O'Neill begins the play by describing Captain Bartlett's "cabin": the fact that O'Neill puts the word cabin in quotes implies that this is not a real cabin, and in fact the room has only been arranged to look like a ship's cabin in order to appease Nat's father, who is mad.
The Doctor's presence is an indication of reality. While Higgins is in the room, Nat emphasizes the facts of the case and distinguishes between the myth his father believes and the reality of the sunken ship.
It is really once the Doctor leaves that the reader begins to leave reality. Sue is described much like a ghost:
She is a tall, slender woman of twenty-five, with a pale, sad face framed in a mass of dark red hair. This hair furnishes the only touch of color about her. Her full lips are pale; the blue of her wistful wide eyes is fading into a twilight gray. Her voice is low and melancholy.
The description of Sue is somewhat eerie, and at this point the reader might wonder if something is amiss.
The ghostly descriptions in the book serve as markers that we are leaving reality and entering fantasy. Later in the play, as Nat is talking with Bartlett, O'Neill describes his mysterious expression: "a haunted, fascinated look in his eyes, which are fixed immovably on his father's". His "haunted" appearance is ghostlike, again moving the reader away from the world of reality.
Later, the "dense green glow" that floods the stage suggests that an otherworldly, supernatural scene is occurring. The light sets the scene for the figures who emerge next - the dead men who are decomposing and swaying to the rhythm of the sea. We are now fully in the realm of fantasy, and only return to reality with the reappearance of the Doctor.