QUANTON FIELDS : EVOLUTION AND DEGREES OF FREEDOM Quanton fields : evolution and degrees of freedom.

For long time the nature of spacetime had been the subject of debate ,here another version will be discussed in the form of space and time fields where a new concept of energy constraining can explain the interactions between those fields. This model comes in three parts : energy constraining , where the evolution of the quanton fields and their different transitions are discussed, the second part ,energy fields, their degrees of freedom and the third part : electromagnetic waves as relativistic quantons and the generic form of Maxwell quations in terms of space and time fields . This work links many of the physical phenomena back to the quanton based world .


Introduction
This model deals with an evolutionary process of the quaton fields out of a singularity event.
Given our state of knowledge, it is rather premature to determine whether it was an initial expansion out of a singularity event or it was rather a single quanton in a recursive inflationary -contraction process.
Yet, a process of quanton evolution out of singularity was detailed to allow for a comprehensive review of the behaviour those fields and their interactions.
There are cosmological implications based on this model which were dealt with previously [1], [2] The concept of quantized spacetime is not new [3] [4][5] [6] , however this work provides a novel aspect in the sense that it employs the concept of energy degrees of freedom as a unification origin of all space and time fields.

The physical basis of this model
This model is based on the following two concepts a-The relationship between quanton energy density ϱ and its parameters (defined in terms of parameters: k , ω , or ( quanton radius )) is an energy degree of freedom relationship.
b-The complex nature of the energy expansion in the form of space-varying and time-varying fields.
As energy expands from a singularity state (energy non-varying in space or time ) , It creates fields with symmetric nature of variation in space and in time and as a result of this symmetry, the relationship between those space and time-varying fields is governed by energy degrees of Freedom.

Quantons
1-Quantons are two complex orthogonal fields, each one is composed of space-and time-varying energy fields, as those fields vary at periodic rate , they possess wave like behaviour.
Each quanton is composed of two different type of energy fields (free and constrained) which interact to form a binding relationships.

QUANTON FIELDS : EVOLUTION AND DEGREES OF FREEDOM
Quantons vary in their energy content with time as they expand and split., as a result quanton frequencies are statistically distributed versus the energy density, as this statistical distribution ensures equi-partition of energy throughout space.
Quanton stability is ensured due to the effect of inter and intra-quanton interactions of energy fields.
Though the quantons are stable but due to the imbalance of these interactions the quantons split up, then expand which is at the origin of expanding universe.

2.2.Anti quantons
Anti quanton fields are the anti-symmetric to those of the quanton as the dominant nature of those fields is of constrained type which differs from that of the quanton (free type) Both quantons and anti quantons exist in pairs as they become a quantum entity of the form Q+AQ Fig.1 provides a representation of quanton -antiquanton fields

Energy constraining
Energy constraining describes evolution and interactions of energy fields which is summarized as a-Containment free energy fields E , E (this will be discussed in the section : Maxwell equations role in the evolution of quantons ) Expansion of the free energy by variation in space or time which must be accompanied by constraining and expansion of constrained energy fields must also be accompanied by constraining of those fields.
When energy is released from a field constraining process for free or constrained energy field as in , it is released in the form of singularity state E E E (energy non-varying in space or time) which expands in the form of electromagnetic radiation .
As a result, a cycle of expansion and constraining is not a reversible process due to losses and effect of entropy (irreversible process) (will be further clarified in the section energy constraining and the

Release of radiative energy)
Since the quanton is a quantum entity, its total energy content is governed solely by the Planck -Einstein relationship so, quanton energy is determined by its wave parameters ( k , ω or r ) , while an energy degree of freedom-which is defined in terms of the constant ( c ) , is just a mechanism of division of energy between the various space and time-varying fields.
Fields of the following forms do not exist independently a-E ds E dt ( free or constrained energy field cannot expand in space and in time simultaneously without having a complimentary field of an opposite nature ) Though quanton includes both field of both natures (free and constrained), but there is a dominant type of energy field, this is based on which type of field has the majority of Dof's ( higher field strength).
For the quanton, the free energy field is the dominant while for anti-quanton ,the constrained type of field is the dominant type.
A quanton volume is an equivalent volume since quanton fields are infinite in range and expanding at the rate of (c) and the equivalent volume can be estimated indirectly as E ϱ dV (22-5)

