With current technology, I don't think it is possible without causing great harm. The atomic bomb dropped on Japan during WWII burned some shadows into sidewalks, but this was due mostly to bodies blocking out the excessive heat.
The way that a camera film works has to do with chemical reactions that react to light. With digital cameras, it has to do with light reactions within a sensor being recorded onto a storage device. Neither of these could be exposed for long periods of time without distortion, especially with fast moving subjects.
This is not to say that it may not happen in the future, but with our current amount of technology, photographs are the way to go.