The Photon
Quantum of Energy of the Observable Universe
Pavle I. Premović,
Laboratory for Geochemistry,
Cosmochemistry&Astrochemistry,
University of Niš, pavleipremovic@yahoo.com., Niš, Serbia
According to the Big Bang theory,
cosmological redshift (or more commonly just redshift), denoted here as zG, is the result
of the Universe's expansion during the flight of light from nearby/distant galaxies[1]
to Earth. In contrast, Lerner [1, and references therein]
reported that the ultraviolet surface brightness data of nearby/distant galaxies,
over a very wide redshift range, are in agreement with the hypothesis of the
non-expanding (Euclidean) Universe (NEEU). Moreover, a detailed analysis of the gamma ray-burst sources performed
by Sanejouand {2} suggests that the observable Universe has been Euclidean and
static over the last 12 Gy. To explain the redshift, Premović {3} suggested a
possibility that the speed of light emitted by nearby/distant galaxies in NEEU
is superluminal. However, if a photon loses part of its energy in transit
to Earth, it is possible to explain this redshift only by that.
Redshift for nearby galaxies is defined as
zG = (λG –
λ)/λ … (1)
where λG is the wavelength of
light emitted by nearby galaxies and measured by the Earthlings, and λ is
the wavelength of light generated by the corresponding source
on Earth.
According to elementary physics, λG = c/νG and λ = c/ν where c (≈ 3×108 m sec-1) is the speed of light and νG and ν are corresponding frequencies. Multiplying these
formulas with Planck’s constant h (= 6.63 × 10-34 J sec) and then the products hc/νG
and hc/ν plugging into eqn. (1) we get
∆E = = hν – hνG = (zGhc/λG) = zG(hνG) … (2)
where ∆E is the difference of energy. There are two opposing views about
this difference. According to one view, a photon emitted by nearby or distant galaxies traveling through intergalactic space
loses energy due to the expansion of the Universe or due to other possible causes. In contrast, another view is
that there is no energy loss. In this case, the energy difference arises from
the fact that observers in the
Earth’s and galaxy’s frames of reference measure different energies of a photon
emitted by nearby or distant galaxies. In the following part of this communication, we will only deal with
nearby galaxies.
Hubble’s law states that there is
a linear relationship
between the distance DG of nearby galaxies to Earth and the redshift
of light coming from them. It is usually written
as follows:
awhere H0
is the Hubble constant which ranges from 50 km sec-1 (Mpc)-1
to 100 km sec-1 (Mpc)-1. We are going to use H0
= 72 km sec-1 (Mpc)-1 = 2.3 × 10-18
sec-1. (When considering distant galaxies, the
Hubble linear relationship (3) cannot be used, and we have to consider a
non-linearity option, which is beyond
the scope of this communication).
Combining equations (2) and (3) we arrive at
∆E
= zGhνG
= (DG/λG)hH0 … (4).
Of course, this equation is only valid for
nearby galaxies. To estimate their energy change ∆E using eqn. (4) we have to know their distance to Earth –
DG, provided that λG is known. This distance is unknown for most of the
nearby galaxies except for a few whose distance is directly measured by the
megamaser method. The distance of these “megamaser galaxies” ranges from 62 Mly
to 447 Mly [3, and references therein].[1]
A graph of their distance vs.
redshift shows a linear relationship between them with a slope c/H0 of
about 13.65 Gly {3}.
This slope corresponds to the above value of H0 = 72 km sec-1 (Mpc)-1.
For convenience, we can write eqn. (4) as
∆E/hH0 = (DG/λG).
The wavelength of electromagnetic radiation ranges from about 1.2 × 10-14 nm (the hard-gamma photon
wavelength) to about 1.2 m (the far-infrared photon wavelength). Taking into account this wavelength range, a simple analysis shows that
for nearby galaxies
∆E/hH0 =
(DG/λG) >>
1.
The ratio DG/λG for nearby galaxies must be either
a very large rational number or even (likely?) a natural number NG. So,
we write eqn. (4) as
∆E = NG(hH0) …
(5).
