[Clare:] I'm at a loss because I am in love with a man who is standing before me with no memories of me at all. [...] I'm flooded with years of knowledge of Henry, while he's looking at me, perplexed and fearful. (1.1.6.)
In the universe of Clare's life, Henry already plays a big role. His presence has changed her life – he has become part of who she is. In the reality of Henry's present life, however, she's a complete stranger to him.
[Henry to Clare:] "Could we back up? Could we pretend that this is a normal first date between two normal people?" (1.1.50)
Henry seems to be insecure about the fact that Clare knows more about him than he knows yet about himself. That's why he asks her to level the playing field and pretend that they don't know each other.
[Clare:] I stand there, holding the lipstick. I feel a little sick. I wonder what she looks like, what her name is. I wonder how long they've been going out. […] Well, whoever you are, I'm here now. You may be Henry's past, but I'm his future. (1.1.120)
Clare struggles at first with the reality that in Henry's present he is or has been with another woman. Yet she knows that Henry will choose her for his future, which reassures her that this woman poses no real danger to her. That woman now inhabits Henry's past.
[Henry to Clare:] "I don't usually tell myself stuff ahead of time unless it's huge, life-threatening, you know? I'm trying to live like a normal person, you know." (1.1.120)
Henry doesn't like to interfere with the lives of his other selves. He wants all of them to experience life as a normal person, which means not knowing what the future brings.
[Henry:] I remember. I remember. I woke up in the morning and it was all a wonderful dream. Mom laughed and said that time travel sounded fun, and she wanted to try it too. (1.2.78)
The first time Henry time traveled at the age of five, he believed it all to be a wonderful dream the next morning, not reality, which allowed him to enjoy it.
[Henry:] "Maybe [fairytales] are real. Or some little thing in them is real and then people just added to it, you know?" (1.4.194)
His experience of being a time traveler has made Henry more open to the possibilities of other realities out there that most people just consider fiction, such as fairytales.
[Clare:] […] just recently it's started to dawn on me that most girls don't have a Henry. (1.4.217)
Clare realizes that the reality she's living in might not be the reality her peers live in as well. It finally dawns on her that her relationship with Henry has changed her life and has made her different from her friends.
[Henry:] "The choices we're working with are a block universe, where past, present and future all coexist simultaneously and everything has already happened; […] a Christian universe in which God made everything and it's all here for a purpose but we have free will anyway. […] And what do you vote for?" [Clare:] "I don't know. I want God. Is that okay?" (1.4.261-264)
Although Clare is not sure which of the two possibilities is the truth, she chooses to believe in God. What advantages might a Christian universe have for her thirteen-year-old self?
[Gomez to Clare:] "And then he – vanished, and I was standing there, and I just… had to. Believe." (1.8.194)
Like most people faced with Henry's condition, Gomez has to first see Henry disappear before he can believe the man's a time traveler. So it seems that most people's sense of what's real or not real depends on if they can see it or not. What might someone not have to see to believe?
[Clare to Henry:] "I wouldn't want you to miss it. […] All the things that happened. When I was a kid. I mean, so far they have only halfway happened, because you aren't there yet. So when they happen to you, then it's real." (1.8.458)
Although Clare remembers a wealth of real experiences from her childhood with Henry, she doesn't feel like they're real before he has experienced them in his present reality as well.
[Clare:] […] Henry appears, doing up his cuff links. He's wet, dirty, and unshaven. He looks about forty. But he's here, and he gives me a triumphant smile as he walks through the doors of the church and down the aisle. (1.14.46)
Only Clare knows that the Henry who is walking down the aisle to marry her is not present Henry, but an older version of him. It's interesting because the older version of Henry is the man that Clare fell in love with in the first place, when she was a child.