3. Commutation of space-time with the principle of conservation of energy

In our early studies [14–16], we suggested that the change of a function in relation to its local position (Δf/f1) could be a sufficient entity for the identification of change. The non-unitary function Δf/f1 with the fractional feature has a "quantum mechanical behavior": the classic operator in the form of Δf/f1 portion describes the fraction of the change (spinning or vibration) of a function around its dynamical initial locality to repeat its origin. Similarly, the operator ΔS/S<sup>1</sup> describes the fluctuation of space with the applied force in relation to its origin, while the operator Δt/t<sup>1</sup> describes the fluctuation of time about instant of action.

In the conjugated space-time field frame, the position of a particle, localized within the space-time frame in relation to its origin, is not a point; it exists within a very certain discrete non-virtual space-time manifold, commuting dynamic energy, which is distributed within space and time fields. On this basis, the origin of spacetime is the energy, which generates space-time and holds its conservation within space and time phases.

In accordance with the above-described principle of conservation of energy within the space-time frame, the space-time becomes the resulting non-unitary inner product of energy distribution, which comprises the portions of energy consumed in space phase (event mass) and restored in time phase:

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

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

$$
\lambda = \frac{\mathbf{E\_{ap}}}{\mathbf{E\_s}} - \mathbf{1} \tag{3}
$$

at λ = 1, Eap = 2Es.

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. On this basis, the space and time phases, which "absorb" applied force and carry energy, attain features of an energetic field. The minimum portion of quanta generates an elementary space-time frame.

approach is the locality of the quanta, while any particle or antiparticle cannot have

According to Rovelli's opinion [12], there is no difference between a gravitational field and space-time, and the locality of a particle can be defined with respect to the gravitational field. This approach is similar to the Newtonian concept that acceleration has a meaning with respect to the gravitation field. However, any field, particularly a gravitational field, cannot have an independent existence; therefore the relation of locality to the gravitational field leads to the uncertainty in quantum

Smolin [13] developed quantum field theory and suggested that at the Planck scale, space exists in the form of fundamental discrete units instead of general relativity's continuous space-time frame. But quantum field theory, similar to Newtonian physics, do not have space-time structure, which interacts with the event. The origin of discrete space and the condition of its independent existence is also

Therefore, different views on space-time and the absence of the origin of the background of space-time frame in both theories is the main problem for reconciling these theories into the unified theory. One of the main problems of these

Einstein showed that space and time are simply different dimensions of the same space-time continuum. By his opinion, energy and momentum are the same quantities of space-time, which has four dimensions. The relative quantity of energy and

The problem of this approach is that the dynamical nature of the space-time variables connected within the continuum framework, which did not allow distinction of the local properties of time and space identities. General relativity determines the dynamics of matter by the geometry of space-time and does not explain the origin of the mass and energy, which curves the structure of space-time. The problem of Newtonian physics, regarding how the moving body responds to action

Unfortunately, the basic formulation of general relativity does not provide the answers to these questions. That is why the theory of relativity itself became the

It is necessary to note that problems of founding a unified theory are due to the problems of energy conservation, which is not complete in the theory of relativity and quantum physics. The approaches related to the generation of a unified theory do not use the principle of conservation of energy as the basis for the unification of relativity and quantum physics. The theory of relativity has a problem with the conservation of energy, which leads to the problem of singularity at small scales. Quantum mechanics suggests that particles borrow energy for some time and then return them. However, quantum mechanics does not explain the origin of this

It is clear that for the generation of unified theory, we have to find a proper mathematical formulation of the conservation of energy, covering the higher scale space-time of relativity and the small-scale quanta of quantum mechanics. The model connecting relativity and quantum mechanics should involve the dynamic local state of space and time variables which, independent of the energy input, can operate between the small scale of quantum physics and large scale of relativity. The known statements of Noether's theorem on conservation of energy, being philosophical in nature, are not applicable for generation of a mathematical formu-

Lagrange and Hamilton have suggested the conservation of energy in the form of differential equations, which is widely used in classical and quantum mechanics.

theories also is the locality of a particle in the space-time frame.

