The most likely interpretations...

So going with the assumption that none of the Sci-Fi elements and explanations in the film are actually real but just for context, this leaves you with two most likely interpretations.

1. It's all a child's imagination in that moment of trying to decide between two paths in his life back at the train station or more correctly 3 paths but that requires accepting the fact that in that span of 10 seconds or how ever long it was he was able to foresee his future.

or

2. It's all told from the viewpoint of the old man and it shows instead the choices and outcomes that would have happened had he opted for different decisions thereby taking different paths in life. Judging by everything that was shown in the film this one to me is the one that makes the most sense. Also the fact that we are introduced into the film from his viewpoint. To me it's another take on the faulty narrator theme. Real memories mixed with imaginations, vivid dreams and lucid thoughts. I think the focus is more on regrets and what could have been when faced with death and old age and not taking chances in life. Regretting more those things you didn't do then the ones you did. The ending could be then interpreted two ways: The old man makes his decision and mentally travels back to his time with Anna with his last dying breath or if you believe the science "The Big Crunch" really does happen and he gets to travel backwards to that point in time when he and Anna are both kids and perhaps start over from there.

3. Another possible interpretation is the only real timeline and real relationship was that which he had with the Asian girl and she had him committed to a psyche ward after trying to commit suicide. This would explain the scenes with the therapist and why that relationship wasn't explored further. Also, it's the only one in which he doesn't try to change the outcome on purpose. It would also explain why he lived to such an old age being wealthy enough to be afforded good care. Then again the old man and the future world could be imaginations or lucid dreams being conjured up by his younger self while in the mental hospital.

4. A combination of 2 and 3 maybe? Assuming he actually got to live to old age and the future world is real.

To me the science is not real and it comes down to the imagination of a child or the regrets of an old man.

But in either case, the real message is choose "Love" follow your heart, find your passion!

~What if this is as good as it gets?!~