[[WMG:Richard never went back in time.]]
Richard was simply driven crazy by his mad desire to have Elise, eventually becoming delusional. This explains why their romance was so ideal even though they barely knew each other. Robinson was a manifestation of Richard's subconscious which "knew" he couldn't really get Elise. Of course, Robinson failed and Richard [[ADateWithRosiePalms had sex with Elise]], causing him to snap out of it.
** The penny in his pocket snapped him back to reality, which gives some credibility to your theory. Had he really been back in time, what could a penny do to snap him back to the present?
*** Well, you'd have to explain how you'd found a penny with a date 70 years in the future in the first place, and wonder where you had found it, and where it came from, and why it was dated that way, and... eventually the reasoning would finally break down.
** It should be noted that the book strongly supports the idea of it being a delusion. Most of the book is written as the memoir of a man who was recently diagnosed with an inoperable brain tumor (that's what kills him in the end, not self-starvation as in the movie), and an epilogue by Richard's brother explains that the entire time-traveling experience was merely a series of hallucinations. The book ultimately leaves it up to readers to decide, but unlike the film, there is very little outside evidence to verify that it actually occurred, and the book relies heavily on the the device of the UnreliableNarrator. The old Elise never hands young Richard a watch or converses with him. The character of the Professor whom Richard meets a little-boy version of in the past was invented for the film. Richard does describe finding his signature in the old hotel record, but that could be part of his delusion, too.
*** There's some evidence in the book that it isn't a delusion. Richard reads in Elise's biography that she had a dramatic personality change after 1896 or 1897, after a period of ten months when she was in isolation. [[spoiler: Richard says while they're making love that he wants to make sure she's carrying their child, and they fuck a few times. Think about it: Elise begged Richard to not leave her. If she lost both the man she loved and their child (this was the 1890s. No doubt her mother and her manager both made her give up the child for adoption. Plus, keeping her in isolation would have made the news of her pregnancy to hide) then she would never have been the same after that point.]] Plus Richard brings back Elise's watch, and why would he have put down an incorrect inscription?
[[WMG:Robinson was also a time traveller]]
Based on Elise talking about how he "knows things" and "knew a lot of things before they happened." He'd been a fan of McKenna and went back to discover why she'd suddenly stopped acting, and figured that it was because of a man she'd met. So she became her manager -- another stable time loop? -- and tried to change history by preventing her from getting with anyone.