"observer" between Newton's physics and quantum mechanics.

energy, which is borrowed and conserved in the wave function.

lation of the space-time picture of a particle.

148

momentum depends on the observer.

in relativity theory, also remains an open question.

independent existence.

Advances in Quantum Communication and Information

mechanics.

not clear.

The portion of energy conserved in space phase (Es) generates momentum of a particle with the mass, which curves the space-time frame to bring energy conservation to the initial state. Therefore, the space-time itself generates curvature to hold the conservation of energy within the boundary-mapped space-time frame. As Eq. (2) shows, the increase of Es and the reduction of (Eap Es) function gradually generate a curved space-time which in the form of gravitation returns an event to the initial state.

4. Matter-antimatter asymmetry

DOI: http://dx.doi.org/10.5772/intechopen.88722

protons.

of quarks with 1:2 relations.

the space-time field.

151

The space-time symmetry, which may present matter-antimatter symmetry, is possible only when energy is equally distributed between two phases. In this case, "energy is not consumed and not destroyed." This is the timeless symmetry, which violates the classical principles of energy conservation that "energy is neither gen-

At the small scale, energy distributed in the small portion of the space phase in the form of mass is low, and energy is predominantly distributed in time phase ingredients, performing as antiparticles. This situation takes place in the case of a proton. The total mass of quarks, forming protons, is much smaller than the mass of

We can now explain matter-antimatter asymmetry and the generation of more particles than antiparticles in a pair of collision experiments. To conserve energy, any action should lead to the consumption of energy (Eap < 2Es) in order to eliminate infinite timeless symmetry. The condition Eap = 2Es describes symmetry which is possible when two particles exist in symmetry with one antiparticle. This condition takes place only in proton-neutron pairs, which carry discrete symmetry

In accordance with Eq. (2), due to the consumption of kinetic energy of collisions for the locality of generated particles, the energy carried by the produced particles is less than the energy required to restore particle-antiparticle symmetry. The boundary-mapped space-time frame, involving a limitation on maximum velocity of the speed of light, is a requirement for energy conservation. Equation (2) presents the boundary of space-time by 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, which carried by

The left side of Eq. (2) involves the dynamic conservation of the space-time frame as non-unitary "grains," while the right side shows the non-uniform conservation of the energy-momentum exchange relation, carrying the dynamic flux of the energy portion to the local S1/t<sup>1</sup> metric of space-time frame. The gradient of energy in relation to the initial state (Eap Es)/Es as an equivalent form of spacetime "grain" becomes the "non-unitary quanta" which describes the change of the 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

It is easy to show that the non-uniform conservation of energy has to be the ground concept for the unification of relativity and quantum physics. Starting from the basic statement of general physics that energy is conserved through its conversion from one form to another, we arrive at 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 theory of black body radiation, which changes the frequency of energy with radiation. The change of frequency of radiation is the

The known statement of energy conservation that energy can neither be created

nor destroyed but can only be transformed from one form to another does not involve the space-time frame of this transformation. Noether's theorem, describing energy and momentum conservation, separately also does not describe change of energy in space-time frame because time and space are not separable entities.

strength of force and repulsive reaction (inertia) of matter.

result of non-uniform locality of energy within the space-time field.

erated nor destroyed but rather is transformed from one state to another."

