7. Transformation of variables and conservation of energy

Here it is necessary to give Sean Carrol analysis of energy conservation who gave excellent comments on the conservation of energy in general relativity. By his opinion [32], "if energy and momentum evolve in response to the behavior of space-time around it, as GR suggests, when space-time is not constant, energy will change in a completely unambiguous way. Therefore, you cannot find the energy or curvature of space-time at every point in space. Photons loss energy as space expands, so total energy decreases. It leads to the violation of energy conservation. Energy is not conserved because space-time changes."

time phase, while Es presents the portion of energy consumed in space phase. The condition (Eap Es)/E<sup>s</sup> ≥ 1 comprises positive electromagnetic energy, while Eap = 0 leads to the

The rate of acceleration of energy conservation has a trend to approach the background speed of light. That is why any event has a trend to move to the maximum velocity through

The origin of matter in GR has no connection with the space-time frame and GR's space-time cannot remove matter from its structure and return to the background space-time state, while GR has no background state. However, the non-uniform energy conservation concept shows that any space-time frame, which does not involve mass, is not able to be the energy carrier. The non-uniform conservation of energy in space-time frame gives very specific concept of mass: the mass is the energy density in space field. As follows from model (5), discrete nonuniform energy conservation may generate only non-invariant dynamical mass in the form of location of energy in the certain space-time frame. The energy flux (Eap/Es 1) determines the density of energy in space phase, therefore mass changes with the change of frequency of the energy conservation. Thus, space is the materialization phase of energy, while time phase destroys everything material and returns the space matter discretely to the initial state, carry-

The discrete, non-uniform conservation of energy, leading to the non-invariance of actionresponse parity of energy-mass relation within space-time field and asymmetry of their bound-

Due to the discrete non-uniform conservation, energy as the resulting quantity of exchange interactions, distributed within dynamic space-time phases, has no meaning as the static quantity. This is the "quantization" of discrete non-uniform energy conservation, which makes all of the interactions as the "classic resulting quantity," having the same meaning of quanta.

The forces of virtual space-time frame at λ = 1 annihilates each other as the electromagnetism and gravity, but in the non-virtual space-time frame they get a new feature—action-response parity of exchange interactions: electromagnetic force at long distance generates gravity, but at short range with the weak force leads to the generation of strong nuclear force. Transformation of energy from space phase to time phase generates gravitational force, while transformation

Later, we will describe the weak force in detail, which is needed for generation of discrete symmetry at minimum atomic space scale to make performance of atomic scale space-time grain stable.

Here it is necessary to give Sean Carrol analysis of energy conservation who gave excellent comments on the conservation of energy in general relativity. By his opinion [32], "if energy and

of energy from time phase to space phase generates electromagnetic interaction.

7. Transformation of variables and conservation of energy

minimum space and maximum available portion of energy.

ing the phenomenon, called "Poincare paradox" [31].

aries is the missing quantity in the equation of general relativity.

negative energy solution.

168 Advanced Technologies of Quantum Key Distribution

We will show that the problems of conservation of energy within energy-momentum and space-time framework, described by Carrol [32], cannot be solved without dynamical model, involving local asymmetric space-time position.

The non-uniform conservation of energy, which holds due to discrete space-time frame (5), is valid only through transformation of asymmetric space and time variables. Consumption of energy during non-uniform conservation in space phase (change of space in relation to the local position—ΔS/S1) generates its conjugate variable—gradient of time in the form of time arrow in relation to the local origin—Δt/t1. Generation of non-virtual space-time frame through coupling of its variables and translation of time phase energy to space-time frame leads to the nonuniform consumption of energy. Consumption of energy in space-time frame and decrease of frequency of photons energy leads to the decrease of frequency of change of local (instant) time.

If to apply Noether's theorem to quantum physics, time translational antimatter-matter symmetry should be associated with the conservation of energy. However, quantum physics time independent antimatter-matter annihilation or classic space-time translations need application of continuous unlimited resources of energy to hold the continuous symmetry.

In accordance with model (6), conversion of energy from one phase to another is possible only if conversion takes place within asymmetric space-time translations. If there is no uniform energy resources, space-time translation in any local position will end in space phase. On this basis, matter-antimatter annihilation ends at the matter formation phase. The amount of energy repulsed after matter generation phase is less than initial amount of applied energy. That is why the repulsive energy in the form of electromagnetic force is not translational invariant.

Model (6) shows that at Eap = 0, decay of space-time and contraction of space back to Planck's scale generates negative energy of antimatter (called gravitational energy) which approaches to its maximum value (vacuum value) where takes place change of sign to positive energy, distributed in space- time frame with space expansion. The state of zero space has no sense while it leads to the runaway of energy to infinity. The state of minimum, non-zero space is needed for change of sign of negative energy of antimatter to positive energy of space-time frame of matter.

The condition when portion of energy, conserved in space phase is equal to the portion of energy of time phase (8), we can call this condition as uniform conservation of energy at background state of "super-symmetry." At this condition, unlimited fluctuation should lead to the generation of unlimited amount of energy. On this basis, there cannot be a continuous uniform state of super-symmetry or even usual symmetry, which can exist on permanent basis. Therefore, the non-uniform conservation of energy does not allow existence of continuous symmetry.

Super-symmetry is a theory of particle physics that connects boson with integer spin and fermions with half integer spin. In accordance with this theory, "each particle from one group is associated with a particle from the other group known as super partner."

However, as we showed earlier, the spin and mass, as the non-separable entities, arrive from the non-uniform conservation of energy in space-time field. The electron mass is not due to the electromagnetic self-interaction and its energy is not due to the potential self-energy; its energy, mass, and spin are results of the energy-mass exchange interaction that carried within

The Concept of Mass Based on Accelerated Conservation of Energy within Asymmetric Space-Time Phases

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171

Hestenes [34] showed that spin may arise from helical world line of space-time, but classical arguments do not produce the properties of spin. It is necessary to note that the abovementioned approach describes quantum level interactions without space-time frame. For example, Dirac equation describes energy-momentum relation, spin, and position for a point particle.

