Earlier papers have stated the astrophysical framework of the New Redshift Interpretation [1] and GENESIS are the same. Thus these two designations will be used interchangeably. In Section 4 of their paper [2] Carlip and Scranton (C&S) use the static model assumption to infer the New Redshift Interpretation (NRI) flux equation will have only one factor of (1 + z)^{−1}. On that basis they attribute to the NRI their Eq. (22), which is contrary to the Hubble diagram. Hence, they say, the NRI must be a failure. The problem is, as has already been discussed in Part 1, the NRI represents an expanding universe, not a static one, as C&S assume. Creationism evidence, creationism evidence,theory of creation,creation science,
More specifically, none of their Eqs. (20) to (22) pertain to the NRI because they all assume the single (1 + z)^{−1} factor that pertains to the static model flux equation. It has been known for some time that this representation is incorrect because my eprint [3] — which C&S cite in their paper [2] — points out there are two redshifts combined in Eq. (2) of my NRI paper [1], one from gravity and the other from relativistic Doppler effects.A more detailed version of GENESIS' magnitude-redshift (m, z) relation is now obtained. It is based partially on Ellis' derivation [4] when considering only gravitational and special relativistic Doppler redshifts but differs from his in two respects. First, the NRI's, gravitational redshifts originate with a gravitational potential due to (i) ordinary mass/energy in the visible universe and that in the outer shell of galaxies and (ii) vacuum energy from C to the outer shell. Second, GENESIS does not assume curved spacetime [1]. These differences lead to an (m, z) relation that differs from ref. [4].
- Derivation of GENESIS' (m, z) relatio
Let L be a galaxy's luminosity (in ergs s^{−1}) and r_{g} represent the source-to-receiver distance (in cm) as measured in the galaxy's rest-frame. Thus r_{g }is the galaxy observer distance [4]. In the absence of gravity the proper flux (in ergs s^{−1}cm^{−2}) measured by a detector fixed in the galaxy's rest frame, would be
In contrast the NRI's redshift expression in ref. [1] contains r, the observer area distance, which is the galaxy's quasi-Euclidean distance as measured by a stationary local observer. Ellis shows [4] that aberration due to special relativistic effects gives rise to a reciprocity relation between these distance measures such that r_{g} = r (1 + z_{d}), where 1 + z_{d} = (1 + v / c) / √1 − (v / c)^{2} is the special relativistic Doppler redshift factor, and v is the galactic recessional velocity measured by a fixed local observer. Creationism evidence
In the NRI framework, as described in refs.[1,3] and in Part 1, the combined relativistic Doppler and gravitational redshifts of the receding galaxy will cause its clocks to run slower by a factor of (1 + z)^{−1} — where z now refers to the redshift due to these combined effects — relative to the local observer's clocks. Thus photons will arrive at the local observer's detector by a factor of (1 + z)^{−1} slower than the rate of emission in the rest frame of the receding galaxy. Furthermore, each photon impinging on the local observer's detector will likewise have its energy diminished by this same redshift factor. These redshift factors facilitate a transfer of the flux expression determined by an observer in the galaxy's rest frame, which is Eq. (1), to that of a fixed local observer in the NRI, or GENESIS, framework. Thus the NRI flux expected from any receding source of intrinsic luminosity L that exhibits both Doppler and gravitational redshifts, as measured by a fixed local observer, with a detector having unit cross section, is
F_{NRI} = | L 4πr_{g}^{2} (1 + z)^{2} | = | L 4πr^{2} [(1 + z)(1+ z_{d})]^{2} |
| (2) |
after utilizing the r_{g} = r (1 + z_{d}) substitution. The difference between Ellis' expression for the flux, and that of the NRI in Eq. (2), lies in the Doppler factor. Ellis' derivation [4] yields a (1 + z)^{−4} dependence rather than the NRI's[(1 + z)(1 + z_{d})]^{−2} dependence.