The Hot Disputes Related to the Generation of a Unified Theory Combining the Outcomes…

In accordance with Eq. (2), 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 space and time are the resulting non-unitary portions of a non-uniform distribution of energy, consumed in space phase (forming mass) and restored in time phase:

In accordance with Eq. (2), the energy portion inserted to the space-time frame travels through wave of exchange interaction and determines the exact pathway of a particle. The right side of Eq. (2) describes the frequency of energy consumption in space by the matter particles, while the left side shows the frequency of the change of space and time wave fields. Following Einstein's approach that energy and momentum are the same quantities of space-time, we can show that the right side of Eq. (1) shows the ratio of available energy and momentum, commuted with the left side space-time frame. The entities Δt, t<sup>1</sup> and ΔS, S<sup>1</sup> perform as the same identities of energy carrier, existing in the opposite phases. Equation (1) describes a mathematical formulation of the energy-momentum relation where space and time are the products of energy conservation and energy-momentum ingredients are the conjugated outcomes of space-time. Therefore, energy and momentum are same quantities as Einstein stated; moreover, space and time are the inner products of the energy-momentum conservation.

Now we may give specification of space, which is different from Caroll's [10] statement. We think that the relationship between space-time curvature and energy is the natural consequence of a non-uniform conservation of energy, which generates a space-time frame, carrying non-separable portions of boundarymapped energy.

We can now give specifications of entanglement based upon the conjugation of the space-time frame with the energy resources. The phenomenon called entanglement may appear only within conjugated space and time phases, carrying conservation of energy-momentum pairs though growth of the space-time frame.

Thus, any interaction of two different pieces of space (entanglement) in reality is the entanglement of space and time phases carrying out the conservation of energy through portions of energy, distributed within these phases. The space phase without entanglement with time cannot exist. The identity called space is the materialized portion of energy, while time destroys the material portion of energy, bringing an event to the initial state. When all the available energy is consumed in space (Eap = 0), "space" particles decay to "time" antiparticles.

The entanglement of space and time phases as displayed in the form of gravitation appears with the accumulation of energy in space phase and generation of tendency to return space phase back to the background state.

The right side of Eq. (1) describes particle and antiparticle relations. Equation (2) treats the matter field through space phase, while the antimatter field is treated with the time phase. The coupling of these phases in space-time unit carries the non-uniform conservation of energy. Therefore, mass does not exist out of spacetime and does not appear by sudden spontaneous symmetry breaking; at zero mass of particles, energy is not conserved.

The Hot Disputes Related to the Generation of a Unified Theory Combining the Outcomes… DOI: http://dx.doi.org/10.5772/intechopen.88722

### 4. Matter-antimatter asymmetry

The portion of energy conserved in space phase (Es) generates momentum of a particle with the mass, which curves the space-time frame to bring energy conservation to the initial state. Therefore, the space-time itself generates curvature to hold the conservation of energy within the boundary-mapped space-time frame. As Eq. (2) shows, the increase of Es and the reduction of (Eap Es) function gradually generate a curved space-time which in the form of gravitation returns an event to

Advances in Quantum Communication and Information

In accordance with Eq. (2), 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 space and time are the resulting non-unitary portions of a non-uniform distribution of energy, consumed in space phase (forming mass) and restored in

In accordance with Eq. (2), the energy portion inserted to the space-time frame travels through wave of exchange interaction and determines the exact pathway of a particle. The right side of Eq. (2) describes the frequency of energy consumption in space by the matter particles, while the left side shows the frequency of the change of space and time wave fields. Following Einstein's approach that energy and momentum are the same quantities of space-time, we can show that the right side of Eq. (1) shows the ratio of available energy and momentum, commuted with the left side space-time frame. The entities Δt, t<sup>1</sup> and ΔS, S<sup>1</sup> perform as the same identities of energy carrier, existing in the opposite phases. Equation (1) describes a mathematical formulation of the energy-momentum relation where space and time are the products of energy conservation and energy-momentum ingredients are the conjugated outcomes of space-time. Therefore, energy and momentum are same quantities as Einstein stated; moreover, space and time are the inner products of the

Now we may give specification of space, which is different from Caroll's [10] statement. We think that the relationship between space-time curvature and energy is the natural consequence of a non-uniform conservation of energy, which generates a space-time frame, carrying non-separable portions of boundary-

We can now give specifications of entanglement based upon the conjugation of the space-time frame with the energy resources. The phenomenon called entanglement may appear only within conjugated space and time phases, carrying conservation of energy-momentum pairs though growth of the space-time frame.

