In some states, it's illegal for an adult not to have ID in public, but in California there's no such law and we can walk (but not drive) without our license or DMV ID in public. Correct me if I'm wrong, but it seems that police in California can't demand to see your ID or arrest you if you don't have one or refuse to show it.
But say a police officer stops you on the street and asks who you are. If you refuse to say anything at all, besides "Officer, am I under arrest, because I'd like to go now?" Or is it the law in California that you must identify yourself to law enforcement upon request, or else risk being arrested or cited and fined?
Here police have no probable cause to arrest, just a suspicion. And you're not carrying guns or contraband, so a patdown would turn up nothing.