I am exploring this Bitcoin thing and yesterday installed the Bitcoin-Qt. The first thing that I noted, is that the after syncing with the network that took me 12 hours, the database grew to 13GB. I know that these are all the blocks in a chain from the beginning of time. My question is what is the sense and the theoretical practicality behind this approach? Imagine if all the world will start to use bitcoins, the blockchain will grow to terabytes and will multiply exponentially on a daily basis. Imagine if USA will embrace Bitcoin as its official currency, the size of blockchain will grow few Petabytes daily. The bottom line is that at these sizes it will become impossible to validate transactions and even simply store or use the blockchain.
My question is if I am missing something here, because I don't see any long term and general usage capabilities here?