A Wrinkle In Time
Philippa Pearce was extremely interested in the concept of wrinkles in time, popularized by both Ursula le Guin in her novel of the same name, and also later by Stephen Hawking. She believed that it was possible to find certain gaps in time where one could slip back into an age gone by, and this is what her hero Tom Long did in the novel; at least, that is what we at first are led to believe, although by the end of the novel it seems that he may be entering someone else's dreams at night and living them.
Tom is able to bridge the gap between the ghost world and the real world by going into the garden; Hatty is not a ghost, she is a living little girl, and it is Tom who is joining her in her time not the other way around. However, there are ghost characters in the novel and this is what makes it difficult to tell where time travel ends and a ghost story begins.
Belief in Magic
It does not occur to Tom for a moment that he is dreaming his experiences in the garden. He knows that he is opening the front door onto Victorian times. He is so confident in the complete possibility of this that he writes to his brother, Peter, and recounts his adventures with the same air of normalcy that he would if he was recounting a day at the beach or an afternoon in the movie theater. Peter, for his part, believes what Tom tells him without question and does not think for a second that his brother is just making things up.
Mrs Bartholomew also knows that Tom is telling the truth because he has been included in her dreams each night, which would really not be possible without the help of magic because the two had never met before.
The Child Inside
Mrs Bartholomew wants Tom to know that not only did she used to be Hatty, but she still is. Although on the outside she is an elderly lady, on the inside she is the same person he has come to know. Tom, for his part, realizes this too. When he leaves he hugs her much like children hug each other, not like a child hugging a much older person. He also realizes that she has not changed on the inside despite her aged appearance on the outside.