Step-by-step explanation:
It depends on what you mean by logical.
As far as modern societ knows, time travel has not been invented yet. In this sense, no traveling backward in time is not logical.
If we move past this known hurdle, then we can also define logical by perserving the former era's authenticity. Since we would be from the future, we could easily (and even accidentally) introduce new concepts, ideas, and inventions that would otherwise never have been thought of or created at that time. This changes both the past and future which means it is not logically possible to live in a former era without it changing the course of history entirely.
Another obstacle would be just the imbalance in general. Since we did not originally exist in the former era, we would affect everything around us. For instance, say we meet a stranger who we fall in love with and have children. Now they will never be with their intended partner or have the children they were supposed to have. Imagine if the children who no longer existed were extremely important to the foundations of education or society, such as Albert Einstein.
Overall, if we were to live in a former era everything from the past to the future would be altered so we could never logically experience the former era in its true nature. However, disregarding the fact time travel doesn't exist at the moment, it is - at the bare minimum - logically possible to live in a former era.