Additional corroboration that Eq. (2)'s dependence on the redshift factors is correct comes from the fact that if only Doppler effects are responsible for the redshift, then, as MTW [5] show, the flux expression is F_{dopp} =L / 4πr^{2} (1 + z_{d})^{4}, which is likewise obtainable from the brightness theorem. MTW [5] also point out that expansion's flux expression is proportional to (1 + z)^{−2}, instead of (1 + z_{d})^{−4} for Doppler recession. This difference is confirmed by Sandage [6], who utilizes the flux expression for expansion's dependence on the redshift — namely, F_{exp} ~ (1 + z)^{−2} — as a cornerstone feature of the Friedmann-Lemaitre expansion hypothesis.
- Comparison of GENESIS' magnitude-redshift (m, z) relation with observation
Continuing with the derivation of the (m, z) relation, we follow standard procedure [4] and define an effective luminosity distance as d_{L} = r_{g} (1 + z) = r (1 + z) (1 + z_{d}). Comparison of the NRI redshift expression from ref. [1],
1 + z = (1 + Hr / c) / √1 − 2 (Hr / c)^{2}, | (3) |
with the NRI's Doppler redshift factor, 1 + z_{d} = (1 + Hr / c) / √1 − (Hr / c)^{2}, shows that (1 + z) ≈ (1 + z_{d}) for z < 1, in which case d_{L} = r (1 + z)^{2}. In this same redshift interval Eq. (3) can be approximated by Hr / c ≈ z / (1 + z), which leads to d_{L} = cz (1 + z) / H. This expression can then be inserted into the distance modulus expression [6],m − M = 5(log d_{L} − 1), to obtain
m − M = 5[log cz − log H] + log (1 + z)] − 5. | (4) |
If we write ℳ = M − 5[log H − log(1 + z)] − 5, then Eq. (4) reduces to
which is the usual linear Hubble relation between m and log cz for z < 1. In this same redshift interval Eq. (4) can be rewritten as
m − M = 5[log cz − log H] + 2.17z − 5. | (6) |
Eq. (6) can be compared with the SNe Ia results of Riess et al. [7], Fillipenko and Riess [8], and Perlmutter et al. [9] by referring to big bang's redshift expression for m − M in terms of its parameter q_{o}, namely [6],
m − M = 5[log cz − log H] + 1.086(1 − q_{o}) z − 5. | (7) |
Supernovae results leading to estimates of q_{o} < 1, and in one case with q_{o} ≈ −1 [7], are easily seen to make the NRI's Eq. (7) indistinguishable from big bang's prediction in Eq. (6).
The foregoing results for the NRI apply to the interval 0 < z < 1. The NRI's (m, z) expression for the approximate redshift interval 1 < z < 2 also deserves comment. We retain Hr / c ≈ z / (1 + z) as a very rough approximation — for example, for Hr / c = 0.6, z_{exact} = 2.02 versus z_{approx} = 1.50 — but no longer assume 1 + z ≈ 1 + z_{d}. In this case we use the definition d_{L} = r(1 + z)(1 + z_{d}), which leads to
m − M ≈ 5[log cz − log H] + 5 log (1 + z_{d}) − 5. | (8) |
Since 1 + z_{d} increases more slowly than 1 + z as z increases to higher redshifts, then Eq. (8) shows that galaxies in the interval 1 < z < 2 would, in general, be brighter than if this equation contained the 1 + z term. For much higher redshifts we find from Eq. 3 that z → ∞ as Hr / c → 1 / √2, which leads to d_{L} = (c / √2H)(1 + z)(1 + z_{d}). Thus,
m − M ≈ 5[log c − log H] + 5 log (1 + z)(1 + z_{d}) − 5(1 + log√2), | (9) |
and again the expectation is that very high redshift galaxies should appear brighter, but only on the condition that they have the same intrinsic luminosity. It is known, of course, that this standard candle assumption is only a rough approximation. More on this later. We now turn attention to the question of angular size.
