Revised Work on Absolute Position and Energy of a Particle and Its Anti-particle

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Introduction
In this paper we will discuss the concept of an absolute position for a particle and its anti-particle. The concept was first introduced in , [Brodet 2018], [Brodet 2019]. In this paper we will update and develop this concept further and will consider it as a parent quantity for all the particle's other quantities. It will be argued that the particle's absolute position summarizes all the external and internal information of the particle in a unique and absolute manner. The experimental indication that the universe expands may be used to fix an absolute reference frame which allows to define the absolute position of a particle in the universe. The absolute position is built on the space-time structure of special relativity but ads the absolute reference frame fix and also includes the particle's mass and information related to the particle's charge and spin. Defining the particle's absolute position may subsequently allow to also define its absolute energy and momentum. Furthermore, we shall show that by adopting a deterministic approach to the decay time of a particle we may get novel absolute expressions for the particle's internal energy and for its mass, charge and magnetic moment. The absolute expressions we get for the energy, momentum, charge, mass and magnetic moment are all related to the running of the coupling constant and to the absolute reference fix. The absolute quantities discussed above are defined for a particle and its anti-particle. In this context, the relationship between a particle and its anti-particle are discussed as well. Relative energy and momentum may be defined using relative velocity while keeping all the internal quantities in their absolute form as will be described in the text. Experimental ways to investigate the suggested additional information related to the fundamental quantities and to the relationship of a particle and its anti-particle are discussed.
Section 4 describes how it may be possible to experimentally test the suggestions made in sections 2 and 3.

Absolute Position
In previous works , [Brodet 2018], [Brodet 2019] we have introduced the possibility of an absolute reference frame that may be related to the universe expansion velocity exp v . Therefore, it was argued that we may define particle's i distance with respect to the above absolute frame in terms of its internal distance and external distance such: Let us first consider the internal contribution (int) i D . As the general expression for distance is described using the formula t V X   , we may use the particle's i internal time and internal velocity, such: The particle's internal time may be its decay time for unstable particles or its internal time for stable particles as was discussed in the context of the hidden variable in time possibility that was first introduced in [Brodet 2010]. The value of ) (Tot i c may be related to two known internal quantities namely charge and spin such: where i c is related to the particle's charge and i v to the particle's spin.
Based on special relativity 4-Vector in space structure, we may define particle's i absolute distance by: The distance in equation 2 is with respect to an absolute reference frame. If we define abs V to be particle's i velocity with respect to the center of the universe, then the distance in equation 2 descries a particle's i absolute distance with respect to the center of the universe. At this stage, in special relativity, equation 2 transforms into an energy-momentum equation by dividing all the terms by the time 2 ) 0 ( i t and multiplying all the terms by However, in this paper, we choose to recognize that the invariant quantity in equation 2 is We also recognize that according to electricity and magnetism the external velocity, abs V of a charge particle is http://apr.ccsenet.org Applied Physics Research Vol. 15, No. 1;2023 131 known to be associated with a magnetic field. Therefore, since the shape of the magnetic field and magnetic force is circular, it would mean that a moving charged particle defines external and therefore also internal angular momentum. Therefore, it is suggested that equation 2 may transform to an angular momentum equation such: where ) (abs i P is defined as the particle's absolute position. This is where i M is the particle's mass and min t is the minimum internal time defined in the particle's exponential distribution as will be explained in section 2.4. The absolute position of a particle is given in the dimensions of angular momentum and it may reflect a point on the circumference of a circle centering the universe.

Absolute Energy and Momentum
One may identify the absolute energy, Which leads to the energy-momentum relationship of: Which is consistent with special relativity energy momentum of: The value of abs V may be given by special relativity velocity law such: Where exp v is the universe expansion velocity at the production position of the particle, prod v is the velocity of the particle relative to its production position, ) (Tot i c is the total internal velocity of the particle with a value around the speed of light c.
Relative energy and momentum may be defined using relative velocity while keeping ) (Tot i c and i M in their absolute form.

