2. The concept of mass

Mechanism of symmetry breaking and generation of mass is the main problem of particle physics. Three independent groups, Higgs [5], Englert and Brout [6], and Guralnik et al. [7–10], published mechanisms on how particles get mass. All three, starting from very different viewpoints, proposed essentially the same mechanism based on spontaneous symmetry breaking. It postulates that matter obtains mass by interacting with a field, known as Higgs field.

In accordance with that mechanism, universe is filled with remarkable new Higgs field and Higgs boson of the field gives mass to gauge bosons and to all other particles. The mass of the Higgs particle itself is not explained in the theory, but appears as a free parameter [10]. Higgs mechanism does not describe how Higgs boson itself gets a mass and the origin of mass in all its forms is not clear [10, 11]. A standard model does not involve gravity therefore, the primary role of mass in this model is not known. The reason why spontaneous symmetry breaking causes and leads to generation of mass remains one of the questions of quantum physics [12–18].

It is necessary to note that the concept of mass needs understanding of the true nature of spacetime. The space-time phenomenon was the hot subject of long debates between Newtonian and Leibniz physics [19, 20]. Later, Kant analyzed Newtonian and Leibniz space-time concepts within his metaphysical principles. Kant's metaphysical understanding of space-time was close to the Newtonian absolute space and time representation. In accordance with Kant's metaphysics, "space and time are substances in their own right (as Newtonian absolute space) and they exist independently of all objects and relations" [19].

Leibniz's view on space and time was different [20]. By Leibniz's opinion, the space-time is "inhere" in objects and relations [19], which is close to Einstein's representation of space-time [21, 22].

However, many questions related to Standard Model of particle physics are waiting for answers, such as locality of elementary particles in space-time frame and its connection with

In our previous papers [1–4], we showed that discrete performance of space-time frame is the necessary background for unification of quantum physics with the relativity theory. In the present paper, we will expand our analysis on non-uniform conservation of energy to show that the space-time phenomenon arises from the non-uniform conservation of energy to carry locality of photons within space and time frame. The non-uniform conservation of energy becomes the only reason for generation of mass and gravity within asymmetric boundaries of

In this paper, we will describe that the elementary particles appear as an energy portions, distributed within conjugated asymmetric space-time fields, where energy contents of space and time phases generate different particles, such as bosons and leptons, emerging from the asymmetric background translation of space-time phases and energy content of the space-time frame. On this basis, we will discuss performance of space-time as an energy-mass carrying non-invariant field, generated from background coupling of space and time ingredients of

Mechanism of symmetry breaking and generation of mass is the main problem of particle physics. Three independent groups, Higgs [5], Englert and Brout [6], and Guralnik et al. [7–10], published mechanisms on how particles get mass. All three, starting from very different viewpoints, proposed essentially the same mechanism based on spontaneous symmetry breaking. It postulates that matter obtains mass by interacting with a field, known as Higgs field.

In accordance with that mechanism, universe is filled with remarkable new Higgs field and Higgs boson of the field gives mass to gauge bosons and to all other particles. The mass of the Higgs particle itself is not explained in the theory, but appears as a free parameter [10]. Higgs mechanism does not describe how Higgs boson itself gets a mass and the origin of mass in all its forms is not clear [10, 11]. A standard model does not involve gravity therefore, the primary role of mass in this model is not known. The reason why spontaneous symmetry breaking causes and leads to generation of mass remains one of the questions of quantum physics

It is necessary to note that the concept of mass needs understanding of the true nature of spacetime. The space-time phenomenon was the hot subject of long debates between Newtonian and Leibniz physics [19, 20]. Later, Kant analyzed Newtonian and Leibniz space-time concepts within his metaphysical principles. Kant's metaphysical understanding of space-time was close to the Newtonian absolute space and time representation. In accordance with Kant's metaphysics, "space and time are substances in their own right (as Newtonian absolute space)

and they exist independently of all objects and relations" [19].

the principles of quantum mechanics.

154 Advanced Technologies of Quantum Key Distribution

light photons.

[12–18].

2. The concept of mass

space-time frame to eliminate singularities from physical laws.

In accordance with Einstein's general relativity theory, space and time are relative and consist in the form of space-time unit. The gravitational force between masses leads to the warping of space-time. However, Einstein's space-time is geometric and does not give explanation as to where space-time comes from.

Zeeya, in his paper published in nature [23], very correctly concluded that, "many researchers believe that physics will not be complete until it can explain not just the behavior of space and time, but where these entities come from."