Thus, any interaction of two different pieces of space (entanglement) in reality

The entanglement of space and time phases as displayed in the form of gravitation appears with the accumulation of energy in space phase and generation of

The right side of Eq. (1) describes particle and antiparticle relations. Equation (2) treats the matter field through space phase, while the antimatter field is treated with the time phase. The coupling of these phases in space-time unit carries the non-uniform conservation of energy. Therefore, mass does not exist out of spacetime and does not appear by sudden spontaneous symmetry breaking; at zero mass

is the entanglement of space and time phases carrying out the conservation of energy through portions of energy, distributed within these phases. The space phase without entanglement with time cannot exist. The identity called space is the materialized portion of energy, while time destroys the material portion of energy, bringing an event to the initial state. When all the available energy is consumed in

space (Eap = 0), "space" particles decay to "time" antiparticles.

tendency to return space phase back to the background state.

the initial state.

time phase:

energy-momentum conservation.

of particles, energy is not conserved.

150

mapped energy.

The space-time symmetry, which may present matter-antimatter symmetry, is possible only when energy is equally distributed between two phases. In this case, "energy is not consumed and not destroyed." This is the timeless symmetry, which violates the classical principles of energy conservation that "energy is neither generated nor destroyed but rather is transformed from one state to another."

At the small scale, energy distributed in the small portion of the space phase in the form of mass is low, and energy is predominantly distributed in time phase ingredients, performing as antiparticles. This situation takes place in the case of a proton. The total mass of quarks, forming protons, is much smaller than the mass of protons.

We can now explain matter-antimatter asymmetry and the generation of more particles than antiparticles in a pair of collision experiments. To conserve energy, any action should lead to the consumption of energy (Eap < 2Es) in order to eliminate infinite timeless symmetry. The condition Eap = 2Es describes symmetry which is possible when two particles exist in symmetry with one antiparticle. This condition takes place only in proton-neutron pairs, which carry discrete symmetry of quarks with 1:2 relations.

In accordance with Eq. (2), due to the consumption of kinetic energy of collisions for the locality of generated particles, the energy carried by the produced particles is less than the energy required to restore particle-antiparticle symmetry.

The boundary-mapped space-time frame, involving a limitation on maximum velocity of the speed of light, is a requirement for energy conservation. Equation (2) presents the boundary of space-time by 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, which carried by the space-time field.

The left side of Eq. (2) involves the dynamic conservation of the space-time frame as non-unitary "grains," while the right side shows the non-uniform conservation of the energy-momentum exchange relation, carrying the dynamic flux of the energy portion to the local S1/t<sup>1</sup> metric of space-time frame. The gradient of energy in relation to the initial state (Eap Es)/Es as an equivalent form of spacetime "grain" becomes the "non-unitary quanta" which describes the change of the 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 force and repulsive reaction (inertia) of matter.

It is easy to show that the non-uniform conservation of energy has to be the ground concept for the unification of relativity and quantum physics. Starting from the basic statement of general physics that energy is conserved through its conversion from one form to another, we arrive at 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 theory of black body radiation, which changes the frequency of energy with radiation. The change of frequency of radiation is the result of non-uniform locality of energy within the space-time field.

The known statement of energy conservation that energy can neither be created nor destroyed but can only be transformed from one form to another does not involve the space-time frame of this transformation. Noether's theorem, describing energy and momentum conservation, separately also does not describe change of energy in space-time frame because time and space are not separable entities.

