if the Federal Reserve so chooses your currency could have half the purchasing power tomorrow that it has today. Admittedly that is very unlikely, but no one has that kind of influence over the price of gold, because it can't simply be created on demand.
This, right here, is the usual logical error that gold bugs typically make. While the physical amount of gold in existence can't readily be changed (we'll neglect the small amount of 'new' gold added to the economy through mining), the supply of gold - reserves available for sale - and the overall demand for gold are very much vulnerable to both general volatility and deliberate manipulation. Changes in supply and demand in turn significantly shift the perceived value of gold, leading to swings in its market price and in its effective purchasing power.
This has been illustrated quite graphically over the last few years. Fifteen years ago, gold was trading below $300 US per ounce. Ten years ago, it was pushing $400. Five years ago, it was around $900. A year ago, it was nudging $1800. Now it has slid back down to $1300, and shows no sign of slowing its decline. There was a similar spike around 1980. There wasn't a sudden reduction in the amount of gold in the world over the last decade or so, but for some reason the price of an ounce increased six-fold (before plummeting again). Either U.S. dollars really did lose five-sixths of their value between 1998 and 2012 - a conclusion not supported by their ability to buy pretty much any good, commodity, or foreign currency - or the 'intrinsic' value of gold generally accounts for only a relatively small portion of its market price, and the majority of its 'value' is just as imaginary as that of any fiat currency.
A currency which is backed by something represents a liability against the issuer to provide a fixed amount of that something on demand in exchange for each unit of the currency. The United States used to have this form of paper currency; in going off the gold standard the U.S. government repudiated its very real debts as the currency's issuer.
The price of gold under the various iterations of the gold standard was stable not because of gold's intrinsic value, but because the currency (or currencies) pegged to it had a perceived stable value. In a very real and practical sense, the strength of the U.S. dollar was backing the price of gold for much of the 20th century, and not the other way around.