What you are saying is any currency not just the USD. The contract between two individuals is that they agree that this currency is what is perceived. After that its the banks that make these two people believe that this value of this currency is what is on the note ie.100 dollars. The banks are then backed by the governing country, in your case the US government, The USD is the faith of the American government and the economy which is backed by all the US banks which is back by the Federal Reserve.
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which prints money out of thin air, then the banks distribute to people so they can produce and consume more goods, ending up with where we are wasting electricity making bitcoin transactions :D