The Proceedings of the Eighth International Conference on Creationism (2018)

gravitational potential of the Galaxy in the Solar neighborhood is approximately ten times larger than the gravitational potential of the Sun, i.e., the Solar System rotates about ten times faster around the center of the Galaxy than the Earth rotates around the Sun. The gravitational potential of the Galaxy does not affect the dynamics within the Solar System for the same reason that astronauts in orbit about the Earth are weightless: in both cases, the orbiting objects are in centrifugal balance, with their rotational energy being equivalent to the gravitational potential energy of the mass they orbit. The fact that gravity cannot be dynamically felt in these situations does not imply that it is not there. Assuming that the Galactic potential is the dominant source of gravity in the Solar neighborhood (although it may in fact be dominated by larger structures such as the Local Group or the Virgo cluster), the speed of light in the Galaxy would be determined by the solution of equation (6) using the Galactic distribution of baryonic (visible) matter. Rather than solving equation (6), I will estimate the speed of light in the Galactic plane by using a simple model for the Galactic mass distribution (McMillan 2011) and a model for c that is calibrated to give c = c 0 at R = 8.5 kpc: c = c 0 (ρ/ρ 0 ) -2/3 , ρ 0 = 0.083 M ʘ pc -3 . (7) The rest mass of a particle in the theory of Dicke (1957) scales with the speed of light as m ~ c -3/2 (this scaling is required in order to satisfy the weak equivalence principle, see Dicke 1957), so that expression (7) is a plausible model for c , but the only requirement for solving the distant starlight problem is a model in which c varies inversely with mass and/or gravitational potential. The model for the Galactic mass distribution consists of a sum of simple functions, one that captures the inner bulge and one that captures the outer disk: (8) (9) where z and R are cylindrical coordinates in kpc. A plot of the speed of light normalized to c 0 using the sum of (8) and (9) in (7) is shown in Figure 1. In this model, c ~ 100 c 0 in the outskirts of the Galaxy. Extrapolating this result much beyond that is not warranted due to the fact that the Galaxy is embedded within larger structures, although it seems clear that c will attain a value much larger than c 0 in galactic voids because of the absence of any massive gravitating objects there. The gravitational potential in voids, which make up 80% of the volume of the universe, is many orders of magnitude smaller than the gravitational potential in galaxies, so that the speed of light could easily be large enough there to put the entire universe in causal contact with Earth on the Biblical time scale. Notice that expression (7) exacerbates the light travel time problem for signals emanating from the Galactic Center, since c ~ 0.01 c 0 at r = 0. The light travel time, t = ∫ dR/ c , (10) can be numerically calculated from (7) and is found to be 10 5 years. The stellar density distribution modeled by expressions (8) and (9), however, is an average density distribution, and the actual stellar distribution is inhomogeneous, with significantly fewer stars in between the spiral arms of the Galaxy. If the interarm stellar density were lower by a factor of 10 the speed of light would be larger by a factor 5 of based upon (7). The fact that the Solar System is located in the fourth spiral arm of the Milky Way would reduce the light travel time by another factor of 4 since light signals from the Galactic Center propagate through 4 interarm regions as they travel to Earth. The combination of these factors reduces the light travel time from the Galactic Center to 8 x 10 3 years, a result that is remarkably close to the Biblical time scale of 6 x 10 3 years. Afinal indication that the model described here is based in physical reality can be seen by considering the Tolman test for the redshift evolution of the surface brightness (luminosity per surface area) of galaxies (Hubble and Tolman 1935). This quantity can be used to test the reality of an expanding universe, since in such a universe the surface brightness of galaxies should vary with redshift as (1 + z ) 4 . One factor of 1 + z arises from the decrease in photon energy with redshift, two factors come from an apparent increase in galactic surface area due to aberration, and one factor comes from a decrease in the flux of photons with time (Sandage and Lubin 2001). The first factor is present in any self-consistent model for the redshifts since photon energy is coupled to wavelength through the conservation of wave action (Whitham 1965). It is the only factor present in the tired light model, which assumes that redshifts are due to light interacting with matter during propagation (Sandage and Lubin 2001). The next two factors are present in both an expanding universe model and the model described here, although for different reasons. Rather than being due to aberration, in a gravity dependent speed of light model they are due to the variation in atomic length scale with c , with a surface area (length squared) giving rise to two factors of 1 + z . The final factor is present only in an expanding universe. The present model thus predicts a total Tolman surface brightness factor of (1 + z) 3 rather than (1 + z) 4 . Results for this test found an exponent of 2.28 - 3.55 (Lubin and Sandage 2001), values that are consistent with the result predicted by a spatially varying speed of light model (three) and inconsistent Johnson ◀ Young universe cosmology ▶ 2018 ICC 49 Figure 1. The variation of the speed of light within the Galaxy based upon expression (7).