A: There are several things that could be happening with your newborn. We really do not know whether or not babies have dreams but they do have sleep/wake cycles with the phases of sleep just like other people, so dreams are possible. Newborns also have a variety of involuntary movements because their nervous system is still figuring out the best way to meet their needs. It is possible for newborns to have seizures although this is uncommon. The best place to start would be to see if you can capture what is happening on your cell phone and show it to your child's doctor so they can help you figure out if you should be worried or not and if more workup (an EEG - looking at the brain waves) is needed.