What happens when googlebot attempts to crawl old.html and new.html? Assuming old.html is already indexed by google, should new.html get indexed given the scenario above? What happens to pagerank for old.html?
old.html is the URL. new.html exists only as a filepath inside your server, and is not visible to clients unless you link to it somewhere.
This is a URL-to-filepath rewrite only. As far as visitors are concerned, there has been no change to your site, because all you have done is changed the filename, and then mapped the old URL to that new file. Since Web clients see only URLs and not filepaths inside the server, they see no change.