Raamsdonk [23] suggested, "In some sense, quantum entanglement and space-time are the same thing." By Maldacena's opinion "quantum is the most fundamental and space-time emerges from it [23]. However, Barbouir [24] believes that if time is removed from the foundation of physics, we shall not all suddenly feel that the flow of time has ceased".

Therefore, our present knowledge does not give any information about the origin of space-time and what we know is only our representation of space, produced from Euclidean geometry.

Description of locality of a matter and energy within space-time frame is the main problem for unification of physical laws. First, for description of mass it is necessary to understand the main principle of Newton's law: when a system having constant velocity tends to continue its constant velocity in a straight line. Where does a system get this behavior from and what are the energy resources that a system uses for motion in space with the non-vanishing constant velocity in straight line in infinite time? It is clear that conservation of energy at this particular condition of Newton's physics becomes a very abstract concept.

If a system tends to keep its constant velocity in straight line in infinite time during its motion in abstract space, as Newton's first law states, it has to consume constant amount of energy to carry a body within space in time independent infinite uniform motion otherwise it cannot keep constant velocity.

Newton's first law is valid only in inertial frame of reference, but the inertial frame itself needs condition to be in a state of uniform motion. We can expand the above-mentioned discussion on energy resources for uniform motion of time independent inertial frame as well, which also has to follow principles of energy conservation. Here appears one important question, which needs clarification. If different frames of reference have different uniform velocities, there should not be any preference in selection of the particular reference frame. In this case, translation from one reference frame with constant velocity to another one with the other constant velocity will change space-time coordinates and produce acceleration, which will vary with the variation of reference frames. The difference between inertial frames with different uniform velocities appears in the form of different space-time frame and generation of some identity, which we call mass.

From an energy point of view, when different inertial frames have the same velocity, they are not energetically different inertial frames. In accordance with the energy conservation principle, frame of references comprise the set of space-time coordinates and the difference between such a frame of reference has to be related to the energy, distributed in space-time structure of that reference frames. As we have shown [1–4], to be the same reference frame, these frames should have the same energy/momentum relation. It is clear that when energy applied to the systems is completely consumed, all reference frames moved from some state of constant velocity by application of energy, and have to "fall back" to the initial state for restoration of energy. In this case [1–4], there should be a uniform "gravitational free fall" for all of the reference frames to the initial state, which is the only reference frame, produced by the non-uniform conservation of energy. This statement is the modification of Newton's second law, where the uniform acceleration is explained through the cancelation of each other's ingredients in the formula of F/m.

In our earlier papers, we showed [1–4] that conservation of energy does not exist without localization in space-time frame and the localization has to be non-uniform. It is easy to show that the space and time are the resulting non-unitary portions of non-uniform distribution of energy, consumed in space phase (forming mass) and restored in time phase:

$$\frac{\frac{\Delta \mathbf{S}}{\mathbf{S}\_1}}{\frac{\Delta \mathbf{t}}{\mathbf{t}\_1}} = \frac{\mathbf{E}\_{\mathbf{a}\mathbf{p}} - \mathbf{E}\_{\mathbf{s}}}{\mathbf{E}\_{\mathbf{s}}} \tag{1}$$

The left side of Eq. (3) shows addition of change of a position to the initial space-time frame in the form of acceleration. The right side of Eq. (3), in the form of non-unitary energy portion, is the relation of the energy of a force carrier field to the initial energy content of a body of the space-

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

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

Equation (3) at ΔS/Δt = 0, could be considered as the symmetry of an energy carrier field with the energy of a particle or unification of energy-mass relation within space-time frame. In this case, use of equivalence between energy and mass of a particle in simple form is not an approximation. Later, we will show that during exchange interaction, Eap and Es may exchange their behavior, and Es of Eq. (3) describes inertial energy of a particle, which at background state of space-time frame is equivalent to the mass. Using this principle in conver-

> <sup>a</sup> <sup>¼</sup> <sup>F</sup> m

In accordance with Eqs. ((1)–(3)), the portion of energy, consumed for locality of a zero mass virtual particle in space-time frame, can be described as "transformation of energy to mass," which presents the non-uniform conservation of energy within energy-mass relations. The non-consumed portion of energy determines the local strength of the "force carrier particle." This approach explains the nature of mass in more details than that of Newtonian inertia of a body. Here, mass appears as the response of an initial local energy state of a body to the change of its space-time frame, which appears as an exchange interaction with the applied energy. On this basis, mass in the dynamical model (3) changes with the content of the energy portion,

