The key to the thought experiment is perspective: we make everything identical materially to try to isolate a conceptual difference. We make the two clones identical in every way, and from nearly all perspectives they are identical (but distinct) entities. The sole difference in this scenario is the perspective of the clones, who have two distinct consciousnesses. Looking at your clone, you don’t see yourself, you see someone who looks like you. Because when we distill it to its pure essence, the one thing that is uniquely you is your perspective, your present conscious experience. You are looking through your eyes, thinking your thoughts, as is this entity materially identical to you. But it’s not seeing and thinking as you, thus it is something different.

There’s something that ties your pure essence to its material composition, such that even a molecularly identical entity wouldn’t have your consciousness (just an identical consciousness, removed from your own).

We can explore the bounds of this experiment by tweaking variables: you teleport a la star Trek, whereby your old body is disintegrated and a new identical one is immediately constructed. Or maybe you upload your consciousness when you die, so the list of variables that in theory comprise you are preserved. But in all cases, the essence that is you, your continuity of perspective, doesn’t transfer over. When you die, everything goes black, and that’s it. It’s only from external perspectives that “you” continue. But the you that is you, you as you experience yourself, is gone.