4. Gravity

Model (5) shows that when the entire available energy portion is consumed for expansion of space (Eap = 0), space-time decays which has to radiate energy, accumulated in the space-time frame (negative λ = 1). In this case, the energy, consumed in space-time frame of any scale, has to move to the initial state through translation of asymmetric boundaries of space-time variables. While space and time are the phase fields of energy conservation, translation of variables presenting conversion of energy from one form to another became an obvious event. The space-time frame in this case decays to virtual space and time field particles moving to the background state, where generation of new space-time frame takes place.

accordance with the available portion of energy. In a simple form, if there is a local position,

The left side of model (5) involves the dynamic conservation of space-time frame as the nonunitary "grains," while the right side shows the non-uniform conservation of energy-mass exchange relation, carrying the dynamic flux of energy portion to the local S1/t1 metric of space-time frame (6). The gradient of energy in relation to the initial state (Eap Es)/Es as an equivalent form of space-time "grains" becomes the non-unitary quanta, which describe change of local space-time frame as an exchange interaction of a particle with the applied force. The portion of energy, distributed in space and time phases, determines the strength of

The model of non-uniform energy conservation (5) shows that space-time is the energetic field, which carries localization of energy conservation within dynamical space-time frame. The space-time, which has to carry conservation of energy, generates a non-virtual local frame,

The condition Eap = 0 of model (5) is the background state of discrete space-time field, where asymmetric space and time variables, for holding of conservation cycles, undergoes to the discrete translation as the portions of energy in the different fields. At this state, all types of

In accordance with model (5), energy appears as the non-uniform inner product of coupling of space and time fields (right-handed translation) and in reverse order, the origin of space-time variables is the decay of space-time into virtual space and time entities (left-handed translation), with the discrete restoration of energy at background state. This is the non-uniform nonstatic conversion of energy from one form to another. On this basis, time appears as the product and boundary of the discrete non-Noetherian dynamic conservation of energy, carry-

Time takes its origin only from discrete energy conservation cycle and starts when energy, accumulated in time phase, translated to the formation and expansion of space-time frame with exchange interaction, controlling the boundary of space-time framework. Due to the relation of motion to the discrete local frame of space-time, description of time only by unitary

Model (5) eliminates singularity in space-time frame and energy: the zero boundary of energy Eap = 0 and its product zero time instant (t1, frequency) cancel each other. The zero Es and its product zero space (S1) similarly cancel each other, which generates singularity free dynamic

Model (5) shows that when the entire available energy portion is consumed for expansion of space (Eap = 0), space-time decays which has to radiate energy, accumulated in the space-time frame (negative λ = 1). In this case, the energy, consumed in space-time frame of any scale,

there should be a boundary of the change of the energy that carries a space-time field.

a force and repulsive reaction of a matter.

160 Advanced Technologies of Quantum Key Distribution

the interactions discretely unified.

ing energy within space-time frame.

intervals leads to the uncertainty.

model of an event.

4. Gravity

and moves it relative to the state of energy restoration.

In accordance with these principles, gravity is not a space-time geometric curvature itself, but a result of discrete non-uniform conservation of energy, localized within finite space-time field. The parameter (Eap/E<sup>s</sup> 1) of Eq. (6), in the form of energy-mass exchange interaction, generates gravity for controlling of space-time and energy boundaries. Therefore, gravity is not a result of simple existence of energy itself in space-time, but it is the result of non-uniform conservation of energy through space-time field.

The right side of model (5) as the energy-momentum content of space-time frame leads to the "warping of space-time structure" as general relativity suggests.

The flux of energy to space-time frame expands Planck scale space in direction of localization of background energy in the expanded space-time frame. The non-uniform conservation of energy (5) involves two space-time structures: non-uniform conservation of energy in differential form within discrete, non-virtual space-time frame and in integral form when space-time decays to virtual space and time phases with restoration of energy at background state with the continuous spectrum (Eap = 0) of uniform conservation. At this condition, there is no exchange interaction and the difference between inertial and gravitational masses disappears. Therefore, the key ingredient of the space-time is not the gravity itself, but non-uniform conservation of energy, which generates mechanism (gravity) restoring energy at its origin. On this basis, gravity appears as the gradient of the energy between background vacuum state and the condition where energy portion transformed to the local space-time phase with generation of space mass.

In the non-uniform energy conservation concept, energy and mass appear as two forms of the same unit, distributed differently within asymmetric coordinates of space-time field. This approach is different from special relativity concept, which connects energy-mass relation with the uniform speed of light. Without mass, there is no non-virtual space-time frame, which has to carry conservation energy. At the background state, emerged non-virtual space-time frame leads to the consumption of energy and growth of the non-virtual space-time frame of the matter.

