I go with the theory (or "Rule") that you can't change the past but you can change the future. He couldn't save the waitress because she had already died in his linear timeline. He couldn't go back and change what had already happened to him. He can go forward, check out the future, return to...
The easiest explanation would be that he exchanges himself for whatever is present in the new location. Air is fairly invisible (depending on where you live) but we could have a stone statue if he landed inside a mountain.