I wouldn't read this if you haven't seen the film.
The main initial reaction to the premise 'Another Earth' is "the physics doesn't make sense". But that comment, in my opinion, misses the point of the film: it's not so much a science fiction film as a character study, and a philosophical thought experiment.
The question is inherent in the title of the film: What would you do if there was an identical earth in the sky, and along with it, another you?
The film adresses this question from the point of view of Rhoda, a young woman who is driving drunk on the night of first contact with Earth 2, and is involved in an accident. The mother and her son die, the father recovers from a coma. 4 years later Rhoda is released from prison and tries to confront her guilt by befriending John, the man whose life she ruined, as she is not able to apologise to him. The existence of Earth 2 adds another element to this familiar storyline: Rhoda has an escape route, by winning an essay contest to win a trip to Earth 2. As the mirroring of the two worlds might have ended at first contact, there is a chance the Rhoda on Earth 2 was not responsible for the deaths of two people.
So there are two Rhodas: one with the unbearable guilt of her crime, the other maybe free to pursue her scientific dreams.
The first question this raises relates to identity. Is the me on the other Earth the same as the me on this Earth? Biologically, they must be. The radio contact with the other Earth also suggests that the versions of people on Earth 2 have the same memories and experiences. But Rhoda is perhaps unique in this: the experiences she had over the 4 years between initial contact and the present have formed her identity. Without the singular moment of the accident, she would be a completely different person.
But then what does Rhoda stand to gain by visiting the other Earth? Even if she discovers that Rhoda 2 did not cause an accident, Rhoda 1 must still bear the responsibility of her actions on Earth 1. Earth 2 can only be a temporary escape route to her guilt, it is not a blank slate. I think Rhoda discovers over the course of the film that there are no blank slates, and she cannot hope to forgive herself by visiting Earth 2. To do this she must accept her crime and confess her guilt to John, which she does near the end of the film. She then gives him her ticket, so he can find out whether his family are still alive on the other Earth. She realises that he needs it more than she does.
The final twist comes at the very end of the film, four months after John has departed for Earth 2. Rhoda turns around and sees a slightly different looking Rhoda 2, on Earth 1. So what does this mean? My initial reaction was, the accident did happen on Earth 2, but this means something must have happened on Earth 2 differently, as Rhoda did not give her ticket to John, either because he died in the crash, never met Rhoda, or Rhoda confessed to him earlier. This could leave the rather bleak conclusion of two unhappy, lonely Johns on Earth 2. However there are some other possibilities:
(i) The accident didn't happen on Earth 2, and Rhoda won the trip for some other reason, maybe her interest in astronomy and her academic achievements. This would explain why Rhoda 2 looked slightly different, but it leaves John to find his family intact, which would create an awkward situation with John 2.
(ii) John reaches Earth 2 to be reunited with his family, and gives Rhoda 2 his return ticket to Earth 1, because he wants to send some sort of message to Rhoda. I'm not sure about this one but it seems to be the most optimistic.
Any other theories?
I'm personally inclined to think my first reaction was correct, because Rhoda's position on the flight was so connected to the accident. That's not to say the accident may not have occurred differently on Earth 2, John could still find his family. That's as optimistic a conclusion as I can think of!