Energy Degrees of freedom
As energy density expands in space or in time, it is said to have an energy degree of freedom where quanton energy density can be defined in terms of the degrees of freedom of its wave parameters (ω, k , or r ) Qanton energy density (ϱ )will be shown to be directly proportional to ω , k or .
While the energy density of the quanton is defined in terms of ω , k or , the energy fields are defined in terms of field strength or in terms of the constant ( c) as follows D = c , Dof : degrees of freedom of free space-varying field.
(transformation from formulation in terms of wave parameters, to degree of Freedom formulation in terms of constant (c )).
Which is the relationship between rate of field variation in space and in time Recalling the Lagrangian (L) of an action as 0 (9-6) Given that momentum P= (10-6) We get or alternatively c (11-6),(12-6) An energy degree of freedom: the rate of change of the total energy of the system with respect to its momentum.
The same result can be obtained directly from the energy momentum relationship E P c m c (13-6) differentiating both sides 2 EdE 2PdP (14-6) ) c , and c (15-6),(16-6) Where for space fabric case ( m zero ) , E= P c which is an alternative definition of the energy degree of freedom.
Both results of (12-6 ) and (16-6) are the same , given that ψ ψ ψ Using the Schrödinger equation for time and space derivatives Based on the above points, the division of energy density between space and time-varying fields can be done where strength of space and time-varying energy fields ( Dof ) is expressed in terms of the constant ( c) that defines the relationship between their rate of variation.
It is worth noting that energy field degrees of freedom (field strength) is not related to the total energy of the quanton , as it is only a mechanism for the division of the quanton energy density between the various space-and time-varying energy fields, and what differs the total energy content of any quanton from another is only the rate of variation of fields with time and space according to The energy degrees of freedom can be classified as follows 1-Active (actual degrees of freedom) that belong to the energy fields (field strength ) .
2-Kinetic degree of freedom which expresses the propagation of energy fields (in the form of electromagnetic waves) in one direction, this kinetic degree of freedom is subtracted from the existing four degrees of energy freedom for space and time-varying fields (discussed in the section: electromagnetic waves as space and time fields), where Dof's = (2)+1 instead of (3)+ (1) 3-Scalarized degrees of freedom: when a degree of freedom of an energy field becomes part of its intensity parameter instead of its strength parameter [9]

7.Superposition principle for energy fields
The linear superposition [7], [8] of energy fields still applies with a resultant Field which equals to the addition of the individual field intensities on condition that a-Those fields must be of the same type (free or constrained) and b-Have the same degree of freedom While for the case of fields of different nature (free / constrained) or fields that do have different energy Dof's , the superposition is then done by adding their field strength ( ie exponential degree of freedom ) and multiplying their intensities.
The exponential form of superposition applies, as energy fields are defined in terms of energy degree of freedom (Dof ), which is expressed as the exponent of c ) The resulting superposition will not be a linear one instead it is an exponential superposition where And for the quanton as a whole For energy fields, instead of the addition of the same type of energy, the exponential addition can be between two different types of energy fields (space and time-varying fields) and of two different natures (free / constrained) to give a complex energy field.
The main reason behind this is that free and constrained fields cannot be considered as an independent energy entity individually, since neither of them does possess four degrees of freedom and hence their individual Dof's must be added exponentially to obtain either a complex field equivalent to the total energy density of the quanton if the addition is for all four energy fields.

8.Definition of directional field directional components
Those are 6 components, 3 are constrained space / time free and 3 are free space / time constrained, It is worth noting that 1-Spatial and time-varying energy fields cannot exist independently of each other, as discussed previously 2-The quanton fields E , E , E , E neither have the dimensions of energy nor the energy density but their product has the dimension of energy divided by three dimensional volume .

