You can say the same for a changed personality :p
You can say the same for a changed personality :p
All that means is that they are somehow connected.
They are still 2 different environments, which different rules -- which is what people actually mean when they say "alternate reality", and not "complete isolated reality space".
So the counter-proof is more like saying "If there's Canada, and we get to there from here, the they are no longer Canada".
What are the borders of reality?
That place would just have to comply with a different set of rules compared to anywhere else to be justified to call it an "alternate reality" (e.g. no gravity, fire is cold, etc).
Heck, we even call experiences like living with the Amish an "alternative reality", and those are on our very same universe/world, and with all the known laws of physics and basics intact.
[1] https://en.wikipedia.org/wiki/Big_Five_personality_traits
[2] https://en.wikipedia.org/wiki/Personality_psychology#Persona...