5. Unification of quantum mechanics and relativity

It is easy to show that the non-uniform conservation of energy has to be the ground concept for unification of relativity and quantum physics. Starting from the basic statement of general physics that energy conserved through its conversion from one form to another, we will arrive to the concept that a dynamical event of energy conversion has to have locality within finite space and time coordinates. In principle, the features of energy conservation during its conversion from one form to another are clear from Planck's black body radiation, which changes the frequency of energy with radiation. Change of frequency of radiation is the result of nonuniform locality of energy within space-time field.

The non-uniform conservation of energy leads to the collapse of the concepts on uniformly moving different reference frames in relation of which all physical laws are valid. It is clear that even light cannot be the reference frame, while light energy is non-uniformly conserved.

In this case, the question "in relation to what background state all physical laws are the same" appears to be a big problem for physics. General relativity, describing space-time "as a geometrical structure, curved by existence in it energy and matter," does not produce a reference frame and mechanism of space-time behavior, while mathematical formulation of GR has no background state. The theory of special relativity, describing constant speed of light in vacuum, does not help much; while within non-uniform conservation of energy in space-time, light is not a space-time independent uniformly moving reference frame.

Within principles of non-uniform conservation of energy, the concept of uniform reference frames without uniform energy resources has no meaning at all. The main problem of quantum mechanics and relativity is the reference frame: we cannot determine the position and momentum at the same time because when we determine momentum, position also will change and its change will be uncertain.

Therefore, the problem described by quantum mechanics appears due to the absence of local position and deterministic formulation of local position by dynamical laws of classic physics. The general relativity has the same problem. The importance of local position arises from the non-uniform conservation of energy, localized in space-time field through change of space and time coordinates of a local position.

Here, it is necessary to give analysis of uncertainty principles in more detail, where changes in position and momentum shown as a change of simple gradients. Description of space-time frame and dynamical events only through gradients of energy and space-time variables or tensors leads to the problems, associated with the loss of local positions (boundary) of spacetime field, carrying distribution of energy. The boundary or local position is the energy density of the phase field. The same question related to the change of momentum, which also needs 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 could be completely different.

coupling of these forces in reverse order in cyclic mode re-generates strong force. Later, we will

It is easy to show that the non-uniform conservation of energy has to be the ground concept for unification of relativity and quantum physics. Starting from the basic statement of general physics that energy conserved through its conversion from one form to another, we will arrive to the concept that a dynamical event of energy conversion has to have locality within finite space and time coordinates. In principle, the features of energy conservation during its conversion from one form to another are clear from Planck's black body radiation, which changes the frequency of energy with radiation. Change of frequency of radiation is the result of non-

The non-uniform conservation of energy leads to the collapse of the concepts on uniformly moving different reference frames in relation of which all physical laws are valid. It is clear that even light cannot be the reference frame, while light energy is non-uniformly conserved.

In this case, the question "in relation to what background state all physical laws are the same" appears to be a big problem for physics. General relativity, describing space-time "as a geometrical structure, curved by existence in it energy and matter," does not produce a reference frame and mechanism of space-time behavior, while mathematical formulation of GR has no background state. The theory of special relativity, describing constant speed of light in vacuum, does not help much; while within non-uniform conservation of energy in space-time,

Within principles of non-uniform conservation of energy, the concept of uniform reference frames without uniform energy resources has no meaning at all. The main problem of quantum mechanics and relativity is the reference frame: we cannot determine the position and momentum at the same time because when we determine momentum, position also will

Therefore, the problem described by quantum mechanics appears due to the absence of local position and deterministic formulation of local position by dynamical laws of classic physics. The general relativity has the same problem. The importance of local position arises from the non-uniform conservation of energy, localized in space-time field through change of space and

Here, it is necessary to give analysis of uncertainty principles in more detail, where changes in position and momentum shown as a change of simple gradients. Description of space-time frame and dynamical events only through gradients of energy and space-time variables or tensors leads to the problems, associated with the loss of local positions (boundary) of spacetime field, carrying distribution of energy. The boundary or local position is the energy density of the phase field. The same question related to the change of momentum, which also needs

light is not a space-time independent uniformly moving reference frame.