- Introduction to GENESIS' angular size-redshift relation
If Δθ is the angular size of any one of a collection of distant galaxies all having about the same diameter, d, then, as Ellis notes [4], an observer in the galaxy's moving frame will measure an angular size Δθ_{g} = d / r_{g} at proper distance r_{g} from the galaxy, on the assumption that the galaxy is oriented with its major axis perpendicular to the line of sight. As ref. [4] also points out, a fixed local observer will measure an angular size Δθ = d / r, where, as before, r is the observer-source distance in the reference frame of the fixed local observer. The GENESIS framework deals with observations of the local observer, in which case we utilize the expression Δθ = d / r.
- GENESIS' galactic angular size relation for 0 < z < 0.5
For z < 1 we can use the NRI approximation, r ≈ cz / H(1 + z), to obtain Δθ = d / r ≈ dH(1 + z) / cz for the locally measured value of the angular size. Since 1 / z is a rough approximation for (1 + z) / z in the interval 0 < z < 0.5, then a stationary local observer would be expected to measure an approximate Euclidean dependence Δθ ≈ dH / cz for this redshift interval. To a first approximation this expectation agrees with the observations of Sandage [10], who noted a Δθ ~ z^{−1} Euclidean dependence for low-redshift, first-ranked E cluster galaxies in the redshift interval 0.0023 < z < 0.46. But there are known difficulties in using galaxies to test the NRI's Δθ − z relation at higher redshifts. Sandage [6] has noted that observational uncertainties at high redshifts are large due to the small size of the galactic disk and the difficulty in defining a true metric diameter. This fact, when taken together with the wide range of angular sizes found in a survey of faint blue galaxies [11], strongly suggests that the underlying "standard" galaxy diameter assumption is not valid. Thus we turn to other astronomical sources to test the NRI's, or GENESIS', Δθ − z relation for higher redshifts.
- Radio astronomical testing of GENESIS' Δθ − z relation for z > 0.5
For the interval 0.5 < z < 1 the approximation (1 + z) / z diminishes in a quasi-Euclidean fashion more slowly than z^{−1}. For z > 1 we find from Eq. 3 that z → ∞ as Hr / c → 1 / √2, in which case Δθ = d / r ≃ √2dH / c for any class of astronomical objects that are presumed to exhibit a "standard" diameter, d. Thus, the NRI predicts the angular size for higher redshift objects should approach a constant angular size for z > 1 and for a specific value of d. Three sets of radioastronomy observations [12-14] appear to be consistent with the NRI angular size expectation for higher redshifts. These observations concern extended double-lobed radio sources, whose linear extent is typically hundreds of kiloparsecs, and compact radio jets, whose separation are typically less than a hundred parsecs [13].In a 1998 study of 103 extended double-lobed radio sources with z > 0.3, Buchalter et al. [14] found essentially no change in the apparent angular size in the range 1 < z < 2.7. This study, which stands in contrast to the Euclidean z^{−1} dependence of similar sources found, and subsequently discussed, by earlier investigators [15-16], is said to have addressed and corrected a range of problems that compromised those earlier studies. A 1993 analysis [12] of compact radio sources similarly found the angular size to be essentially independent of redshift in the interval 0.5 < z < 3. More recently this analysis was extended to include the angular size-redshift relation for compact radio sources based on 330 5-GHz VLBI contour maps [13]. In this latter case the redshift interval was 0.011 ≲z ≲ 4.72, and again the median angular size for compact radio sources for z > 0.5 appeared to be independent of redshift with median values ranging from about Δθ_{m} ≃ 2 mas to Δθ_{m} ≃ 5 mas. It is interesting that the NRI's angular size expectation of Δθ = d / r ≈ √2dH / c for a nominal radio jet separation of d ≈ 80 parsecs [13] lies near the upper end at Δθ ≃ 5 mas. However, this apparent agreement cannot necessarily be interpreted as confirmation of the GENESIS framework because there is no independent method of validating the constancy of d. The best that can be said is that the prediction of GENESIS appears to be consistent with the Δθ − z relation for z > 0.5.
