Some food for thought.
I think, therefore I am. - René Descartes
Is thinking real in your mind? Ideas and concepts? Are they tangible? You can claim they are real because they are a particular arrangement of neural memory and synapses, but as far as I know, that is a theory based on what we know, but has not been scientifically proven. (Where is a map of someone's synapses showing what the person is thinking?) However we could say that ideas are real, because we experience them—assuming you think the ideas are in a real person. (Contrast with asking if Santa Claus' ideas are real.)
If we're in the Matrix (from the movie, The Matrix), is what we are experiencing "real?" I believe you are asking a question that only has subjective perspectives, rather than a logical and objective proof. i.e., there is no provable single definition of "real."
Does anyone have a piece of dark matter? Some scientists believe the universe must have more tangible mass than we have observed to explain other measured phenomena. As a result, there "must" be as-of-yet undetected dark matter. But that is just a theory to explain observed phenomena. Would you consider dark matter real?
You may find it comforting to believe that if it isn't tangible then it isn't real, but it is not possible to prove that assertion. The best you can do is to say that is what you believe.
On the other hand, you could say that God is real and everything he created is real, whether tangible or not, and that may very well be true, but we still wouldn't be able to prove it scientifically—nor theologically (as far as I know). God does not specifically say that there is nothing else other than himself and what he created, but says this:
For by him all things were created: things in heaven and on earth, visible and invisible, whether thrones or powers or rulers or authorities; all things were created by him and for him. (Colossians 1:16, 1984 NIV)
If you believe heaven is real, does that mean it must have a location in our physical universe? If it doesn't, is it real?