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

In accordance with the non-uniform conservation of energy, the spin as the space-time identity is the "face" of a particle. The particle may have identity of baryonic structure if it has the space-time frame in discrete symmetry at Eap = 2Es

The Hot Disputes Related to the Generation of a Unified Theory Combining the Outcomes…

Therefore, within the principles of non-uniform conservation of energy, light is not a uniformly moving reference frame. Light photons cannot exist without spacetime frame and, due to the moving within the non-uniform space and time phases,

The space-time, which has to carry conservation of energy, generates a non-

The condition Eap = 0 of Eq. (2) is the background state of the discrete spacetime field where asymmetric space and time variables, for maintaining conservation cycles, undergo the discrete translation as the portions of energy in the different

In accordance with Eq. (2), the gravitational field is the reverse phase of the electromagnetic field (negative energy solution), which restores energy at the origin. In the gravitational field, there is no space-time frame, while the electromagnetic field generates the space-time field and moves in the form of a wave through this frame. Due to the conservation of electromagnetic waves through the spacetime frame, it propagates through transverse waves, while gravity moves back to

It is necessary to note that it is not possible to get singularity-free quantization of space without a background space-time frame. The time parameter in quantum mechanics is an external entity, and quantum theories do not provide a dynamical space-time frame. The model in the form of Eq. (2) provides an entirely new

Model (2) shows that energy appears as the inner product of the coupling of space and time fields (right-handed translation), and in reverse order, the origin of space-time variables is the decay of energy into virtual space and time entities (left-handed translation), with restoration of energy at the background state. This is the non-uniform, non-static 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 the space-time frame. Due to the action-response interaction (2), we observe an event

Model (2) describes a background-dependent space-time frame where the background state is not a fixed state but the dynamical origin of energy conserva-

The space and time phases of energy conservation at the background Planck scale do not have a space-time frame; rather, they exist in the form of condensate without a shape. This approach is different from Wheeler's opinion that at Planck

According to Rovelli, [11] the state of the system may be certain when it has reference to a second physical system. In accordance with model (2), the second system is the applied force (energy) which generates the exchange interaction.

5. Detailed features of the uncertainty principle of quantum mechanics

Now based on model (2), we can explain details why the combination of momentum-position in quantum physics leads to uncertainty. Model (2) predicts that local position in the form of a point cannot give information about momentum or position, which can be relevant only to the exchange interaction with the applied

virtual local frame and moves it relative to the state of energy restoration.

fields. At this state, all types of the interactions are discretely unified.

with the participation of dynamic three jet particles.

have features of electromagnetic wave.

DOI: http://dx.doi.org/10.5772/intechopen.88722

background state through a longitudinal wave.

scale space and -time have a space-time foam [11].

function for the quantization of time.

only in the past.

tion cycles.

153

Eq. (1) shows that the space-time frame, which emerges from the non-uniform splitting of photons, is the fundamental building block of energy and matter: the space-time frame generates ordinary matter, which in energy-mass exchange interaction carries accelerated conservation of energy.

Within the non-uniform conservation of energy through the space-time frame, the unification of electromagnetism with the space-time frame becomes an obvious concept. The multiple S1/t<sup>1</sup> (Eap/Es � 1) of Eq. (2) is the localization of the electromagnetic field (Eap/Es � 1) within the local space-time S1/t<sup>1</sup> frame. The local space-time S1/t<sup>1</sup> metric undergoes change with the consumption of energy flux. The energy flux (Eap/Es � 1) is not uniform and presents the local energy portion, remaining from the exchange interaction. That is why electromagnetism is not Galilean invariant.

Equation (2), due to the involvement of the local frame of space-time and exchange energy-mass interaction, predicts the precise measurement of velocity and the local position of a particle; the exchange interaction eliminates the reference frame phenomenon, and different observers will have the same measurement if they have the same exchange interaction, coupled with the local position.

Equation (2) explains the uncertainty principle in a way that, in order to probe the small scale of space, we have to apply large amounts of energy. Probing the state of a particle to get information is possible only through an exchange interaction. At the Planck scale, there is no space-time frame, and the exchange interaction (2) is the reason why we cannot obtain any information and probe the state of a particle at Planck's scale. On this basis, by probing vacuum we can get information only on discrete uniform conservation of energy in the form of particles-antiparticles, breaking the symmetry with the formation of the space-time frame.

