Distant Galaxies in the Non-Expanding (Euclidean) Universe: the Light Speed Redshift

 

   

Distant Galaxies in the Non-Expanding (Euclidean) Universe:

The Light Speed Redshift

Pavle I. Premović

Laboratory for Geochemistry, Cosmochemistry&Astrochemistry,

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

Abstract. The superluminal speed of light coming from distant galaxies in the non-expanding (Euclidean) Universe may explain the redshift of that light.

Keywords: Universe, cosmology, Big Bang, galaxy, redshift, speed of light.

 

Introduction

 

Redshift and blueshift in cosmology are characterized by the relative difference between the observed and emitted wavelengths (or frequencies) of light (or in general electromagnetic radiation) sourced by an astronomical object such as a galaxy. The (wavelength-based) redshift is expressed z = (λ_G – λ_E)/λ_E where λ_G is the wavelength of light emitted by the source of the galaxy and λ_E is the wavelength of light generated by the same source on 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.

Blueshift is rarely important, in contrast to the redshift which is of great use. The majority of distant galaxies (outside the Local Group: the total size is about 10 Mly across) show a redshift in their spectra and we will mainly deal with them. According to cosmology, they are expanding in all directions away from the Earth and each other.

There are at least three types of redshift that occur in the Universe: gravitational redshift, redshift due to motion (Doppler effect) and cosmological redshift. Gravitational redshift is rarely important, the other two are far more important in cosmology, especially cosmological redshift.

In general, the Hubble Law shows that a redshift of a galaxy is correlated with its distance from the Earth. This law is only applicable to distant galaxies (or say for relatively long-distance galaxies); for nearby galaxies (in the Local Group), it does not hold. Most cosmologists believe that Hubble’s law indicates a constant cosmic expansion of the Universe.

The simplest expression for the Hubble law valid for a redshift z  ≤ 0.1 is

D_G = zc/H₀    … (1)

where D_G is the distance of a distant galaxy to the Earth, c (~ 3×10⁵ km sec^-1) is the current speed of light and H₀ is a constant known as the Hubble constant; at present time itis estimated that H₀ =  72 km sec^-1 (Mpc)^-[1] or = 22 km sec^-1× (Mly)^-1 [= 2.2(1) × 10^-18 sec^-1].¹ This expression shows that there is a linear relationship between redshift z and the distance of galaxies D_G if the redshift z ≤ 0.1. This linearity however breaks down at large distances. Applying eqn. (1) we find that the Hubble distance, c/H₀ = 13.6 Gly for H₀ = 2.21 ×10^-18 sec^-1. The Hubble distance provides the natural distance scale for the expanding Universe. Further details about Hubble’s law the reader may find in many standard astronomical textbooks and related publications.

The Big Bang Universe vs. the non-expanding (static[1]) Universe. The (standard) Big Bang model of the Universe is based on the General theory of relativity.  It states that the Universe started as a point singularity of infinite density and temperature that included all matter and energy of the current Universe. It then expanded rapidly over the next about 13.8 Gy to the current version. This is the expansion of space itself (or better space-time itself) that is still occurring. It appears that the Big Bang hypothesis is supported by numerous evidence, including cosmological redshift.[2] However, they

can, also, be interpreted without this model.

An alternative to the Big Bang model is the (standard) non-expanding model of the Universe. This Universe is unlimited in both space and time with no singular beginning or ending like in the Big Bang model. Many of their galaxies can be much older than about 13.8 Gy allowed by the Big Bang hypothesis. Lerner [2, and references therein] reported that the ultraviolet surface brightness data of galaxies, over a very wide redshift range, are in agreement with the hypotheses of the non-expanding (Euclidean) model of the Universe. A detailed analysis of the gamma-ray burst (GRB) sources performed by Sanejouand {3} suggests that the observable Universe has been Euclidean and static over the last 12 Gy.

The non-expanding models of the Universe have serious difficulties in explaining many observations (for instance cosmological redshift). It appears now that the Big Bang theory is dominant in cosmology but it is still subjected to various criticisms and discussions, although most of them are theoretical.

In the further text, we adopt the non-expanding (Euclidean) Universe (hereinafter NEEU) although some derivations and considerations may be applied to other models of the non-expanding Universe.