5. Unification of quantum mechanics and relativity

uniform locality of energy within space-time field.

change and its change will be uncertain.

time coordinates of a local position.

describe these forces in detail.

164 Advanced Technologies of Quantum Key Distribution

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 of conservation laws.

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 naturally to the existence of oppositely charged particles.

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 origin of generation of discrete performance of physical laws.

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 outcome is uncertain.

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."

The general view of quantum mechanics on conservation of energy is that the energy-time uncertainty has a meaning that a state of a body that exists only for a short time cannot have a definite energy because to have a definite energy, the frequency of a state must be accurately defined. It is easy to show that model (5), which conjugates energy flux of exchange interactions and local position of a state, covers the above-mentioned requirements.

of energy is non- invariant translation, therefore cannot give local symmetry of general relativity or even any type of invariant translations. In dynamical events, comprising non-uniform conservation of energy within space-time frame cannot be any static state of rest or uniform motion, accepted as a reference frame. The static energy conservation law does not fit with the conservation of finite amount of energy. Without coupling of local energy state and local space-

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With the increase of energy of a body Es (classic inertial energy/mass content of a body), the space-time unit requires more energy flux to keep the initial action of exchange interactions. This principle appears as a trapping of more energy by the space phase leading to the "acceleration of space expansion;" but in reality, it is the acceleration of energy conservation. Consumption of energy and expansion of space leads to the condition, where any amount of energy trapped in space-time "black hole" structure. When all available portion of energy is consumed, (Eact = 0), the energy trapped in the space-time frame, has to be radiated back to the initial state through translation of asymmetric energy conservation phases. The frame called "black hole" is the boundary of space-time frame, where the entire portion of energy is going to be consumed. At Eap = 0, the local discreteness of electromagnetism is invariant with the global discreteness of gravity which is the integral equivalent of Maxwell's differential invari-

Model (5) shows that for inversion of space-time from one local frame to its previous state more energy portion than locally available is necessary to apply, therefore the temporal Galilean transformation is non-invariant. This prediction of model (6) is the alternative to the statement of special relativity that with the increase of mass of a particle, more energy is necessary to apply to get constant velocity. This effect is the internal "gravitational property" of energy conversion from one form to another within space-time frame, which can be called

Acceleration of non-uniform conservation of energy arises from exchange interaction and conservation itself produces the exchange interaction. With the growth of space-time frame and consumption of energy, more flux of energy required to keep the local state. In reverse order, when space-time collapses, more energy portion than locally available is necessary to apply to stop decay of space-time of matter, moving to the background to start a new cycle of

In relativity theory, the concept of mass is the part of energy-momentum tensor; but in model (5), mass is the part of energy-momentum exchange interactions (Eap/Es 1), coupled with the local position of space-time. The positive value of exchange interaction plays a role of right-

In accordance with the non-uniform conservation of energy, the main problem of conservation laws is the description of energy conservation in Lagrangian or Hamiltonian in the form of sum of energies. Energy exists and conserved as a waves, passing through space and time fields with formation of different energy density within these phases. That is the reason why model (5) describes an event dynamics through exchange interaction of the energy portions, distributed in space and time waves. Eap Es describes the available portion of energy in

"acceleration of non-uniform conservation of energy."

discrete conservation of energy.

handed Lagrangian.

time frame, energy conservation in GR is approximate and leads to the singularity.

ance dF = 0.

In accordance with the non-uniform conservation of energy, the deterministic state of a body requires description of an event in the form of exchange interaction, comprising actionresponse conservation. The parameter (Eap � Es)/E<sup>s</sup> of model (5) describes exchange interaction that conjugates with the local space-time frame for generation of deterministic path of a particle. In quantum field theory, the space-time metric does not vary with the flux of energy. However, our concept presents dynamical space-time metric, which is the dynamical local space-time field.

