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

where the subscripts e and o denote a quantity in the emitted and observed region, respectively. In a moving medium the frequency is replaced with the doppler- shifted frequency ω ± v k , where v is the velocity of the medium, so that in general ω = ( c ± v) k . A shift in the wavelength of a wave can thus occur due to either a variation in the wave speed or motion of the background medium. For a shift due to motion of the background medium, the ratio of wavelengths is given by λ o / λ e = ω e / ω o = 1 ± v / c (2) if it is assumed that the wave speed remains constant between emitter and observer. These considerations apply to light waves as well as to sound waves, as long as the motion of the background is non-relativistic. Equation (1) applies to light propagating through a medium whose index of refraction varies from unity, and equation (2) is the expression for a non-relativistic Doppler shift. In Big Bang cosmology, the ratio of wavelengths is given by λ o / λ e = a o / a e , (3) where a is the scale factor of the universe. A comparison of expressions (1) and (3) indicates that the cosmological redshift of light could be attributed to a spatial variation in the speed of light rather than (or in addition to) the expansion of the universe. While I believe the above considerations alone provide sufficient motivation to explore the implications of a varying speed of light for creationist cosmology, I would like to point out two additional considerations that strengthen the case for pursuing this line of research. First, Dicke (1957) goes through the constraints required to ensure that a varying speed of light is consistent with known physics. If the fine-structure constant remains fixed, for example, atomic energy levels remain unchanged. This requires μ ∝ ε, so that c ∝ ε -1 , a constraint that Barceló et al. (2011) refer to as a “somewhat unphysical restriction.” On the contrary, what this in fact implies is a constraint on the impedance of the medium. The impedance of a medium, which reduces in vacuum to the impedance of free space , is a measure of the resistance of the medium to the propagation of electromagnetic waves through it. In addition, the impedance of an optical or acoustic medium is the quantity that governs the amount of reflection and transmission that occurs as a wave propagates through regions in which the properties of the medium change significantly on length scales that are short compared to the wave length of the propagating wave. Just as discrete transmission components must be impedance matched to provide optimal transmission with minimal reflection, a constant impedance in a continuous medium allows a wave to propagate freely without reflection. Rather than being unphysical, then, μ ∝ ε implies a constant impedance , a profound physical constraint that suggests that a varying speed of light may have a basis in physical reality. If what we refer to as the space-time continuum behaves like a dielectric medium, this constraint would be necessary to allow the propagation of light through the cosmos without reflection. Second, Dicke (1957) covers some of the cosmological implications of a variable speed of light, and shows that the speed of light varies with the square of the redshift: c = c 0 (1 + z ) 2 , (4) a scaling that arises from a combination of a change in atomic length scales (the Bohr radius scales as c 1/2 ) and the wave length change during propagation given by expression (1). Since the redshift of the Cosmic Microwave Background (CMB) is z ~ 1000, this in turn implies that the speed of light is 10 6 times faster at the CMB than it is on Earth. This is close to the discrepancy between the age of the universe in Big Bang cosmology and the Biblical age (10 10 / 10 4 ), an encouraging result. If light were to propagate at 10 6 c 0 throughout its entire route, this would imply that the edge of the observable universe is in causal contact with the earth on the time scale of Biblical history. Such a claim cannot be made, however, based upon cosmological redshifts alone. The reason for this is that z > 1 only for r > r H ≡ c 0 / H 0 ~ 4Gpc (for H 0 ~ 70 km/s/Mpc), i.e., cosmological redshifts are negligible over a volume that is billions of light years across. The fact that c ~ 10 6 c 0 near the CMB does not resolve the light time travel problem and further considerations are required to reconcile the two disparate time scales. Before getting into those additional considerations, an important implication follows from what has been discussed thus far. It is natural to assume that if cosmological redshifts are in fact due to a spatial variation in c , the cosmological parameters that are currently associated with the expansion of the universe would instead reflect gradients in the speed of light. The Hubble constant H would be a measure of dc / dr and the deceleration parameter q would be a measure of d 2 c / dr 2 . Using the definitions H 0 ≡ dc / dr| r =0 and q 0 ≡ −( c 0 / H 0 2 ) d 2 c / dr 2 | r =0 , one can construct an expression for the speed of light that is valid for small redshifts: c = c 0 (1 + r / r H + 0.25 r 2 / r H 2 ), (5) where I have used q 0 = −0.5. This expression is only valid for r ≪ r H . In general c ( r ), would be determined by the redshift distance relation, which does not admit a simple analytic form. What is readily apparent from expression (5) is that what is interpreted as an accelerated expansion in Big Bang cosmology is simply a reflection of the fact that the speed of light varies non- linearly with radius. This obviates the need for dark energy. However, while removing the need for dark energy is a fortuitous side benefit of a varying speed of light, we are still left with the problem of distant starlight, because as discussed above, the observed cosmological redshifts are simply not large enough to bring the universe into causal contact with Earth on the scale of 10 4 years. If the redshift distribution traces the variation in the speed of light emitted from distant galaxies, we are still left with the possibility that light travels even faster in regions of low gravity. This would be consistent with the theory outlined by Dicke (1957), with the additional assumption that c 0 is set by the dominant gravitational potential in the Solar neighborhood. The gravitational Poisson equation, derived by taking the steady-state limit of Dicke’s theory and given by his equation (53), takes the form c -1/2 2 c -1/2 = −( K /4)ρ, (6) where the constant K is determined to be 16π G by solving (6) for a spherically symmetric source and assuming that c = c 0 at infinity (away from the gravitational source). It is not the case, however, that gravity is negligible at large distances from the Sun. The Johnson ◀ Young universe cosmology ▶ 2018 ICC 48