Ignore the clone part though. That's just how I'm extending the time frame. The same problem exists with a "transporter". The instance coming out the other side

Ignore the clone part though. That's just how I'm extending the time frame. The same problem exists with a "transporter". The instance coming out the other side appears to be identical, but there's no way to know if that instance is actually a continuation or yourself. Is it the same consciousness/self? Is that even possible to know?