"Article I, Section 10, Clause 1: No State shall enter into any Treaty, Alliance, or Confederation; grant Letters of Marque and Reprisal; coin Money; emit Bills of Credit; make any Thing but gold and silver Coin a Tender in Payment of Debts [emphases added]; pass any Bill of Attainder, ex post facto Law, or Law impairing the Obligation of Contracts, or grant any Title of Nobility."
Note that Constitution-ignoring FDR made the unconstitutional (imo) executive order to confiscate gold.
Executive Order 6102
You could still have electronic transactions, IMO, but they would simply all have to be backed by silver and/or gold.