 

Varying speed of light. In the cosmological literature, the issue of the speed of light in the early Universe is more recent. Troitskii {4} suggested that the speed of light continuously decreased over the lifetime of the Universe. He argued that at the origin of the Universe, light might have traveled at 10¹⁰ times its current speed c. Albrecht and Magueijo {5} suggested that at a very limited time during the formation of the Universe, the speed of light was much higher (about 10⁶⁰ times) than its current speed c. Earlier, a similar idea was proposed by Moffat {6}. In contrast, Barrow {7} proposed that the speed of light has decreased from the value suggested by Albrecht and Magueijo down to its current value over the lifetime of the Universe. Sanejouand {8} hypothesized that the speed of light decreased by about 2 × 10^-5 km sec^-1 y^-1 during the cosmological history of the Universe. All of these authors have shown that several intriguing cosmological issues associated with the Big Bang model could be unraveled by such a high initial speed of light. However, there are many problems in their theoretical approaches. This is not the place to deal with these issues. Instead, we recommend the reviews by Magueijo {9} and Farrell and Dunning-Davies {10} to the interested reader. It is important here to note that Alfonso-Faus {11} proposed a non-expanding explanation for cosmological redshift. He argues that this shift is due to a decreasing speed of light in the fractal universe.

We hypothesize that the redshift of distant galaxies of NEEU is caused by the superluminal speed of their light, i. e. the speed of light coming from distant galaxies is greater than the current speed of light c.

Derivation, Results and Discussion

As we pointed out above, it appears that the cosmological redshift of distant galaxies arises from the uniform expansion of space (or better space-time itself), not from their motion. In this case, the energy E_G (= hν_G) of photons coming from distant galaxies is lower than the energy of photons E_E (= hν_E) generated by the same source on the Earth; h (= 6.63 × 10^-34 J sec) is the Planck constant and ν_E and ν_G are the appropriate frequencies. Of course, ν_E > ν_G. The difference between these two energies is ΔE_EG = E_E – E_G[1]. Let us denote with λ_G the wavelength of light emitted (and measured by an Earth’s observer) by distant galaxy G and with λ_E the wavelength of light generated by the same source on the Earth. Since ν_E = c/λ_E and ν_G = c/λ_G we have λ_E < λ_G.

The galaxies interact with each other via gravity, which gives them a component of velocity that is not due to the expansion of the Universe, but related to their real (“peculiar”) motion and it is called “peculiar” velocity. In reality, we deal only with the radial component of each galaxy’s peculiar velocity: v_pec. The expansion largely predominates, since the average v_pec of galaxies v_pec is usually between about 100-300 km sec^-1 [12, and references therein] then it is very likely that v_pec ≤ 0.001c (≤ 300 km sec^-1).

 

Assume now that all distant galaxies of NEEU are moving relative to the Earth at a non-relativistic speed v_pec ≤ 0.001c. These galaxies continuously emit a stream of monoenergetic photons in all directions. These photons were emitted in the cosmic past, usually millions and billions of years ago. In other words, we could conceive them as the “ancient photons” or “the photon fossils” from the cosmic past. For the sake of simplicity, let us ignore for a moment the effect of the velocity v_pec on the redshift of a distant galaxy. As above, we denote the energy of these photons with E_G and with E_E the energy of the photons generated by the same kind of source on the Earth; ν_G and ν_E are the corresponding photon frequencies. Distant galaxies are in the same frame of reference as the Earth since v_pec ≤ 0.001c. Now we can apply the Principle of Conservation of energy. In this case, we have E_E = hν_E = E_G = hν_G, and, accordingly, ν_G = ν_E =ν[5]. Since we are dealing with the redshift λ_G > λ_E. We know that the wavelength of a photon is given by the ratio of its speed and frequency. It follows that the speed of light emitted by distant galaxies c_G > c.[6]

However, the total redshift of galaxy z = z_G + z_pec where z_G is the redshift due to the speed of the galaxy’s light c_G and z_pec is the redshift due to the velocity v_pec. Of course, depending on the direction of the peculiar motion z_pec can be positive, equal to zero, and negative. In the case of the galaxy’s superluminal light, the “peculiar” redshift can be approximated with z_pec ~ v_pec/c_G < 0.001 (or 1000v_pec < c_G), then if z ≥ 10z_pec we can write that z = z_G ≥ 0.01. Therefore, if the total redshift z ≥ 0.01 then the redshift of superluminal light coming from distant galaxies, z_G, largely predominates in the total redshift z. Now the redshift of this light can be defined by the following relation z_G = (λ_G – λ_E)/λ_E (= z) or z_G = (c_G – c)/c. After a bit of algebra, the speed of the photons c_G coming from distant galaxies is given as

c_G = (1 + z_G)c    … (2).

Thus, if the total shift of superluminal light emitted by distant galaxies z > 0.01 then the speed of this light is (1 + z_G) times larger than the current speed of light c.