The energy-momentum exchange interaction, coupled with the dynamical local space-time frame, eliminates point particle problem. Model (5), which describes conservation of energy in space-time field, is the wave function of energy distribution involving asymmetric space and

Formation and expansion of space-time takes place by the non-uniform electromagnetic force with the participation of charged particles, while decay of space-time field and delivery of the energy to the background takes place by neutral current of weak force. The weak force makes a distinction between left and right due to the non-uniformity in energy-mass exchange interaction during conversion of energy from one form to another. Conversion of energy from one

The non-uniform conservation of energy requires two opposite motions: electromagnetic acceleration of energy consumption with the expansion of space-time frame, and decay of space-time frame with the uniform restoration of energy at background state by neutral current. In accordance with model (5), coupling of space-time variables generates separate charges and electromagnetic energy, while coupling of charges generates separate space-time

The static continuous energy conservation described by Noether's theorem does not involve locality of an event and does not limit the boundary of the conserved quantity, therefore leads

The traditional concept of continuous energy conservation, described by Noether's time independent frame "energy can be neither created and not be destroyed, but it transforms from one form to another" is not a complete theory, while it describes conservation of energy in the form of time independent symmetry in abstract space, similar to Newton's abstract space. It does not involve driving force of conservation and transformation of energy from one form to another in space-time frame that is why continuous conservation of energy within unlimited

Model (5) has a feature of quantum physics, while energy and the produced space-time entity within non-uniform energy distribution have discrete performance and are the non-continuum "quantum portions." Model (1) at Eap = 0 describes restoration of energy and virtual asymmetric space and time products at background state. It is similar to the asymmetric wave equation

form to another does not involve invariant translation.

variables moving uniformly to the background state.

time is not a valid concept to use in dynamical laws.

of quantum mechanics:

to the singularity in the dynamical laws of classic physics.

space-tine field.

time variables.

The non-uniform energy conservation concept, as we described above, gives different requirement for symmetry: the symmetry is the condition where total spin numbers of particles, forming this symmetry is equal. It follows from the condition when energy portions, distributed within space and time phases are equal (8), which corresponds to the condition Eact = 2Es. This state corresponds to the discrete symmetric performance of space-time grain containing three family quarks. The total spin numbers of bosons and fermions and triplet performance of quarks family arise from the discrete symmetry of space-time variables of baryonic frame at Es = 1/2Eap.

Equation (5) at (Eap/Es � 1) 6¼ 1 describes electromagnetic force, while condition Es = 1/2 Eap represents the strong force. Model (5) describes the identity of particles as bosons and fermions through exchange interactions. The energy flux makes position and momentum as separable variables; but at Eap = 0, these variables merge together to form non-separable boson compensates of indistinguishable particles, occupying the same state.

The non-uniform conservation of energy requires existence of "three particles tandem" only in discrete mode. The Exclusion Principle on existence of a particle in a certain energy state does not consider energy conservation principle and does not involve time ingredient of the conserved energy to keep a particle at this energy state.

Therefore, photons, holding Bose-Einstein statistics, exist in discrete mode within three family particles frame, which appears in the form of three-color frame. Similar to the existence of binuclear structure of matter, the antimatter structure of photons exists within discrete flavor of three colors (Eap = 2Es), changing between two frames. Light photons travel through waves of space-time color flavors, alternating within two frames of three-color flavors. Therefore, change of photons' frequency is not possible without the three family color flavors.

The space-time frame of non-uniform energy conservation explains classic physics clarification of light photons. The condition Eap = 2Es, produced from energy-mass exchange interaction shows that coupling of two identical half integer particles produces a particle with the integer spin, called boson. This prediction of model (5) corresponds to the quantum physics statement that the wave function of the identical half-integer spin particles changes sign when two particles swapped.

By quantum mechanics, two fermion particles cannot occupy the same quantum energy state. However, in accordance with the non-uniform energy conservation principles, two particles cannot exist unlimited time at the same position of these particles. The particle having certain space-time position may temporarily move and occupy the state of another particle through absorption or radiation of energy.

Here we may show that the non-uniform conservation of energy leads to the understanding of electron self-interaction problem as well. By literature information [33, 34], the electron mass and spin can be identified with the energy and angular momentum of the electromagnetic selfinteraction.

However, as we showed earlier, the spin and mass, as the non-separable entities, arrive from the non-uniform conservation of energy in space-time field. The electron mass is not due to the electromagnetic self-interaction and its energy is not due to the potential self-energy; its energy, mass, and spin are results of the energy-mass exchange interaction that carried within space-tine field.

Super-symmetry is a theory of particle physics that connects boson with integer spin and fermions with half integer spin. In accordance with this theory, "each particle from one group

The non-uniform energy conservation concept, as we described above, gives different requirement for symmetry: the symmetry is the condition where total spin numbers of particles, forming this symmetry is equal. It follows from the condition when energy portions, distributed within space and time phases are equal (8), which corresponds to the condition Eact = 2Es. This state corresponds to the discrete symmetric performance of space-time grain containing three family quarks. The total spin numbers of bosons and fermions and triplet performance of quarks family arise from the discrete symmetry of space-time variables of baryonic frame at Es = 1/2Eap.

Equation (5) at (Eap/Es � 1) 6¼ 1 describes electromagnetic force, while condition Es = 1/2 Eap represents the strong force. Model (5) describes the identity of particles as bosons and fermions through exchange interactions. The energy flux makes position and momentum as separable variables; but at Eap = 0, these variables merge together to form non-separable boson compen-

The non-uniform conservation of energy requires existence of "three particles tandem" only in discrete mode. The Exclusion Principle on existence of a particle in a certain energy state does not consider energy conservation principle and does not involve time ingredient of the con-

Therefore, photons, holding Bose-Einstein statistics, exist in discrete mode within three family particles frame, which appears in the form of three-color frame. Similar to the existence of binuclear structure of matter, the antimatter structure of photons exists within discrete flavor of three colors (Eap = 2Es), changing between two frames. Light photons travel through waves of space-time color flavors, alternating within two frames of three-color flavors. Therefore,

The space-time frame of non-uniform energy conservation explains classic physics clarification of light photons. The condition Eap = 2Es, produced from energy-mass exchange interaction shows that coupling of two identical half integer particles produces a particle with the integer spin, called boson. This prediction of model (5) corresponds to the quantum physics statement that the wave function of the identical half-integer spin particles changes sign when two

By quantum mechanics, two fermion particles cannot occupy the same quantum energy state. However, in accordance with the non-uniform energy conservation principles, two particles cannot exist unlimited time at the same position of these particles. The particle having certain space-time position may temporarily move and occupy the state of another particle through

Here we may show that the non-uniform conservation of energy leads to the understanding of electron self-interaction problem as well. By literature information [33, 34], the electron mass and spin can be identified with the energy and angular momentum of the electromagnetic self-

change of photons' frequency is not possible without the three family color flavors.

is associated with a particle from the other group known as super partner."

sates of indistinguishable particles, occupying the same state.

served energy to keep a particle at this energy state.

170 Advanced Technologies of Quantum Key Distribution

particles swapped.

interaction.

absorption or radiation of energy.

Hestenes [34] showed that spin may arise from helical world line of space-time, but classical arguments do not produce the properties of spin. It is necessary to note that the abovementioned approach describes quantum level interactions without space-time frame. For example, Dirac equation describes energy-momentum relation, spin, and position for a point particle.

The energy-momentum exchange interaction, coupled with the dynamical local space-time frame, eliminates point particle problem. Model (5), which describes conservation of energy in space-time field, is the wave function of energy distribution involving asymmetric space and time variables.

Formation and expansion of space-time takes place by the non-uniform electromagnetic force with the participation of charged particles, while decay of space-time field and delivery of the energy to the background takes place by neutral current of weak force. The weak force makes a distinction between left and right due to the non-uniformity in energy-mass exchange interaction during conversion of energy from one form to another. Conversion of energy from one form to another does not involve invariant translation.

