sign in sign up
<<
Home , Active galactic nucleus, EGSY8p7, Galaxy, GRB 090423, Lists of galaxies, List of galaxies

Distant in the Non-Expanding (Euclidean) : the Pavle Premovic

To cite this version:

Pavle Premovic. Distant Galaxies in the Non-Expanding (Euclidean) Universe: the Light Speed Redshift. The General Journal, The General Science Journal, 2021. ￿hal-03216407￿

HAL Id: hal-03216407 https://hal.archives-ouvertes.fr/hal-03216407 Submitted on 4 May 2021

HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés.

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

Pavle I. Premović Laboratory for Geochemistry, Cosmochemistry and Astrochemistry e-mail: [email protected]

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

Keywords: universe, , , , redshift, speed of light

Introduction.

Redshift and in cosmology are characterized by the relative difference between the observed and emitted (or ) of light (or in general electromagnetic ) which is sourced by an such as a galaxy. The (-based) redshift is expressed z = (λG – λE)/λE where λG is the wavelength of light emitted by the source of the galaxy and λE is the wavelength of light generated by the same source on the . 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 : the total 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: , redshift due to () 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 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

DG = zc/H0 … (1)

5 -1 5 -1 where DG is the distance of distant galaxy to the Earth, c (= 2.99792×10 km s ~ 3×10 km s ) is the current speed of light and H0 is a constant known as the Hubble constant; at present time it

1

-1 -1 -1 -1 -18 -1 is estimated that H0 = 72 km sec (Mpc) or = 22 km sec × (Mly) [= 2.2(1) × 10 sec ]. This expression shows that there is a linear relationship between redshift z and distance of galaxies DG if the redshift z ≤ 0.1. This linearity however breaks down at large . Applying eqn. (1) -18 -1 we find that the Hubble distance, c/H0 = 13.6 Gly for H0 = 2.21 ×10 sec . Apparently, the Hubble distance provides the natural distance scale for the expanding Universe. Further details about Hubble’s law the reader may find in many astronomical textbooks and related publications.

The Big Bang Universe vs. the non-expanding (static2) Universe. The (standard) Big Bang model of the Universe is based on the General . It states that the Universe started as a point singularity of infinite and that included all and of the current Universe. It then expanded rapidly over the next about 13.8 Gy to the current version. This is the expansion of itself (or better of space-time itself) that is still occurring. It appears that the Big Bang hypothesis is supported by numerous evidence, including cosmological redshift.3 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 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 has been Euclidean and static over the last 12 Gy.

The non-expanding models of the Universe have serious difficulties in explaining many (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 applicable to other models of the non- expanding Universe.

Varying speed of light. In the cosmological literature, the issue of 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

11 megaparsec (Mpc) = 106 = 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 background (CMB).

2

[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 a number of 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 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 EG (= hνG) of coming from distant galaxies is lower than the energy of -34 photons EE (= hνE) generated by the same source on the Earth; h (= 6.63 × 10 J sec) is the constant and νE and νG are the appropriate frequencies. Of course, νE > νG. The difference 4 between these two is ΔEEG = EE – EG . Let us denote with λG the wavelength of light emitted by distant galaxy G and with λE the wavelength of light generated by the same source on the Earth. Since νE = c/λE and νG = c/λG we have λE < λG.

The galaxies interact with each other via , which gives them a component of 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 : vpec. The expansion largely predominates, since the average vpec of galaxies -1 vpec is usually between about 100-300 km sec [12, and references therein] then it is very likely -1 that vpec ≤ 0.001c (≤ 300 km sec ).

Assume now that all distant galaxies of NEEU are moving relative to the Earth at a non- relativistic speed vpec ≤ 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 fossils” from the cosmic past. For the sake of simplicity, let us ignore for a moment the effect of the velocity vpec on the redshift of distant galaxy. As above, we denote the energy of these photons with EG and with EE the energy of the photons generated by the same kind of source on the Earth; νG and νE are the corresponding photon frequencies. Distant galaxies are in the same as the Earth since vpec ≤ 0.001c. Now we can apply the Principle of . In this case, we have EE = hνE = EG = hνG, and, accordingly, νG = νE =

4 As ΔEEG > 0 it appears that the energy is lost. Actually, the energy of the space expansion rises by the same amount compensating for this loss.

3

5 ν . Since we are dealing with the redshift λG > λE. We know that the wavelength of a photon is given by the ratio of its speed and . It follows that the velocity of light emitted by 6 distant galaxies cG > c.

