3. Generation of classic space-time field model

The new concept, which we present, involves conjugation of the change of a function (Δf) with the local value which is the relative locality of a particle (fn). In this formulation, the reciprocal discrete transform within change (Δf) and function (fn) can be generalized within boundary of canonical variables. In this case, we have a purpose eliminating problem of classic physics and quantum mechanics, which describes an event as a change of state of something without relation to something itself. The formulation (Δf)/f1 is useful while it allows description of an interaction of a body and force carrying field through exchange interaction.

The formulation (Δf)/f1 has also "quantum mechanics behavior:" the new classic operator in the form of (Δf)/f1 describes change (spinning or vibration) of the function around dynamical initial locality to repeat its origin. Similarly, the operator ΔS/S<sup>1</sup> describes the fluctuation of space around its origin due to the applied force, while operator Δt/t<sup>1</sup> describes the fluctuation of time about instant of action. On this basis, space and time phases, which carry energy, get features of an energetic field.

In the conjugated space-time field, a position of a particle, located within space-time frame is not a point; it exists within very certain discrete non-virtual space-time manifold, commuting dynamic energy, and is distributed within space and time fields.

In accordance with the non-uniform energy conservation concept, the space-time is the resulting non-unitary inner product of energy distribution, which comprises portions of energy consumed in space phase (event mass) and restored in time phase.

$$\frac{\frac{\Delta \mathbf{S}}{\mathbf{S}\_1}}{\frac{\Delta \mathbf{t}}{\mathbf{t}\_1}} = \frac{\mathbf{E}\_{\text{ap}} - \mathbf{E}\_{\text{s}}}{\mathbf{E}\_{\text{s}}} \tag{5}$$

$$\frac{\Delta \mathbf{S}}{\Delta \mathbf{t}} = \frac{\mathbf{S\_1}}{\mathbf{t\_1}} \left( \frac{\mathbf{E\_{ap}}}{\mathbf{E\_s}} - \mathbf{1} \right) \tag{6}$$

$$
\lambda = \frac{\mathbf{E\_{ap}}}{\mathbf{E\_s}} - \mathbf{1} \tag{7}
$$

at λ = 1, Eap = 2Es.

However, Feynman's Lagrangian action is not conserved and even modified Lagrangian for

Another important feature of the model (3) is that from classic physics position it is possible to get limitation of velocity by the speed of light, which cannot follow from Newton's second law and does not need special relativity formulation. When energy of a body is equal to the light energy (Eap/Es = 1), ΔS/Δt parameter in Eq. (3) became zero, and therefore there is no change of velocity in relation to the initial state (background state) and there is no acceleration. Besides that, with the expansion of space (1) and accumulation of energy in space in the form of mass, more energy is required to move a body with the same velocity therefore a body never can reach the speed of light. It is the boundary of maximum velocity. Such an outcome from Eq. (3) on the limitation of maximum velocity to the speed of light is completely different from principles of special relativity. Model (3) describing the velocity in relation to the initial local space-time frame and the relation of the action energy to the initial energy content of a particle in the form of exchange interaction unifies F/m formulation of classic physics and E/m relation of special relativity. Model (3) shows that if a particle will have velocity equals to the speed of light, there

The above-mentioned analysis of model (1) reveals one very important question: a particle to feel the effect of force or effect of any type of field should have minimum non -zero mass,

It is necessary to explain one question, which has no explanation in the special relativity theory. The question is why there should be a maximum velocity, which is limited by the speed of light. In accordance with our concept, maximum velocity of light is necessary to hold conservation of energy, elimination of infinite energy and space-time singularity. In addition, the finite maximum velocity limit needed for translation of space-time variables to each other through ΔS/Δt. Without boundary velocity, there cannot be finite space-time frame and no energy conservation. It is obvious that boundary of light velocity leads to the boundary of

Based on model (1), we may analyze energy-mass equivalence and the concept why energy conversion to mass is needed. This question has a connection to the discussion given above. Our concept shows that there is no static Noether's conservation of energy [26], and only nonuniform conversion of energy from one form to another can hold conservation principle. The non-invariance of energy-mass relation is the only way for conservation of energy during its conversion from one form to another, which is carried within non-uniform space-time frame. This is an alternative approach on the existence of mass and energy-mass equivalence for limitation of velocity to the speed of light. This approach is different from the relativity concept

The new concept, which we present, involves conjugation of the change of a function (Δf) with the local value which is the relative locality of a particle (fn). In this formulation, the reciprocal

space-time frame, which correlates this boundary through translation of variables.

strong interactions needs renormalization [25].

158 Advanced Technologies of Quantum Key Distribution

will be no acceleration and universe will not undergo the change.

otherwise a particle will not have limited velocity.

of increase of relativistic mass with the increase of velocity.

3. Generation of classic space-time field model

where S<sup>1</sup> and t<sup>1</sup> are the space and time variables corresponding to the dynamic local boundary, Eap and Es are the energies of action and under action systems of interaction at conditions corresponding to the local boundaries of S<sup>1</sup> and t1. In accordance with model (5), energy portion inserted to the space-time frame, travels through wave of exchange interaction, which determines the exact pathway of a particle. The right side of the model describes the frequency of energy consumption by the matter particles, while the left side shows the frequency of the change of space and time waves fields. The entities Δt, t<sup>1</sup> and ΔS, S<sup>1</sup> perform as the same identities of energy carrier, existing differently in the opposite phases.

Model (5) treats the matter field through space phase, while antimatter field with the time phase which couples in space-time unit carries the non-uniform conservation of energy. Later, we will show in detail how the boundary mapped space-time frame, involving limitation of maximum velocity to the speed of light is the requirement for conservation of energy. Model (5) presents the boundary of space-time by the local position, dynamically growing in accordance with the available portion of energy. In a simple form, if there is a local position, there should be a boundary of the change of the energy that carries a space-time field.

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

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

http://dx.doi.org/10.5772/intechopen.75988

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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

The right side of model (5) as the energy-momentum content of space-time frame leads to the

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

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

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.

background state, where generation of new space-time frame takes place.

conservation of energy through space-time field.

generation of space mass.

matter.

"warping of space-time structure" as general relativity suggests.

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 a force and repulsive reaction of a matter.

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, and moves it relative to the state of energy restoration.

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 the interactions discretely unified.

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, carrying energy within space-time frame.

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 intervals leads to the uncertainty.

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 of an event.
