Minimum Quantum Energy of the Observable Tired-Light Universe

 

Minimum Quantum Energy of the Observable Tired-Light Universe

 

Pavle I. Premović

Laboratory for Geochemistry, Cosmochemistry7Astrochemistry,

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

The tired-light theory argues that the light of nearby or distant galaxies[1] is redshifted because it loses energy as it passes through intergalactic space. In his recent communication, Premović {3} derived basic equations related to the tired-light hypothesis. According to it, the initial energy of photon E₀ emitted by a nearby or a distant galaxy (hereinafter galaxy) and its energy E after traveling a distance d in the intergalactic space are related by

E = E₀e^-βd

where β is the energy attenuation or the rate of energy attenuation {4}. Premović {5} has also found that the value of β is 0.071 Gly and the above equation can be written as

E = E₀e^-0.071d    ... (1).

Premović [6] estimated that the minimum quantum energy of the observable Universe, ε, is about 1.5 × 10^-51 J. Eqn. (1) allow us to calculate a distance d_ε at which a photon emitted by a galaxy would have a final energy equal to the minimum quantum energy ε (= 1.5 × 10^-51 J) or

ε = E₀e^-0.071dε     ... (2).

Example 1:

A Lyman-alpha (-α) emitter is a type of distant galaxy that emits the Lyman-α line of the hydrogen atom. The relationship between the energy of this line E_α and its wavelength λ_α (= 121.6 nm) can be described by the following equation

E_α = hc/λ_α

where h (= 6.63 10^-34 J sec) is called Planck's constant and c (= 2.99792 × 10⁸ m sec^-1) is the speed of light. Putting the given values for h, c and λ_α we find that E_α = 1.6 × 10^-18 J.

 In the tired-light terminology, E_α represents E₀ and eqn. (1) can be written as

E = E_αe^-0.071d

The Lyman-α photon would reach its minimum quantum energy of the observable Universe ε when E = ε (= 1.5 × 10^-51 J). So, we can write after a bit of algebra

E_α/ε = e^0.071de

where d_ε is the distance from the galaxy emitter at which these energies would be equated. Logarithmizing this expression and after a bit of algebra, we get 

d_ε = ln(E_α/ε)/0.071. 

Introducing into this equation the above values for E_α and ε we have

d_ε = ln(1.07 × 10³³)/0.071 = [ln(1.070) + ln(10³³)]/0.071 = 1100 Gly.

The time of flight of this photon up to this distance away from the galaxy emitter is about 1100 Gy.

Example 2:

GRB 190114C was an extreme gamma-ray burst explosion whose radiation detected is the highest energy ever observed for a GRB: 1TeV or E_GRB is about 1.6 × 10^-7 J. In this case, employing eqn. (2) and similar mathematical procedure as in Example 1, one gets

d_ε = ln(E_GRB/ε)/0.071.

If we plug the above values for ε and E_GRB we find that

d_ε = ln(1.07 × 10⁴⁴)/0.071 = [ln(1.07) + ln(10⁴⁴)]/0.071 = 1465 Gly.

The time of flight of this photon up to this distance away from GRB 190114C is 1465 Gy.

As we have shown in our previous communication [3], for the Hubble law case of a linear relationship between the redshift z and the distance D between the Earth and a nearby galaxy there is the following relationship

β = H₀/c

where H₀ is the Hubble constant [= 72 km sec^-1 (Mpc)^-1] and c (= 299792 km sec^-1) is the speed of light. In Hubble terminology, H₀/c represents the inverse of Hubble’s distance, 1/D_H. Plugging 1/D_H instead of β = 0.071 (Gly)^-1 and D instead of d and into eqn. (1) we have

ε = E₀e^-D/DH.

References

{1}P. I. Premović, Distant galaxies in the non-expanding (Euclidean) Universe: the light speed redshift. The General Science Journal, December 2021.

{2} P. I. Premović, The age of the “megamaser” galaxies in the Big Bang Universe. The General Science Journal, December 2021.

{3} P. I. Premović, The tired-light hypothesis: derivation of basic relations. The General Science Journal, November 2022.

{4} P. A. LaViolete, Is the Universe really expanding? ApJ. 301, 544-553 (1986).

{5} P. I. Premović, Expanding Universe vs. Tired-light Universe: the rate of energy attenuation and the cosmological distance. The General Science Journal, December 2022.

{6} P. I. Premović, Minimum quantum energy of the observable Universe. The General Science Journal, January 2023. 

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[1] We define nearby galaxies as those whose redshift z is from 0.001 to 0.1 (or 0.001 ≤ z ≤ 0.1) and distant galaxies with z > 0.1 {1, 2}. Of course, there is no sharp line between nearby and distant galaxies.