 

If the currently observed upper limits of z_G is about 11 then, according to eqn. (2), c_G → 12c. Note that this upper limit would change if galaxies with higher z_G are discovered. It is possible that in the near future Earthlings may measure the speed of the light coming from distant galaxies with a new highly sophisticated instrumentation.

If z_G = z ≥ 0.01 then the distance D_G between distant galaxies and the Earth can

D_G = c_Gt_G

where t_G is the “cosmic age” of the photons[7] emitted from the galaxies. This formula can be rewritten

as

t_G = D_G/c_G    … (3).

“Megamaser” galaxies of NEEU. Distance measurement is very important in cosmology but also is difficult. The distance from the Earth to distant galaxies can be estimated using standard candles. However, these estimation methods require a complex and uncertain ladder of calibration and the use of uncertain Hubble constant H₀ and redshift z.

Direct geometric distance measurements by the megamaser method provide an independent way to accurately measure the distance of distant galaxies D_G up to about 650 Mly. This method also does not require the complex ladder of calibration and Hubble’s constant H₀.

For the present purpose, we consider six prominent “megamaser” galaxies whose redshift z (= z_G) is known and their distance D_G is determined by the megamaser method, Table 1. NGC 4258 galaxy has a total redshift of z = 0.001541, so the contribution of its v_pec to this shift can be significant (tens of percent).

Table 1. “Megamaser” galaxies.

Name of galaxy	zS	DG [Mly] Megamaser	cG1 [km sec-1]	tG2 [My]
NGC 4258	0.001541	23.7 {13}	300 000	-
NGC 1052	0.004930	65 {14}	301 000	70
UGC 3789	0.010679	162 {15}	303 000	170
NGC 6323	0.02592	349 {16}	307500	360
NGC 5765B	0.02754	411{17}	308 000	420
NGC 6264	0.03384	447 {18}	310 000	460

 ^SFrom Simbad (Astronomical database, Centre de données astronomiques de  Strasbourg,

                               Université de Strasbourg); ¹calculated using eqn. (2); and, ²calculated using eqn. (3).

Table 1 also shows the speed of light c_G emitted from the megamaser galaxies and the cosmic ages of

the associated photons t_G.

Fig. 1. Distance D_G – redshift z relation among “megamaser” galaxies.

Fig. 1. Distance D_G – redshift z relation among “megamaser” galaxies.

Fig. 1 is a graph of the measured distance D_G of these galaxies vs. their redshift z (= z_G). This graph shows a linear relationship between their distance D_G and redshift z and its slope is (c/H₀)~ 13.65 Gly. In other words, D_G is linearly proportional to z. This can be mathematically expressed as Hubble’s equation (1) valid for z  ≤ 0.1.

aD_G = z_Gc/H₀.[8]    … (4).

If we combine eqns. (2) and (3) we get

D_G = (1 + z_G)ct_G    … (5).

For z_G < 0.1 then this equation becomes

D_G = ct_G    … (6).

The only way to equate these eqns. (4) and (6) is to have t_G equal to c/H₀. Now eqn. (5) takes the following form

D_G = (1 + z_G)z_Gc/H_0.

For convenience, this equation can be rewritten as

D_G = 13.65(1 + z_G)z_G    … (7)

where D_G is Gly.

Table 2. Selected distant galaxies

. 

Name of galaxy	zW	cG1 [km sec-1]
3C 273	0.158339	350 000
BX442	2.1765	950 000
TN J0924-2201	5.19	1 850 000
TGSS J1530+1049	5.72	2 000 000
Q0906+6930	5.47	1 950 000
ULAS J1342+0928	7.085	2 400 000
GRB 090423	8.2	2 800 000
EGSY8p7	8.68	2 900 000
GN-z11	11.09	3 600 000

^WRedshift from Wikipedia, (List of galaxies); ¹calculated using eqn. (2).

   

Selected galaxies. We know that the redshift z_G of light emitted from distant galaxies is known then we can estimate their speed c_G employing eqn. (2). In Table 2 are given values for this parameter for selected distant galaxies[9] whose redshift z (= z_G) is much larger than 0.01. These are: the optically brightest quasar in the sky 3C 273; the remote grand design spiral galaxy BX442; the most remote radio galaxies TN J0924–2201 and TGSS J1530+1049 and; the most remote blazar Q0906+6930 and quasar ULAS J1342+0928[10]; the most remote gamma-ray burst (GRB) host galaxy GRB 090423; and, the two most remote “ordinary” galaxies EGSY8p7 and GN–z11.

 

In conclusion, it is shown that the redshift of the light coming from distant galaxies of NEEU is possible to explain by the superluminal speed of this light. 