The non-uniform conservation of energy requires two opposite motions: electromagnetic acceleration of energy consumption with the expansion of space-time frame, and decay of space-time frame with the uniform restoration of energy at background state by neutral current. In accordance with model (5), coupling of space-time variables generates separate charges and electromagnetic energy, while coupling of charges generates separate space-time variables moving uniformly to the background state.

The static continuous energy conservation described by Noether's theorem does not involve locality of an event and does not limit the boundary of the conserved quantity, therefore leads to the singularity in the dynamical laws of classic physics.

The traditional concept of continuous energy conservation, described by Noether's time independent frame "energy can be neither created and not be destroyed, but it transforms from one form to another" is not a complete theory, while it describes conservation of energy in the form of time independent symmetry in abstract space, similar to Newton's abstract space. It does not involve driving force of conservation and transformation of energy from one form to another in space-time frame that is why continuous conservation of energy within unlimited time is not a valid concept to use in dynamical laws.

Model (5) has a feature of quantum physics, while energy and the produced space-time entity within non-uniform energy distribution have discrete performance and are the non-continuum "quantum portions." Model (1) at Eap = 0 describes restoration of energy and virtual asymmetric space and time products at background state. It is similar to the asymmetric wave equation of quantum mechanics:

$$\mathbf{at} \to\_{\text{ap}} = \mathbf{0}\_{\prime}$$

$$\frac{\Delta \mathbf{S}}{\mathbf{S}\_1} + \frac{\Delta \mathbf{t}}{\mathbf{t}\_1} = \mathbf{0} \tag{8}$$

In this chapter, we will discuss how the non-uniform energy conservation concept is to be the alternative mechanism of mass generation. The non-uniform distribution of energy portions within asymmetric space and time phases requires generation of the fields with the different energetic properties (frequency and amplitude), which is the only way for carrying conservation of energy through these fields. Coupling of two fields with the different energetic properties as an energy consuming and energy restoration phases generates the non-virtual space-time frame, which appears to be the non-uniform conservation of energy through energy-mass exchange

The Concept of Mass Based on Accelerated Conservation of Energy within Asymmetric Space-Time Phases

The background state of space-time frame is the relation of virtual asymmetric space and time phases, which proceeds conversion of energy from one form to another (8), through translation of asymmetric entities, such as ΔS/S1, Δt/t1, carrying energy portions as a virtual matter and

We can describe the non-uniform background energy-mass translation by conversion of light photons to electron/positron pairs, which is well-known quantum mechanics translation event. Quantum mechanics states that during this translation, energy conservation is hold by fluctuations, such as particles borrow energy and after very short time return the borrowed energy back:

The energy-matter translation given by relation (9) does not count time phase of energy conservation and locality of the produced particles, while photons-leptons translation takes place in the abstract space. Equation (9) could be the discrete translation of energy in the form of infinite fluctuations of the background quantum state. It is clear that in this case there is no natural way for breaking of the continuous symmetry of discrete fluctuations, forming time independent infinite symmetry of matter-antimatter relations. Equation (9) does not reflect the

Conservation of energy requires a certain finite frame for locality that is why space and time cannot exist as separate variables. Formation of a particle within any time scale without locality in space phase leads to the missing of energy conservation. By Landau's opinion [35], infinite fluctuations of virtual matter-antimatter pairs should lead to the "Ultraviolet Catastrophe due to the accumulation of infinite amount of energy of collisions and it is impossible to

γ=γ ¼ � eþ=e� þ νe=ν<sup>e</sup>

The right side of Eq. (10) involves additional identity in the form of neutrinos to cover missing part of energy conservation in time dependent frame. Equation (10) represents mechanism of energy conservation, which involves decay of energy into asymmetric space and time fields particles having different energy density. Conversion of light photons from one form to another for conservation needs generation of phase difference, which appears with the forma-

prove the mathematical basis of elimination of "Ultraviolet Catastrophe."

γ=γ ¼ eþ=e� (9)

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173

� ð Þ (10)

transformations (Eap/Es � 1).

borrowed time in the change of energy.

On this basis, we replaced Eq. (9) with the relation:

� pairs.

antimatter particles.

tion of e<sup>+</sup>

/e� + νe/ν<sup>e</sup>

In accordance with Eq. (8), the energy consumed in space phase is equal to the energy restored in time phase. The total energy in opposite phases is conserved E=0.

When energy is inserted to space-time frame for space expansion, one of time variables (instant of time) gets performance of space coordinate for expansion of space with the decrease of frequency of energy: (2;2) ! (3;1). Generation of an event starts with the translation one of time variables to space variable. The arrow of time, which is due to the consumption of energy in space phase (appears as an energy Eap � Es gradient), generates thermodynamic arrow of heat loss. Decrease of energy frequency Eap � E<sup>s</sup> leads to the increase of time arrow Δt, which is the move from the past to the future, carrying energetic information of the past.

This is the mechanism of generation arrow of time. Therefore, the phenomenon called entropy is due to the translation of time phase energy to the space-time frame with the loss of frequency of energy. Due to the maximum frequency of time phase energy in the past and consumption of energy in space phase, the parameter called "entropy" has its minimum value in the past.

The condition (Eap � Es)/Es = 1 of model (1) describes the minimum space-time frame, where the condition Eap = 2Es is in hold. This condition corresponds to the state where space-time frame exist as Planck's scale unit, carrying energy portion in discrete symmetry. In this case, there is no difference in performance of time and space variables. However, this condition takes place only in discrete mode.

The background state Eap = 0 of model (8) is the vacuum state of particle physics and classic field, where all the components of stress-energy tensor is zero. At Eap = 0, the space-time frame is broken to the separate space and time fields and there is no arrow of time. At Eap = 0, the gravitational energy appears as the separate force through inversion of variables. In this case, the entire energy portion, distributed in space phase (with negative sign) absorbed by the initial background state. On this basis, gravitation appears as energy-mass relation of asymmetric space-time variables rather than mass-mass relation of Newton's physics.

#### 8. Generation of mass

One of the main problems related to the generation of mass by spontaneous breakdown of continuous symmetry, given by Higgs mechanism, is that this mechanism does not connect generation of mass with the space-time locality of a particle, which gets mass and does not explain why background continuous symmetry has to be broken by un-natural way. The mechanism of mass generation also has to explain why collision experiments produce more matter particles than antimatter particles.

In this chapter, we will discuss how the non-uniform energy conservation concept is to be the alternative mechanism of mass generation. The non-uniform distribution of energy portions within asymmetric space and time phases requires generation of the fields with the different energetic properties (frequency and amplitude), which is the only way for carrying conservation of energy through these fields. Coupling of two fields with the different energetic properties as an energy consuming and energy restoration phases generates the non-virtual space-time frame, which appears to be the non-uniform conservation of energy through energy-mass exchange transformations (Eap/Es � 1).

