Absolute Position and Energy

In this paper we will develop further the absolute position of a particle defined in Brodet (2017a, b) which involves the particle's decay time or when relevant internal time and the particle's velocity with respect to the expanding universe. We will refine the previous definition to give two separate absolute position definitions, one termed the absolute position at rest and the other termed the absolute position which includes also a contribution of the particle's velocity with respect to the velocity of the expanding universe. Next we will discuss how we may define the particle's absolute energy from the particle's absolute position definition. We will show, how the absolute energy definition may help us to identify a dependence between the particle's decay time, as measured in its rest frame, and its velocity with respect to the expanding universe. Consequently, we will relate the above to the particle's mean lifetime and discuss the affect and relationship of the running coupling constant and the possible mean lifetime dependence on velocity. Finally, experimental ways by which one may investigate and test the above are presented.


Introduction
In this paper we will develop further the absolute position definition given in Brodet (2017a, b) which uses the particle's decay time or when relevant internal time and the particle's velocity with respect to the expanding universe.We will refine the previous definition and get two separate definitions for the particle's absolute position: the first an absolute position that depends only on the particle internal properties and doesn't depend on velocity, and the second an absolute position that additionally includes a contribution from the particle's velocity with respect to the velocity of the expanding universe.Next, we will show how one may obtain the particle's absolute energy from the particle's absolute position definition.We will also show, how the absolute energy expression may help us identify a dependence between the particle's decay time at its rest frame and the particle's velocity with respect to the expanding universe.Consequently, we will relate the above to the particle's mean lifetime and discuss the affect and relationship of the running coupling constant and the possible mean lifetime dependence on velocity.Finally, experimental ways to investigate and test the above are presented.This paper is divided into six sections.Section 2 discusses the absolute position of the particle that doesn't depend on velocity.Section 3 discusses the absolute position of the particle that depends on velocity and the possible consequence of the particle absolute energy.Section 4 discusses the particle's absolute energy at rest and section 5 discusses the experimental implications.Section 6 contains the conclusions.

Absolute Position that does not Depend on Velocity
The absolute position, ( ) , is defined in Brodet (2017a) as: ) ( 1 a ) Where i t is particle's i decay time(or internal time in the case of a stable particle), ' ) ( is the particle's velocity with respect to the expanding universe, )) ( ( is the total particle's velocity, ( ) is the particle's position in some arbitrary frame of reference and as defined in Brodet (2018).
Choosing a frame in which ( ) = 0 gives: factor) we get: Where i c and ( ) may be given by Brodet (2017bBrodet ( , 2018): Or may be given by: It is unclear yet if , ( ) should take the form of equations 3a,3b or 3c,3d.It is possible that one set of equations is suitable for particles and the other to anti-particles.This should be determined experimentally as will be discussed in section 5 and in Brodet (2016Brodet ( , 2017aBrodet ( , 2017bBrodet ( , 2018)).Try if it can be solved assuming that A=B ( )= ( 4 a ) i.e.where √ could be equal to: Finally, based on equations 1a,4a,b, we may define an absolute position for particle i that doesn't depend on its velocity and external position and depends only on its internal properties.Therefore, the above may be termed internal absolute position or rest absolute position, ( )_( ) , given by (choosing ( ) = 0): ) ( 5 a ) Equation 5a will be modified further later on in section 4. Notwithstanding, we may define from the above, an absolute four-vector: ( 5 b ) Which has a constant length of: ≈ , (assuming = ℎ = 1), we may modify Equation 5b to be consistent with special relativity arbitrary position four-vector( by changing to an arbitrary position ( ) and using ( ) that depends on ( ) instead of ( )( ) ) such: Which defines an arbitrary but invariant length of ( ) , , while temporarily removing the mass factor, , and considering its position with respect to a frame in which = 1, we get a consisted expression to special relativity, such: 4 ( )_( ) = ( ) − ( 6 a ) The values of ( ) , may be viewed by a frame of reference traveling in velocity with respect to the frame of ( ) , by using special relativity modified Lorentz transformation based on Brodet (2016): A more complete transformation of a position four-vector as defined above will be discussed later on in the text.

Absolute Position that Depends on Velocity
The total absolute position of the particle should depend on its internal properties but also on the particle's velocity and therefore describes the sum of the space and time contributions.The above is related to the discussion in Brodet (2017) where initially the absolute of the complex number Since, in this case, we are interested in including the contribution of the particle's velocity to its absolute position definition, we adopt the plus sign for the time contribution such: ) ( 8 a ) The geometric meaning of ( ) is shown in Figure 1 with respect to the geometrical meaning of ( )_( ) .
Choosing ( ) = 0 gives: One can see that we actually get the time and position components at the end of the universe frame of reference ( i.e. a frame resting on the edge of the expanding universe), which could be used as an absolute frame of reference.Therefore, we may define: − Which allows us to express ( ) in terms of ( ) , ( ) : ( 1 0 a ) The above experiment may be repeated many times with different particles and different velocities in order to produce a distribution for the photon energy values which may allow a careful investigation of the above.

Lifetime Implications
The suggested dependence of on the particle velocity ( ) should clearly have an effect on the particle mean lifetime measurement.As we know from the Standard Model, the mean lifetime measurement depends on the particle's charge.Thus it should be affected from the running coupling constant effect (Halzen & Martin, 1984).Therefore, combining the above, we may suggest that ′ possible dependence on ( ) may be a part of the description of the running coupling constant effect.This is in fact manifested in the expression for the particle's charge given in Brodet (2017b) and also from equation 18b where there is a dependence of ( )_( ) on .From the experimental point of view, the running coupling effect is known to be related with energy.It is suggested here to investigate this effect more specifically and attempt to measure the running coupling constant as a function of the particles velocity.i.e. to base the measurement of this effect on a direct measurement of the particle's velocity rather than energy, using detectors as Cherenkov detectors (Arnold et al., 1988).This may allow us to test if the expression given here for ( )_( ) describes the running coupling constant effect correctly or not.

Conclusions
The absolute position of a particle was discussed in terms of two separate definitions.The first definition describes the particle's absolute position at rest and the second describes an absolute position containing also a contribution from the particle's velocity with respect to the expanding universe.Furthermore, a definition for the particle's absolute energy was calculated from the particle's absolute position.Moreover, from the calculation of the particle's absolute energy, it was possible to identify a dependence of the particle's decay time in its own rest frame on the particle's velocity with respect to the expanding universe.Consequently, the above was related to the particle mean lifetime and was discussed in the context of the running coupling constant and the possible mean lifetime dependence on the particle's velocity.Finally, experimental ways to investigate and test the above were presented.