The condition, when the portion of energy conserved in space phase is equal to the portion of energy in time phase, could be considered as a uniform conservation of energy in the form of "Noether's symmetry." This condition corresponds to the relation:

$$\mathbf{E\_{ap} = 2E\_s \ (2) \ \Delta \mathbf{S} / \mathbf{S\_1} = \Delta t / t\_1 \ (3) \ \Delta \mathbf{S} / \Delta t = \mathbf{S\_1} / t\_1 \tag{4}$$

At the condition (3), the unlimited translation of energy portions between the opposite phases of space-time variables in the form of matter-antimatter fluctuations should lead to the "ultraviolet catastrophe." However, annihilation takes place within an asymmetric space-time frame; therefore, the non-uniform distribution energy moves in the direction of space expansion, which eliminates the ultraviolet catastrophe. On this basis, continuous uniform conservation of energy, matter-antimatter symmetry, and uniform continuous existence of any type of symmetry is impossible.

In symmetry, the space-time manifold of a particle after the change should look the same (4). But at Eap = 2Es (2), the space and time fields are symmetrically interchangeable only in a discrete mode (2) where after the change the space-time frame holds the local state (4) only within the frame of discrete symmetry.

We think that the performance of the three particles of baryonic space-time n-p matter in the form of boson-fermions relations follows this requirement. Therefore, without discrete performance of energy-mass exchange interaction in an elementary space-time unit, baryonic matter cannot exist in a symmetric manner. The strong and weak forces appear as the coupling product of exchange interaction in order to hold the discrete symmetry of the space-time frame of the baryonic matter.

#### The Hot Disputes Related to the Generation of a Unified Theory Combining the Outcomes… DOI: http://dx.doi.org/10.5772/intechopen.88722

In accordance with the non-uniform conservation of energy, the spin as the space-time identity is the "face" of a particle. The particle may have identity of baryonic structure if it has the space-time frame in discrete symmetry at Eap = 2Es with the participation of dynamic three jet particles.

Therefore, within the principles of non-uniform conservation of energy, light is not a uniformly moving reference frame. Light photons cannot exist without spacetime frame and, due to the moving within the non-uniform space and time phases, have features of electromagnetic wave.

The space-time, which has to carry conservation of energy, generates a nonvirtual local frame and moves it relative to the state of energy restoration.

The condition Eap = 0 of Eq. (2) is the background state of the discrete spacetime field where asymmetric space and time variables, for maintaining conservation cycles, undergo the discrete translation as the portions of energy in the different fields. At this state, all types of the interactions are discretely unified.

In accordance with Eq. (2), the gravitational field is the reverse phase of the electromagnetic field (negative energy solution), which restores energy at the origin. In the gravitational field, there is no space-time frame, while the electromagnetic field generates the space-time field and moves in the form of a wave through this frame. Due to the conservation of electromagnetic waves through the spacetime frame, it propagates through transverse waves, while gravity moves back to background state through a longitudinal wave.

It is necessary to note that it is not possible to get singularity-free quantization of space without a background space-time frame. The time parameter in quantum mechanics is an external entity, and quantum theories do not provide a dynamical space-time frame. The model in the form of Eq. (2) provides an entirely new function for the quantization of time.

Model (2) shows that energy appears as the inner product of the coupling of space and time fields (right-handed translation), and in reverse order, the origin of space-time variables is the decay of energy into virtual space and time entities (left-handed translation), with restoration of energy at the background state. This is the non-uniform, non-static 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 the space-time frame. Due to the action-response interaction (2), we observe an event only in the past.

Model (2) describes a background-dependent space-time frame where the background state is not a fixed state but the dynamical origin of energy conservation cycles.

The space and time phases of energy conservation at the background Planck scale do not have a space-time frame; rather, they exist in the form of condensate without a shape. This approach is different from Wheeler's opinion that at Planck scale space and -time have a space-time foam [11].

According to Rovelli, [11] the state of the system may be certain when it has reference to a second physical system. In accordance with model (2), the second system is the applied force (energy) which generates the exchange interaction.