The background state of space-time frame is the relation of virtual asymmetric space and time phases, which proceeds conversion of energy from one form to another (8), through translation of asymmetric entities, such as ΔS/S1, Δt/t1, carrying energy portions as a virtual matter and antimatter particles.

We can describe the non-uniform background energy-mass translation by conversion of light photons to electron/positron pairs, which is well-known quantum mechanics translation event. Quantum mechanics states that during this translation, energy conservation is hold by fluctuations, such as particles borrow energy and after very short time return the borrowed energy back:

$$\mathbf{\color{red}{y/y = e^+/e^-}}\tag{9}$$

The energy-matter translation given by relation (9) does not count time phase of energy conservation and locality of the produced particles, while photons-leptons translation takes place in the abstract space. Equation (9) could be the discrete translation of energy in the form of infinite fluctuations of the background quantum state. It is clear that in this case there is no natural way for breaking of the continuous symmetry of discrete fluctuations, forming time independent infinite symmetry of matter-antimatter relations. Equation (9) does not reflect the borrowed time in the change of energy.

Conservation of energy requires a certain finite frame for locality that is why space and time cannot exist as separate variables. Formation of a particle within any time scale without locality in space phase leads to the missing of energy conservation. By Landau's opinion [35], infinite fluctuations of virtual matter-antimatter pairs should lead to the "Ultraviolet Catastrophe due to the accumulation of infinite amount of energy of collisions and it is impossible to prove the mathematical basis of elimination of "Ultraviolet Catastrophe."

On this basis, we replaced Eq. (9) with the relation:

at Eap = 0,

172 Advanced Technologies of Quantum Key Distribution

in the past.

takes place only in discrete mode.

8. Generation of mass

matter particles than antimatter particles.

ΔS S1 þ Δt t1

in time phase. The total energy in opposite phases is conserved E=0.

move from the past to the future, carrying energetic information of the past.

In accordance with Eq. (8), the energy consumed in space phase is equal to the energy restored

When energy is inserted to space-time frame for space expansion, one of time variables (instant of time) gets performance of space coordinate for expansion of space with the decrease of frequency of energy: (2;2) ! (3;1). Generation of an event starts with the translation one of time variables to space variable. The arrow of time, which is due to the consumption of energy in space phase (appears as an energy Eap � Es gradient), generates thermodynamic arrow of heat loss. Decrease of energy frequency Eap � E<sup>s</sup> leads to the increase of time arrow Δt, which is the

This is the mechanism of generation arrow of time. Therefore, the phenomenon called entropy is due to the translation of time phase energy to the space-time frame with the loss of frequency of energy. Due to the maximum frequency of time phase energy in the past and consumption of energy in space phase, the parameter called "entropy" has its minimum value

The condition (Eap � Es)/Es = 1 of model (1) describes the minimum space-time frame, where the condition Eap = 2Es is in hold. This condition corresponds to the state where space-time frame exist as Planck's scale unit, carrying energy portion in discrete symmetry. In this case, there is no difference in performance of time and space variables. However, this condition

The background state Eap = 0 of model (8) is the vacuum state of particle physics and classic field, where all the components of stress-energy tensor is zero. At Eap = 0, the space-time frame is broken to the separate space and time fields and there is no arrow of time. At Eap = 0, the gravitational energy appears as the separate force through inversion of variables. In this case, the entire energy portion, distributed in space phase (with negative sign) absorbed by the initial background state. On this basis, gravitation appears as energy-mass relation of asym-

One of the main problems related to the generation of mass by spontaneous breakdown of continuous symmetry, given by Higgs mechanism, is that this mechanism does not connect generation of mass with the space-time locality of a particle, which gets mass and does not explain why background continuous symmetry has to be broken by un-natural way. The mechanism of mass generation also has to explain why collision experiments produce more

metric space-time variables rather than mass-mass relation of Newton's physics.

¼ 0 (8)

$$\mathbf{\gamma}/\mathbf{\gamma} = - (\mathbf{e}^+/\mathbf{e}^- + \mathbf{v}\_\mathbf{e}/\mathbf{v}\_\mathbf{e}^-) \tag{10}$$

The right side of Eq. (10) involves additional identity in the form of neutrinos to cover missing part of energy conservation in time dependent frame. Equation (10) represents mechanism of energy conservation, which involves decay of energy into asymmetric space and time fields particles having different energy density. Conversion of light photons from one form to another for conservation needs generation of phase difference, which appears with the formation of e<sup>+</sup> /e� + νe/ν<sup>e</sup> � pairs.

The space field particles, comprising e�/e+ pairs have more energy density, while time phase particles, comprising νe/ν<sup>e</sup> � pairs, have energy portions of high frequency. That is why the mass for neutrinos is significantly less than that of an electron's mass. The right-handed antineutrino and left-handed neutrino pair together with the electron/positron pair represent distribution of energy within virtual space and time phases. Due to the locality within space, close to Planck's size, performance of virtual matter particles became time dependent and it get velocity less than speed of light photons that is why parity translation (10) became non-invariant.

At Eap = 0, decay of the ordinary matter particles e+

through longitudinal wave of neutral current e<sup>+</sup>

which gets peculiar properties of superconductivity.

time (Eap = 0) represents negative energy solution.

consumes huge amount of energy which makes produced W+

particles, which in individual form have no space-time frame.

frame comprising of three-color structure.

total energy conserved.

vector bosons. Generation of mass and its stable existence is possible if W+

Separation of e/e+ + νe/ν<sup>e</sup>

W+

W+

/ν<sup>e</sup> + e/ν<sup>e</sup>

The Concept of Mass Based on Accelerated Conservation of Energy within Asymmetric Space-Time Phases

/e + νe/ν<sup>e</sup>

pairs and transformation to the frame of quarks e+

of gravitational force. The energy, released from the continuous decay of space-time frame,

moves to the background state. The absence of exchange interaction generates longitude wave. In the absence of energy flux, decay of space-time frame leads pairing of electron/positron and neutrino/antineutrino pairs to composite bosons with continuous spectrum. The composite bosons do not obey Pauli Exclusion Principle and can occupy the same ground to form fluid,

The empty space is the medium where particles form fluid with continuous spectrum. They become as massless particles moving with superconductivity to the initial state. The uniform fluid motion of complex boson to the background state appears as the uniform gravitational field.

