People often make a distinction between asset backed currency, (where each dollar is a claim to some physical good, such as the gold standard), and fiat currency (where each dollar is simply a government printed piece of paper).
The distinction that people generally draw is that fiat currency can be produced in arbitrarily large amounts (i.e. printing tons of paper money), while asset backed currencies limit the sovereign's wealth to his stocks of the asset in question (unless he wants to dilute the currency, by reducing the amount of gold in each coin if it's literally a commodity currency, or reducing the amount of gold that each piece of paper is claim to for an asset backed currency).
In reality, all these arrangements are arbitrary - money works because people believe other people will accept it, and the gold and paper and whatnot are just coordination mechanisms to help us agree on what to accept.
The idea that the key distinction is the ability to print more money obscures a second aspect of asset-backed currencies that was less prominent historically but is actually more relevant today - the fact that people are accepting a notional instrument as a claim to some other less convenient instrument that they would say that they value more.
With gold, it was inconvenient to actually carry it around, so people were happy to carry around convenient pieces of paper that were claims to a fixed amount of gold, as long as everybody believed that the paper system was always going to work and be accepted. Eventually people got sufficiently used to the paper that the fiction of convertability was unnecessary. The Supreme Court took it away, and people barely noticed.
The parallel today is that we have a 'paper standard'.
The real money in today's society is ones and zeros in bank accounts, in SWIFT computers, and in Federal Reserve bank deposits.
Just like the gold standard before it, people are happy to transact in this fully abstract money because each digital dollar is a notional claim to a piece of paper printed by the US treasury. You can go to the bank and redeem your digital dollars for paper dollars whenever you want.
In the modern world, the digital dollar is vastly more convenient than the paper dollar, just as the paper dollar was more convenient than the gold bar. And while people do still withdraw dollars for some purposes, it's becoming increasingly rare. Can you imagine someone actually taking all their wealth out of the bank and leaving it in dollars under the mattress? The vast majority of the cash holdings for the vast majority of people are already in digital form.
At the moment though, people still like the fiction that they might convert all their digital dollars to paper dollars. If things were entirely on computers, what would happen if the computers crashed?
In reality, that ship sailed decades ago. If the computers crashed, the rich would be left with their houses and that's about it. But most people don't worry about this, just like most people in the 90s in America didn't worry about the government printing zillions of paper dollars, even though people in 1800 would have viewed this insouciance as insane naivete.
It seems likely that eventually the fig leaf of paper convertability will be removed. Young people already would be comfortable with this - they barely use cash, it's all credit cards. Eventually, the anachronism of paper money will be removed altogether.
When that happens, it will raise a number of intriguing economic possibilities.
The biggest of these is that there will no longer be any binding zero lower bound on interest rates. The biggest obstacle to negative interest rates is that people have the option of just hanging onto their dollars and earning zero. When the dollars are only in the bank, that's trivial to change. Every dollar in your account is depreciating at a continuously compounded interest rate equal to 3% per year.
If you could do that, the 2008 recession might have been a damn lot shorter. You don't want to spend and are trying to deleverage and hoard liquid assets? Does your answer change if those liquid assets are earning you -8% a year? Hell, even a Porsche doesn't depreciate much more than that - why not just enjoy the car instead? Hey presto, spending is back.
Don't get me wrong, there will likely be a huge psychological obstacle to negative interest rates. People will view it as the government or the bank taking their money (in a way that they don't view it as the government giving them money with positive interest rates). If the fed wants to do it, there's not much choice though - where are you going to take your money instead when there's no paper to redeem it for? If probably would fuel asset inflation, as people rush to put their assets into anything that will hold its value.
In addition, the difference between fiscal and monetary policy becomes much harder for the average person to see. If the government is taking out 1% per month from your account, does it really matter whether that amount is getting transferred to the government's account (under a tax) or destroyed altogether (under a negative interest rate)?
The eventual disappearance of paper money seems like it will only be forestalled by civilisational collapse or a massive change of governing arrangements. When the first government has the balls to announce negative nominal interest rates is another question.
I suspect that you and I may well live to see this reality.