Description of an event as a change of velocity in relation to the local initial space-time frame gives more information on the dynamics of an event and nature of mass than that of description of force as a change of the momentum or double change of space-time with the non-

The effect of a force is the action and the local initial content of the energy of a body (Eq. (1)) describes conservation of action through the action-response exchange relation, while Newton's effect of force does not involve action-response exchange relation that is why Newtonian response appears in the form of independent uniform inertia. That is why action in Newton's formulation is not conserved. Model (1) describes the response of a system in exchange interaction (Eap � Es)/E<sup>s</sup> in the form of Es, which appears as the carrier of dynamic inertia (or gravitational mass) of a body

It is necessary to note that presently there is no complete theory of dynamics, which may describe change phenomenon where action is conserved. The action is the integral of a Lagrangian over time between the initial and final time of the system. For the action integral to be well defined, the trajectory should have its boundary simultaneously in time and space. However, Lagrangian action principle does not cover these requirements, therefore is not a complete theory for analysis of the simultaneous change of variables and cannot be a proper law for conservation of energy. Feynman applied Lagrangian action to quantum mechanics.

(4)

157

sion of entities, we can get the equation of classic physics:

which is consumed in the space-time frame of a particle.

vanishing mass in the abstract space within change of universal time.

to the non-uniform flux of the available portion of energy to the space-time field.

time frame.

where Eap is the applied energy, and Es is the local energy of a body. When carrying of energy, the parameters ΔS/S<sup>1</sup> and Δt/t1 represent the changes of space and time variables in relation to their local values as spinning of the change around their local state, respectively. The detailed features of the model will be explained later. Model (1) can be written as follows:

$$\frac{\frac{\Delta \mathbf{S}}{\mathbf{S}\_1}}{\frac{\Delta \mathbf{t}}{\mathbf{t}\_1}} = \frac{\mathbf{E\_{ap}}}{\mathbf{E\_s}} - \mathbf{1} \tag{2}$$

$$\frac{\frac{\mathbf{S\_1}}{\mathbf{t\_1}} + \frac{\Delta \mathbf{S}}{\Delta \mathbf{t}}}{\frac{\mathbf{S\_1}}{\mathbf{t\_1}}} = \frac{\mathbf{E\_{ap}}}{\mathbf{E\_s}} \tag{3}$$

We will consider that due to the carrying of energy, the space and time phases are energetic fields, having all the behavior that is a characteristic for any energy field. The special feature of the model (3) is that acceleration as a phenomenon appears as the change of space-time in relation to the initial local space-time position. The special feature of this approach is that the effect of the action is determined as the result of exchange interaction (Eqs. (1) and (2)). When Eap-Es 6¼ 0, change of velocity is proportional to the applied energy (Eap) and while at Eap = 0, "inertial" and "local" energy contents of different masses cancel each other.

This concept is completely different from Newton's acceleration, which describes acceleration as the derivative of the velocity or second-order derivative of space-time in abstract space within universal time.

The left side of Eq. (3) shows addition of change of a position to the initial space-time frame in the form of acceleration. The right side of Eq. (3), in the form of non-unitary energy portion, is the relation of the energy of a force carrier field to the initial energy content of a body of the spacetime frame.

principle, frame of references comprise the set of space-time coordinates and the difference between such a frame of reference has to be related to the energy, distributed in space-time structure of that reference frames. As we have shown [1–4], to be the same reference frame, these frames should have the same energy/momentum relation. It is clear that when energy applied to the systems is completely consumed, all reference frames moved from some state of constant velocity by application of energy, and have to "fall back" to the initial state for restoration of energy. In this case [1–4], there should be a uniform "gravitational free fall" for all of the reference frames to the initial state, which is the only reference frame, produced by the non-uniform conservation of energy. This statement is the modification of Newton's second law, where the uniform acceleration is explained through the cancelation of each other's

In our earlier papers, we showed [1–4] that conservation of energy does not exist without localization in space-time frame and the localization has to be non-uniform. It is easy to show that the space and time are the resulting non-unitary portions of non-uniform distribution of

> <sup>¼</sup> Eap � Es Es

where Eap is the applied energy, and Es is the local energy of a body. When carrying of energy, the parameters ΔS/S<sup>1</sup> and Δt/t1 represent the changes of space and time variables in relation to their local values as spinning of the change around their local state, respectively. The detailed