Addition of neutrinos to Eq. (9) replaces the concept of electron self-interaction. The condition of space expansion describes positive energy solution while consuming all the energy in space-

ever, heavy bosons are not a fermions because they do not have own non-virtual space-time frame. As in the case of Eq. (10), when there is no energy flux (absence of force carrier scalar bosons) to hold the condition of Eq. (11), due to the absence of non-virtual space-time frame,

, W vector bosons have a trend to decay back to γ/γ photons in the form of beta decay. The

, W bosons have a performance as left- and right-handed particles, which is why they are

form a non-virtual space-time frame. On this basis, non-uniform conservation of energy requires translation of background asymmetric time phase energy to space-time frame, which leads to the generation of baryonic space-time structure. Here, it is necessary to give specifications: baryonic particles are the particles, which have space-time frame, and leptons are the

Energy of YY photons converted to energy of massive W and W+ vector bosons for generation of virtual space-time frame. In the second step, flux of the energy for generation of non-virtual space-time frame of quarks takes place within n-p structure. The energy of exchange interactions composes energy of gluons to hold discrete locality of quarks in the non-virtual spacetime frame. The difference of the energy of W bosons and quarks in relation to quarks mass (at discrete symmetry energy-mass equivalence is in hold) becomes the energy flux for discrete exchange interactions. That is why quarks mass is less than that of W bosons. Due to the three body interactions (Eact = 2Es) which keeps discrete symmetry of n-p transformations (8), gluons participate in exchange interactions also in the form of non-zero mass particles in three family

Due to the existence of quarks family in proton-neutron frame in discrete mode, energy portion consumed from force carrier scalar in exchange interactions (Eact Es)/Es generates the symmetric three particles frame of quarks. In the process of cyclic n-p transformations, the

takes place with the generation

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of complex bosons condensate

/ν<sup>e</sup> + e/ν<sup>e</sup>

, W bosons could

, W bosons very heavy. How-

175

Generation of e�/e+ + νe/ν<sup>e</sup> � particles (10) is the translation of photons energy to virtual space and time phase particles which could be specified as an "empty space" particles. The "empty space" is the medium where e�/e+ + νe/ν<sup>e</sup> � particles form fluid with continuum spectrum. In the absence of energy flux, Eap = 0 (5), takes place loss of the virtual space frame (10) and translation of virtual particles backward to photons. However, particles before giving the "borrowed' energy back should loss localization in space phase and loss some portion of energy which has to go in parallel with the absorption of photons by e�/e+ pairs. This phenomenon is the main feature of energy non-conservation during return of "borrowed" energy of quantum fluctuations. Generation of space phase and distribution of energy in space field leads to the non-uniform conservation of energy in space by absorption of photons by e�/e<sup>+</sup> pairs with formation of pairs of heavy bosons:

1. Generation of mass for bosons: passing of photons through e+ /e� + νe/ν<sup>e</sup> � field

$$\mathbf{m}\mathbf{\gamma}\gamma + (\mathbf{e}^+/\mathbf{e}^- + \mathbf{v}\_\mathbf{e}/\mathbf{v}\_\mathbf{e}^-) = \mathbf{n}\gamma\gamma + \mathbf{e}^+/\mathbf{v}\_\mathbf{e}(\mathbf{W}^+) + \mathbf{e}^-/\mathbf{v}\_\mathbf{e}^-(\mathbf{W}^-) \tag{11}$$

2. Generation of mass for leptons

$$(\mathbf{n}\gamma\gamma + \mathbf{e}^+ / \mathbf{v}\_\mathbf{e}(\mathbf{W}^+) + \mathbf{e}^- / \mathbf{v}\_\mathbf{e}^-(\mathbf{W}^-) = (\mathbf{u}\mathbf{d}\mathbf{d}...\mathbf{Gluons}...\mathbf{d}\mathbf{du})\tag{12}$$

In accordance with condition (10), the pair of leptons e�/e+ + νe/ν<sup>e</sup> � has a performance of virtual bosons (similar to the Nambu Goldstone bosons) and in the form of four leptons describes the "fermionic quanta" or virtual particles of space phase. From model (5) and Eqs. (10) and (11), it is followed that photons energy may be conserved only through exchange interaction with the non-zero mass particles.

The two pair of particles e�/e+ + νe/ν<sup>e</sup> � in the form of virtual neutral boson field is the alternative to the Higgs field which absorbing photons generates heavy W bosons.

Exchange interaction of yy photons with the e�/e+ + νe/ν<sup>e</sup> � particles lead to the observance of light which became a composite particle. When Eap = 0, the leptons in the form of pair of particles e�/e+ + νe/ν<sup>e</sup> do not form space-time frame and do not obey Pauli exclusive principle and perform as bosons condensate with the integer spin number. Composite fermions with bosonic "face" due to the absence of exchange interactions, has a performance similar to Bose-Einstein bosons condensate, which in the form of superconductive neutral fluid carry energy to the background state. The left side of Eq. (10) describes bosons superconductive fluid, while the right side presents superconductive fermionic medium.

At Eap = 0, decay of the ordinary matter particles e+ /ν<sup>e</sup> + e/ν<sup>e</sup> takes place with the generation of gravitational force. The energy, released from the continuous decay of space-time frame, through longitudinal wave of neutral current e<sup>+</sup> /e + νe/ν<sup>e</sup> of complex bosons condensate moves to the background state. The absence of exchange interaction generates longitude wave.

The space field particles, comprising e�/e+ pairs have more energy density, while time phase

for neutrinos is significantly less than that of an electron's mass. The right-handed antineutrino and left-handed neutrino pair together with the electron/positron pair represent distribution of energy within virtual space and time phases. Due to the locality within space, close to Planck's size, performance of virtual matter particles became time dependent and it get velocity less than

and time phase particles which could be specified as an "empty space" particles. The "empty

the absence of energy flux, Eap = 0 (5), takes place loss of the virtual space frame (10) and translation of virtual particles backward to photons. However, particles before giving the "borrowed' energy back should loss localization in space phase and loss some portion of energy which has to go in parallel with the absorption of photons by e�/e+ pairs. This phenomenon is the main feature of energy non-conservation during return of "borrowed" energy of quantum fluctuations. Generation of space phase and distribution of energy in space field leads to the non-uniform conservation of energy in space by absorption of photons by e�/e<sup>+</sup>

� ð Þ ¼ nγγ þ eþ=ν<sup>e</sup> W<sup>þ</sup> ð Þþ e�=ν<sup>e</sup>

virtual bosons (similar to the Nambu Goldstone bosons) and in the form of four leptons describes the "fermionic quanta" or virtual particles of space phase. From model (5) and Eqs. (10) and (11), it is followed that photons energy may be conserved only through exchange

light which became a composite particle. When Eap = 0, the leptons in the form of pair of particles e�/e+ + νe/ν<sup>e</sup> do not form space-time frame and do not obey Pauli exclusive principle and perform as bosons condensate with the integer spin number. Composite fermions with bosonic "face" due to the absence of exchange interactions, has a performance similar to Bose-Einstein bosons condensate, which in the form of superconductive neutral fluid carry energy to the background state. The left side of Eq. (10) describes bosons superconductive fluid, while

alternative to the Higgs field which absorbing photons generates heavy W bosons.

speed of light photons that is why parity translation (10) became non-invariant.