The statement of general relativity (GR) that "space-time of GR is the gravitational field" [27] does not explain origin of space-time. GR does not explain why space-time has to involve gravity and curvature if its space-time has no boundary. These questions have direct connection with the classic physics concept of inertia, which does not explain why a body resists in its uniform motion to the applied force. In accordance with Eq. (5), the dynamics of a body is the result of the coupling of energy with the space-time frame: a body has a tendency to keep its local state, but it cannot hold this state uniformly because energy applied to a system is nonuniformly conserved. This leads to the growth of the internal force of inertia (called gravitation), which has a trend to return a system uniformly back to the energy restoration state.

At Eap = 0 of model (5), the space-time field undergoes to the decay which leads to the loss of the information, generated by the energy flux. Therefore, generation of a new cycle of spacetime frame is the generation of new event and "an event when it travels backward does not meet with itself" because an event returns with the loss of space-time information. Without space-time frame, there is no ordinary matter to carry information.

The antimatter having no space-time frame is the "dark" ingredient of energy phase of Higgs field. Running Eq. (6) at Eap = 0 to background Planck scale generates phase translation of "dark" ingredient of energy to the visible space-time matter. Dark energy does not carry space-time frame. It has only time phase in the form of condensate, which after interaction with the generated space-time frame forms vector bosons with integer spin. Photon energy is the reversed reflection from space-time frame. Photon transforms to electron/positron pairs, which absorbs photon to produce vector bosons as the precursors of

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It is necessary to note that the non-invariant translation of variables of space-time gives alternative mechanism for generation of spin property of particles. In accordance with quantum mechanics, the spin number is the quantum state where fermions are half spin particles and have to follow Pauli Exclusion Principle. This means that one fermionic particle can occupy only one quantum energy state. Quantum theory suggests that spin appears as the

Model (5) suggests that the spin is the space-time phenomenon, which appears in the form of energy-mass and action-response relation (Eap Es)/Es. Conservation of energy takes place through its distribution within space-time phases, which generates energy-mass exchange relation. Consumption of energy in right-handed space expansion is carried by electromagnetic energy, while accumulation of energy in space-time frame is in the form of mass that moves the space-time in the left-handed direction. The opposite forces of exchange interaction curves space-time and produce angular momentum, rotating particles of space-time frame

The spin as the identity is the "face" of a particle: every particle with its energy content can have only one local space-time structure. Fermion has "face" as a particle of baryonic structure that exists within non-virtual space-time frame in discrete symmetry at Es = 1/2Eap (7) of nuclear. This structure generates half spin number for fermionic particles. Model (7) shows that half spin behavior of fermions Es = 1/2Eap and spin one performance of bosons is generated from exchange interactions to carry discrete symmetry through translation of energy to space-time field. The full recovery of discrete symmetry of a fermionic particle involves two

In the absence of Eap, (Es = 0) all the particles lose space-time frame and spin: helicity becomes the dynamical behavior for conservation of energy at the origin. Later, we will show that without

Based on model (5), we can explain the quantum level particle-antiparticle interactions in deterministic way. At Eap = 0, particle radiates energy and loses its space-time field (virtual for non-baryonic particles, non-virtual for baryonic particles), where two states of energy merge together forming neutral particle. This is the phenomenon which divides fermionic

From non-uniform conservation of energy follows, that gravitation together with the electroweak force holds nuclear stability in discrete mode. On this basis, all the forces unified within three families: decomposition of strong force generates week and gravitation forces and

helicity of neutrinos space-time cannot restore energy conservation at background state.

pieces of full cycle between discrete exchanges of quarks within n-p frame.

quarks.

around local position.

particles "face" between two states.

momentum of a particle around its own axis.

It is necessary to note very important statement of special relativity (SR) that space and time do not exist separately, but form a four-dimensional space-time unit. In accordance with the principles of SR, conservation of energy has to be valid in "flat space-time." This statement of SR is based on Minkowsii concept [28] of a flat four-dimensional space-time frame. Special relativity describes energy-mass equivalence through uniform relation E = mc2 (or Eo = mc2 ), but conservation of energy-mass relation within non-uniform space-time field eliminates invariant features of the conservation laws. The additional statements of SR such as "space contraction" and "time delay" do not explain mass-velocity relation, while these supplementary concepts follow from Lorentz's invariant translation principles.

In accordance with the non-uniform energy conservation model (5), "flat space-time" without mass does not comprise a frame of the non-virtual space-time and cannot carry any information on energy conservation. On this basis, model (5) treats mass as a discrete space-time field of energy-mass unit of non-uniform conservation of energy.

