In a lucid dream, we are capable of asking whether or not we are dreaming while dreaming. This leads to the question of whether our wake state is also a very vivid dream albeit one that is harder to wake up from. But since the waking up is what defines a dream, it may not be proper to lable our day to day experience as a dream. A 'dream that we never ever wake from' is an oxymoron. However, there is still a lesson to learn about reality from the fact that we can dream about reality and convince ourselves that it is real at least within the dream.
First of all if you want to compare our wake experience with a dream, it may be far more insightfull to say that what we term it as a dream is infact an experience of some reality than to say that what we experience as real is infact a dream. Contrary to how you may think, we unwittingly decide what is or is not real by just agreeing on what the word 'real' should unambiguosly rifer to and/or what it should not rifer to. Since we will perform the relevant, ostensive definition while wake, it would be self defeating to again assert that what we experience in the wake state is not real.
The mainstream science and also many people will try to use the wake state to attempt to understand the dream. We do experience that we have a body and senses and whether or not we perceive the world depends on whether or not information get to our senses and then to our brains. Since the signal serves to creat some transductions at verious places in the nervous system, it is easy to imagine similar transductions happening albeit caused by something else other than the object we are to perceive. Thus it is easy to imagine a case where we perceive something that does not exist like it does when we are receiving information from the external. So we say such a process might simply be what is happening when we dream.
COMPARISON BETWEEN A DREAM AND AN HOLOGRAM
For this purpose, we will consider a dream or imagination of a pictoral image. If certain 'pixels' fire in the retina, hippocampus or the visual cortex, an image will appear in your awareness telling you that you are seeing something at some distance away from you, even upto milions of miles aways! In this case, the visual cortex is behaving in a way analogous to an hologram. When you see through an hologram, a 3d virtual image appears that seems located far at the back of the hologram even though the relevant event of bouncing light off is all happening on the surface of the hologram. If you are not aware of the hologram, you can formed the false idea that the light you see is caused by something far at the back when it is infact caused by events on the surface. Somthing close to that happens when things akin to bouncing light off a surface happens in the visual cortex.
You can then see that thus if you are not aware of the hologram, it is not at all easy to infer that thus whathever you are seeing is infact an holographic projection by studying the projection itself. This is because the image bears little recemblance with the hologram. One then might say that why should we categorise anything as a dream at all? If seeing at tree during wake is due to events that begines with light bouncing off the surface, and seeing a tree in the dream is due to events that begines with charges bouncing off somewhere in your brain. Why don't we rather define dream as just a perception in some other realm? The answere ultimately boils down to permanence and if the world out there is not permanent, then it is like a dream in that sense. It is only a longer dream. When we know that hologram is easy to get damaged, we then also know that the image will get lost alongside the hologram. This would not be the case if we were seeing something independent on the hologram.
PHYSICS IN THE DREAM
Is it possible to conclusively tell that you are dreaming while dreaming. Then we could use such a technique to exermine if the world we see is like a dream. Even though the scenario you are perceiving is caused by neurones that are firing, you can't easily see the neurones firing within the dream. Rather, you see an image such as a tree that bears little recemblance to neurones.
If you use some reasoning, you can still tell that you are dreaming while dreaming. One of the ways to do that is checking the permanence of the scene. We use the intuition that nothing can come out of void, supposedly blind things cannot behave like intelligent things etc. If you see a simple stone doing such a complex thing as math, then you can tell that this stone must be caused by some underlying mind that you are not seeing. If you see that things surreptitiously appear and disappear, or get easily transformed to different forms, then you can tell that what you are seeing is more akin to an energy than a thing. It must be an exitation in some other invisible entity such as visual cortex. This is the reason why temporality mean almost the same as dream. There is not so much difference between a bark you hear of once and dreaming of one. Finaly if things appear to be much within your control then what you are seeing is probably just your own dream.
Let us now see if our world fit that of a dream in a 'nervous system' that connects all of us. In other words, we might be dreaming and we all have a single, huge 'brain'!! Because there are countless consciousnesses operating the same 'brain', then we cannot espect the dream to be in much control of a single individual. The only way we can achieve such a control is through the coherence of our wills. This is not so in our world. Everybody has his own different and at many time conflicting will. We can see though that if at least we interprate quantum mechanics in a certain way, then yes we have some good control of the scenario at least in quantum world. The only reason quantum mechanics doesn't appear in our world is that there is no quantum coherence between many particles.
We also see that things behave more like energy. Particles end up being exitations in a strange, unseen ocean termed quantum field. If we were to liken the world with a dream, then this invisible quantum field out of which particles emerg as exitations in it will be akin to the neurons that are not visible in the dream. Farthermore, the quantum word indead appear and disapears surreptitiously and constantly changing form just like a dream.
Finaly, we see things akin to stones doing math. For instance the moon knows how to orbit the earth and where it is! Its behaviour then appears to be cause by some underlieing, unseen mind.