Some nagging questions in modern physics can be resolved rigorously using a basic mathematical formalism, albeit with the need to admit that non-isomorphic realities arise to various degrees in a given universe. Let <i>U=(m', m")</i> be an unordered pair of distinct massive objects in different reference frames. A dark experiment is an ordering <m_u, m_v> of the elements of <i>U</i>, either <m', m"> or, exclusively, <m", m'> , where the left-hand member of the ordered pair is called <i>the observer</i>, and where there exists a 1-to-1 mapping <i>f</i>:{<m_u}→{events}, m_v> , such that both elements of an ordered pair in a dark experiment agree on the events that unfold in the experiment. However, since <m', m">≠ <m", m'>, it follows that <i>f</i>(<m', m">)≠<i>f</i>(<m", m'>). This describes non-isomorphic realities where in both elements of each ordered pair mapping two distinct sets of unfolding events will agree on their respective events. Consequently, there is an inherent limitation on what can be determined directly from experimentation. Examples arise in the context of the Hawking information paradox, relativistic time travel, and cosmic ray experiments

The purpose of the present paper is to assume that the expanding spacetime of our cosmos was created by the big bang. It then follows that there exists a finite instantaneous radial extent dR_U to spacetime as observed from anywhere in spacetime by comoving observers. The consequences for gravity are explored by first considering the scalar field of a central mass that defines the dynamic properties of a circular orbit for each radius R ≤ dR_U under the postulate of weak equivalence. These properties include an orbital velocity and an escape velocity. For a central mass of galactic proportion, the escape velocity becomes large even at cosmological distances. By considering the dynamics of a smaller mass occupying the last orbit, we find that the established laws of physics lead to different rotation curves than they do when applied to the solar system. Since galactic rotation curves reveal the existence of dark matter, this is anticipated to have some consequences for our understanding of dark matter.