On the Absence of Dark Matter in the Milky Way

 

On the Absence of Dark Matter in the Milky Way*

Pavle I. Premović

Laboratory for Geochemistry, Cosmochemistry&Astrochemistry,

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

The Milky Way is one of billions of galaxies in the Universe. Cosmologists estimated that the Milky Way is approximately 13.6 billion years old. It is a large spiral system containing hundreds of billions of stars embedded in a large gas reservoir - mostly hydrogen and helium. Most stars in this galaxy exist either as single stars or as double stars. One of the single stars is the Sun. Besides these two, there are clusters of stars and stellar groups with tens to thousands of stars. Most stars, as our Sun, have at least one planet orbiting them.

 

Current cosmology estimates that 25 % of the Universe is made up of “dark matter” and about 70 % of “dark energy” and the rest about 5% is ordinary matter. These two things do not interact with ordinary matter and light (and other forms of electromagnetic radiation) so it is impossible to detect employing modern instrumentation. Their existence is mainly based on the observable indirect evidence of their strong gravitational effect on the galaxy’s stars. We will here focus our attention on some recent concerns related to the dark matter of the Milky Way. 

The current astronomical data suggest that the stars in the outer part of the Milky Way orbit much faster than the inner ones which is against the third Kepler’s law. This observation is explained by the presence of dark matter associated with this galaxy[1] whose gravitational effect makes the faster-than-expected orbital speeds of outer stars. This matter forms a halo around our galaxy but ordinary matter is mainly situated in its central part where most of stars dwell. It is important to note here that the Earth resides in the halo of the Milky Way. 

Based on the effects of gravity in the Milky Way, scientists believe that there is a high concentration of dark matter near the galaxy's center, around the supermassive black hole that resides there. The current cosmology states that during the history of the Milky Way, this matter has guided and sustained the formation and evolution of our galaxy. It seems that dark matter prevents the disintegration of the Milky Way due to its rotation and thus the disintegration of its star systems with their planets, including the Earth. The gravitational attraction of this matter keeps stars, dust, and gas together in our galaxy. In other words, dark matter maintains the existence of the Milky Way. Simply speaking no dark matter, no Milky Way, no the Solar system and its planets including the Earth and its life. 

Recently, Ou et al {2} published their measurement of the speed of the stars in the Milky Way and suggested the stars closer to the edge of the Milky Way rotate more slowly than expected. They reason that there is less dark matter in the center of our galaxy. Moreover, recent research carried out by Gupta {4} appears to indicate dark matter is absent from the Universe.[2] If this is true the following intriguing question arises: how a massive galaxy such as the Milky Way was formed without dark matter?

Now, the second intriguing question appears: how does this galaxy survive without dark matter for 13.6 Gy? The origin of the Milky Way in the Universe without dark matter and its existence for so many billion years is a cosmological mystery. We leave this mystery in the hands of cosmologists. 

Entropy is a fundamental concept in thermodynamics and statistical mechanics that measures the degree of disorder or randomness in a system. This is a key concept for understanding the behavior of physical systems.

 

In physical science, a system may be an isolated system, a closed system, or an open system. A physically isolated system that does not exchange matter or energy with its surroundings. A closed physical system allows only the energy exchange with its surroundings but not matter. An open physical system can interact with its surroundings by exchanging both matter and energy. The Milky Way is a thermodynamically closed system. The current definition of the Second law (of thermodynamics) states that the entropy of a closed system tends to increase over time. So, the entropy of the Milky Way tends to increase.

The Milky Way can be considered a highly organized complex cosmic structure. In a first approximation, this galaxy can be thermodynamically viewed as a low-entropy physical system. Without dark matter, for this structure to be stable during 13.6 there would have to be a constant external input of energy. The question is, what is the source of this energy? Dark energy? Unlikely. Cosmologists have to deal with this issue too.

Within biblical teaching, one can hypothesize that the Spirit of God maintains, instead of dark matter, the survival of the Milky Way, the Solar system, the Earth, and its life. For this reason, we remind the reader again of the sayings in the Letter Diognetus: "God loved men. For their sake, He made the cosmos and subjected everything on earth to them. To them alone He gave understanding and speech, them alone He allowed to look up to heaven, them alone He formed in His image,..." 

References

{1} P. I. Premović, On the absence of dark matter in the galaxy NGC 1277. GSJ, April 2024.

{2} X. Ou, A.-C. Eilers, L. Necib, A. Frebel, The dark matter profile of the Milky Way inferred from its circular velocity curve. MNRAS, 528, 693-710 (2024).

{3} S. Comerón, I. Trujillo, M. Cappellari, et al., The massive relic galaxy NGC 1277 is dark matter deficient - From dynamical models of integral-field stellar kinematics out to five effective radii. A&A, 20, 1-30 (2023).

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* See also {1}.

[1] The evidence for dark matter in the Milky Way comes from the rotation curve of this galaxy.

[2] Of note, there are few galaxies without dark matter. For instance, new findings by the research team led by Comerón {3} indicate dark matter is absent from the massive lenticular galaxy NGC 1277.

 

The Principle of Energy Conservation and the Light Emitted

by the Nearby or Distant Galaxies

Pavle I. Premović,

Laboratory for Geochemistry, Cosmochemistry&Astrochemistry,

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

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/λ_t    … (1)

where λ_t 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 = cν_t/cν = ν_t/ν

where ν_t/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 = hν_t/hν

where hν_t is the energy E_t 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 > λ_t or ν_t > ν then E_t > 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, a_t, and the time when it is examined, a, by an Earth’s observer or mathematically

1 + z = a/a_t.

