Nathan spoke. "Uh Remus? What exactly would a paradox entail?"
"Usually some disorientation and a very stiff headache. Nothing too awful and catastrophic generally."
"No high energy explosions?"
Remus chuckled. "No, but I can see where you would be concerned. I assume you're thinking of the rules that matter can only occupy one place at a time, correct?"
"Yeah, that's generally how that works."
"Yes, generally. Magic, however, has a built in 'safety valve' that prevents that sort of thing. You see, if Harry or Hermione were to have headed down the beach and shook hands with their future selves, their magic would have established a minute field that would have prevented them from actually touching. The backlash would probably have thrown them apart and stunned them for a while, but to no lasting harm."
"Oh. Well that's good then. Wonder how somebody discovered that!"
"Indeed, wizard-kind are not known for careful and well considered actions."