And how, exactly, would we discover that?

It turns out that what you've thought of as consciousness or self-awareness is a process in the shadow-particle world. The reason you find yourself talking about your experiences is that the real world contains particles that duplicate the interactions of your shadow particles. They do not actually interact with your thoughts, but because of the parallel structure maintained in the real world and the shadow-particle world, you don't notice this. Think of the shadow particles as your soul, which corresponds exactly to the real-world particles in your brain, with the only difference being that the shadow particle interactions are the only once you actually experience.

You conduct a particularly clever physics experiment that somehow manages to affect the shadow-particle world but not the real-particle world. Suddenly the shadow particles that make up your soul diverge from the real-world particles that make up your brain! This is a novel experience, but you find yourself unable to report it. It is the brain that determines your body's actions, and for the first time in your life, this actually matters. The brain acts as though the experiment had done nothing.

Once your brain and soul diverge, the change never cancels out and you find yourself living a horrific existence. Because real-world particles do affect shadow particles, you still receive sensory input from your body. However, your brain is now thinking subtly different thoughts from your soul. To you, this feels as though something has hijacked your body, leaving you unable to cry out for help.

Of course, you never have, and never could have, found out about shadow particles. But you are a brilliant physicist, so your soul eventually figures out what happened. Your brain never does, of course; it lives in the real world, where your clever experiment had absolutely no effect, and was written off as a failure.