� pairs, have energy portions of high frequency. That is why the mass

� particles (10) is the translation of photons energy to virtual space

� particles form fluid with continuum spectrum. In

/e� + νe/ν<sup>e</sup>

� W� ð Þ¼ ð Þ udd…Gluons…ddu (12)

� in the form of virtual neutral boson field is the

� particles lead to the observance of

� field

� W� ð Þ (11)

� has a performance of

particles, comprising νe/ν<sup>e</sup>

174 Advanced Technologies of Quantum Key Distribution

Generation of e�/e+ + νe/ν<sup>e</sup>

space" is the medium where e�/e+ + νe/ν<sup>e</sup>

pairs with formation of pairs of heavy bosons:

interaction with the non-zero mass particles.

The two pair of particles e�/e+ + νe/ν<sup>e</sup>

2. Generation of mass for leptons

1. Generation of mass for bosons: passing of photons through e+

mγγ þ eþ=e� þ νe=ν<sup>e</sup>

nγγ þ eþ=ν<sup>e</sup> W<sup>þ</sup> ð Þþ e�=ν<sup>e</sup>

Exchange interaction of yy photons with the e�/e+ + νe/ν<sup>e</sup>

the right side presents superconductive fermionic medium.

In accordance with condition (10), the pair of leptons e�/e+ + νe/ν<sup>e</sup>

In the absence of energy flux, decay of space-time frame leads pairing of electron/positron and neutrino/antineutrino pairs to composite bosons with continuous spectrum. The composite bosons do not obey Pauli Exclusion Principle and can occupy the same ground to form fluid, which gets peculiar properties of superconductivity.

The empty space is the medium where particles form fluid with continuous spectrum. They become as massless particles moving with superconductivity to the initial state. The uniform fluid motion of complex boson to the background state appears as the uniform gravitational field.

Addition of neutrinos to Eq. (9) replaces the concept of electron self-interaction. The condition of space expansion describes positive energy solution while consuming all the energy in spacetime (Eap = 0) represents negative energy solution.

Separation of e/e+ + νe/ν<sup>e</sup> pairs and transformation to the frame of quarks e+ /ν<sup>e</sup> + e/ν<sup>e</sup> consumes huge amount of energy which makes produced W+ , W bosons very heavy. However, heavy bosons are not a fermions because they do not have own non-virtual space-time frame. As in the case of Eq. (10), when there is no energy flux (absence of force carrier scalar bosons) to hold the condition of Eq. (11), due to the absence of non-virtual space-time frame, W+ , W vector bosons have a trend to decay back to γ/γ photons in the form of beta decay. The W+ , W bosons have a performance as left- and right-handed particles, which is why they are vector bosons. Generation of mass and its stable existence is possible if W+ , W bosons could form a non-virtual space-time frame. On this basis, non-uniform conservation of energy requires translation of background asymmetric time phase energy to space-time frame, which leads to the generation of baryonic space-time structure. Here, it is necessary to give specifications: baryonic particles are the particles, which have space-time frame, and leptons are the particles, which in individual form have no space-time frame.

Energy of YY photons converted to energy of massive W and W+ vector bosons for generation of virtual space-time frame. In the second step, flux of the energy for generation of non-virtual space-time frame of quarks takes place within n-p structure. The energy of exchange interactions composes energy of gluons to hold discrete locality of quarks in the non-virtual spacetime frame. The difference of the energy of W bosons and quarks in relation to quarks mass (at discrete symmetry energy-mass equivalence is in hold) becomes the energy flux for discrete exchange interactions. That is why quarks mass is less than that of W bosons. Due to the three body interactions (Eact = 2Es) which keeps discrete symmetry of n-p transformations (8), gluons participate in exchange interactions also in the form of non-zero mass particles in three family frame comprising of three-color structure.

Due to the existence of quarks family in proton-neutron frame in discrete mode, energy portion consumed from force carrier scalar in exchange interactions (Eact Es)/Es generates the symmetric three particles frame of quarks. In the process of cyclic n-p transformations, the total energy conserved.

Generation of space-time frame of quarks through alignment of "empty space field" particles e+ /e� + νe/ν<sup>e</sup> � to "Dirac particles" e+ /ν<sup>e</sup> + e�/ν<sup>e</sup> � requires huge amount of energy flux from force carrier scalar bosons. The decay of mass and translation of space-time energy back takes place at Eact <sup>=</sup> <sup>0</sup>, (<sup>λ</sup> <sup>=</sup> �1) with transformation of e+ /ν<sup>e</sup> + e�/ν<sup>e</sup> � ingredients (Dirac particles) to the longitudinal wave of neutral current correlating the helicity of neutrinos with the negative Eigen value:

$$\mathbf{e}^+/\mathbf{v}\_\mathbf{e}(\mathbf{W}^+) + \mathbf{e}^-/\mathbf{v}\_\mathbf{e}^-(\mathbf{W}^-) \to (\mathbf{e}^+/\mathbf{e}^- + \mathbf{v}\_\mathbf{e}/\mathbf{v}\_\mathbf{e}^-) + \mathbf{Y}\mathbf{Y} \tag{13}$$

when more energy portion applied to the space-time frame, the gravitational mass added. The gravitational mass appears as the energy portion distributed in space-time frame to control conservation of energy within certain boundary of this frame. Eap in energy flux (Eap � Es)/Es is the bosonic part of the frame, while Es is the fermionic ingredient of exchange interactions. The energy flux (Eap � Es)/Es through coupling with the local position of space-time S1/t1 describes interaction of bosonic and fermionic particles through exchange of energy. In case when interaction takes place between two fermions, the ingredients of the energy flux (Eap � Es)/Es describes interaction of energy or mass content of these fermions. Therefore, model (5) con-

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177

Generation of mass is the combination of electromagnetic and weak forces. The electromagnetic force needed for generation of non-virtual space-time frame, while weak force is necessary to keep the existence of space-time frame of a matter "grain" through discrete symmetry, which requires violation of local CPT symmetry. Weak interactions are the result of nonuniform discrete conservation of energy, which takes place with translation of asymmetric

Now appears a question, why electromagnetic force is carried by charged particles, while neutral particles are responsible for gravitation. Charged bosons are needed for generation of non-zero mass quarks of space-time frame to carry conservation of energy in expansion phase of space, while neutral bosons are needed for translation of space-time energy back to the background state. At Eap = 0, decay of space-time frame releases graviton in the form of neutral

Within non-uniform conservation of energy in space-time frame we may explain how spacetime, carrying energy distribution may lead to the generation of chargers. The space-time to carry non-uniform conservation of energy leads to the formation of phase difference between

In non-uniform conservation of energy, boundary of space and time variables is asymmetrically different, and background coupling of asymmetric space-time variables does not produce symmetrical particles-antiparticles pairs. At Planck scale, when space boundary is small, the left side of Eq. (8) has a huge trend to change and the duration of change at this scale is very small. Therefore, space and time variables, carrying the same portions of energy, have very asymmetric boundaries, which is the driving force for selection of the direction in non-uniform

Due to this reason, the symmetry of strong force and permanent performance of the protonneutron pairs is possible only through discrete uniform translation of scalar energy to the

Due to the requirement of discrete symmetry Eap = 2Es, neutrinos also exists in three family mode; Two types of neutrinos couple and produce third type neutrino; asymmetric decay of the third neutrino leads back to the realization of discrete symmetry of neutrino's existence. At Eap = 0, neutrinos do not participate in electromagnetic force but at Eap 6¼ 0, neutrino, being part of quark structure, participates in the discrete symmetry of baryon frame. The neutrino's mass is small for realization of neutron-proton discrete symmetry with high frequency.

boundaries of space-time phases, carrying non-uniform conservation of energy.

space and time coordinates which appears in the form of charges.

