementary space, the difference in the relative deformation of the space with which the elementary space touches or overlaps causes a difference in the time of movement.

2.      the difference in the time of movement kinematically deforms the elementary space and causes kinematic tension in the elementary space

3.      kinematic tension causes additional movement of the elementary space in the direction of the time difference of movement.

 

 

 

 

 

 

The condition for the formation of a structure is the collision of elementary spaces. The three-axis space does not move in relation to the surrounding space and the deformation of the three-axis space is not kinematically deformed. After colliding with the three-axis space, the biaxial space moves on its her surface. The kinematic interaction with a triaxial space causes the following changes in the movement of a biaxial space:

1.      point A touching the three-axis space moves "slower" and stretches the biaxial space

2.      point B performs a centripetal movement in the surrounding space and wraps the biaxial space on the surface of the three-axis space, the contact of the biaxial space with the surface of the three-axis space increases

3.      point B, curling the biaxial space, "catches up" with point A

4.      overlapping extends the biaxial space, in the surface layer of the biaxial space the tension stresses increase, after the maximum value of the tension stress is exceeded, the surface layer breaks and the biaxial space forms a biaxial ring.

The basic elementary structure is formed by three mutually perpendicular biaxial rings rotating on a triaxial space. In the places of intersection (overlapping) of the biaxial rings, the deformation of the space is the sum of the deformation of the spaces of the biaxial rings. At right angles between the intersecting biaxial rings, the difference in tension has a circumferential direction and does not cause the biaxial rings to slide out of the triaxial space. Biaxial rings that differ in the type of space do not form an elementary structure.

The sum of the turnover of the three biaxial rings determines the turnover of the elementary structure. The direction of rotation (L, R) is defined in relation to the direction of linear movement of the elementary structure. Due to the turnover, we distinguish:

1.      right-handed elementary structure

2.      left-handed elementary structure.

For every torsion, the basic elementary structure exists in three kinds of biaxial space. Together we get six basic elementary structures (3 kinds x 2 torsions).

After colliding with a three-axis space, the uniaxial space moves on the outer surface of the three-axis space. The kinematic interaction with a three-axis space causes the following changes in the movement of a uniaxial space:

1.      point A touching the three-axis space moves "slower" and stretches the uniaxial space

2.      point B performs linear motion, rotational motion and centripetal motion in the surrounding space

3.      times A and B points are aligned, uniaxial space moves in protolinear motion

The rotary movement prevents the uniaxial space from curling up on the triaxial space. A uniaxial ring is not formed. If the triaxial space is part of the elementary structure, the uniaxial space may contact the biaxial space before the movement times of points A and B align. The kinematic interaction between the uniaxial space and the biaxial ring causes the following changes in the movement of the uniaxial space and the biaxial ring:

3.      the uniaxial space is in contact with the biaxial ring

4.      the overlap of the uniaxial space on the biaxial ring increases, the parts of the uniaxial space inside the biaxial ring move "slower", the uniaxial space is stretched

5.      the kinematic interaction (difference in movement time in the ambient space and inside the biaxial ring) pulls the uniaxial space under the surface of the biaxial ring

6.      point B "catches up" with point A, the uniaxial space forms a uniaxial ring rotating under the surface of the biaxial ring

7.      the transverse rotary movement of the uniaxial space is synchronized in a plane perpendicular to the direction of movement with the natural frequency of the ring

8.      the movement time of the biaxial ring at the point of contact with the uniaxial space increases, the difference in the movement time between the places of the biaxial ring contacting the triaxial space and the parts in contact with the uniaxial space decreases, the radius of the centripetal movement of the biaxial ring increases

9.      creating a uniaxial ring completely superimposed on the biaxial ring increases the radius of the centripetal movement of the biaxial ring around its entire circumference, the biaxial ring with the applied uniaxial ring has a larger diameter.

The kinematic interaction between the uniaxial ring and the biaxial ring deprives the uniaxial ring of all degrees of freedom of movement relative to the surrounding space. In relation to the biaxial ring, the uniaxial ring has one degree of freedom of circumferential rotation.

When the uniaxial ring is applied to the biaxial ring, the deformation of the space changes. We analyze the movement time of the uniaxial ring. With opposite rotation of the biaxial ring and of the uniaxial ring, the time of one complete revolution of the uniaxial ring is longer and it is shorter for the concurrent rotation. Longer movement time is interpreted as the sum of uniaxial and biaxial space deformation. We interpret shorter movement time as the difference of biaxial and uniaxial deformation of space. For the opposite rotational movements, we assign a positive sign to the uniaxial ring. For rotational movements, we assign a negative sign to the uniaxial ring. Uniaxial rings placed on biaxial rings require synchronization of rotational movements. Synchronization requires the same sign of uniaxial rings and the same kinds of uniaxial rings and biaxial rings.

The derivative elementary structure is formed by basic elementary structures in which a uniaxial ring is superimposed on at least one biaxial ring.

The following types of derivative elementary structures can arise:

1.with one uniaxial ring

2.with two uniaxial rings

3.with three uniaxial rings.

Each of the types of derivative elementary structures can differ in torsion, the sign of uniaxial rings and the kinds of space. Together we get twelve derivatives of elementary structures for each type (3 kinds x 2 torsions x 2 signs).

 

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36 minutes ago, olencki said:

quote by prof. Meissner:

“The Planck length, as a measure of such small distances (or so high energies) at which the effects of quantum gravity should begin to play a role, is indeed in contradiction with the Lorentz transformations...

Can you provide the source of this quote?

Are there any testable predictions from your conjecture?

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The deformed space model, and more precisely the model of elementary structures, is a theoretical model of structures that may arise under certain conditions in a three-dimensional compression deformed one. Such a model may be correctly formulated or there may be concepts or quantities assumed without definitions or internal contradictions. So far, no one has found internal contradictions or undefined concepts in the model of elementary structures.  The model of elementary structures as a model of deformed space is not a model of anything else, including elementary particles or fundamental interactions, and no can predict anything. If we find that the model is correctly formulated, then we can then ask whether there are very important analogies between the known properties of elementary particles and the properties of elementary structures. With a positive answer to such a question, a hypothesis about elementary particles and fundamental interactions can be formulated. This hypothesis, apart from explaining why we have such and not another number of elementary particles with such and no other properties, why we have such and no other fundamental interactions, and why the constant of the fine structure has such and no other value, predicts, among other things, a greater gravitational mass of neutrinos about a thousand times greater than the inertial mass (this dependence is a consequence of electromagnetic mass; I recommend volume 2 chapter 28 of Feynman lectures). Since such models have not been discussed in physics so far, the model is extensive. Attached is the entire model without hypotheses with drawings that I found difficult to copy elementary spe.docx

 

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