The Principle of
Energy Conservation and the Light
Emitted
by the Nearby or Distant Galaxies
Pavle I. Premović,
Laboratory for Geochemistry, Cosmochemistry&Astrochemistry,
Abstract. By postulating
that the Principle of energy conservation is not valid for the energy of
photons emitted by the nearby and distant galaxies we find that the speed of
light and the fine structure constant are invariant throughout the age of the
Universe, but the rest of energy of the Universe’s atomic hydrogens follows the
above principle. In contrast to the standard cosmology, we find that time flows at a lower rate
in the current Universe than in the past Universe. However, if the energy of these photons follows the above
principle then the speed of light and the rest energy of the Universe’s atomic
hydrogens decrease throughout the age of the Universe but the fine structure
constant and time flow are invariable.
Keywords: Principle of energy conservation, galaxy,
speed of light, scale factor, time flow, fine structure constant, rest energy.
Introduction. Cosmological redshift
z is characterized by the relative difference between the observed and emitted
wavelengths of light which is sourced by a nearby or a distant galaxy[1]
(hereinafter galaxy). This shift
is a direct consequence of the cosmological expansion. It can be defined as
1 + z = λ/λt
… (1)
where λt is the
wavelength at which the light (in the cosmological past) has been emitted by
the source of the galaxy and λ is the wavelength of this
light measured by an observer after its arrival to the Earth. If z > 0
then the galaxy’s light redshifted; if z < 0 the galaxy
then its light blueshifted. Often, a blueshift is referred to as a
negative redshift.
Results/Discussion/Conclusions. Knowing that the product of the speed
of light c (≈ 3 × 108 m sec-1) and frequency a
photon equals to its wavelength, eqn. (1) can be expressed in the following
form
1+ z = cνt/cν = νt/ν
where νt/ν are the corresponding photon frequencies.
Multiplying/dividing the central part
of this expression with Planck’s constant h (= 6.34 × 10-34 J
sec) and after a bit of algebra and canceling c, we get
1+ z = hνt/hν
where hνt is the
energy Et of a photon (or light) emitted by a galaxy and hν is the
energy E of this photon (or light) measured by Earth’s observer. As λ
> λt or νt > ν then Et > E or the
photon energy is non-conserved. This apparent violation of the Principle of
energy conservation by the cosmological expansion is one of the major sources
of concern in cosmology. This principle, as one of the basic laws of physics,
is not violated by any known process. Several approaches have been offered to
solve this problem but none of them is completely satisfactory.[2]
The
redshift of galaxy’s light z is directly linked to the scale factor
values at the time when this light is emitted, at, and the
time when it is examined, a, by an Earth’s observer or
mathematically
1 + z = a/at.
At
present time the scale factor a is considered to be 1 and we
write
1 + z = 1/at = λ/λt
= νt/ν.
So, the expansion of the
Universe decreases the frequency of the light coming from a galaxy. Since the frequency is inversely proportional to the
period, it increases In other words, by the expansion of the Universe time
dilated. According to the standard cosmology[3], time in the cosmological past is dilated or it is
inversely proportional to the age of the Universe.
The fine-structure constant, α (dimensionless
number, α = 1/137.03599) can be expressed by
α = k/c … (2)
where k
is a constant.[1]
Since the speed of light c has been constant throughout the age of the
Universe so has the fine structure constant α.
Most
astronomers and cosmologists believe the Universe’s formation started with the
Bing Bang about 13.8 Gy ago. Atomic hydrogen comprises about 90 % of the
current Universe by number density or about 75 % of the Universe by mass. It
was created in the early Universe after the Big Bang event. We call it the Universe’s
atomic hydrogen.
The total
energy E of the moving Universe’s atomic hydrogen is E = γm0c2, where m0 is
its rest mass, c is the speed of light, γ = 1√(1 − υ2/c2) and υ is its speed to a laboratory frame. This atom
is the non-relativistic particle with υ/c
<< 1, so we have γ ≈ 1, and the Universe’s atomic hydrogen has the
rest of energy
E0 = m0c2 … (3).
We can
extend this equation to the rest energy of all the Universe’s atomic hydrogens.
So, having in mind the mass conservation law and that the speed of light is
constant we conclude that the rest energy of atomic hydrogen atoms is constant
over cosmological time. This is in agreement with the Principle of energy
conservation.
By adopting in advance, the Principle
of energy conservation, Premović {1} recently proposed that the speed of light ct
emitted (in the cosmological past) by a galaxy with the cosmological redshift z
is lower by the factor (1 + z) than the (current) speed of this light c
(≈ 3 × 108 m sec-1) after its arrival to the Earth. In
the equation form
ct = c/(1 + z) … (4).
For Earth’s observer, the speed of light is
not constant throughout the Universe but increases with cosmic time reaching its
current speed c (≈ 3 × 108 m sec-1). This increase
can be interpreted as a result of the Universe’s expansion as implied by
Premović {1}.
