Acausal Processes and Astrophysics: Case When Uncertainty Is Non-statistical (fuzzy?)

In Newtonian physics, if we know the state of the world at some moment of time, then we can precisely predict the state of the world at all future times. In this sense, Newtonian physics is deterministic. In modern physics (starting with quantum mechanics), theories are usually non-deterministic in the sense that even if we know exactly the initial state of the world, we cannot uniquely predict the future state of the world. In quantum mechanics (and in most modern quantum-based physical theories), the best we can get is probabilities of diierent future states. In this sense, in the majority of modern physical theories, uncertainty is of statistical nature. Lately, a new area of acausal (causality violating) processes has entered mainstream physics. This area has important astrophysical applications. In this paper, we show that acausal processes lead to non-statistical uncertainty. The main purpose of this paper is to inform specialists in uncertainty representation about this situation, with a hope that formalisms for describing non-statistical uncertainty that have been developed to represent uncertainty of human knowledge (such as fuzzy logic) will help in formalizing physical non-statistical uncertainty as well.