How does the body wake itself up in the morning?
Excluding environmental stimuli (e.g., light), the transition from sleep to wakefulness in the morning is due to two physiological process.
One is the circadian rhythm, which promotes wake during the daytime and promotes sleep at night. The circadian drive for wakefulness typically begins to increase a couple of hours before regular awakening. This includes telling the pineal gland to stop producing the sleep-promoting hormone melatonin in preparation for awakening.
The other factor is sleep homeostatic pressure. Across the night, sleep pressure dissipates due to the clearance of sleep-promoting substances from the brain. This means there is less and less drive to remain asleep.
Together, these two factors promote the onset of wakefulness in the morning.
The brain is not able to immediately transition from sleep to fully alert wakefulness. In the first minutes of awakening, people typically feel very groggy and their cognitive performance is exceptionally poor. This phenomenon is referred to as sleep inertia.
As long as you only press “snooze”, your body will still chemically be in its sleeping state. So, if you fall right back to sleep between the snoozing, then it is not likely to stop sleep inertia when you get up later.
Normally, it takes around 1-2 h to fully dissipate sleep inertia. The reason sleep inertia exists is not known, but it has been hypothesized that different parts of the brain may take different amounts of time to transition from sleep to wakefulness. Certainly the opposite is true: the thalamus falls asleep several minutes before the cortex.
Acute effects of caffeine
Caffeine acts as a competitive antagonist of adenosine, which is one of the sleep-regulatory substances that accumulates in the brain during wakefulness. In effect, it makes people temporarily less sensitive to (or “masks”) the sleep-promoting effects of the adenosine. This can help people to stay awake or make the transition from sleep to wakefulness more rapid.
Taking caffeine has been shown to reduce the effects of sleep inertia following naps. Unfortunately, it is more difficult to achieve this in the morning, since it takes ~1 h for ingested caffeine to reach peak levels in the blood, by which time the worst of sleep inertia has already passed.
Chronic effects of caffeine
The average half-life for caffeine is approximately 7 hours. However, caffeine pharmacokinetics and caffeine sensitivity vary enormously between individuals. For example, oral contraceptives have been found to approximately double the half-life in some individuals. Some individuals will feel a large effect from a morning coffee while others will not.
On average, there is some effect of morning caffeine intake on sleep that night. This study found that a 100mg dose of caffeine (about a small cup of coffee) at 7:10am resulted in lighter sleep that night on going to bed at 11:00pm.
Long-term caffeine use has been shown to increase the number of adenosine receptors in the brain and increase their sensitivity. This means that more caffeine is required to elicit the same response. It also means that the brain becomes progressively more sensitive to the regular levels of adenosine. For somebody who suddenly stops drinking caffeine, this can result in caffeine withdrawl and higher levels of sleepiness (and presumably greater difficulty transitioning from sleep to wakefulness) than prior to the caffeine use.