9.Dimesional energy symmetry (DES)
Dimensional energy symmetry is the mechanism which ensures the uniformity and homogeneity of Given that Note : The chain rule was applied for differentiation and change of variables for the case of integration.
As energy density expands along one axis it must not only expand along other spatial and temporal axes but be constrained along the spatial and temporal axes as well, this leads to the conclusion that events in one direction are immediately reflected in the other spatial and temporal directions.
The uniformity and the homogeneity of space fabric is ensured through the role time plays as the link between all the three space-varying fields and via the constant (c) .
To satisfy dimensional energy symmetry for quanton , the degrees of freedom must be symmetric with respect space and time-varying energy fields.
Define the Dof , D (in terms of c ) where the degree of freedom parameter In other words,for free and constrained fields the degree of freedom must be expressed in a symmetric way across all spatial and time-varying fields The analytical value of the statistical constant is unknown for now, however an alternative method to assess the energy density and to arrive at the density degree of freedom relationship can be made in terms of mean wave parameters.
Recalling first that the quanton fields are infinite in range, and the definition of the variation parameters of E , E fields which corresponds to an exponentially decaying field away from the quanton , the free and constrained fields can be put as quanton energy density is in the form ϱ : represents the average energy density over time.
To assess the entire energy stored in both fields, the quanton total energy would be equal to the volumetric integration. in other words , Quanton field energy density is linearly proportional to the four degrees of freedom as expressed by either ( ω ,k or ) The same result can be reached alternatively, when calculating the vacuum energy density ϱ at any point in space as the summation of individual energy density contributions of ( N ) quantons.
ϱ ∑ ϱ , which leads to the same integration and the same energy density constant, and in general the vacuum energy density is equivalent to the quanton average energy density ϱ ϱ (13-10) To relate the average energy density ϱ to it maximum value (ϱ ) over time, we use the quanton /anti quanton wave model. which represents the release of energy in a singularity state due to the constraining of part of the free and constrained fields.
This non-varying energy expands and it is released from the quanton in the form of radiative energy , Fig. 4. Shows the expansion of the quanton and the subsequent release of radiative energy . The idea that a free expansion process gives off heat is rather odd, since expansion is closely related to reduction in temperature, in fact any release of thermal energy is more than offset by the effects of inflation, so the net result would be a reduction in temperature (observed as thermal degradation of CMB photons) This free expansion process of the universe, which according to the second law of thermodynamics, is an irreversible process, this irreversibility is due to losses in the form of space fabric giving off heat during expansion.
The origin of this release of thermal energy: is energy constraining.
Based on the previous results, we can conclude that the CMB origin is due to release of thermal energy during free expansion of the space fabric itself.
The extraordinarily high degree of CMB homogeneity with variation of the order of ( 10 ) , reflects the high degree of homogeneity of space fabric itself as it releases radiation during the free expansion process and, in fact energy constraining is behind that release of this radiation energy.

Why do quantons split ?
The question how the quantons split is discussed in the following section , but why this happens resides in the fast that the quanton energy density is four dimensional , as the quanton expands from an equivalent volume ( V ) to (V ) ,the quanton radius r and its volume V should change in the following manner which is expected in case of an expansion in three dimensional energy density.
Quanton energy fields change periodically with time, this variation at the rate of ω rad /sec , and vary in space at the rate of k ) , the total energy of the quanton (as a quantum entity ) is governed by Planck Einstein relationship ( function only in its wave parameters ) , namely E hf the relationship between quantons of different energy content can be put as (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13) which means that the quanton radius and the wave length of its characteristic wave behaviour are inversely proportional to its total energy content.
Recalling here the Dof relationship between quanton energy density and its wave parameters, energy density can be assessed as substituting for , and (

We get (3-13)
Which deviates from what we would expect in a classical volume / density relationship of the form This is due to the fact that energy density is inversely proportional to r and not to r and this relationship can be obtained directly from the equation ( 14-11 ) , namely ϱ π h or ϱ ) As quantons expand into a three dimensional space, they have to release energy, in the form of radiation but energy release from such a process would be excessive.
Instead, the quantons, as they expand do split , to allow for subsequent expansion , put this time with minimal release of thermal energy.

14.Mechanism of quanton splitting and expansion.
This model for quanton splitting serves as preliminary and introductory one where the splitting is symmetric, but since the CMB radiation has a statistically distributed frequencies it is inferred that the quanton frequencies are also statistically distributed and the splitting occurs non symmetrically.
There are two mechanisms that can cause the quantons to expand, namely a-Splitting action of the quantons due dimensional energy asymmetry b-The sole release of energy from the quantons as for the first mechanism.

