Children's stories are full of characters who move back and forth between different realms of reality. Take Cinderella, for example. You know the story of four mice pulling a pumpkin, whisking Cinderella away from poverty into an exalted moment of acceptance and glory. In one transforming moment, the servant is transformed into the queen of the ball. Suddenly, everyone can see Cinderella's beauty and worth. Or take the story of The Lion King, where Simba, a young lion cub, makes a series of selfish choices that lead to his father's death. He has to flee. After a long exile, he is challenged to return. While wrestling with the decision, he sees in a pond his own image, mysteriously transfigured into the image of his deceased father. In that moment, he sees the purpose of his life and discovers the courage to return. Or take Beauty and the Beast, where the beast is transformed by love back into a prince.
In these stories, reality is seen in a whole new way. As for the disciples, during these very mysterious moments on the mountain, the one they had followed up the mountain was transfigured before them.