It is clear that an event can have its own reference frame if its energy-mass conservation is described by the true mathematical space-time formulation. Model (5) involves interaction of an event space-time field with its own reference frame. The condition Es 6¼ 0 describes an acceleration of event dynamics in relation to the initial condition, while the condition Eap = 0 is the uniform translation of an event to the initial state. In this case, the laws of classic and relativistic classic physics unified with the quantum mechanics within singularity free deterministic physical frame of non-uniform conservation of energy. In the absence of the energy flux "moving in space became equivalent to the moving relative to the space," which restores the classic physics concept of relation of a motion to the space "ether."

Thus, the non-uniform conservation of energy comprises the acceleration of space expansion in forward direction and uniform backward process of energy restoration at the initial state.

### 6. Unification of space-time frame with the electromagnetism

While energy is non-uniformly conserved within space-time frame with asymmetric boundaries, unification of electromagnetism with the space-time frame becomes an obvious concept. The multiple S1/t1 (Eap/Es � 1) of model (6) is the combination of electromagnetic field (Eap/Es � 1), which describes flux of the energy to the space-time frame and local position in space-time, where S1/t1 metric is not fixed and changes with the change of the energy flux field. The energy flux (Eap/Es � 1) is not uniform and presents local energy portion, remained from the exchange interactions with the particle. That is why electromagnetism is not Galilean invariant. Due to the coupling of the local energy portion with the local space-time position the multiple S1/t1 (Eap/Es � 1), as a deterministic function, describes trajectory of a particle. In the multiple S1/t1 (Eap/Es � 1), the space-time and energy-mass relation have reciprocal relations: the non-uniformity of energy-mass relation generates asymmetry of space-time variables and in reverse order, asymmetric space-time leads to the non-uniformity of energy-mass relation.

The asymmetric boundaries of space-time variables allow only global conservation laws. On this basis, during discrete non-uniform conservation of energy in space-time frame the change of energy is non- invariant translation, therefore cannot give local symmetry of general relativity or even any type of invariant translations. In dynamical events, comprising non-uniform conservation of energy within space-time frame cannot be any static state of rest or uniform motion, accepted as a reference frame. The static energy conservation law does not fit with the conservation of finite amount of energy. Without coupling of local energy state and local spacetime frame, energy conservation in GR is approximate and leads to the singularity.

The general view of quantum mechanics on conservation of energy is that the energy-time uncertainty has a meaning that a state of a body that exists only for a short time cannot have a definite energy because to have a definite energy, the frequency of a state must be accurately defined. It is easy to show that model (5), which conjugates energy flux of exchange interac-

In accordance with the non-uniform conservation of energy, the deterministic state of a body requires description of an event in the form of exchange interaction, comprising actionresponse conservation. The parameter (Eap � Es)/E<sup>s</sup> of model (5) describes exchange interaction that conjugates with the local space-time frame for generation of deterministic path of a particle. In quantum field theory, the space-time metric does not vary with the flux of energy. However, our concept presents dynamical space-time metric, which is the dynamical local

It is clear that an event can have its own reference frame if its energy-mass conservation is described by the true mathematical space-time formulation. Model (5) involves interaction of an event space-time field with its own reference frame. The condition Es 6¼ 0 describes an acceleration of event dynamics in relation to the initial condition, while the condition Eap = 0 is the uniform translation of an event to the initial state. In this case, the laws of classic and relativistic classic physics unified with the quantum mechanics within singularity free deterministic physical frame of non-uniform conservation of energy. In the absence of the energy flux "moving in space became equivalent to the moving relative to the space," which restores

Thus, the non-uniform conservation of energy comprises the acceleration of space expansion in forward direction and uniform backward process of energy restoration at the initial state.