However, the total redshift of galaxy z = zG + zpec where zG is the redshift due to the speed of galaxy’s light cG and zpec is the redshift due to the velocity vpec. Of course, depending on the direction of the peculiar motion zpec can be positive, equal to zero and negative. In the case of galaxy’s superluminal light, the “peculiar” redshift can be approximated with zpec ~ vpec/cG <

0.001 (or 1000vpec < cG), then if z ≥ 10zpec we can write that z = zG ≥ 0.01. Therefore, if the total redshift z ≥ 0.01 then the redshift of superluminal light coming from distant galaxies, zG, largely predominates in the total redshift z. Now the redshift of this light can be defined by the following relation zG = (λG – λE)/λE (= z) or zG = (cG – c)/c. After a bit of algebra, the speed of the photons cG coming from distant galaxies is given as

cG = (1 + zG)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 + zG) times larger than the current speed of light c.

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

If zG = z ≥ 0.01 then the distance DG between distant galaxies and the Earth can be expressed as

DG = cGtG

7 where tG is the “cosmic age” of the photons emitted from the galaxies. This formula can be rewritten as tG = DG/cG … (3).

“” galaxies of NEEU.

Distance 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.

5 Of course, the frequency-based redshift zν = 0. 6 This is the most critical assumption of this communication. To the best of the author's knowledge, the light velocity 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].

4

Direct geometric distance by the megamaser method provide an independent way to accurately measure the distance of distant galaxies DG 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 (= zG) is known and their distance DG is determined by the megamaser method, Table 1. NGC 4258 galaxy has a total redshift of z = 0.001541, so the contribution of its vpec to this shift can be significant (tens of percent).

Table 1. “Megamaser” galaxies.

S 1 2 Name of z DG [Mly] cG tG [My] galaxy Megamaser [km sec-1] 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 cG emitted from the megamaser galaxies and cosmic ages of the associated photons tG.

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

Fig. 1 is a graph of the measured distance DG of these galaxies vs. their redshift z (= zG). This graph shows a linear relationship between their distance DG and redshift z and its slope is (c/H0)

5

~ 13.65 Gly. In other words, DG is linearly proportional to z. This can be mathematically expressed as Hubble’s equation (1) valid for z ≤ 0.1.

8 DG = zGc/H0. … (4).

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

DG = (1 + zG)ctG … (5).

For zG < 0.1 then this equation becomes

DG = ctG … (6).

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

DG = (1 + zG)zGc/H0.

For convenience, this equation can be rewritten as

DG = 13.65(1 + zG)zG … (7) where DG is Gly.

Table 2. Selected distant galaxies.

W 1 Name of z cG -1 galaxy [km sec ] 0.158339 350 000 BX442 2.1765 950 000 TN J0924- 5.19 1 850 000 2201 TGSS 5.72 2 000 000 J1530+1049 Q0906+6930 5.47 1 950 000 ULAS 7.085 2 400 000 J1342+0928 GRB 8.2 2 800 000 090423 EGSY8p7 8.68 2 900 000 GN-z11 11.09 3 600 000 WRedshift from Wikipedia, (); 1calculated using eqn. (2).

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

6

Selected galaxies

We know that the redshift zG of light emitted from distant galaxies is known then we can estimate their speed cG employing eqn. (2). In Table 2 are given values for this parameter for 9 selected distant galaxies whose redshift z (= zG) much larger than 0.01. These are: the optically brightest in the sky 3C 273; the remote grand design BX442; the most remote galaxies TN J0924–2201 and TGSS J1530+1049 and; the most remote Q0906+6930 and quasar ULAS J1342+092810; the most remote gamma-ray burst (GRB) host galaxy GRB 090423; and, 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 [.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, with varying light speed. Phys. Rev. D 59, 043515 (1999). [8] Y.-H. Sanejouand, A simple Hubble-like law in lieu of . 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).

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 ) and quasar (a quasi-stellar object) are a type of active galaxies.

7

[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 in a nuclear gas disk. , 400, 539-541 (1999); C.-Y. Kuo The megamaser cosmology project: geometric distances to megamaser galaxies and accurate od supermassive holes at their centers. PhD Thesis, Department of , University of Virginia, USA (2011). [14] P. van Dokkum , S. Danieli1, Y. Cohen , et al., The Distance of the 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- 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 at z = 5.72. MNRAS, 480, 2733-2742 (2018).

8