The three consciousness states of Dreaming Sleep, Awake and Deep Sleep can be understood by analogy with Einstein's theory of General Relativity - in terms of time always running at the same speed as experienced from within a state, but being perceived to run at relative different speeds when observing one state from a different state.
Time runs at the same rate for every state from within that state. One hour always feels like one hour, whether a person is dreaming, awake or deeply asleep.
But, for instance, if awake is taken as the reference point; then one hour of being awake seems to be able to encompass many hours, even days, of dreaming. On the other hand, many hours in deep sleep feel like an absence, or just a few moments - from the perspective of being awake.
So Deep Sleep passes almost like no time at all (as when somebody wakes-up and says: "how long have I been asleep?", and he can't believe that the answer is three hours because while deeply asleep it felt like a few moments); while dreaming can encompass what is experienced as a very long, complex, vivid, perhaps exhausting dream - and on wakening the dreamer find that they have only been asleep 45 minutes.
Perhaps there is a helpful analogy in considering falling into deep sleep as an acceleration, and falling into deep sleep as a deceleration - a slowing.
Thus, from the perspective of an observer located on Earth, an astronaut on a spaceship which accelerates away from earth to high relative speed, for example in a round trip to Jupiter, will be found to have 'aged more slowly'; when he returns to Earth. For the observer on Earth time has slowed down for the astronaut - for the astronaut, time on Earth has speeded-up.
Thus, dreaming sleep is like an acceleration to high speed: within the dream the time is unaltered, but from the awake perspective the dream can cram more into each unit of time than is possible for the awake mind.
And presumably the opposite is true of deep sleep; where (from the awake perspective) very little seems to be happening per unit of time.
So our lives are spent oscillating between different times. Being awake is in the middle of two states, and when we are awake we see events speeded-up or slowed-down, or time running slower or and faster: in dreaming events are speeded-up or time appears to run slower to allow more to happen per unit time; and in deep sleep events are slowed-down or time seems to run quicker so that not much happens per unit time.
This provides a way of understanding why our memories of the times when we are asleep are so limited: when we are dreaming, too much is happening, too fast for memory to 'take it all in': like a videotape sped up to 1000 times normal speed, and reduced to a mere blur of shapes and colours.
But when we are deeply asleep, not enough is happening for the memory systems to make sense of it - it is like a sound recording played back a thousand times too slowly: a single word becoming just a deep, incomprehensible, modulating rumble.
However, it would be reasonable to assume that although the waking mind, and waking memory systems cannot make much explicit sense of what happens in dreams and deep sleep - the experiences of dreaming and deep sleeping do change things (presumably by their own memory systems): although how this happens is only indirectly knowable to the awake state - being mostly unconscious, inaccessible, implicit.