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- https://phys.libretexts.org/Bookshelves/Relativity/General_Relativity_(Crowell)/01%3A_Geometric_Theory_of_Spacetime/1.01%3A_Time_and_CausalityYou may have heard that relativity is a theory that can be interpreted using non-Euclidean geometry. The invariance of betweenness is a basic geometrical property that is shared by both Euclidean and ...You may have heard that relativity is a theory that can be interpreted using non-Euclidean geometry. The invariance of betweenness is a basic geometrical property that is shared by both Euclidean and non-Euclidean geometry. We say that they are both ordered geometries. With this geometrical interpretation in mind, it will be useful to think of events not as actual notable occurrences but merely as an ambient sprinkling of points at which things could happen.
- https://phys.libretexts.org/Bookshelves/Relativity/Special_Relativity_(Crowell)/02%3A_Foundations/2.01%3A__CausalityOur intuitive belief in cause-and-effect mechanisms is not sup- ported in any clear cut way by the laws of physics as currently understood. For example, we feel that the past affects the future but no...Our intuitive belief in cause-and-effect mechanisms is not sup- ported in any clear cut way by the laws of physics as currently understood. For example, we feel that the past affects the future but not the other way around, but this feeling doesn’t seem to translate into physical law. For example, Newton’s laws are invariant under time reversal, as are Maxwell’s equations. In fact, the weak nuclear force is the only part of the standard model that violates time-reversal symmetry.
- https://phys.libretexts.org/Bookshelves/Relativity/General_Relativity_(Crowell)/07%3A_Symmetries/7.03%3A_Penrose_Diagrams_and_CausalityA Penrose diagram, also known as a Penrose-Carter diagram or causal diagram, can be used to visualize spacetime with a symmetry, so the relevant properties the whole thing by considering a lower-dimen...A Penrose diagram, also known as a Penrose-Carter diagram or causal diagram, can be used to visualize spacetime with a symmetry, so the relevant properties the whole thing by considering a lower-dimensional part of it. For example, for a spacetime that is spherically symmetric, then we can reduce the four-dimensional to a two-dimensional one, with each point representing a two-sphere.
