The neuroscience of sleep and dreams teaches us that there are three basic brain states: waking, REM (rapid eye movement), and non-REM (NREM) sleep.
We have our most vivid dreams in REM while physiologically restorative sleep occurs in association with slow waves of NREM. What determines or creates and maintains each of these three states is a differing mixture or profile of brainstem-generated neurotransmitter (aminergic and cholinergic modulation) activity levels as well as differing forebrain activation and deactivation patterns. The three different brain activity profiles that give rise to the three different brain states must be thought of as probabilistic profiles.
Each brain state’s profile can be fully engaged or only partially engaged. The transitions between the brain states can also be only partial. Because the mechanisms that control brain states are probabilistic, transitions between states are virtually always partial and incomplete. When transitions between states are partial, we get a hybrid brain state—for example, a mixture of REM and waking, a mixture of NREM and waking, or REM with NREM. When these hybrid states occur, we tend to get uncanny, weird, and bizarre experiences.
For example, sleep paralysis represents a hybrid of REM and waking.
The patient is conscious and awake but he is paralyzed and cannot move because the muscle atonia associated with REM is persisting into the waking state. In addition, the patient hallucinates an intruder possibly because many REM dreams are about potential threats and so on. But what about the closely-related false awakening experience?
Presumably, when we falsely believe we have woken up (but are in fact still dreaming), the brain is moving towards the awake state and for some reason thinks it has arrived. If some degree of activation of the dorsolateral prefrontal cortex is the standard physiological cue that the brain uses to think it is awake, then it seems reasonable to argue that that clue can sometimes be used incorrectly. But the dream within a dream phenomenon is not only about being fooled that you are awake because there is still full-on dreaming happening. The dream within a dream requires some other explanation than its mere re-description as a partial waking.
Perhaps the dream within a dream is more like lucid dreaming, which results from a hybrid of REM and waking states because the dorsolateral prefrontal cortex is partially activated. When the dorsolateral prefrontal cortex is activated during REM, the individual gains some awareness of self and so becomes aware that he is dreaming. A false awakening would involve skipping the awareness of self as a dreaming step that occurs with lucid dreaming, and that is associated with moving toward the waking state. Instead, the awakening process would discontinue and the individual who was anticipating an awakening would continue dreaming. But why dream about normal morning rituals and awake activities? We do not know the answer to this question.