I was right. Someone else not only thought of it but implemented something like it. See http://www.timebanks.co.uk/.
See also http://www.ithacahours.com/
I am being serious (except for the part about getting paid with clocks). Fiat currency is a promise to pay more fiat currency. Expressing value in time makes it concrete. Time is in limited supply for all of us. Our time and energy are all we have to contribute to society. Most of us contribute time to a job so we can have time for ourselves. We are all born with some time to invest/spend, unlike gold or paper currency.
The same way they do now. Command economies appoint a group of super smart people to determine everyone's wealth. Free market economies turn everyone loose and see how much they can grab. Most economies fall somewhere along that axis, with some free market and some price controls/tax credits/tarriffs for restraint. The standard (gold, fiat, time, etc.) doesn't determine how value is assigned to most goods and services, with the notable exception of goods used as currency (i.e. gold).
So, in fact, you've just changed the units we're working with.
Yes, it's just an alternate currency standard, not an alternate economy. The connection between currency standards and economies is complex. The gold standard expresses the value of everything in terms of gold. If a lot of gold is discovered everything costs more because there is more gold to be spent. Whoever discovered the gold can trade it for more goods and services. The time standard expresses the value of everything in time. We can't discover more time, but we can optimize and amplify our use of it with wisdom and technology. Automation and efficiency (any use of time that saves time) would be rewarded with a higher modifier. They already are in other currency standards, but a time standard would make the calculations more obvious and direct.
Then there's the quality of time. It may be worth five hours from me and 40,000 other fans to share a couple of hours observing a music or sports performer because we value the way that experience enhances the quality of our time.
Another alternative I've read about is an energy standard, where the value of everything is expressed in joules, calories, horsepower, or what have you. This suffers some of the same arbitrariness as precious metal standards, since some people happen to live on top of stuff that releases energy with ease. Pumping water puts you in debt while pumping oil makes you rich.
ThereAintNoSuchThingAsAfreeLunch?. If everyone using an energy standard currency had to pay for putting energy back into matter after they release it, there would be only negative wealth due to inefficiency of the conversion process. Luckily we live on a planet with solar powered carbon sequestration devices.
Petroleum is solar energy, just really old sunlight.