Ok, how can you prove another dimension, when there is no interaction between this other dimension and our reality. Only 'being in another state of awareness' is the only way to detect the existence of this other dimension. How are you going to prove the existence of this parallel universe?
For example: Suppose that sleepparalysis is a state of mind wich allows you to discover a parallel universe of 'beings in the room' while the room was empty when you went to sleep. How can you prove that?
You can't, and thus it isn't.
See, this is where you run up against the definition of "exists" and hit a brick wall. Your hypothetical other dimensions and sleep-paralysis demons are only an interesting thought experiment; by any meaningful definition of existence, they are not real.
What it comes down to is that, to exist, a thing must have some sort of observable effect on the universe. If there is no observable effect, ever, under any circumstances, then there is no difference between that and nonexistence - and thus, it doesn't exist. Follow me so far?
In case you don't, here's it boiled down a bit:
In order to be said to exist, a thing must have some sort of detectable effect on the rest of the universe. As a corollary,
if something exists, removing it from existence will have an effect on the rest of the universe - and, as the inverse of that,
if something does not exist, removing it from existence will have no effect on the rest of the universe.
So let's look at your two given examples:
- Alternate dimensions, observable through altered states of mind (presumably achieved through drug use).
- Sleep-paralysis entities, observable when experiencing sleep paralysis.
You might, hypothetically, be thinking "Well, these things are theoretically detectable, albeit through unusual means, so ha! They exist! You just don't accept my evidence and are close-minded!" But that's not true.
See, the problem with both your given examples is that they are effectively adding hypothetical entities to situations that we already know have mundane causes. We know that drug use causes hallucinations; your proposed alternate dimensions are indistinguishable from these. We know that sleep paralysis causes what are essentially nightmares; your proposed sleep paralysis entities are indistinguishable from these.
In both cases, your hypothetical entities do not actually change the situation in any way. Removing from the equation changes absolutely nothing; thus, by definition, they are not real, because they have zero effect that can actually be detected by any means. They cannot be distinguished from the mundane phenomena that we
know exist and offer explanations from their existence. They violate the corollaries.
So in both of your proposed situations, the answer to your question is: you can't. Because they aren't real.