"three particles tandem of" space-time-energy frame (5).

nects all the interactions of particles physics.

current back to the initial state.

distribution of energy.

The transformations, described by Eqs. (10)–(13), are symmetrical only in discrete mode within closed loop. The absence of invariant translations between ingredients of Eqs. (10)–(13) is due to the non-uniform conservation of energy. In accordance with model (6), in the presence of energy for reverse translation, matter particle in exchange interaction (Eact � Es)/Es should have more energy than that of force carrier scalar (gluons). Due to the same reason, it is impossible to separate quarks-antiquarks pairs. Separation of individual quarks is possible only at Eact = 0, when three family space-time frame of proton collapses. This behavior of quarks describes color confinement phenomenon.

Model (5) explains the phenomenon called "nonlocality" or entanglement paradox of quantum mechanics. The function Eap � Es/Es of model (5), which describes action-response parity, is the origin of local action. At Eap = 0, particle has no space-time frame and has no certain locality. When particle has no space-time (Eap = 0), all particles are the non-distinguishable ingredients of antimatter "condensate."

At Eap � Es ˃ 0, particle has its own space-time frame and therefore independent locality. The condition Eap = 0, eliminates action-response behavior of a particle which losing spin response moves to the background state with the velocity not less than speed of light.

You cannot isolate virtual space phase from virtual time phase that is why it is impossible to separate the quark-antiquark frame. Meson alone has no space-time frame that is why it is not observable as a separate particle, but it is a piece of non-virtual space-time frame of p-n frame, having a motion in baryon structure.

The exchange interaction of model (5) (Eap � Es)/Es explains why the weak interaction acts only on left-handed particles and right-handed antiparticles. The right-handed particles in exchange interactions lead to the expansion of space matter, while left-handed matter particles generate gravitational force to hold the boundary of the conserved energy. The non-invariant translation of a body to the initial state takes place with the decay of space-time frame and realignment of the neutrinos helicity with formation of neutral current. Composite bosons with the continuum spectrum comprise the phenomenon called gravitation.

The first step described by Eqs. (10) and (11) is the generation of non-zero mass virtual particles having virtual space-time frame, while the step (12) involves transformation of a lepton particles from virtual space-time manifold to the minimum grain of non-virtual spacetime frame. That is why mechanism of generation of mass for space-time frame particles (quarks) and bosons is different.

From model (1), it follows that at zero value of Es, the space-time frame moves to the singularity. Therefore, the inertial energy of a particle in cyclic mode can never have zero value and when more energy portion applied to the space-time frame, the gravitational mass added. The gravitational mass appears as the energy portion distributed in space-time frame to control conservation of energy within certain boundary of this frame. Eap in energy flux (Eap � Es)/Es is the bosonic part of the frame, while Es is the fermionic ingredient of exchange interactions. The energy flux (Eap � Es)/Es through coupling with the local position of space-time S1/t1 describes interaction of bosonic and fermionic particles through exchange of energy. In case when interaction takes place between two fermions, the ingredients of the energy flux (Eap � Es)/Es describes interaction of energy or mass content of these fermions. Therefore, model (5) connects all the interactions of particles physics.

Generation of space-time frame of quarks through alignment of "empty space field" particles

carrier scalar bosons. The decay of mass and translation of space-time energy back takes place at

/ν<sup>e</sup> + e�/ν<sup>e</sup>

dinal wave of neutral current correlating the helicity of neutrinos with the negative Eigen value:

The transformations, described by Eqs. (10)–(13), are symmetrical only in discrete mode within closed loop. The absence of invariant translations between ingredients of Eqs. (10)–(13) is due to the non-uniform conservation of energy. In accordance with model (6), in the presence of energy for reverse translation, matter particle in exchange interaction (Eact � Es)/Es should have more energy than that of force carrier scalar (gluons). Due to the same reason, it is impossible to separate quarks-antiquarks pairs. Separation of individual quarks is possible only at Eact = 0, when three family space-time frame of proton collapses. This behavior of

Model (5) explains the phenomenon called "nonlocality" or entanglement paradox of quantum mechanics. The function Eap � Es/Es of model (5), which describes action-response parity, is the origin of local action. At Eap = 0, particle has no space-time frame and has no certain locality. When particle has no space-time (Eap = 0), all particles are the non-distinguishable ingredients

At Eap � Es ˃ 0, particle has its own space-time frame and therefore independent locality. The condition Eap = 0, eliminates action-response behavior of a particle which losing spin response

You cannot isolate virtual space phase from virtual time phase that is why it is impossible to separate the quark-antiquark frame. Meson alone has no space-time frame that is why it is not observable as a separate particle, but it is a piece of non-virtual space-time frame of p-n frame,

The exchange interaction of model (5) (Eap � Es)/Es explains why the weak interaction acts only on left-handed particles and right-handed antiparticles. The right-handed particles in exchange interactions lead to the expansion of space matter, while left-handed matter particles generate gravitational force to hold the boundary of the conserved energy. The non-invariant translation of a body to the initial state takes place with the decay of space-time frame and realignment of the neutrinos helicity with formation of neutral current. Composite bosons with

The first step described by Eqs. (10) and (11) is the generation of non-zero mass virtual particles having virtual space-time frame, while the step (12) involves transformation of a lepton particles from virtual space-time manifold to the minimum grain of non-virtual spacetime frame. That is why mechanism of generation of mass for space-time frame particles

From model (1), it follows that at zero value of Es, the space-time frame moves to the singularity. Therefore, the inertial energy of a particle in cyclic mode can never have zero value and

moves to the background state with the velocity not less than speed of light.

the continuum spectrum comprise the phenomenon called gravitation.

� W� ð Þ! eþ=e� þ νe=ν<sup>e</sup>

� requires huge amount of energy flux from force

� ingredients (Dirac particles) to the longitu-

� ð Þ þ YY (13)

/ν<sup>e</sup> + e�/ν<sup>e</sup>

e+

/e� + νe/ν<sup>e</sup>

� to "Dirac particles" e+

quarks describes color confinement phenomenon.

of antimatter "condensate."

having a motion in baryon structure.