While energy is non-uniformly conserved within space-time frame with asymmetric boundaries, unification of electromagnetism with the space-time frame becomes an obvious concept. The multiple S1/t1 (Eap/Es � 1) of model (6) is the combination of electromagnetic field (Eap/Es � 1), which describes flux of the energy to the space-time frame and local position in space-time, where S1/t1 metric is not fixed and changes with the change of the energy flux field. The energy flux (Eap/Es � 1) is not uniform and presents local energy portion, remained from the exchange interactions with the particle. That is why electromagnetism is not Galilean invariant. Due to the coupling of the local energy portion with the local space-time position the multiple S1/t1 (Eap/Es � 1), as a deterministic function, describes trajectory of a particle. In the multiple S1/t1 (Eap/Es � 1), the space-time and energy-mass relation have reciprocal relations: the non-uniformity of energy-mass relation generates asymmetry of space-time variables and in reverse order, asymmetric space-time leads to the non-uniformity of energy-mass relation.

The asymmetric boundaries of space-time variables allow only global conservation laws. On this basis, during discrete non-uniform conservation of energy in space-time frame the change

tions and local position of a state, covers the above-mentioned requirements.

the classic physics concept of relation of a motion to the space "ether."

6. Unification of space-time frame with the electromagnetism

space-time field.

166 Advanced Technologies of Quantum Key Distribution

With the increase of energy of a body Es (classic inertial energy/mass content of a body), the space-time unit requires more energy flux to keep the initial action of exchange interactions. This principle appears as a trapping of more energy by the space phase leading to the "acceleration of space expansion;" but in reality, it is the acceleration of energy conservation. Consumption of energy and expansion of space leads to the condition, where any amount of energy trapped in space-time "black hole" structure. When all available portion of energy is consumed, (Eact = 0), the energy trapped in the space-time frame, has to be radiated back to the initial state through translation of asymmetric energy conservation phases. The frame called "black hole" is the boundary of space-time frame, where the entire portion of energy is going to be consumed. At Eap = 0, the local discreteness of electromagnetism is invariant with the global discreteness of gravity which is the integral equivalent of Maxwell's differential invariance dF = 0.

Model (5) shows that for inversion of space-time from one local frame to its previous state more energy portion than locally available is necessary to apply, therefore the temporal Galilean transformation is non-invariant. This prediction of model (6) is the alternative to the statement of special relativity that with the increase of mass of a particle, more energy is necessary to apply to get constant velocity. This effect is the internal "gravitational property" of energy conversion from one form to another within space-time frame, which can be called "acceleration of non-uniform conservation of energy."

Acceleration of non-uniform conservation of energy arises from exchange interaction and conservation itself produces the exchange interaction. With the growth of space-time frame and consumption of energy, more flux of energy required to keep the local state. In reverse order, when space-time collapses, more energy portion than locally available is necessary to apply to stop decay of space-time of matter, moving to the background to start a new cycle of discrete conservation of energy.

In relativity theory, the concept of mass is the part of energy-momentum tensor; but in model (5), mass is the part of energy-momentum exchange interactions (Eap/Es 1), coupled with the local position of space-time. The positive value of exchange interaction plays a role of righthanded Lagrangian.

In accordance with the non-uniform conservation of energy, the main problem of conservation laws is the description of energy conservation in Lagrangian or Hamiltonian in the form of sum of energies. Energy exists and conserved as a waves, passing through space and time fields with formation of different energy density within these phases. That is the reason why model (5) describes an event dynamics through exchange interaction of the energy portions, distributed in space and time waves. Eap Es describes the available portion of energy in 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 negative energy solution.

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

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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,

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

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

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

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.

of continuous unlimited resources of energy to hold the continuous symmetry.

is not conserved because space-time changes."

involving local asymmetric space-time position.

invariant.

frame of matter.

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 minimum space and maximum available portion of energy.

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

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

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

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.
