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 U...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 U=(m', m') be an unordered pair of distinct massive objects in different reference frames. A dark experiment is an ordering u, mv> of the elements of U, either or, exclusively, , where the left-hand member of the ordered pair is called the observer, and where there exists a 1-to-1 mapping f:{u}→{events}, mv> , such that both elements of an ordered pair in a dark experiment agree on the events that unfold in the experiment. However, since ≠ , it follows that f()≠f(). 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.展开更多
文摘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 U=(m', m') be an unordered pair of distinct massive objects in different reference frames. A dark experiment is an ordering u, mv> of the elements of U, either or, exclusively, , where the left-hand member of the ordered pair is called the observer, and where there exists a 1-to-1 mapping f:{u}→{events}, mv> , such that both elements of an ordered pair in a dark experiment agree on the events that unfold in the experiment. However, since ≠ , it follows that f()≠f(). 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.
