The scenario you describe is commonly known as the "grandfather paradox" in time travel discussions. It presents a logical contradiction that arises when a time traveler interferes with events in the past, potentially leading to a chain of events that prevents the time traveler's existence in the first place.
If a person were to accidentally or intentionally kill their ancestor in the past, several theories attempt to explain what might happen:
Self-Erasing Paradox: One possibility is that the time traveler would create a paradox, leading to a logical inconsistency. If the ancestor dies before they can have children, the time traveler's lineage would be disrupted, preventing their own birth. Consequently, they would not exist to travel back in time and cause the ancestor's death, creating a paradox.
Alternate Timelines/Parallel Universes: Another way to resolve the paradox is through the theory of alternate timelines or parallel universes. In this interpretation, the time traveler's action creates a new branch of reality, where the ancestor is killed, but the original timeline where the time traveler exists remains unchanged. The time traveler would then be trapped in the new timeline without a way to return to their original one.
Predestination Paradox: Some theories propose that time travel events are predestined, meaning that the time traveler was always meant to go back in time and be involved in their ancestor's death. Therefore, even if the time traveler causes the ancestor's death, it was already part of history, and nothing would change.
Novikov Self-Consistency Principle: This principle suggests that any actions a time traveler takes in the past were already part of the past and won't alter the future significantly. So, even if the time traveler tried to kill their ancestor, they would somehow fail or be prevented from doing so.
It's important to note that time travel remains a theoretical concept, and there is no consensus among physicists about its feasibility or the resolution of associated paradoxes. As a result, the consequences of time travel, including the scenario you describe, remain speculative and a subject of fascination in science fiction rather than a scientifically established reality.