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

(2) entail the unreality of the creation week; (3) imply that the existence of sin, redemption, and judgement are likewise eternal. For instance, Christ is eternally on the cross. These are clearly rejected by the biblical revelation. So then, fundamentally, presentism is the only biblically consistent position. We cannot, on Christian presuppositions, maintain that the creation is, in anyway, coeternal with God and that all events in salvation history are eternally present. As above, this would mean Christ is forever on the cross and other equally abhorrent implications. And finally, eternalism is philosophically incoherent. It replaces the mystery of the reality of a single flow of time with billions of subjective flows of time. To summarize, eternalism is untenable. (1) It is contrary to Scripture. (2) Philosophically it is incoherent and, in fact, self- refuting. (3) And finally, contrary to some opinion, it is not a consequence of the theory of relativity. 1. AYEC cosmological solution So then, to develop a solution of the starlight problem we turn to inhomogeneous models within GR interpreted according to a biblically consistent presentist philosophy of time. GR is a widely successful theory of gravity and due to the relativity of time (“time dilation”) within the theory, GR is recognized as possessing the theoretical framework for solving the time issue. Inhomogeneous models present the possibility of providing different time dilations in different regions of the universe. However, relying on time dilation alone by way of inhomogeneities is not adequate to overcome the large orders of magnitude of the age-to-size ratio. Therefore, we will need to discover another path, in addition to mere inhomogeneity, to solve the light travel time problem. As it turns out, the inhomogeneous solutions contain the seed of the solution since they contain “chronological enigmas” due to issues of the ambiguity of “simultaneity,” and the requirement of different lifetimes for different regions of the cosmos. 2. Foundations of the Solution Our solution to the light travel time problem will be based on presentism and the fact that GR specifically and the relativity principle in general prohibits any empirical method of determining a putative hypersurface in space-time that is the present. Thus, any spatial 3-surface that represents an actual “now” (which must exist according to presentism, though in principle operationally undetectable) and explains the distant light arrival is acceptable. As mentioned above, we will construct such a solution motivated by an examination of cosmological solutions with “chronological enigmas” that, when interpreted in the presentist view, imply that there must be “non-simultaneous” (according to a conventional requirement of “cosmic time”) yet when interpreted via presentism and a proper selection of a “now” surface accommodate a YEC cosmology. The solutions we will examine are the maximal Schwarzschild geometry and the inhomogeneous L-T models. These cases correspond to time dependent spherically symmetric space-times. We will discuss the Schwarzschild case first then turn to the construction of “crude” inhomogeneous models from the FLRW solution by way of an examination of the general L-T solutions. To develop an inhomogeneous model cosmology that exhibits “chronological enigmas” we will employ the “cut and stitch” method of assembling solutions frompieces of several cosmological solutions. 3. The “Cut and Stitch” Approach to GR Solutions We will begin the mathematical investigation of a YEC cosmology guided by the topological method of constructing solutions of the Einstein field equations (EFE) of General Relativity (GR). The object of study in GR is a pseudo-Riemannian manifold denoted by the ordered pair ( ) , M g . Here, M is a C ∞ (“smooth”) 4-dimensional Hausdorff manifold and g is a Lorentzian metric tensor. We call the ordered pair ( ) , M g a space-time. See for example, Hawking and Ellis (1973, p. 56-59). A key point made by Hawking and Ellis is that two models denoted by ( ) , M g ′ ′ and ( ) , M g ′′ ′′ are equivalent if there exists a diffeomorphism : M M θ ′ ′′ → which carries (by way of the differential map, * θ  ) the metric g ′ on M ′ into the metric g ′′ on M ′′ , i.e. * g g θ ′′ ′ = . We say that two space-times are locally equivalent (in the regions , N N ′ ′′ ) if for some open subsets N M ′ ′ ⊂ and N M ′′ ′′ ⊂ the space-times ( ) , N N g ′ ′ ′ and ( ) , N N g ′′ ′′ ′′ are diffeomorphic. Here N g denotes the restriction of g to the set N . It follows that any two locally diffeomorphic space-time manifolds will be physically equivalent in their mutual regions of overlap. We will later use this property to note that our proposed solution, in as much as it matches the FLRW metric, will retrodict all the properties of the FLRW within the common region. An illustration of this can be seen by considering a 2-dimensional example. Consider the unit two-sphere 2 S embedded in 3-dimensional Euclidean space, 3 R , with induced metric: 2 2 2 2 sin ds d d θ θ ϕ = + . For a second manifold consider the “polar cap” specified by the open set given by ( ) { } 0 , , 0 2 P θ ϕ θ θ ϕ π = < ≤ < . This is a submanifold of 2 S and is isomorphic to the same region of 2 S consequently the polar cap region has all the same local Dennis ◀ Young earth relativistic cosmology ▶ 2018 ICC 18 Figure 1. Causal structure of space-time.