> <sup>¼</sup> Eap Es

We will consider that due to the carrying of energy, the space and time phases are energetic fields, having all the behavior that is a characteristic for any energy field. The special feature of the model (3) is that acceleration as a phenomenon appears as the change of space-time in relation to the initial local space-time position. The special feature of this approach is that the effect of the action is determined as the result of exchange interaction (Eqs. (1) and (2)). When Eap-Es 6¼ 0, change of velocity is proportional to the applied energy (Eap) and while at Eap = 0,

This concept is completely different from Newton's acceleration, which describes acceleration as the derivative of the velocity or second-order derivative of space-time in abstract space

<sup>¼</sup> Eap Es

� 1 (2)

(1)

(3)

energy, consumed in space phase (forming mass) and restored in time phase:

ΔS S1 Δt t1

features of the model will be explained later. Model (1) can be written as follows:

ΔS S1 Δt t1

S1 t1 þ ΔS Δt S1 t1

"inertial" and "local" energy contents of different masses cancel each other.

ingredients in the formula of F/m.

156 Advanced Technologies of Quantum Key Distribution

within universal time.

Equation (3) at ΔS/Δt = 0, could be considered as the symmetry of an energy carrier field with the energy of a particle or unification of energy-mass relation within space-time frame. In this case, use of equivalence between energy and mass of a particle in simple form is not an approximation. Later, we will show that during exchange interaction, Eap and Es may exchange their behavior, and Es of Eq. (3) describes inertial energy of a particle, which at background state of space-time frame is equivalent to the mass. Using this principle in conversion of entities, we can get the equation of classic physics:

$$\mathbf{a} = \frac{\mathbf{F}}{\mathbf{m}}\tag{4}$$

In accordance with Eqs. ((1)–(3)), the portion of energy, consumed for locality of a zero mass virtual particle in space-time frame, can be described as "transformation of energy to mass," which presents the non-uniform conservation of energy within energy-mass relations. The non-consumed portion of energy determines the local strength of the "force carrier particle." This approach explains the nature of mass in more details than that of Newtonian inertia of a body. Here, mass appears as the response of an initial local energy state of a body to the change of its space-time frame, which appears as an exchange interaction with the applied energy. On this basis, mass in the dynamical model (3) changes with the content of the energy portion, which is consumed in the space-time frame of a particle.

Description of an event as a change of velocity in relation to the local initial space-time frame gives more information on the dynamics of an event and nature of mass than that of description of force as a change of the momentum or double change of space-time with the nonvanishing mass in the abstract space within change of universal time.

The effect of a force is the action and the local initial content of the energy of a body (Eq. (1)) describes conservation of action through the action-response exchange relation, while Newton's effect of force does not involve action-response exchange relation that is why Newtonian response appears in the form of independent uniform inertia. That is why action in Newton's formulation is not conserved. Model (1) describes the response of a system in exchange interaction (Eap � Es)/E<sup>s</sup> in the form of Es, which appears as the carrier of dynamic inertia (or gravitational mass) of a body to the non-uniform flux of the available portion of energy to the space-time field.

It is necessary to note that presently there is no complete theory of dynamics, which may describe change phenomenon where action is conserved. The action is the integral of a Lagrangian over time between the initial and final time of the system. For the action integral to be well defined, the trajectory should have its boundary simultaneously in time and space. However, Lagrangian action principle does not cover these requirements, therefore is not a complete theory for analysis of the simultaneous change of variables and cannot be a proper law for conservation of energy. Feynman applied Lagrangian action to quantum mechanics. However, Feynman's Lagrangian action is not conserved and even modified Lagrangian for strong interactions needs renormalization [25].

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

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

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

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

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

> <sup>¼</sup> Eap � Es Es

> > Eap Es � 1

<sup>λ</sup> <sup>¼</sup> Eap Es

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

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

(6)

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

� 1 (7)

(5)

159

ΔS S1 Δt t1

ΔS <sup>Δ</sup><sup>t</sup> <sup>¼</sup> S1 t1

identities of energy carrier, existing differently in the opposite phases.

interaction of a body and force carrying field through exchange interaction.

dynamic energy, and is distributed within space and time fields.

in space phase (event mass) and restored in time phase.

features of an energetic field.

at λ = 1, Eap = 2Es.

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

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, otherwise a particle will not have limited velocity.

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

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 of increase of relativistic mass with the increase of velocity.