Hence,
ε = hH0
(= 6.63 × 10-34 J sec × 2.3 × 10-18 sec-1)
= 1.5 × 10-51 J is the Hubble photon quantum of energy of the observable
Universe with a frequency νε
= H0 = 2.3 × 10-18 sec-1. Of course, if NG is a natural number, then the
change of the photon energy ∆E is quantized with the Hubble photon quantum
of energy ε = hH0 (= 1.5 ×
10-51 J).[1]
To
the Hubble photon quantum of energy ε corresponds a momentum pε = ε/c = hH0/c (= 1.5 × 10-51
J/3 × 108 m) = 5 × 10-60 N sec and a rest mass mε = ε/c2 (= 1.5 × 10-51
J/9 × 1016 m2 sec-2) = 1.7 × 10-68
kg. These values are given in Table 1.
Eqn.
(5) can also be expressed as follows
∆E = NG(hH0) = NGε (= NGhνε).
Using
the above value for H0
and after a bit of elementary physics, we find
that the wavelength of the Hubble photon quantum
of energy ε is λε = c/H0 = 13.65 Gly which is
the Hubble length and λε/c = 1/H0
= 14.4 Gy which is the Hubble time.
For comparison, we also give the values of
related Planck units: energy = 1.96 × 109
J, frequency = 1.86 × 1043 sec-1, momentum = 6.53 N sec and mass = 2.18 × 10-8 kg.
Table 1. The Hubble photon quantum of energy ε and related physical
quantities calculated using H0 = 72 km
sec-1 (Mpc)-1.
|
Physical
quantity |
Expression |
Value/unit |
|
Quantum of
energy |
ε
= hH0 |
1.5 × 10-51
J |
|
Frequency |
νε = H0 |
2.3× 10-18 sec-1 |
|
Momentum |
pε
= ε/c |
5 × 10-60 N sec1 |
|
Rest mass |
mε
= ε/c2 |
1.7×
10-68 kg |
Previously, Alfonso-Faus [4,
and references therein] had reported in another context that a minimum quantum
energy (self-gravitational energy of the visible Universe) EG ≈ kT ≈ ћH0
where ћ = h/2π (= 1.05 × 10-34 J sec and k (= 1.38 × 10-23
J K-1) is Boltzmann constant. This energy is about 10-52
J with an equivalent mass of about 10-69 kg corresponds to a
temperature of about 10-29 K. Plugging h/2π instead ћ into EG
≈ ћH0 after a calculation we obtain that 2πEG ≈ hH0
≈ 10-51 J and associated mass of about 10-68 kg at 10-29
K. At the average temperature of the Universe today approximately of
2.73 K this minimum quantum energy
would be about 10-23 J.
References
{1} E. J. Lerner, Observations
contradict galaxy size and surface brightness predictions that are based on the
expanding universe hypothesis. Monthly notices the Royal Astron. Soc. (MNRAS) 477, 3185-3196 (2018).
{2} Y. –H Sanejouand, A simple Huble-like in lieu of dark energy.
ArXiv: 1401.2919 [astroph.CO]. 2015.
{3} P. I. Premović, Distant
galaxies in the non-expanding (Euclidean) Universe: the light speed redshift. The General Science Journal, December 2021.
{4} A. Alfonso-Faus, Fundamental principle of information/to-energy conversion. Recent Advances in Information Science, Proc. 7th
European Computing Conference (EEC'13), June 2013.
[1] We define nearby galaxies as those whose redshift zG is from 0.001 to 0.1 (or 0.001 ≤ zG ≤ 0.1) and distant galaxies with
zG > 0.1. Of course, there is no sharp line between nearby and distant galaxies.
[2] The contribution of the peculiar motion to their redshift is negligible {3}.
[3] The graph of this equation is a straight line with a slope c/H0 that passes through the origin and it applies to the “megamaser galaxies” {see below and also {3}.
[4] We will discuss this issue in one of our next communications.
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