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A complex motion and complex momentum due to relativistic phenomenon has been deduced in this paper. This procedure leads to explain the generation of a field which is the result of energy momentum complexity (tensor). In this work, a form of complex momentum of photon has been derived. This momentum reveals the construction of electromagnetic field. These procedures have been applied to explain the electromagnetic field of fundamental charged particle and leads to the assumption of fundamental charge. In this works trial would be made to derive a relation between gravitational field and electromagnetic field.

In the theory of relativity, mass velocity relation gives a large quantity of kinetic energy attributed to the particle of rigid configuration [

For composition of three velocities we may visualize six inertial frames as discussed in [_{5} would be

Inverse of this operation would be

Considering four inertial frames where, velocity and angle in [

(3)

(4)

Above conditions imply that Frames and have both their co-ordinate axes aligned and _{ }is moving at a velocity along axis as observed by. The inertial frame has another co-ordinate reference frame, where _{ }axis of, is rotated by an angle counter clockwise with respect to on plane. Frames and have both their co-ordinate axes aligned and is moving at a velocity along axis as observed by [

In (5) it is clear that and are two linear velocities in different directions and rotational angle between and is. From these implications we get Case-1: When and as in [

Case-2: When but is linear then it may be called rotation-linear (i.e. R-L) interaction and that will be S-L interaction if the particle is present at the origin of.

Case-3: When and both are linear motions then it is called L-L interaction.

Following [

So

where, also, and are normal to each other.

represents velocity along space coordinate and

represents velocity along time coordinate. So,

in (7) is a four velocity and from it we get a four velocity matrix where,

Hence to an observer in resultant velocity in (7) is of complex nature. And the relativistic mass of the particle

and relativistic Lagrangian would be

which leads to the form of relativistic momentum

where, , and

when θ = 90˚, then we get from (7)

where, are mutually normal to each other which leads to the form of momentum

where, and

It is seen that Equations (10) and (12) represents a complex momentum of the particle. For a relativistic particle taking we get from (11)

For R-R interaction, and .

For R-L interaction and (i.e. direction of linear velocity of)

So, following (12) momentum would be

It is understood that due to every relativistic motion kinetic energy respective virtual mass is attributed to the particle and due to every relativistic spin it rotates about the axis with relativistic velocity approaching that of light [

So, we can write a function of field as below

where, is canonically conjugate to

here, and are real fields, and are constants.

Light is electromagnetic wave. It carries electric and magnetic fields which is proved by Faraday effect and Kerr effects. But photon is a particle whose kinetic energy is, having mass. Photon has spin motion about an axis and it may be considered as a small mass concentrated in a ring of radius and rotates at velocity of light and it also has linear motion with velocity along the axis of rotation [10, 11]. It is one kind of S-L interaction which is homogeneous with R-L interaction. So resultant velocity would be as in (13) which gives the complex momentum of photon as shown below

This leads to the electromagnetic wave function as specified in [12,13] respectively

where, Now we can write and

where, and are respectively the momentum density energy density and poynting vector of electromagnetic field of photon, So we can write stress energy tensor of this field as

where is the Maxwell stress tensor [

Again from [6,7,15] a concept is that photon charge is possible with both types, positive and negative, and also upper limit of photon charge is of elementary charge. It is also possible that photon has two types of spins (i.e. clockwise or anti-clockwise). Since directions of field depend on the direction of momentum so, nature of charges (i.e. positive or negative) would be determined by the type of spins. It is understood that reveals the field. Photon carries electric and magnetic fields which are functions of energy (or virtual mass) and momentum as given in Equation (17). From the concept of photon we can write energy-momentum tensor due to S-L interaction of a particle which appears as an electromagnetic field. From this we can assume that tensor due to S-S interaction of the particle generates electromagnetic field and the particle would be a rest charged element to the view of an observer in S. So a particle of rigid configuration may be charged having electromagnetic field if it possesses S-S or S-L interaction with corresponding relativistic speed. It is to be pointed out that electron, proton carry electric charge as well as electromagnetic field with its rigid configuration. Hence we can write, in (16) is an electromagnetic field function and to make a rest charged particle S-S interaction of it is required.

Let gravitational field function in the frame in Section 2 be and which would be as observed by

where

Then using (3) and (4) we get the relation between and as

Inverse of this operation is given as

It is understood that a particle of rigid configuration may be charged having S-S or S-L interaction with relativistic speed as in [2,10]. So we can write performing two superimposed motions (which is associated with) generates electromagnetic field function which would be homogeneous with in (22). So we can consider a relation

This leads to the form

Similarly, using four velocity matrix as in (7A) we can consider the above relation as

where and are two constants which depend on the medium.

A particle can possess two simultaneous superimposed spins (i.e. S-S interaction). To get an electromagnetic field, energy-momentum tensor due to complex motion as well as complex momentum of a relativistic particle as in (7) and (10) are required. But to make an elementary rest charged particle, to the view of an observer, S-S interaction of it is required. In such manners a particle of rigid configuration having gravitational field generates electromagnetic field. Equation (26) reveals the relations between electromagnetic field and gravitational field.

Author thanks the authorities of Satmile High School, Satmile-721452, W. B., India for their continuous encouragements.