Every sub-atomic particle exchanges all the affectance/energy/mass of which it is made every second. You don’t need to wait to become a new person.
You see a light in the night sky. It seems to be hovering, slowly moving a bit. You discuss the light that you saw with a friend. He tells of someone else who had seen a different light the night before. You discover that the color of light was different, one was reddish and the other was bluish. You and your friend then discuss the red and the blue night lights with your old college professor.
The professor laughs a bit and apologizes. He begins an explanation, but then he interrupts himself. “Wait…” he says, “How many lights did you see?” You explain that there was only one red light and one blue light. “And for how long did you see these lights?” You explain that you watched it for perhaps 30 seconds. So he asks how that could be, “The light that enters your eye cannot go back out and come in again for 30 seconds. How did the image persist?”
Now you are figuring that the professor was merely being pedantic and perhaps getting a little too much “the old professor”, so you explain, “Okay, okay, we saw something in the sky that was glowing.” “Are you sure that it was merely one light each night?” he asks.
The professor, who had picked yet another PhD, this time in Philosophy, then explained that some students were experimenting with laser phasing and producing spots of light mid-sky. When the phasing of the lasers was correct, the humid air at the point of convergence would glow. Of course the air and moisture that is glowing is never the same molecules, as they float freely and quickly around, in and out of the glowing region. So again, the professor asks, “Each night, how many lights did you actually see?”
How many lights were actually there?
…same question as Theseus’ ship. Nothing is ever exactly identical to itself for more than an infinitesimal of time. The mind could not even begin to track the changes. Thus the mind tracks only what is relevant: “It is the same basic configuration in basically the same location with roughly the same relevance to me, thus it is the same object by declaration of rational definition.”