Fethi Ramazanoğlu, Koç University, Istanbul, Turkey — February 3, 2025

We can know the future if we are given the state of a system right now. This is the essence of "time," which is a central concept in our theories of nature. There are well-known guidelines about how to mathematically implement the flow of time in a theory. In this talk, we will see how these guidelines can be broken in a surprising manner in some of the simplest field theories. Namely, time evolution exists for a finite duration in our examples, but dynamics becomes impossible afterwards in a phenomenon called "loss of hyperbolicity". Such results are especially valuable today, since ideas to modify general relativity are abundant, but there is a relative scarcity of experiments and observations to test them. Hence, we will discuss how time evolution problems can be utilized to constrain or rule out many alternative theories of gravity.