The Particle's Internal Energy, (int)
i E The possibility of a hidden variable in time was first introduced in [Brodet 2010]. The idea was that may be a hidden frequency, ) (i f f , within the particle that is related to its decay time or internal time for stable particles.

Subsequently,
) (i f f was also related to the particle's Briet-Wigner distribution (The expression here includes a normalization addition with respect to [Brodet 2016], ). Finally, if ) (i f f indeed describes a hidden frequency within a particle then its period would naturally be ) 0 ( i t . Therefore we may get three expressions for where K is given by: Using equation 5 and 5a we may get an expression for and using equation 3d we may get the expression for the particle's mass

Equation 6a
2.4 The Value of min Therefore, in order to get a more detailed expression for Where E is the electric field, B is the magnetic field and q is the electric charge.
If the electric field has the units of energy then we may identify the units of the charge q as 1/meter.
If we assume the electric charge is indeed related to i c then we may define i q as: The question is now what may be the expression for Note that the expression for the gravitational force is non-relativistic. In the relativistic case the gravitational force expression would indeed change but so would the value of the balancing electric field. Therefore, the value of i c wouldn't change by the relativistic change in the gravitational field. However i c would indeed change by particle's i absolute velocity, abs V as will be discussed later on in this section.
Before we continue let us first recall the suggested relationship between  Now, the electron's magnetic moment may be given by: where i L may be given by: Therefore, the energy that is given to the electron by the external magnetic field may be given by: where B is the external magnetic field.
We may equate equation 11 and 11c for electrons and positrons such: which gives: while this may not be necessarily the case and may depend on the sign of the magnetic moment. We may substitute for i c from equation 10c to give: Therefore, using equation 10d  2 ) ) ) 1 ( ( and 2 , 1 ) 0 ( We can see from equation 10d, 10h that ) (Tot i c depends on ) 0 ( i t . However, if i c is indeed related to the electric charge it should also depend on the particle's velocity. We know this from the running of the coupling constant [Aitchison and A. Hey, 1982], [R.D. Field, 1989]. This dependence may be expressed in the value of the particle's width,  . We know that in the units 1   c h ) ) 1 ( ( Note that in equation 11, 2 ) (Tot i c and therefore also 2 i c is equal for a particle and its anti-particle. This may not be necessarily the case and should be investigated experimentally by analyzing the distribution of a negatively charge particle and its corresponding positive charge distribution.

The Absolute Position, Energy, Momentum and Time of a Particle and Its Anti-particle
In section 2.1, equation 3 we have defined particle's i absolute position such: Therefore, the total derivative of ) (abs i P is given by: and from deriving equation 6 we get: Using the total derivative ) (abs i P  we may construct particle's i+ and its anti-particle i-absolute position such: Equation 14a means that if we know Therefore, since we may know ) 0 ( i t Therefore, for each particle and anti-particle i we may define: where ) (true i t  are the true internal times or measured decay times of particle/anti-particle i and Therefore, substituting

Experimental Investigation
If indeed there is an additional information in the fundamental quantities of a particle, it should be expressed in their measurements. Therefore, we may suggest to test this in an experiment such as LEP[Large Electron Positron] or a LEP like experiment in which we may look at the process f f e e     and measure the basic quantities of the outgoing fermions, mesons or hadrons produced. The suggested expressions for the particle's energy, momentum, charge and mass given in section 2, includes the particle's decay time or internal time.
Therefore, we may measure the fermions, mesons or hadron's energy, momentum, charge and mass and search for a possible correlation with the particle's decay time. Furthermore, in order to test the particle/anti-particle relationship suggested in section 3, we may measure the correlation between

Conclusions
The concept of an absolute position for a particle and its anti-particle was discussed. The concept was updated and developed further since its previous versions given in , [Brodet 2018], [Brodet 2019]. Subsequently novel expressions for energy, momentum, internal energy, mass, charge and magnetic moment were presented. Furthermore, the relationship between a particle and its anti-particle were discussed in the context of all the novel quantities that were developed in the text. Finally, possible experimental ways to test the suggestions presented in the paper were discussed.