Yes, this question can be answered in both directions,both requiring to accept the assumption implied: 1) everything that is unaccesible in terms of the physic's instruments (look at quantums, or black wholes for example)would fit on the category stablished on the question. 2)Everything refering to different planes of existence (astral, mental, etc.) these areas have been called esotheric, or metaphysic, referring on both cases to that which trascends physics. In either case, however, the only relevant means we have to demonstrate te existence of unaccesible, or metaphysical reality are theoretical. There is, another non-physical reality: the psychological reality, which is different from one person to the other, and from one country or culture to the other.

I assume you mean by "are not perceived" that these things "can not be perceived, even in principle". Well, just because something can't be perceived directly, it can be perceived indirectly by its effects in observed phenomena (such as "dark matter" potentially existing, but only perceivable in terms of its effects on normal matter through gravity). Dark matter is part of physical reality though. In fact, if we can perceive of something even indirectly, it MUST be physical in nature, or else you need to answer the question, how does the (undefined!) non-physical reality interact with the physical reality, which leads to questions about what that intermediary might be. Rene Descartes had this problem with his dualist theory of the mind, wherein the "soul / mind" is non-physical but the "body / brain" is physical. Ultimately there is no satisfactory answer, and this remains one of the harshest indictments against dualist thinking of any sort. Maybe an even more effective approach to this question is "why do we believe or claim certain things exist?". Even the existence of physical reality is ultimately an assumption, a theory or mental model that seems to explain how, seemingly, if we poke things outside of our consciousness with tools, senses, and measuring equipment, we repeated get results, and, in fact, we seem to always get the same or similar result for each like poke, hence we also have the theory (which itself may only be an approximation) of the constancy and predictability of physical laws. Ultimately these beliefs - or better, theories - can have no justification other than their usefulness and practical value at explaining and predicting observed phenomena. Now, with "non-physical" reality, we're posed with two problems. First, it isn't clear what you mean by this - can you define it? Second, how would one come to theorize about something non-physical, if it doesn't interact with the physical (and if it does, how?)? One can only rightfully theorize given observations. If we are talking about whether or not there exist unobservables, I would pose that the very question is really unanswerable, undefinable, unactionable, and meaningless through uselessness. Bertrand Russel once used a thought experiment about an invisible tea pot in space, that was IN PRINCIPLE unobservable; Richard Dawkins recently reinvented that tea pot as the invisible flying spaghetti monster. The fact is if we can't observe something, and speculating about it doesn't lead to any new or more refined explanations or predictions, it doesn't make sense to talk about it. We have our hands full just in thinking about whether we can be certain that physical reality exists, let alone adding this "non-physical" thing. And why only two? What if physical and non-physical are like electric charge, positive and negative, but you can also have a third option, "neutral"? What would THAT be alike? This is an equally absurd and meaningless question. You can make it more absurd by asking if "physical" is only one of an infinite number of possible realities, and we oversimply by simply lumping them all together as "non-physical" (which, in defining them in terms of what they're not, doesn't really define them at all). I hope I made my point.

A non-physical reality is all there is. There is one vast field of consciousness that is timeless, deathless and from this springs everything we have ever known or seen. Even our selves are offshoots of this realm of pure consciousness, and it is only ego that would have us beleive we are separate from it.

My personal views on this are very... minimalist... I take the simpliest possible explanation that gives the same output. E.g. If I ask you how to obtain 5 from 3, I would say +2, but there are a whole plethora of other methods to do it by, my personal opinion is just that you do not need to add unnecessary explanation and depth (E.g. steps) when it makes no difference. I believe what we readily call the mind, the soul, etc, are all just manifestations of, say, the neurons firing in your brain. I have yet to see any requirement FOR a soul or a mind, or even any method for them to exist which doesn't violate laws of physics (see the Conservation of Energy problem with Dualism) I personally believe if we can't (and by cant i mean physically limited, rather than technologically) measure it, if we can't detect it, or if we can't even infer its presence, then there is no point debating it's existance, because a) you will never be able to provide any evidence FOR it, and more importantly, b) it makes no damn difference

WHAT A PHYSICS MEAN IS ALL THAT WE SURROUNDED BY. AS FAR AS THE PHYSICAL REALITY IS CONCERNED, I BELEIVE THAT THOUGH THERE ARE MANY SPHERES IN WHICH PHYSICS HAS NOT GET INTO,LIKE BLACK HOLE. BUT PHYSICS WILL DO IT.

I would be shocked it that wasn't the case.

I believe there is. ( in dr suszes Horton hears a who, the theory was proven, but everyone thought that was just a cartoon)

Fascinating question - I have often pondered the same thing. It may happen that intelligent beings exist which do have the ability to detect and measure properties/entities which we will never be able to. They may be able to communicate with us and tell us about them. Of course we could never know for sure if they were telling the truth, but they could help to explain some of our unsolved physics questions.

Before you wrote your question, you formulated it in your mind; therefore, it had a reality that was non-physical. You have demonstrated to yourself that there is non-physical reality.

I think it's a logical impossibility, or logical contradiction. I think that "exist" and "real" and "physical" are all the same thing. But then, we could be talking about the number 7. Does it exist? Where is it?

Dark Matter is a good example of something undectable, but yet we know exists.

How would you know if they did? There may well be many, many things which exist but do not affect us in any way at all. But, by your very definition, (a) we can never know if they do exist, and (b) it doesn't matter if they do, because by definition they cannot affect us.