It just feels like the span of time of the dream is longer than I have been sleeping. I could sleep for an hour and dream for a day. But it's not really that I go through a day long dream, it's just that it feels like a day has passed.

My theory is that the memory of a dream is actually formed instantaneously in the brain, not over whatever span of time you feel like has passed in the dream.

Have you ever dreamed that you've spent an hour trying to turn off your alarm clock, but in real life you wake up and it's 1-minute past the alarm time? How can you have had this long complicated dream involving an alarm clock that won't turn off, but you've only really slept 1-minute through the alarm? My answer is, as I said, the dreams happen instantly but your brain just thinks time is passing in them because it's a false memory.

That's a good point. I've definitely had that alarm experience before, but not in the context of dreams within dreams.

I think the idea of each inner dream happening faster than the outer one is probably just an Inception thing.

Fast dreams might not need to be an "instant" false memory. It seams possible that a dream could actually happen much, much faster than your "normal" sense of time, it's entirely synthetic so there is no sensory bottleneck. But it would take more energy to experience it this way.

I'm basing this theory off of the time I had several long, detailed dreams in the 9 minutes between pressing snooze and the second alarm. I woke up bewildered and worn out, as though I had been up all day. Worst "snooze" ever.