Stage(1-2) expansion under the effect of self interacting repulsive field
The two types of quanton fields ( free Dominated E and neutral E ) interact , creating a binding relationship but since the energy Dof's (i.e field strength) of both types are not the same, the field of the dominant type of energy( E for quantons and E for anti quantons ) self-interact creating a repulsive interaction that causes the quantons to expand, the self-interacting (unbound) field is ( E E ) for quantons and ( E E for anti quantons [ 9] The unbound field is at the origin of the quanton inflationary energy overcomes this binding and causes the quanton to the expand.
As the quanton expands its wave parameters ( ω , k are altered , while its energy content remains the same since there's no energy release from the quantons at this stage, as a result the quanton has either to a-Release radiative energy to maintain the relationship E = or b-Split thus reducing its overall energy content and allowing further expansion

Stage (2-3) dimensional energy asymmetry occurs and quanton splits
Since the quanton parameters ( ω , k do not reflect its energy content , ( must be equal to while E still equals E ) , this conflict causes quanton to split as a mechanism to restore the relationship ( r r , E , the splitting corresponds to a quanton radius x , x = 2

Stage(3) quanton expands further
Following quanton splitting its total energy becomes E , while wave parameters (ω, k must altered to satisfy the relationship As the quantons expand , they release radiative energy in the form of CMB photons, and to arrive at the final stable state.  The second method is the pure release of thermal energy followed up by a subsequent quanton expansion which is such an inefficient mechanism in comparison to the fore described method of quanton splitting and subsequent expansion.
Given the high efficiency of the splitting process as a mechanism to manage the expansion of the quanton through both inflation and multiplication while on the other hand minimizing the thermal energy release, it is clear that quanton splitting and subsequent expansion is the actual mechanism of space fabric expansion.
The release of the radiative energy during the process of expansion of the quanton is not related to the re-establishment of the wave parameter relationship with the quanton energy.

15.Mathematics behind constraining
As the quanton forms, the nature of the energy field changes (from free to constrained) , to perform such an operation energy fields must transit through a singularity state (energy that does not vary in space or in time ) and as energy field strength is in terms of Dof's , its operator( integration / differentiation) has to be applied at an exponential level, thus the exponent of field variation parameter which is operated upon.
a For evolution of constrained space-varying field

15.1-Expansion term
As mentioned earlier the expansion of constrained fields is handled by integration process

15.2-Constraining term
To summarize, the exponential differentiation / integration would be applied in either of the following cases 1-Change of the nature of the energy field (free / constrained) or (space-varying to time-varying) and vice versa.
2-Change in the degrees of freedom of any energy field ( Dof rearrangement of Dof's between fields)

Wave-like properties of space fabric
Energy which varies in time and varies in space has wave like properties as it changes at periodic rate that equals ω rad sec 2 π f and the space-varying field , where r ) , such that ω r constant πc , in fact the quanton ( or anti quanton ) is represented by two (wave like) equations.

17.Quanton evolution and degrees of freedom
Evolution of the quanton takes place as both free fields ( E and ( E coexist As free energy field expands by variation in space part of this field becomes a constrained spacevarying field . While as the time-varying field E ) expands, a part of it becomes constrained time-varying energy field.
As no field possesses all four Dof's , none of them can exist independently.

Now quanton energy density equation becomes
Which expresses two apparently separate (but otherwise linked) Fields.
For space constrained energy field E ),its energy Dof equals one third of the corresponding free energy field E For constrained time-varying energy field E ) , its energy degree of freedom equals one third of the corresponding free time varying field E .
The previous discussion can be summarized in the following 4 equations by solving them the quanton Dof's for the four energy fields can be obtained

18.Variation of quanton energy fields with time
Not only the unbound energy fields E E of the quanton (or E E for anti quanton ) which change with time as the quanton ( or anti quanton ) expands , but rather all the other energy fields , and this is so , to ensure the uniformity of energy density. 2-Relative rate of variation in time of all energy fields is equal to the ratio between their degrees of freedom and this is due to the uniformity of their variation parameters. ϱ k c K c (7,(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19) The quantity K k can be put as K h k K K K K ( K =energy field intensity parameter ) (9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19) Where