Acknowledgments  

This work is dedicated to my sister Branka Premović. She introduced me to the wonderful world of science and art from my earliest youth. My thanks are addressed to Joseph A. Rybczyk for essential information to this work. His scientific work is impressive.

References

[1] R. K Soberman and M. Dubin, Was there a Big Bang. arXiv:0803.3604 [physics.gen-ph](2008).

[2] 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).

[3] Y. –H Sanejouand, About some possible empirical evidences in favor of a cosmological time variation of the speed of light. Europhys. Lett., 88, 59002  (2009).

 [4] V. S. Troitskii, Physical constants and evolution of the Universe. Astrophys. and Space Sci., 139, 389-411 (1987).

[5] A. Albrecht and J. Magueijo, A time varying speed of light as a solution to cosmological puzzles. Phys. Rev. D,  59, 043516 (1999).

[6] J. Moffat, Superluminary Universe: A possible solution to the initial value problem in cosmology. Intern. J. of Modern Phys. D, 2, 351-365 (1993).

[7] J.Barrow, Cosmologies with varying light speed.  Phys. Rev. D 59, 043515 (1999).

[8] Y.-H. Sanejouand, A simple Hubble-like law in lieu of dark energy. arXiv:1401.2919[astro-ph.CO].  (2015). [9] J. Magueijo, New varying speed of light theories. Rept. Prog. Phys., 66, 2025-2068 (2003). [10] D. J. Farrell and J. Dunning-Davies, The constancy, or otherwise, of the speed of light.

arXiv:physics/0406104[physics.gen-ph] (2004).

[11] A. Alfonso-Faus, Expanding versus non expanding universe. Hadronic J. 34, 165-178 (2011).

[12] S. Mei, M. Scodeggio, D. R. Silva, et al., H₀ measurement from VLT deep I–band surface brightness fluctuations in NGC 564 and NGC 7619. Astron. Astrophys. 399, 441-448 (2003).

[13] J. R. Herrnstein, J. M. Moran, L. J. Greenhill, et al., A 4% geometric distance to the galaxy NGC 4258 from orbital motions in a nuclear gas disk. Nature, 400, 539-541 (1999); C.-Y. Kuo The megamaser cosmology project: geometric distances to megamaser galaxies and accurate masses od supermassive black holes at their centers. PhD Thesis, Department of Astronomy, University of Virginia, USA (2011).

[14] P. van Dokkum , S. Danieli1, Y. Cohen , et al., The Distance of the dark matter deficient galaxy NGC 1052–DF2. Astrophys. J. Lett. 864: L18 (2018).

[15] M. J. Reid, J. A. Braatz, J. J. Condon, et al., The megamaser cosmology project. IV. A direct measurement of the Hubble constant from UGC 3789. Astrophys. J., 767, 154-165 (2013). Updated by Braatz.

[16] C. Y. Kuo, J. A. Braatz, K. Y. Lo, et al. The megamaser cosmology project. VI. Observations of NGC 6323. Astrophys. J. 800, 26-35 (2015).

[17] F. Gao, J. A. Braatz, M. J. Reid, et al., The megamaser cosmology project. VIII. A geometric distance to NGC 5765b. Astrophys. J., 817, 128-145 (2016).

[18] C. Y. Kuo, J. A. Braatz, M. J.  Reid, et al., The megamaser cosmology project. V. An angular-diameter distance to NGC 6264 at 140 Mpc. Astrophys. J. 767, 155-168 (2013).

[19] [13] M. Saxena, R. A. Marinello et al., Discovery of a radio galaxy at z = 5.72. MNRAS, 480, 2733-2742 (2018).

[1] 1 megaparsec (Mpc) = 10⁶ parsec = 3.26×10⁶ ly.

[2] We are referring to its geometry alone, i. e. static means non-expanding.

[3] According to Soberman and Dubin {1}, the Big Bang is supported by only two experimental observations, the cosmological redshift and the cosmic microwave background (CMB).

[4] As ΔE_EG > 0 it appears that the energy is lost. The energy of the space expansion rises by the same amount compensating for this loss.

[5] Of course, the frequency-based redshift z_ν = 0.

[6] This is the most critical assumption of this communication. To the best of the author's knowledge, the light speed of a distant galaxy has not been measured reliably so far.

[7] Or the “time of flight” of these photons between the galaxy G and the Earth {3}.

 [8] Of note, that Lerner [2, and references therein] adopted this relationship for NEEU and for all z.

[9] For the sake of simplicity, this selection is based on the values of z reported by Wikipedia, except for TGSS J1530+1049 {19]}

[10] Blazar (an active galactic nucleus) and quasar (a quasi-stellar object) are a type of active galaxies.