As writers, we can have that same feeling. I came upon this by accident as I was trying to reach my word count for the day. I was quite tired as I'd only gotten about 4 hours of sleep the night before due to homework. I sat there, typing away on my favorite writing machine, the Alphasmart Neo (a tool I think every writer should have in their belt), and I started to doze off. But my writer's intuition took over and I kept going. I typed with my eyes closed -- thank you high school keyboarding class for teaching me to type without looking -- and truly connected with my story. I could see the characters clearly, almost hear their dialogue. I entered the story and left the world around me. I instinctively started rocking back and forth like a pianist during an emotional piece. It was an incredible experience that I have repeated many times since.
Now granted, not everyone can do this (if you can't type without looking and I don't know how well it would work for writing by hand), but I'd suggest if you can that you give it a try. I can see now why composers or other musicians do it. As an artist, you feel a part of your work, the world around you fades and you're in your world. It is a peaceful feeling, a feeling I love repeating and one that I had to share! Post how you feel after trying it below.