Spoilers ahead, don't read until much later in the game, same deal as all the rest of the Bioshock Infinite questions.
Later on in the game, in a sort of side-exploration destination,
you will find a tear in the house of Albert Fink, as you head back to Comstock house after finding the third tear. From it, you will hear a modern song ("Girls Just Want to have Fun", of all things). Jerimiah Fink congratulates his brother for discovering such rifts in a Voxophone, saying "Dear brother, these holes in the thin air continue to pay dividends. I know not which musician you borrow your notes from, but if he has half the genius of the biologist I now observe, well...then you are to be the Mozart of Columbia." This implies that both of them had access to the tears.
After digging through the Voxophone transcripts, I've found even more answers on the significance of this.
A voxophone found in Finkton Proper or in the Good Time Club recorded by Jeremiah Fink:
"I had thought you a fool, dear brother. When you told me that you heard wonderful music trumpetting from holes in the thin air. I began to doubt your mental integrity. But not only have you made your fortune from these doodads, you have lit the path for me as well."
That voxophone doesn't have much significance until later, in the factory:
"These holes have shown me yet another wonder, though I've yet to see the application for it. They illuminate a merger of machine and man that is somehow the lesser, yet the greater, of both parties. The process seems to be irreversible. Perhaps, though, Comstock will have some need of this kind of thing to keep watch in that tower of his."
This likely reveals the origin of
the Handymen, Firemen, and possibly the Motorized Patriots.
The final voxophone loses significance, given these others:
"Dear brother, these holes in the thin air continue to pay dividends. I know not which musician you borrow your notes from, but if he has half the genius of the biologist I now observe, well...then you are to be the Mozart of Columbia."
The real significance of the room...
...lies in the actual tear in the room, since before this point, it's not entirely clear what exactly Fink means by "holes in the thin air"