Quantal logic vs classical logic

摘要

Two methods for the description of physical phenomena, microscopic and macroscopic, are necessary to understand the physical world. We now have two examples. The first one is mechanical, whether classical or quantal, vs thermodynamic treatments, which are characterized by reversibility and irreversibility, respectively. Another one is quantal vs classical theories, which have different forms of logic and lead to various paradoxes in measurement processes. To understand these contradicting aspects, it should be noted that in both cases, chaos and measurement are involved inevitably, and averages over small regions of space and time for measurement are required. In this way, chaos mediates between the two methods of description. We have already made an attempt to treat the former example in terms of ergodicity. In this paper the latter example will be treated with the theory of quantum measurement and the EPR paradox in mind.