Apparently that is what BitCoin want to do. The big question is why.
What BitCoin is — near as I can make out — is a token that you earn by lending your computer’s processing power to some function — I think processing transactions. As you do this you earn more tokens and the idea is that you can exchange those tokens for stuff on the Internet.
Is this crazy? It turns out that it isn’t necessarily crazy. BitCoin is structured to have a fixed supply of tokens and so at some point it will become harder to earn them through your computer. But the quantity theory of money will hold and so the rate of exchange of computer power to goods earned should stay constant in equilibrium (unless something happens to velocity). As Eugene Fama pointed out years ago what you need to have money take off is some scarcity of supply. The people behind BitCoin have thought through that.
So the next question is: what function will it serve? The return in terms of goods acquired for processing power given is something that can be priced now; in existing currency. There is no reason to suppose that BitCoin will change this rate of exchange fundamentally. It may unlock some computer power (liquifying it) but it could do that without launching a new currency. I can’t see the market here.