- GENESIS' apparent brightness relation (bolometric)
The flux given by Eq. (2) is the bolometric flux from the total luminosity over all wavelengths. Corresponding to this flux is the bolometric intensity, or apparent surface brightness, designated by I = F / ΔΩ, where ΔΩ is the solid angle subtended by the source at r, the observer area distance. To obtain this relation for the GENESIS framework we follow the treatment of this topic as given in ref. [4]. In this case the flux diverging from the source along some bundle of geodesics subtends a small solid angle ΔΩ_{g} at the source and has cross-sectional area ΔS_{g} at the observer. The subscript g denotes quantities related to the galaxy being observed. Next, consider a unit sphere centered on the source galaxy and let F_{g} denote the value of F on that sphere. In this case it follows [4] that the source luminosity and F_{g}, the value of F on the unit sphere, are related by the expression L = ∫ F_{g }dS_{g} = 4π F_{g}, where ΔS_{g} = r_{g}^{2}ΔΩ_{g}.
Continuing, if the galaxy's cross sectional area is A, then the solid angle subtended by the source as seen by a local stationary observer is ΔΩ = A / r^{2}. If we substitute this expression and F from Eq. (2) into I = F / ΔΩ, we obtain
I = | {(4π)^{−1}L}r^{2} Ar^{2} [(1 + z)(1 + z_{d})]^{2} | = | F_{g} / A [(1 + z)(1 + z_{d})]^{2} | = | I_{o} [(1 + z)(1 + z_{d})]^{2} |
| (10) |
where I_{o} = Fg / A is the surface brightness of the source. Since 1 + z ≈ 1 + z_{d} for z < 1, then [(1 + z)(1 + z_{d})]^{2} ≈(1 + z)^{4}, and we have
I_{NRI} ≈ I_{o}(1 + z)^{−4}, | (11) |
which reproduces big bang's well-known Tolman redshift dependence [6],
in this redshift interval. An attempt to test this dependence for lower redshift galaxies is given in ref. [17]; but see also ref. [18] for additional comments.
- GENESIS' apparent brightness relation (heterochromatic)
What is measured photometrically through the telescope is not the bolometric intensity, I_{bol}, but instead the specific intensity, I_{v}, which is specific flux, F_{v}, per unit solid angle, over a specified wavelength/frequency range. As usually defined the specific intensity is the energy per unit area per unit time per unit frequency bandwidth per unit solid angle crossing a surface perpendicular to the radiation beam. To obtain this relation for the NRI it is convenient to again follow Ellis' treatment [4] and represent the source spectrum by a function φ (v_{g}), whereLφ (v_{g}) is the rate at which radiation is emitted from the galaxy at frequencies between v_{g} and v_{g} + dv_{g}, with φ (v_{g}) normalized so that ∫_{0}^{∞} φ (v_{g})dv_{g} = 1. The preceding discussions in this paper show the frequency, v, measured by some stationary observer at r is related to the emission frequency, v_{g}, in the galaxy's rest frame by v = v_{g} / (1 + z), which implies dv = dv_{g} / (1 + z). With these substitutions the flux expression, Eq. (2), becomes
F_{NRI} = | ^{ }L^{ } 4π | | ∫_{0}^{∞} φ (v_{g})dv_{g} r_{g}^{2} (1 + z)^{2} |
| = | ^{ }L^{ } 4π | | ∫_{0}^{∞} φ (v)dv r^{2} (1 + z)(1 + z_{d})^{2} |
| , |
| (13) |
which is essentially the same as the modified form of Ellis' Eq. 6.26 — as it appears on p. 161 of ref. [4] — except that the above expression contains the factors (1 + z)^{−1}(1 + z_{d})^{−2} instead of (1 + z)^{−3}. Following Ellis [4] we define the specific flux over the interval dv as
F_{v}dv = | L _{ }4π_{ } | | φ (v)dv r^{2} (1 + z)(1 + z_{d})^{2} |
| , |
| (14) |
in which case, the specific flux itself becomes,
F_{v} = | L _{ }4π_{ } | | φ (v) r^{2} (1 + z)(1 + z_{d})^{2} |
| . |
| (15) |