Different phases of energy conservation in space-time field appear as the virtual fields of different entities, such as particles and antiparticles, representing energy-mass relationship. Light energy exists through conservation between two fields, which appears in the form of particles with positive and antiparticles with negative energy states. However, positive and negative energy states do not follow invariant translations to each other. At Eapp = 0, model (5) describes negative energy solution of antimatter, while Eapp E<sup>s</sup> ˃ 0 represents positive energy solution of matter being localized within space-time frame. The condition when energy content of local state (Eapp Es) is equal to the energy content of background state E<sup>s</sup> (Eap = 2Es) describes space-time symmetry or symmetry of matter-antimatter particles.

Our concept describes space-time in a new representation, responsible for symmetry breaking. The space-time is the product of energy distribution within two phases, which in reverse order is the carrier of energy conservation. The "warping of space-time with energy and matter in it," suggested by general relativity, is the requirement of cyclic performance of space-time for conservation of energy and matter.

At background Planck scale, the space-time appears within annihilation of space and time phases in the form of matter and antimatter annihilation. This transformation leads to the consumption of photons energy by generated space-time frame with formation of matter and expansion of it in space-time frame. In accordance with our concept, spontaneous symmetry breaking is the change of time phase to space-time frame with the generation of mass, carrying discrete conservation of energy.

As follows from model (7), one energy carrier particle is in symmetry with the two matter carrying particles which forms three particles tandem (three particles distribution of quarks in proton and neutron). This is the necessary condition for symmetrical existence of a matter. The antimatter having no space-time frame is the "dark" ingredient of energy phase of Higgs field. Running Eq. (6) at Eap = 0 to background Planck scale generates phase translation of "dark" ingredient of energy to the visible space-time matter. Dark energy does not carry space-time frame. It has only time phase in the form of condensate, which after interaction with the generated space-time frame forms vector bosons with integer spin. Photon energy is the reversed reflection from space-time frame. Photon transforms to electron/positron pairs, which absorbs photon to produce vector bosons as the precursors of quarks.

At Eap = 0 of model (5), the space-time field undergoes to the decay which leads to the loss of the information, generated by the energy flux. Therefore, generation of a new cycle of spacetime frame is the generation of new event and "an event when it travels backward does not meet with itself" because an event returns with the loss of space-time information. Without

It is necessary to note very important statement of special relativity (SR) that space and time do not exist separately, but form a four-dimensional space-time unit. In accordance with the principles of SR, conservation of energy has to be valid in "flat space-time." This statement of SR is based on Minkowsii concept [28] of a flat four-dimensional space-time frame. Special relativity describes energy-mass equivalence through uniform relation E = mc2 (or Eo = mc2

but conservation of energy-mass relation within non-uniform space-time field eliminates invariant features of the conservation laws. The additional statements of SR such as "space contraction" and "time delay" do not explain mass-velocity relation, while these supplemen-

In accordance with the non-uniform energy conservation model (5), "flat space-time" without mass does not comprise a frame of the non-virtual space-time and cannot carry any information on energy conservation. On this basis, model (5) treats mass as a discrete space-time field

Different phases of energy conservation in space-time field appear as the virtual fields of different entities, such as particles and antiparticles, representing energy-mass relationship. Light energy exists through conservation between two fields, which appears in the form of particles with positive and antiparticles with negative energy states. However, positive and negative energy states do not follow invariant translations to each other. At Eapp = 0, model (5) describes negative energy solution of antimatter, while Eapp E<sup>s</sup> ˃ 0 represents positive energy solution of matter being localized within space-time frame. The condition when energy content of local state (Eapp Es) is equal to the energy content of background state E<sup>s</sup> (Eap = 2Es)

Our concept describes space-time in a new representation, responsible for symmetry breaking. The space-time is the product of energy distribution within two phases, which in reverse order is the carrier of energy conservation. The "warping of space-time with energy and matter in it," suggested by general relativity, is the requirement of cyclic performance of space-time for

At background Planck scale, the space-time appears within annihilation of space and time phases in the form of matter and antimatter annihilation. This transformation leads to the consumption of photons energy by generated space-time frame with formation of matter and expansion of it in space-time frame. In accordance with our concept, spontaneous symmetry breaking is the change of time phase to space-time frame with the generation of

As follows from model (7), one energy carrier particle is in symmetry with the two matter carrying particles which forms three particles tandem (three particles distribution of quarks in proton and neutron). This is the necessary condition for symmetrical existence of a matter.

),

space-time frame, there is no ordinary matter to carry information.

162 Advanced Technologies of Quantum Key Distribution

tary concepts follow from Lorentz's invariant translation principles.

describes space-time symmetry or symmetry of matter-antimatter particles.

of energy-mass unit of non-uniform conservation of energy.

conservation of energy and matter.

mass, carrying discrete conservation of energy.

