No, but just imagine the genius being really into classical music, and they hit shuffle, so then when the two characters are transported, they see tall, snow-covered houses and people walking around in long dresses and suits. The one who didn't make the time machine looks around the German atmosphere, saying, "Uh... What song did you select?" and the other just whispers, their face pale and their eyes wide, "Für Elise."
The Beatles shaped not only music but also an entire generation. People mimicked all that they did, including haircuts, clothing, and outlook. Their style and innovative music set the standard for all musicians to follow.