We now utilize the previously defined expression, L = 4πF_{g}, in which case
F_{v} = | F_{g}φ (v) r^{2} (1 + z)(1 + z_{d})^{2} | . |
| (16) |
Again following ref. [4], the specific intensity becomes
I_{v} = F_{v} / ΔΩ = | F_{g}φ (v) A (1 + z)(1 + z_{d})^{2} | = | I_{g}φ (v) (1 + z)(1 + z_{d})^{2} | , |
| (17) |
where I_{g}φ (v) is the surface brightness of the source [4] at frequency v (see ref. [4], p. 163). Since 1 + z ≈ 1 + z_{d} for z < 1, then [(1 + z) (1 + z_{d})]^{2} ≈ (1 + z)^{3}, and we have
I_{v-NRI} ≈ I_{g}φ (v) (1 + z)^{−3}, (for z < 1). | (18) |
If we let I_{g}φ (v) = I_{v-o}, the above expression can be rewritten as
I_{v−}_{NRI} ≈ I_{v-o }(1 + z)^{−3}, (for z < 1 in the NRI). | (19) |
This is exactly the same relation obtained in big bang cosmology — namely,
I_{v-bb} = I_{v-o }(1 + z)^{−3}, (for all z in the big bang). | (20) |
Thus the apparent surface brightness expectation for the NRI is indistinguishable from expansion's dependence on the redshift factor for z < 1. But for higher redshifts the 1 + z ≈ 1 + z_{d} approximation is no longer valid in the NRI framework, in which case Eq. (17) becomes
I_{v-NRI} ≈ I_{v-o }(1 + z)^{−1 }(1 + z_{d})^{−2}, (for z > 1). | (21) |
- The difference between GENESIS' and big bang's heterochromatic dimming factors points to another smoking gun signature of GENESIS
In his recent discussion about observational astronomy and how it is all about the contrast between a celestial object and the background — both that of the local universe as well as instrumental noise — Disney [19] notes that galaxies being just marginally brighter than the night sky is either extraordinary good fortune or that something else is involved which is not presently understood. He comments in particular on how unusual it is to see galaxies at z = 2, since — as per Eq. (12) — in big bang theory their apparent brightness should be dimmer by the inverse of the Tolman factor, which is (1 + z)^{4} ~ 100. But if this is unusual, what is to be said about the highest redshift galaxy reported thus far, for which z = 5.74 [20]? Here the inverse of the Tolman dimming factor is (1 + z)^{4} ~ 2000, far in excess of the 100 which Disney considered unusual [19].We investigate this topic further by considering the difference in GENESIS' and the big bang's dimming factors when comparing their heterochromatic rather than bolometric surface brightness. This approach is more realistic since it is the heterochromatic surface brightness which is actually observed telescopically. For higher redshifts there is an increasingly larger difference between big bang's dimming factor of (1 + z)^{−3}, as given in Eq. (20), and GENESIS' dimming factor of(1 + z)^{−1 }(1 + z_{d})^{−2}, as calculated from Eq. (21), because 1 + z_{d} = (1 + Hr / c) / √1 − (Hr / c)^{2} increases more slowly than does 1 + z = (1 + Hr / c) / √1 − 2 (Hr / c)^{2} for increasing r. Thus we expect that very high redshift galaxies which would be predicted to be virtually invisible in the big bang framework would in fact be somewhat luminous on the basis of the GENESIS model. An outstanding example of this expectation is the very luminous galaxy with z = 5.74 reported by Hu and McMahon [20]. In this instance big bang's dimming factor is (1 + z)^{−3} ~ 0.003, whereas for GENESIS it is only (1 + z)^{−1 }(1 + z_{d}) ^{−2} = [(6.74)(1.89)(1.89)]^{−1} ~ 0.04.Additionally there is the fairly recent photometric redshift determination of 335 faint objects in the HDF-S [21]. Tentatively identified are eight galaxies with z > 10, two of which have z ~ 14 and one of which has z ~ 15 [21]. It is in this very high redshift regime that the difference