It is necessary to note that the non-invariant translation of variables of space-time gives alternative mechanism for generation of spin property of particles. In accordance with quantum mechanics, the spin number is the quantum state where fermions are half spin particles and have to follow Pauli Exclusion Principle. This means that one fermionic particle can occupy only one quantum energy state. Quantum theory suggests that spin appears as the momentum of a particle around its own axis.

Model (5) suggests that the spin is the space-time phenomenon, which appears in the form of energy-mass and action-response relation (Eap Es)/Es. Conservation of energy takes place through its distribution within space-time phases, which generates energy-mass exchange relation. Consumption of energy in right-handed space expansion is carried by electromagnetic energy, while accumulation of energy in space-time frame is in the form of mass that moves the space-time in the left-handed direction. The opposite forces of exchange interaction curves space-time and produce angular momentum, rotating particles of space-time frame around local position.

The spin as the identity is the "face" of a particle: every particle with its energy content can have only one local space-time structure. Fermion has "face" as a particle of baryonic structure that exists within non-virtual space-time frame in discrete symmetry at Es = 1/2Eap (7) of nuclear. This structure generates half spin number for fermionic particles. Model (7) shows that half spin behavior of fermions Es = 1/2Eap and spin one performance of bosons is generated from exchange interactions to carry discrete symmetry through translation of energy to space-time field. The full recovery of discrete symmetry of a fermionic particle involves two pieces of full cycle between discrete exchanges of quarks within n-p frame.

In the absence of Eap, (Es = 0) all the particles lose space-time frame and spin: helicity becomes the dynamical behavior for conservation of energy at the origin. Later, we will show that without helicity of neutrinos space-time cannot restore energy conservation at background state.

Based on model (5), we can explain the quantum level particle-antiparticle interactions in deterministic way. At Eap = 0, particle radiates energy and loses its space-time field (virtual for non-baryonic particles, non-virtual for baryonic particles), where two states of energy merge together forming neutral particle. This is the phenomenon which divides fermionic particles "face" between two states.

From non-uniform conservation of energy follows, that gravitation together with the electroweak force holds nuclear stability in discrete mode. On this basis, all the forces unified within three families: decomposition of strong force generates week and gravitation forces and coupling of these forces in reverse order in cyclic mode re-generates strong force. Later, we will describe these forces in detail.

description in the form of exchange interaction relative to the local momentum of a particle. It is clear that in case of mathematical formulation of dynamical events, involving a local position of a particle in space-time field and its local energy content, the prediction of quantum mechanics

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In accordance with the non-uniform energy conservation principle, coupling of local spacetime field and local energy state of a particle is the necessary approach for elimination of singularity and for removal of renormalization from particle physics theories. Without involvement of local position and exchange interaction, it is impossible to get mathematic formulation

It is necessary to note that Dirac's relativistic quantum theory [29] on existence of an antiparticle appeared due to the uncertainty in position. Dirac suggested that uncertainty in position can be solved if there will be another particle (antiparticle) with the different position to maintain the balance for conservation of quantum number. However, conservation of energy, involving coupling of local position with the energy flux to the space-time frame leads natu-

The concept of non-uniform conservation of energy explains why charges are needed. Coupling of space and time variables within elementary space-time frame of baryonic particle and distribution of energy in extended space-time structure takes place through involvement of charged particles. However, restoration of energy at origin takes place through decay of spacetime field and translation of energy in the form of neutral current to the initial background state. The energy is restored at the origin (Eap = 0) when phase difference, leading to the generation of charges, disappears (5). Conservation of energy through phase difference is the

In accordance with model (5), relation of an event to local position of space-time is not separable from the energy flux to space-time frame because local position, which undergoes to the growth, is the product of energy distribution in space-time frame. In reverse order, change in relation to the energy flux also is not separable from the local position, while the outcome of energy flux determined by the consumption of energy in dynamical local position. Therefore, change of velocity is the product of conjugation of local space-time position of a particle with the exchange interactions, generated from the energy flux to space-time field. This is the deterministic physical law of nature. Without conjugation of local position and energy resources through exchange interactions within space-time field of a particle there is no conservation of energy and there is no correct concept of mass. The position and momentum conjugate of uncertainty principle does not involve resources of action that is why its

In accordance with the quantum field theory, during short time intervals violation of energy conservation is restored. The common view on this statement is that conservation of energy can be temporarily violated and energy can be borrowed from the universe as long as it is returned within a short duration of time. However, Griffits [30] showed that "this principle is based on the false axiom that the energy of the universe is an exactly known parameter at all times."

could be completely different.

rally to the existence of oppositely charged particles.

origin of generation of discrete performance of physical laws.

of conservation laws.

outcome is uncertain.
