Traditional money in the near future will lose its function universal means of payment and will be replaced by electronic money. The main difficulty rejection of coins and banknotes lies not in the level of technology and in human psychology.
In e-money has a number of advantages and disadvantages. Banks and other electronic payments, bills and small change than financial institutions are much cheaper and easier to operate. The development of e-commerce further accelerates the process of eliminating the traditional money.
In the future it could happen, I know digital currency or e-money will rule the world as it gives us the convenience to transact online, and it would be easy to trace our transaction but paper money will not be out in the circulation.
But even then, you're talking about e-money in a form controlled by the government. Our economy and banking system is largely electronic already, but the control of the supply is still down top-down, from the Federal Reserve and the banking institutions it oversees.
E-money is really going to be controlled and manipulated by the government. But about bitcoin if it is going to be implemented to a country they are going hard time to control it.
Because of its decentralization they are going to hard to control it.