What was the parting conversation between Elrond and Arwen?

Question

In The Return of the King, the chapter "Many Partings", it says:

None saw her lasting meeting with Elrond her father, for they went up into the hills and there spoke long together, and bitter was their parting that should endure beyond the ends of the world.

What was this conversation, and why was it bitter? Did they fall out, perhaps because Elrond would rather Arwen go with him to the Undying lands (note that I might be encouraged to think like this because in the films Elrond doesn't seem too impressed with her choice, but based on other questions on this site that might not have been entirely accurate), or by "bitter" does Tolkien mean that it was sad because they wouldn't see each other ever again?

Answer 1

When Arwen chose to marry Aragorn, she also chose mortality. Arwen would die and her spirit would pass out of the world -- where to, no one knew for sure. Elrond was committed to Elvish immortality and would live in the world (in Valinor to be sure, but Valinor was still part of the world) until it ended. He faces a very long life without her, and she faced a short life and then death.

And yes, "bitter" can mean "tragic" or "painful".