In much of the modern world, currency is defined according to a "floating exchange rate." To the best of my knowledge, such an innovation was unknown during the time of the prophet, where the economy directly revolved around gold and silver.
Whereas before, while under the gold standard, "a dollar" was defined by a particular weight of gold. Regardless of how the currency changed through time, or how the value of gold fluctuated in the economy at large, such a fixed currency maintained a solid value of exchange. That dollar would always be worth such-and-such amount of gold, period.
A floating currency, on the other hand, does not have such a guarantee. "A dollar" under a floating exchange is effectively only ever worth a dollar, whatever that may mean. Combined with the effects of inflation, this typically results in the dollar having less and less buying power with every passing year.
In other words, a dollar's worth of gold in 2012 would NOT be the same as a dollar's worth of gold in 2002.
This is very relevant when providing a loan; if the value of a dollar goes down as time goes on, the debtor has a strong motivation to not pay back an interest-free loan immediately, especially if the period of the loan is lengthy or undefined. The longer one waits to return the money, the cheaper it effectively becomes to pay back.
This is not good for the lender, who typically gets less value (despite the same dollar amount) in return than he had originally loaned out. In the non-Muslim world, this risk is often handled by charging interest on any loan; this not only offsets the effects of inflation (as well as providing a profit), but provides debtors with a motivation to pay back a loan as soon as possible so as not to accrue additional debt. Such an option is, of course, not appropriate in Islam as God has explicitly "permitted trade and has forbidden interest."
It occurs to me that, with an interest-free loan, one could effectively mitigate this problem by providing a loan of "effective value" rather than of a particular dollar amount. For example, instead of loaning somebody $50, one could loan them "the cash equivalent of .915g of gold" (which as of the time of this post works out to roughly $50). That way, when the loan is repaid, the exact dollar amount returned would be based on whatever the price of gold is at that time, rather than a straight dollar-for-dollar return.
I realize that this transaction could be performed without stepping on any Islamic laws by simply loaning out the gold directly; arguably even by loaning out the gold and immediately buying it back for market price (and reversing the transaction when the debt is repaid), which would functionally be the same as the above proposal. Of course, most people typically don't deal with gold directly anymore (at least not in Canada), which makes this sort of transaction awkward at best.
So the question lies thus: Would performing such an "equivalent value" transaction be valid according to Islamic law? As Islamic finance in general has received significant study, especially in the wake of the interest-based economic system so favored by the modern world, I would be particularly interested in any scholarly opinions on the matter.