What are the implications of this line for the reader, "For every atom belonging to me as good belongs to you"?

There are a lot of ways to understand this line. I guess the question that naturally comes up is, how? How can "every atom" be the same?

The line could be suggesting that:

1) We are the same in that we each are participants in the democratic spirit of the U.S.

2) We are the same in that we are each living, feeling beings, poetically engaged with the world.

3) We are the same in that we are each poets, writing through our lives our own poems.

To me, the line represents nothing less than a stupendous reinvention poetry itself. By positing that poet and reader are the same -- no matter how you understand it -- Whitman throws into doubt the roles of reader and writer. If we are the same, then, somehow, the reader is as much responsible for the poem as the writer. The idea is that the real poem is the meaning created when the "you" and "me" of the line meet in the lines Whitman has written. In this way, the reader actually becomes a kind of author!