The Schrödinger equation as we know it is linear, but I believe that we don't know that we have discovered all the terms of it.
If there are yet undiscovered terms and the full equation is not linear then it turns out that question of whether the Copenhagen interpretation of quantum mechanics versus the many-worlds interpretation is not just a philosophical question. With a nonlinear Schrödinger equation different "worlds" of the many-worlds interpretation can interact.
Maybe you ran into a you from a different reality.
If there are yet undiscovered terms and the full equation is not linear then it turns out that question of whether the Copenhagen interpretation of quantum mechanics versus the many-worlds interpretation is not just a philosophical question. With a nonlinear Schrödinger equation different "worlds" of the many-worlds interpretation can interact.
Maybe you ran into a you from a different reality.