We demonstrate an unsuspected freedom in physics, by showing an essential unpredictability in the relation between the behavior of clocks on the workbench and explanations of that behavior written in symbols on the blackboard. In theory, time and space are defined by clocks synchronized as specified by relations among clock readings at the transmission and reception of light signals; however spacetime curvature implies obstacles to this synchronization. Recognizing the need to handle bits and other symbols in both theory and experiment, we offer a novel theory of symbol handling, centered on a kind of logical synchronization, distinct from the synchronization defined by Einstein in special relativity. We present three things: (1) We show a need in physics, stemming from general relativity, for physicists to make choices about what clocks to synchronize with what other clocks. (2) To exploit the capacity to make choices of synchronization, we provide a theory in which to express timing relations between transmitted symbols and the clock readings of the agent that receives them, without relying on any global concept of time. Dispensing with a global time variable is a marked departure from current practice. (3) The recognition of unpredictability calls for more attention to behavior on the workbench of experiment relative to what can be predicted on the blackboard. As a prime example, we report on the horse race situation of an agent measuring the order of arrival of two symbols, to show how order determinations depart from any possible assignment of values of a time variable.
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