(quarks) and bosons is different.

eþ=ν<sup>e</sup> W<sup>þ</sup> ð Þþ e�=ν<sup>e</sup>

Eact <sup>=</sup> <sup>0</sup>, (<sup>λ</sup> <sup>=</sup> �1) with transformation of e+

176 Advanced Technologies of Quantum Key Distribution

Generation of mass is the combination of electromagnetic and weak forces. The electromagnetic force needed for generation of non-virtual space-time frame, while weak force is necessary to keep the existence of space-time frame of a matter "grain" through discrete symmetry, which requires violation of local CPT symmetry. Weak interactions are the result of nonuniform discrete conservation of energy, which takes place with translation of asymmetric boundaries of space-time phases, carrying non-uniform conservation of energy.

Now appears a question, why electromagnetic force is carried by charged particles, while neutral particles are responsible for gravitation. Charged bosons are needed for generation of non-zero mass quarks of space-time frame to carry conservation of energy in expansion phase of space, while neutral bosons are needed for translation of space-time energy back to the background state. At Eap = 0, decay of space-time frame releases graviton in the form of neutral current back to the initial state.

Within non-uniform conservation of energy in space-time frame we may explain how spacetime, carrying energy distribution may lead to the generation of chargers. The space-time to carry non-uniform conservation of energy leads to the formation of phase difference between space and time coordinates which appears in the form of charges.

In non-uniform conservation of energy, boundary of space and time variables is asymmetrically different, and background coupling of asymmetric space-time variables does not produce symmetrical particles-antiparticles pairs. At Planck scale, when space boundary is small, the left side of Eq. (8) has a huge trend to change and the duration of change at this scale is very small. Therefore, space and time variables, carrying the same portions of energy, have very asymmetric boundaries, which is the driving force for selection of the direction in non-uniform distribution of energy.

Due to this reason, the symmetry of strong force and permanent performance of the protonneutron pairs is possible only through discrete uniform translation of scalar energy to the "three particles tandem of" space-time-energy frame (5).

Due to the requirement of discrete symmetry Eap = 2Es, neutrinos also exists in three family mode; Two types of neutrinos couple and produce third type neutrino; asymmetric decay of the third neutrino leads back to the realization of discrete symmetry of neutrino's existence. At Eap = 0, neutrinos do not participate in electromagnetic force but at Eap 6¼ 0, neutrino, being part of quark structure, participates in the discrete symmetry of baryon frame. The neutrino's mass is small for realization of neutron-proton discrete symmetry with high frequency.

The weak force is needed to hold permanent performance of the "space-time frame of elementary grain" of the matter in discrete mode within minimum space frame. The conservation of matter "grain" in the form of proton cannot hold continuous symmetry, while in this case there cannot be conservation of energy.

of nature. Therefore, nature requires description only within very precise energy conservation

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We replaced two pieces of conservation laws, comprising conservation of energy as uniformity in time and conservation of momentum as uniformity in space by the new conservation concept suggesting non-uniform conservation of energy within discrete space-time frame. We replaced particles concept of classic physics and wave equation of quantum physics by the boundary mapped discrete space-time frame, which carries the non-uniform conservation of energy. Uniform manifestation of energy in time and uniform manifestation of momentum in space is not possible within space-time frame, which carries energy conservation within the

Therefore, the energy-mass equivalence, limitation of velocity with the speed of light, breaking of background symmetry all originate from the non-uniform conservation of energy. The background state of discrete space-time frame describes quantum level interactions through discrete transformation of space-time variables to each other with generation of discrete virtual particle-antiparticle pairs. Consumption of energy from the background field leads to the formation of the "grain" of the non-virtual space-time frame with generation of mass, energy-

With the increase of energy portion consumed in space phase, it consumes more energy to continue its velocity that is why expansion of space is "accelerated," which is the result of nonuniform conservation of energy. Conservation of energy is accelerated which appears in the form of non-uniform distribution of energy within asymmetric space and time boundaries.

Our concept suggests that the laws of nature comprise simple deterministic formulation of space-time, which holds conservation of energy in a unique way through non-spontaneous background translations of space-time phases. The consumption of energy photons by the space-time matter with the expansion of space generates backup reaction, which becomes the

Finally, discrete, non-invariant translation of asymmetric boundaries of space and time variables to each other for carrying energy portions is the deterministic mathematical beauty of

momentum relation of general relativity and classic physics.

energy conservation and discrete existence of nature.

Address all correspondence to: aghaddinm@gmail.com

Petrochemical Company, Technology Center, Sugar Land, Texas, USA

principles.

9. Conclusion

non-uniform framework.

origin of gravity.

Author details

Agaddin Khanlar Mamedov

The discrete performance of three particles frame Eap = 2Es explains why there are three families of quarks. For generation of discrete stable performance of an n-p pair the energy flux to space-time frame of baryon quarks needs to meet the condition Eap = 2Es. The baryon alone is not stable therefore cannot be the fundamental matter: the two nucleons are coupled with the meson field TB (top-antibottom) to form three flavor structure of space-time frame Eap = 2Es. In this case, the n-p frame holds discrete symmetry with high frequency and n-p transformation event which "after the change looks the same" (8).

The non-uniform conservation concept explains "mass gap problem" of Yang-Mills theory [36], which states "quantum particles have positive mass with regard to the vacuum state." The positive Eigen value of (Eap Es)/E<sup>s</sup> exchange interactions shows that "quantum" particle has a positive mass in relation to the vacuum while translation of time phase vacuum energy to the space-time frame generates positive Eigen value (Eap Es)/E<sup>s</sup> and positive mass. Conversion of mass to energy produces energy with negative sign and this process does not response to the change of time.

Description of the energy flux of model (6) in the form Eigen value (Eap/E<sup>s</sup> Es/Es) involves two terms: the term Eap/E<sup>s</sup> describes performance of charged particles through electromagnetic flux of energy, while Es/E<sup>s</sup> involves neutral particles—neutrinos which have self-coupling performance and do not experience effect of forces.

Recently, due to the dark energy phenomenon of Universe, the subject of energy conservation got more attention. For example, Ref. [37] suggest that without dark energy and dark matter, Einstein's gravitational field equations should not hold conservation of energy-momentum relation.

In accordance with the non-uniform energy conservation concept, we may give specification of ordinary and dark energy. The dark energy generated due to the non-invariant translation of ordinary energy to the virtual space-time frame. Ordinary matter exists when there is spacetime frame; but when space-time frame decays, it disappears with the decay of space-time frame of ordinary matter. Dark matter is not a baryonic matter and has no non-virtual spacetime frame. Matter may have observance when it has non-virtual space-time frame.

The non-uniform phenomenon of energy conservation and non-invariant weak interaction are the necessary laws of nature to give different shapes to the different events: without nonuniform conservation of energy and non-invariant exchange interaction, the events would form a non-separable dark matter without any shape and structure.

In accordance with model (5), both energy and matter to be observable should have space-time frame. In the background, energy and space-time are not observable. On this basis, the nonobservable time phase energy has features of dark energy.

Thus, the space and time are the products of non-uniform energy conservation and in reverse order, energy and mass identities are the inner products of space-time discrete dynamics. This concept completely changes our views on the fundamental interactions and symmetrical laws of nature. Therefore, nature requires description only within very precise energy conservation principles.
