Pretty much a distinction without a difference...money vs. currency. All currency is, by definition, debt; in the beginning it was a certificate issued by a bank entitling the holder to redeem in in gold, silver, or perhaps copper. Personal checks, as promissory notes to personal debt. are negotiable as currency, though denoted in Dollars and almost certainly discounted against face value.
The supply of U.S. government bonds is limited by many factors, the most obvious of which are the ability of buyers to pay for them, and U.S. law limiting sovereign debt. Using diamonds as an analogy, the possible supply of diamonds on the market is far smaller than the number of diamonds that could be put on the market,...De Beers among other near diamond monopolists controlled the diamond market till the '90s by flooding the market to drive down prices and kill off competitors or holding back on their supply to drive prices up.
The Fed and Treasury play the same basic game, controlling demand by controlling interest rates and functioning within the supply limits imposed on them by Congress. The fact that capital routinely flees to Treasuries when the global economy looks rocky, sometimes actually paying for that privilege with negative interest rates, shows that confidence extends far beyond the supposed benefits of cheap oil.
As to debt to GDP ratio, Japan's is now about 230% and their economy chugs along, actually their inflation rate is one of the lower ones among industrial states.
While the sovereign debt ratio doom scenario has been loudly trumpeted I'm not sure how serious it actually is, particularly since much of the U.S. debt is owed to ourselves.
The "backing" of the Dollar is basically the confidence in the U.S. economy and in U.S. governmental institutions...court systems, multi-branch government with regular transfer of power, not to mention civic institutions like a free press, an independent central bank, relatively free market economy.
In any case, you have not responded to my basic question; how does a two bit operation like BTC and the Lightening network replace any of this?
