Оddity of Cosmological Time Dilation

                          

The Оddity of Cosmological Time Dilation

 

Pavle I. Premović

Laboratory for Geochemistry, Cosmochemistry&Astrochemistry, 

University of Niš, pavleipremovic@yahoo.com, Niš, Serbia

A number of my ex-students in Serbia feel that my paper entitled "A Simple Way to Show Space-Time Expansion" published in "The General Science Journal" {1} requires a simpler and more clear thought experimentation. I agreed with their statement and that is the goal of this brief note. 

Let us first clarify some basic issues. With respect to an observer on Earth, a BЕ galaxy[1] is receding from Earth but with respect to a galaxy’s observer, the Earth is receding away from the galaxy at a speed υ. From the reference of the galaxy’s observer, the Earth can expand with υ smaller than the speed of light c (or υ < c), or with υ equal or greater (or υ ≥ c) than this speed.  In reference to this observer, the galaxy’s light at these two last speeds would never reach Earth.

The best estimate of the age of the Earth is 4.55 Gy. Consider a BE galaxy that was born at a distance D_B [in Gly] far away from the just-born Earth (E_B), Fig. 1. This galaxy would be at a distance D from the present-time Earth (E_P) and E_P would be from E_B at a distance: υ × 4.55[Gy] where υ is the recession speed of the Earth (or the galaxy, or the Milky Way). This speed is equal to the recession speed of the galaxy. [2] 

Fig. 1: Position of the galaxy BE respect to the Earth formation about 4.55 Gy. 

A simple analysis shows that the light emitted by G cannot reach the position E_B before or after the Earth is born. In the first case, it would reach the Е_P position before the present time, and in the second case, it would reach this position after the present time, i. e. sometime in the future.

When the light from G reaches the E_B position, the Earth would be closer to the E_P position than this light. As in the previous case, it would not reach this position before or after the present time but at present time. Therefore, the arrival of light at the position Ep would be simultaneous with the arrival at this position by the receding Earth. (It certainly at least sounds оdd).

If this is the case then, mathematically speaking, 

D[in Gly] = D_B + υ × 4.55[in Gy]. 

This distance can be also expressed by

D[in Gly] = c × A_E[in Gy] 

where A_E is the age of Earth from the standpoint of an observer associated with the BE galaxy.  Obviously, A_E > 4.55 Gy. Therefore, we deal with a cosmological time dilation.

Consider now an AE galaxy. ¹ Most of the previous considerations for BE-type galaxies are also applicable to this type of galaxy.

 Let G represent a position in respect to the Earth when an AE galaxy is born and G represents its position after 4.55 Gy, Fig 2. E_B and E_P are defined as above. Now, the light emitted by this galaxy would not reach the before or after the present time but at that time. In other words, it would travel to the Earth as long as it has been since the birth of this galaxy, i.e., A_G. 

 

Fig. 2: Position of the galaxy AE in respect to the Earth formation about 4.55 Gy. 

In expression 

D G = cA_G ... (2). 

So, we again are dealing with a cosmological time dilation but now involving the age of the galaxy, A_G, instead of the age of the Earth A_E. 

Reference 

{1} P. I. Premović, A simple way to show space-time expansion. The General Science Journal, December 2023. 

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[1] Our definition of BE and AE galaxy is given in [1].

[2] The recession speed, according to the standard cosmology, can be lower, higher, or equal to the speed of light c. In all viable cosmological models, this speed exceeds the speed of light for distant galaxies with z > 1.5 [2].