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

( ) ( ) ( ) 2 2 1 1 ' 1 2 2 1 1 2 A B A B B A t t t t t v x t v t ′ ′ = + = + − ′ = − − Substituting the times from the null ray solutions gives: ( ) ( ) 1 ' 2 1 1 2 1 1 1 1 1 1 2 1 1 A B t t t v t x x t v v v t x v v ′ ′ = +  − = − + +     +         − − = + + −           + +         ( ) 1 1 ( ) 2 1 1 1 1 1 1 2 1 1 v x x t t x v v v t x v v   − ′ = + − −     +         − − = − + +           + +         In III M the null rays satisfy: B B A t t vt x t t x − = − − = − or 1 B A t x t v t t x − = − = + . Therefore ( ) ( ) ( ) 2 2 1 1 ' 1 2 2 1 1 2 A B A B B A t t t t t v x t v t ′ ′ = + = + − ′ = − − − ( ) ( ) 1 ' 2 1 1 2 1 1 1 1 1 1 2 1 1 A B t t t v t x t x v v v t x v v ′ ′ = +  + = + + −     −         + + = + − −           − −         ( ) ( ) 2 1 1 2 1 1 ( ) 2 1 1 1 1 1 1 2 1 1 B A x t v t v t x t x v v v t x v v ′ = − − −   + = − − − +     −         + + = + − −           − −         The resulting coordinate lines for the moving observer are shown in Figure 14. The continuity of the coordinates in both space and time and the absence of coordinate anomalies is clear. It is a global and continuous coordinate system derived from first principles of relativity. Every event in the space-time to which coordinates are assigned have necessarily been observed since the procedure is based on the operational requirements of the principle of relativity. APPENDIX B : JOINING EQUATIONS FOR THE INHOMOGENEOUS “BAR BELL” COSMOLOGY. We will construct the bar bell cosmology from two FLRW regions (labeled “1” and “2”) and a Schwarzschild region labeled “3.” We will use comoving coordinates for constructing a global radial coordinate r . We will take our cue for this coordinate by using the embedding diagram and noting that the Novikov coordinate uses the maximum radial coordinate of a freely falling particle as the constant comoving coordinate of the particle. We will use that feature for the FLRW to convert the usual radial “angular” FLRW coordinate to a “linear” radial coordinate. Figure 15 displays the pertinent variables and their relations. The Schwarzschild region lies in the range of Novikov coordinates: 1 2 r r r ≤ ≤ . 1. Embedding Maps To construct a mathematically precise solution we will need to specify the details of the Schwarzschild region mentioned above. To do this we will construct the embedding of a t=constant and / 2 θ π = two-dimensional cross section of the Schwarzschild geometry with surface metric: 1 2 2 2 2 2 1 M ds dr r d r ϕ −   = − +     To embed this in three-dimensional Euclidean space with metric in cylindrical coordinates: 2 2 2 2 2 ds dz dr r d ϕ = + + one writes z as a function of r. Dennis ◀ Young earth relativistic cosmology ▶ 2018 ICC 33 Figure 14. Radar range coordinates for an observer undergoing an impulse acceleration. This is a global and continuous coordinate system derived from first principles of relativity. Every event in the space-time necessarily has been observed before coordinates are assigned.