I'll repeat my comment which kind of triggered this topic.
Am I totally missing something or were they incredibly inconsistent and sloppy about people having to "bring your own oxygen" when inverted? I mean Pattinson is traveling backward in comparison to Washington, right? So, wouldn't that mean any time he is with Washington he would have to be inverted? Even if you ignore that, it seemed like they would use and not use oxygen randomly when we were supposed to know they were inverted. It just all seemed terribly sloppy to me. Also, is Pattinson the only person we see which is traveling backwards through time?
“Extinction is the rule. Survival is the exception.” -- Carl Sagan