How long is now?

Stephen King wrote a book that became a TV show called “The Langoliers” http://www.imdb.com/title/tt0112040/ . These many toothed things eat up reality for a while after now is done and are seen by a group of airplane passengers when they pass through some type of time warp after leaving LAX. The Twilight Zone TV show also had an episode with a similar theme called “A matter of Minutes” The Twilight Zone TV show also had an episode with a similar theme called “A Matter of Minutes" http://www.tv.com/the-twilight-zone-1985/a-matter-of-minutes/episode/75277/recap.html .

While interesting stories, one wonders what modern physics has to say about the length of the current instant. Is now infinitely small or does it have some duration. The shortest time know is one tick of the Planck clock (related to the Planck constant) which is very short indeed. However, relativity defines time as a dimension and all other dimensions have a finite length. It would seem to me that “now” cannot be infinitely small as if so time would not exist. If we consider time as the surface of an expanding balloon then one can ask, how thick is the surface of the balloon? Is the inside of the balloon empty or does the past always exist but is just not accessible to our conscious self?

Food for thought.