At present time the scale factor a is considered to be 1 and we write

1 + z = 1/a_t = λ/λ_t = ν_t/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 c_t 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

c_t = 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 c_t and λ_t 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

c_t/λ_t = c/λ(= ν).

Combining this equation with eqn. (4) we have

λ_t = 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/a_t = λ/λ_t = c/c_t    … (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 = c_min/c

where c_min is the minimum speed of light is a constant characteristic of the Universe. 

Taking into account the mass conservation law and that c_t is lower for (1 + z) or a_t 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/λ_t − 1, but adopting this law we have an additional equation z = c/(c_t – 1). This law is valid for about z ≤ 0.1. For the present-day Earth z = 0 and according to this last formula c_t = 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

c_tz = H_tD_t.

Combining this equation with c_t = c/(1 + z) and 1 + z = 1/a_t we arrive to

a_t = H_tD_t/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/λ_t − 1], see above] by assuming that light emitted from a galaxy in such a universe has a subluminal speed c_t [= 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.

 

 

 

 

How Mathematics and Physics Look at the Sum of 1 plus 1 or Is de Broglie's Theory Applicable to Macroscopic Objects?

 

How Mathematics and Physics Look at the Sum of 1 plus 1

or

Is de Broglie's Theory Applicable to Macroscopic Objects?

Pavle I. Premović

Laboratory for Geochemistry, Cosmochemistry&Astrochemistry,

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

Back in elementary school or often in our parents’ home much earlier, we were taught that 1 plus 1 equals 2. No one doubts that elementary mathematical statement. However, from a physicist's point of view, that claim is doubtful. Indeed, in his opinion, in the macroscopic world, 1 + 1 is not 2. One sand grain cannot be simply added to another because they are different. The same can be said for volcanic ash particles, volcanic bombs, asteroids, comets, planets (and their moons), stars and galaxies (hereinafter macroscopic objects).[1]

Let us consider the microscopic world. The simplest atom is the hydrogen atom H. Two of these atoms are identical.[2] The same can be said for two protons or two neutrons and all other microscopic objects. The simplest molecule is the hydrogen molecule. Two of these molecules are also identical. Thus, in contrast to macroscopic objects, microscopic objects can be added to each other. In other words, the microscopic world and elementary mathematics are even in agreement on the elementary level. In our opinion, the macroscopic and microscopic worlds are so distinct that their reconciliation is pointless.

The foundation for modern quantum physics is de Broglie’s theory. This theory states that all matter has a wave-like nature and can be described through his mathematical equation:

λ = h/mv    … (1)

where h (= 6.63×10⁻³⁴J sec) is Planck’s constant, m and υ is the mass and speed of the object.  According to this equation, the Broglie’s theory is even applicable to the moving microscopic particles as well to the moving macroscopic objects.

Heisenberg's Uncertainty Principle is a fundamental principle of quantum physics. It states that it is impossible to know exactly both the position and the momentum of a particle simultaneously. This principle can be only applied to the microscopic particles and arises from their wave-matter duality. The origin of the uncertainty principle is found in the duality of particles in quantum physics.

Quantum physics states a microscopic particle can be in two places at once. As far as we are aware, this was experimentally demonstrated for the electron but also some complex giant molecules. One can extend this conclusion to the macroscopic objects. Indeed, if a galaxy or a group of galaxies can also occupy two places at once then we have two universes at once.

Quantum entanglement is a quantum physical phenomenon that occurs when the microscopic particles photons, electrons, atoms, or molecules interact quantum-mechanically even when they are separated by large distances in space. Of course, the macroscopic objects as listed above cannot interact quantum-mechanically.

New experiments from two separate teams of researchers {1, 2} reported observing quantum entanglement between two aluminum membranes (“drums”), of about 10 micrometers in size. They managed to simultaneously measure the position and the momentum of the two drums. This is possible since, as we stated above, the Heisenberg uncertainty principle is valid only for microscopic particles but not for macroscopic objects. It appears that the size of these drums is about the upper limit of the microscopic particles and the lower limit of the macroscopic world.

The question now arises as to whether or not there is a sharp boundary between the microscopic and the macroscopic objects? The answer to that question is expected from physicists.

If the three-above quantum "oddities" cannot be applied to macroscopic objects then the question arises: why would de Broglie's theory, as one of the basic theories of quantum physics, be applicable to these objects? We reason that this theory and its equation (1) are not applicable to the macroscopic objects but only to the microscopic particles.

References

{1} S. Kotler, G. A Peterson, E. Shojaee , F. Lecocq, K. Cicak, A. Kwiatkowski , S. Geller, S. Glancy,  E. Knill, R. W. Simmonds, J. Aumentado , J. D. Teufel, Direct observation of deterministic macroscopic entanglement. Science, 372, 622-625 (2021).

{2} Laure Mercier de Lépinay, Caspar F. Ockeloen-Korppi, Matthew J. Woolley, and Mika A. Sillanpää, Quantum mechanics–free subsystem with mechanical oscillators. Science,  372, 625-629 (2021). 

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[1] We excluded living organisms from macroscopic objects because they are fundamentally different from non-living physical systems.

[2] Hydrogen atoms could appear they be similar because our ability to observe them in detail is rather limited. The same can be said for electrons, protons, neutrons and other microscopic particles.