Complex action suggests future-included theory

TL;DR

This paper explores quantum theories with complex actions and introduces a future-included framework where both past and future states are considered, proposing this approach to ensure consistent universe histories across time.

Contribution

It proposes that complex action quantum theories naturally align with future-included models, extending the classification of quantum theories based on action reality and temporal inclusion.

Findings

Complex action theories suggest future-included models.

Future-included theories maintain consistent universe histories.

Classification of quantum theories into four types based on action and temporal inclusion.

Abstract

In quantum theory its action is usually taken to be real, but we can consider another theory whose action is complex. In addition, in the Feynman path integral, the time integration is usually performed over the period between the initial time $T_A$ and some specific time, say, the present time $t$. Besides such a future-not-included theory, we can consider the future-included theory, in which not only the past state $| A(T_A) \rangle$ at the initial time $T_A$ but also the future state $| B(T_B) \rangle$ at the final time $T_B$ is given at first, and the time integration is performed over the whole period from the past to the future. Thus quantum theory can be classified into four types, according to whether its action is real or not, and whether the future is included or not. We argue that, if a theory is described with a complex action, then such a theory is suggested to be the future-included theory, rather than the future-not-included theory. Otherwise persons living at different times would see different histories of the universe.