Each of the characters in Mrs. Dalloway seem to be having internal battles that differ from the others'. In each of the characters' minds, unique thoughts and opinions form; these evolve into fondness or dislike of others. For instance, Clarissa seems to simultaneously feel love and hatred for Peter, and vice versa. These two characters blame the other for their personalities and actions; however, like all the characters, these two are united in their fear of time.
In the introduction of the novel, Clarissa shares her self-perception. She senses that she is aging and often professes her fear with "time itself". She perceives her life as a "share" that is "sliced" with each  year she ages. She favors her youth and misses when she would "fill the room" with her young beauty She even relates the "exquisite suspense" of entering her drawing room to a diver plunging into the sea. However, after many years have gone by she sees her youth fade away and resorts to trying to regain her physical beauty by wearing dresses and throwing parties.
Like Clarissa, Peter also attempts to escape time. When he sits in Trafalgar Square, he attempts to regain his youth and is "utterly free". This occurs when he becomes distracted from his encounters and past with Clarissa. He puts his past-life aside and chases after a young woman to fell an "exquisite amusement". He feels young again, but his infatuation (and rather creepy) with the girl is short lived once the girl goes walks into her home. As a result, Peter is brought back into real-time and with his age, comes to realize that his infatuation with the girl and ultimately  his own youth is "smashed to atoms".
Clarissa and Peter also experience an encounter with time when they are together. During their conversation, they both have feelings towards each other but fail to make them external. Clarissa realizes that if she married Peter, she would have his "gaiety.. all day". Despite this, neither of the characters discuss their feelings but rather "challenge each other". When Peter finally begins to ask Clarissa about her marriage and happiness, Elizabeth interrupts their conversation. In the midst of the situation, Big Ben rings once again, reminding everyone that time is ticking.