I know this question has been asked before, so before you shut it down for being a duplicate, please hear me out. The answers I saw in other similar threads were not satisfactory to me and they left me with more questions than clarifications, mainly because most of the highly rated answers seemed to miss the following point:
People assert that dreams -- including lucid dreams -- are noticeably less vivid than our waking state. But isn't this argument roundabout? If the question is "how do you know that what you currently perceive as reality is not in fact a dream world", then how can you go about arguing "well, dream worlds are not as vivid as the real world"? This misses the point entirely.
We've read Descartes' first Meditations, as well as John Pollock's A Brain in a Vat, in our intro to philosophy course and I'm really intrigued by this subject. One of the things Descartes mentions is how there is really no way to distinguish the dream world from the waking state, or that everything in dreams is an extension of things we have seen in the external world.
Is it possible, then, to prove that one is not, at any given point in time, dreaming?