Do pets dream?  If you are a dog or cat owner, chances are you have wondered if your pets dream. If you've watched your pet sleep, you've seen him quiver, twitch, run in place, swat at phantoms, or even growl or snap during nightmares.  You probably already guessed it; the answer is yes. Like us, our companion animals dream while sleeping.      How Do We Know This? There are two main types of sleep: rapid eye movement (REM) sleep and slow-wave sleep (SWS). Both slow-wave sleep and REM sleep are very similar in pets and humans. During this time, the brain processes information learned during the day. The REM or rapid eye movement stage of sleep refers to the...