I'm not sure you can call this equivalent from the point of view of the observer, since the observer's faculties are different during sleep than while awake.

Precisely. Same mind but different faculties, different perceptions, different reality. Amazing! The mind just goes into a different reality on its own.

Rich

Well, something is missing for me in the problem thesis.
What do you understand under the word "reality"?
Who is the observer? How many dimensions it has? Which dimensions you consider?

Alternate realities are plausible, but some things drive me mad when it comes to majority views on the subject. Especially how people equate extra dimensions with alternate reality (i.e, a Wrinkle in Time, that film is horridly misleading to unknowing people:puzzled:). Or how people mistake a fourth spatial dimension with the 'dimension' of time. God doesn't live in another dimension. We can't percieve 4D, we can however see a 4d model in 3d motion on a 2d computer screen. However, alternative realities are possible, at least in theory. Many theories support the possibility of alternate realities, separate areas of space that aren't linkable. Of course, with many theories, events such as a black hole in our universe have effects elsewhere beyond our understanding.

In the form of alternative realities, I assert myself to the notion propossed by Kant to explain the unintelligibility of such an alternative 'reality' of multi parallels. Kant placed focus on the physical apparatus and the premises for knowledge attainment. He firmly believed, writing in his Prolegomena to Any Future Metaphysics, that most characteristics that our experiences have are contingent: an object of perception can be of this material or that, of this colour or that, of these dimensions or those...etc. He explained that we find out what they are by observing them and reading off their characteristics from our observation, of which we do in our commonsense activities and in our science (of which we can assert belief by after first perceiving the premises of propositions from experiment to conceive to the notion of proposition).
But there are some characteristics of which we can say with certainty in advance that any object of experience has to possess them if it is to be an object of experience at all. We cannot, for instance, perceive any object without perceiving it to be something, and as being capable of being acted on casually by other things, and as having a location in three-dimensional space, and in one-dimensional time. These are not characteristics of the world that we learn about by reading them off our experiences: they are things that we know with certainty in advance of all possible experience. They are preconditions that have to be met before anything can be experience at all. The 'conditions' for conceivability. Kant used an analogical metaphor to describe the apparatus for the ability to conceive knowledge, and that was of a net trying to catch fish. When one swoops One's net in the water in attempt to catch a fish, when the net is pulled out, much material seeps through the net and cannot be collected by the item used. Kant hypothesised an enormous possibility of all what could consist of in all the un-perceivable. This being so, if we carry out painstantingly careful investigation of the forms of all possible experience we shall be discovering the limits what can be possibly be experience or knowledge for us; and anything that falls outside those limits cannot possibly be experience or knowledge for us. This is not to say that nothing outside those limits can exist, but only that if it does exist we have no way to apprehend it. Knowing as he did, the apparatus of which we have in the form of sensual organs for us to interact and perceive with the objective world is limited, we can only mediate is possible experience for us.
This is not at all the same as proposing that nothing can exist that it cannot mediate-to suppose this is one of the commonest error made by scientific an commonsense thinking, an also be empiricist and realist philosophers according to Kant. There are no grounds for making such an assertion. The simple truth is that as far as we can never know there is no limit to what can exist outside the possibility of our knowledge. Of course, because there is no limit on it, one of the infinitely many possibilities is that there is nothing outside the possibility of our knowledge. But this is infinitely unlikely. Kant firmly believed also with confidence that there is an independent reality outside the world of all possible experience.

Post Kant era, technological advances blossomed, and we were acquainted with new knowledge that there are alternative kinds 'stimuli' of which cannot be perceived, such as electroception, magnetoception, and even radiation, all of which are present in this ethos of world of possible experience in the three dimensional world of causality.
With Kant's premises, one should not shun the plausibility of parallel universes coinciding in existence with that of which we are accustomed with believing to be the totality of all.

'Alternative', 'supernatural', 'parallel', 'non-physical'... Is it not philosophically correct just to say 'spiritual'?

When I fly in a dream, my body does not fly, but I truly experience flight. Declaring dreams not real is equal to denying our existence during sleep. I personally find sleep the most enjoyable part of my life when spirit is not dependent on body. If I have an idea of something which does not happen in physical world, this does not mean that my idea does not really exist...

if you consider other dimensions than space, alternative realities are fact.
my reality consists of 3d physical dimensions, but 4th - the time line (even if I consider it as non-real), 5th - relationships, 6th - my imagination, 7th - my descendants and so on...so your reality in my understanding is a l t e r n a t i v e to mine. Init?

What are you even talking about?

There's a grand misconception about TIME as the 4th dimension. Time as a fourth dimension is known as the space-time continuum. The space-time continuum is a totally separate issue from, for example, the proposed 11 spacial dimensions of String theory. Having a 4th or 5th or xth spacial dimension is not contradictory to the spacetime continuum theory, but they certainly have not been unified on a theoretical basis.

Since reality is composed of waves, time is a necessary dimension in order to locate a specific point within our universe. A point lacking any of the three spacial dimensions or the time dimension amounts to an abstraction which purports to model reality.

I'm talking about my reality. I see the time dimension of mine and my environment, even if you don't see that, and even if you consider that as misconception.

Intrigued more on such theories, I took it upon myself to once again seek answers and delve within modern Physics and Cosmology to see whether such a hypothesis made, is actually tangible and in par with axioms of Physics and Cosmology. Once such confrontation that I felt intellectually stimulated bu and emotionally exhilarated from was the theoretical post three minute stage of the 'Big crunch'. One such Professor Paul Davies postulated that Multi-verses as a set of bubble-like realities are entirely possible. The actual term of such a theory 'The Chaotic Inflation Theory' and was first proposed by physicist Andrei Linde. Within such assertion, lay the plausible reality which is in par with the principles of Physics, that outside our infinite universe there lay other 'bubble-universes'. One can only begin to be imaginative and postulate theories what other such realities could consist of. The fundamental problem that is revealed from such conjecture is the conflict that a bubble universe has with infinity of space in the universe. One such elucidation that was used to resolve such a conundrum was that our universe was like a balloon, a balloon that had been twisted as is seen by clowns when they create ballooned-animals by bending sections of the balloon and establishing segregations. We lay inside such a precinct that we can never escape, as the more we attempt to travel out of, the more the section expands accordingly. Inside it would appear that space is infinite as there seems to be no closure of end, but from the outside of such a bubble, a completely opposing view would be perceived. There lay the speculative questions as to whether our bubble was established by an intellectual being as some sort of experiment, or of natural causality. Or as to whether multi-universes are identical, all establishing at the unequivocal exact moment, all with the exact environment with the identical principles of matter and laws. Therefore, we may indeed have other universes with indistinguishable events of past present and future thus giving birth to the reality of multi universes containing identical selves.