When we sleep, we actually do it in repeating cycles of going deeper into sleep and then coming out of that deep sleep. When this cycle starts, your brain releases chemicals that make you sleepy and stop you from moving around so it can do repairs, and when the cycle ends your body flushes those chemicals out so you can wake up feeling refreshed. If you wake up before your body can complete a full cycle and wash out all those sleep chemicals you’ll feel worse than if you hadn’t slept at all.
You can actually have a similar problem if you get too much sleep, because those sleep chemicals start piling up so much your body can’t effectively get rid of them.
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