between the big bang's and GENESIS' predictions are even more pronounced. For z = 10, big bang's dimming factor is (1 + z)^{−3} ~ 1/1300, whereas for GENESIS it is (1 + z)^{−1 }(1 + z_{d})^{−2} ~ 1/60. For z = 15 big bang's prediction is 16^{−3} ~ 2 × 10^{−4} versus z ~ 0.01 for GENESIS. Clearly the latter provides the astrophysical framework for understanding such redshifts as originating with standard candle galaxies, whereas the big bang had to assume all such galaxies were exceedingly luminous.At even higher redshifts the predicted differences between GENESIS and the big bang becomes even more pronounced. In the big bang it was impossible to observe objects with z > 1000, or even z > 50, because these values corresponded to the time when the universe was presumed to be opaque or, in the second instance, before the time when galaxies had formed. In the GENESIS model, however, there are no such constraints. As Eq. (3) shows, in it redshifts for celestial objects can increase without limit as r → c / √2H. Thus, astronomers searching for very high redshift galaxies, quasars, supernovae, and Gamma-Ray Bursters should be alert to the possibility of astronomical objects with extremely high redshifts, meaning those higher — and conceivably much higher — than ten. I should also add that in the GENESIS model there is no constraint on the existence of primordial black holes. Therefore we could even speculate that evaporation of distant primordial black holes might somehow be related to the central engines of GRBs.
Summary
This paper has shown the GENESIS model accounts for: (i) the Hubble redshift-magnitude relation, (ii) the galactic angular size observations for low redshift galaxies (iii) the near-constant median angular size of extended and compact radio sources for higher redshifts, (iv) the z ≲ 1 SNe Ia evidence for an accelerating universe, with the expectation that SNe Ia with increasingly higher redshifts will be brighter than expected, and (v) the Tolman(1 + z)^{−4} dependence for the bolometric intensity and the (1 + z)^{−3} dependence for the specific intensity for z < 1, with the additional expectation that for higher redshifts the apparent brightness will vary as (1 + z)^{−1 }(1 + z_{d})^{−2}. This latter result implies it should be possible to detect galaxies and other distant celestial objects with much higher redshifts than predicted by the big bang model.
If the recent apparent discovery of very high redshift galaxies [21] with z ~ 14 − 15 is confirmed — and if even higher redshifts are discovered and likewise confirmed — then clearly, such results will be additional and unambiguous smoking gun signatures of GENESIS. Moreover, since redshifts for celestial objects can increase without limit in the GENESIS model as r → c / √2H, then astronomers searching for very high redshift galaxies, quasars, supernovae, and GRBs should be alert to the possibility of detecting astronomical objects with extremely high redshifts, meaning those higher — and conceivably much higher — than fifty [22 7^{th} day adventist theology, 7^{th} day adventist theology, 7^{th} day adventist theology, university seventh day adventist church, adventist website, online bible study degree, biblical studies online, online biblical studies, biblical studies, bible studies online, onlinebible, bible videos, the bible online, the end is near, 7^{th} day adventist theology, university seventh day adventist church, adventist website, online bible study degree, biblical studies online, online biblical studies, biblical studies, bible studies online, onlinebible, bible videos, the bible online, the end is near