Elementary
physics states that the frequency equals the
speed of light divided by the wavelength or ν = c/λ. If we denote
with ct and λt the speed and
wavelength of light emitted by a galaxy (in its cosmological past) and with
c and λ the speed and wavelength of this light reaching the Earth then
we have
ct/λt
= c/λ(= ν).
Combining this equation with
eqn. (4) we have
λt
= λ(1 + z).
Therefore,
the wavelength of light emitted (in the cosmological past) by a galaxy with the
cosmological redshift z is lower by the same factor (1 + z), as
the speed of this light, after its arrival to the Earth. The Principle of conservation, as one of the basic laws in
the Universe, implies that the wavelength and speed of light emitted from a
galaxy are higher by the same factor (1 + z) when it reaches the
Earth. Having in mind eqn. (1), we have
1 + z = 1/at
= λ/λt = c/ct … (5).
So, the
expansion of the Universe does not affect the frequency and period of the light
coming from the galaxy opposing the above standard cosmology formulation.
Since the
speed of light has not been constant throughout the age of the Universe. At
first sight, one can conclude that the fine structure constant α has not been
constant during this age. However, according to Premović {1}, the fine
structure constant can be now expressed by the following expression
α = cmin/c
where cmin is the
minimum speed of light is a constant characteristic of the Universe.
Taking
into account the mass conservation law and that ct is lower
for (1 + z) or at times than c ([see the expression (5)]
the rest energy of the Universe’s atomic hydrogen E0 is lower
as many times [see eqn. (3)]. However, this is against the Principle of energy
conservation.
Therefore,
not accepting the Principle of conservation of energy, the energy of light
emitted by a galaxy decreases throughout the Universe and the rest energy of the
Universe’s hydrogen is constant according to this principle. By accepting this
principle, the energy of the galaxy’s light is constant but the rest energy of the
Universe’s atomic hydrogen decreases throughout the Universe.
The question now is which of the two
mentioned possibilities related to the Principle of conservation of energy can
be accepted? Apparently, none.
The cosmological
Hubble law is a consequence of an expanding Universe, as predicted by the Big
Bang theory. Hubble measured the actual distance to the nearby galaxies (using the
concepts of standard candles), and their recessional speed (using the redshift
of their light emitted) to create his Hubble diagram and his law. This law
is usually expressed by the following relationship
cz = H0D0
awhere H0
is the Hubble constant and D0 is the distance between the
Earth and the galaxy. Without adopting the Principle of energy conservation z = λ/λt
− 1, but adopting this law we have an additional equation z =
c/(ct – 1). This law is valid for
about z ≤ 0.1. For the present-day Earth z
= 0 and according to this last formula ct = c.
H0
is
not constant and varies over cosmological time. It is more appropriate to call
it the Hubble parameter and mark it as H(t). Now, in general case, we express
the Hubble law with this equation
ctz = HtDt.
Combining
this equation with ct = c/(1 + z) and 1 + z
= 1/at we arrive to
at = HtDt/H0D0.
Finally, to
explain the redshift of the galaxy's light in the infinite, Euclidean and
static Universe, Premović {4} hypothesized that this light has a superluminal
speed when it reaches the Earth. Now we can explain this redshift [z
= λ/λt − 1], see
above] by assuming that light emitted from a galaxy in such a
universe has a subluminal speed ct [= c/(1 + z), see (5)].
References
{1} P. I. Premović, Fine structure constant and the minimum speed of light. The General Science Journal, August 2023.
{2} J. Hands, Cosmosapiens: Human evolution
from the origin of the universe. Overlook Duckworth, Peter Meyer
Publishers, Inc., p. 144 (2016)
{3} G. F. Lewis and B. J Brewer, Detection of the cosmological time dilation
of high-redshift quasars. Nat Astron (2023). https://doi.org/10.1038/s41550-023-02029-2.
{4} [4] P. I. Premović, Distant galaxies in the non-expanding
(Euclidean) Universe: the light speed redshift. The General Science Journal, December 2021.
[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 and galaxies with z > 0.1. Of course, there is no sharp line between nearby and distant galaxies.
[2] As Hands {2} simply pointed out: “The only reasonable conclusion is that we do not know whether or how the Principle of conservation of energy can be applied to the Universe”.
[3] According to this cosmology, time appears to pass slower in the distant Universe compared to the present. This is cosmological time dilation (predicted by the General relativity) and it is very recently confirmed by Lewis and Brewer [3] by the identification of this dilation in a sample of 190 quasars monitored for over two decades. However, the appearance of time dilation in other less distant sources is less conclusive.
[4]
k = e2/4πε0h = 1/137.03599) where e
is the charge of an electron, ε0 is the permittivity of free space
and h is Planck’s constant.
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