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

Solid Mechanics and is the Chief Technical Officer for CAVS. APPENDIX: Special Relativity Primer This appendix introduces fundamental concepts of Special Relativity that are used throughout the paper, such as: synchrony conventions, Minkowski diagrams, relativity of simultaneity, and light cones. 1. Synchrony conventions The concepts presented in this appendix are based the Einstein Synchrony Convention (ESC), which prescribes that the one- way speed of light is c . Only the round-trip speed of light is a physical quantity, and not the one-way speed, which is why it is chosen by convention. While the ESC is the most commonly used convention because of its convenient mathematical properties, other conventions are also valid and useful for special types of application. For example, Lisle, writing under the pen name Newton (2001) introduced a synchrony convention he called ‘anisotropic synchrony convention’ (ASC), according to which light is reckoned to arrive instantaneously when traveling toward an observer, but whose one-way speed is c /2 when traveling away from the observer. It is important to realize that the choice of synchrony convention does not change the outcome of physical experiments and has no physical significance at all. 2. Minkowski diagrams Special relativity postulates that the speed of light relative to any observer does not depend on the velocity of the observer relative to the light source (Einstein, 1905). This postulate is known as the invariance of the speed of light . The invariance of the speed of light implies, however, that elapsed time and distance measurements are not absolute but depend on the motion of the observer performing the measurement. We will use Minkowski diagrams to illustrate geometrically the application of this postulate and to present our proposed solution to the distant starlight problem. A Minkowski diagram (see Figure 4) is a schematic of spacetime in which one axis represents time, such as the ct -axis in the gure, and the remaining axes represent one or more spatial dimensions. Although often only one spatial dimension is visualized, such as the x -dimension in the gure, the remaining two spatial dimensions are always implied. Furthermore, time measurements are normally scaled by the speed of light c, so that one unit along the time axis represents the distance that light travels during one unit of time. Consequently, the path that a light beam traces on a Minkowski diagram subtends equal angles with the time and space axes (see object d on Figure 4). On the other hand, the tangents to the path that a material particle traces through spacetime, also known as that particle’s world line , must always subtend smaller angles with the time axis than the spatial axes for the particle’s speed to remain less than the speed of light (see object b on Figure 4). A point on a Minkowski diagram corresponds to an event at a particular place and time. For example, object C in Figure 4 corresponds to the event when the light beam d was emitted in the positive x-direction. Similarly, the world line of a particle is made up of many events each representing the particle being in a particular location at a speci c instant in time. While events themselves are objective, in the sense of being independent from the observer who measures them, the time and space measurements of these events are subjective and depend on the motion of the observer. The time and space measurements of an event are in fact the event’s coordinates on a Minkowski diagram. Hence each observer corresponds to a set of coordinate axes on a Minkowski diagram. We use the term inertial reference frame for the set of axes associated with each observer. It is not necessary for the coordinate axis on a Minkowski diagram to be perpendicular to each other. In fact, different inertial reference frames are indicated on a Minkowski diagram by varying the tilt of the coordinate axes. The following subsection uses this diagraming technique to compare two inertial reference frames. 3. Relativity of simultaneity Figure 5 shows two reference frames, primed and unprimed, corresponding to two observers moving with velocity v relative to each other. Speci cally, the primed observer is moving in the negative x -direction of the unprimed reference frame. A particle comoving with (that is, stationary in relation to) the primed observer, moves with velocity v in the negative x -direction relative to the unprimed observer. Consequently, the primed time axis ct' , which may be viewed as the world line of a particle comoving with the primed observer, has a slope of magnitude c / v with respect to the unprimed reference frame. As discussed earlier, due to the invariance of the speed of light, the path of a light beam must subtend equal angles with the time and space axes within each of the two reference frames. Therefore, the primed spatial axis x' must have a slope of magnitude c / v with respect to the unprimed reference frame. Let t A and t B be the coordinates of events A and B , respectively, in relation to the unprimed reference frame, and let t ' A and t ' B be their coordinates in relation to the primed reference frame. As illustrated on Figure 5, we find that t A > t B while t ' A < t ' B . The implication is that the objective ordering between Events A and B is indeterminate. Tenev et al. ◀ Creation time coordinates solution to the starlight problem ▶ 2018 ICC 93 Figure 4. Minkowski diagram showing an example event E , a world line b of some particle, and a beam of light d emitted at event C . The vertical axis ct represents the time dimension, while the horizontal axis x represents one of the spatial dimensions. The other two spatial dimensions are implied but omitted from the diagram for clarity. Note that the time dimension is measured in units of time t multiplied by the speed of light c .