Only fools rush in. But why not? Elvis did:
Great song, right? This is an arrangement of a much older song by Jean Paul Martini (1741-1816). Here is a performance by Elisabeth Schwarzkopf of the original:
The first couple of notes of the melody are a bit different, but the rest is the same.
I put this up because I find it interesting that as recently as 1962, when this was released as the 'B' side of an Elvis Presley single, pop music and classical music were still within shouting distance. There are occasional examples of classical music "crossing over" into popular territory, but they are usually sparked by association with a film, such as the second movement of Mozart's Piano Concerto No. 21, K 467 and the 1967 film Elvira Madigan, or even an advertising campaign such as the British Airways use of a duet from Delibes' Lakme. But since the Beatles and all the other profound changes in pop music, pieces of classical music are less likely to find their way into popular culture. Can anyone imagine Lady Gaga doing a cover of a classical tune?
The aesthetic gulf between classical music and popular music has become immense. What are the elements that divide them? First off, we have to distinguish between avant-garde music and traditional classical music as there too is another aesthetic gulf. Traditional classical music which probably includes Stravinsky and Shostakovich, but not John Cage or Steve Reich, has certain features such as voice-leading and harmonic structure, that are deeply rooted in past music. John Cage, Steve Reich and also current pop music no longer share these fundamental characteristics. I haven't worked out the details, but I suspect that the Beatles may have started the process in pop music. While Elvis could quite easily accommodate an old Italian song in his style, the Beatles (let along the Rolling Stones or the Grateful Dead) could not. Just as the only place for a bit of traditional classical music in a piece of John Cage, would be in the form of an ironic quotation.
Now the interesting thing is that some current composers like Osvaldo Golijov have returned to a more traditional aesthetic which includes tonal harmony. His Tenebrae for string quartet is loosely related to some music by Francois Couperin, for instance.
So it seems that in classical music it is now possible to re-connect with the great tradition. What are the odds in popular music? Is the industrialization of pop music an irrevocable process? I don't have the answer and I'm not even sure if I stated the question clearly.