Energy field parameters
It must be noted that while h constant The division of the field intensity parameter does not follow the energy degree of freedom but follows the division of field types ( free / constrained and space or time-varying fields ) otherwise energy fields E , E or E , E could exist independently.
One can be drawn to think that the division of K ) between various energy fields such that K K K . , or K K K . , but since there are no wave parameters in nature of k .
or ω . due to the symmetry of the wave behavior between various fields which is previously defined as constant and This leads to the following result : Finally, we can write the energy fields themselves as A unified value of ( K for all energy fields ensures that the relationship between the different fields depends only on their degrees of freedom and not on the intensity of such fields. In general a field energy can be seen as the product of two terms: field energy = field intensity ( defined in terms of : K ) * field strength ( D ∶ defined in terms of energy degrees of freedom )

20.Dimensions of vector energy fields
While being a scalar quantity, energy as it expands in the form of space-and time-varying fields which are vector quantities.
Individual energy content of various fields in the form E E dV does not exist . and this is due to the fact that quanton energy fields are inextricably linked to the quanton volume in a dependence relationship, this does not make it possible to determine the total energy of each individual field .
The energy fields must be defined in terms of the quanton dimensions, in addition to energy dimensions and degrees of freedom for each energy field.
The quanton radius ( r and , its equivalent volume(V are not constant but rather inversely proportional to its total energy content.

Anti quanton evolution and its degrees of freedom
The reason behind the evolution of the anti quanton from quanton fields lies in the fact that quanton self-interactions (binding/repulsive) could not generate potential energy (binding or inflationary potential) on its own as those interactions possess only two degrees of freedom while it is required to have four degrees of freedom for an interaction to create a real potential energy [9] The existence of anti quanton as a stable part of space fabric may seem to be problematic, however other evidence still weighs in its favour, namely 1-Its role in the electromagnetic wave generation and formation of the negatively charged particles (electrons , down quarks ) .

2-Anti quanton is stable under expansion conditions (no degeneration)
3-The interactions generated by anti quanton energy fields are symmetric to those of the quanton ,hence it cannot affect the space fabric homogeneity and integrity

24.Electromagnetic waves as relativistic quantons
The main difference between quanton -anti quanton pair (Q+AQ) and quantons of electromagnetic waves lie in the fact that electromagnetic waves propagate in linear directions, and consequently one degree of freedom is subtracted from space (free and constrained) fields, as it becomes a kinetic degree of freedom, this relativistic effect is split equally between free and constrained fields (E , E ) in other words each of the free and the constrained space fields have one half of Dof's less than the corresponding quaton fields of space fabric,

25.Representation of EM field as space and time fields
Here , an integrated approach is provided for the treatment of electromagnetic field as as a quantized phenomenon which was attempted previously [10], [11] The formulation of electromagnetic waves in terms of energy fields depends on the system of units, under the (Esu) system volumetric electromagnetic energy density (4-25),  where E x is the electric field due to the free dominated field E of the quanton while E x is the electric field due to the constrained field E of the anti quanton.
B x is the magnetic field due to the free dominated field E of the anti quanton , B x is the magnetic field due to the constrained field E of the quanton

31.Conclusions
The inflation of the universe involves expansion of energy density whose constituent free and constrained fields are inextricably linked, neither free nor constrained fields are capable of expansion individually and precisely this inseparable linkage is at the origin of the constraining term as a byproduct of energy density expansion of space fabric.
As free and constrained fields expand part of those fields is transformed as non-dimensional energy packet that expands in the form of relativistic quanton or a CMB photon As a further evidence to support this conclusion we must draw parallels between the uniformity and the homogeneity of CMB radiation and that of space fabric itself as had been proposed by the general principle of cosmology.
The inflationary process of the universe, is considered as a free expansion process and the second law of thermodynamics states that there must be losses accompanying this process which brings further confirmation the conclusion that the about the thermodynamic origin CMB radiation as a direct result of the space fabric expansion, this gives a gate way for further understanding of the quanton interactions.