Outside the Middle East, declining global energy prices could have equally destabilizing effects. Russia rode its way out of the post-Soviet doldrums on a wave of rising revenues from oil and natural gas sales. Today, roughly half the country’s 83 regions could not stay afloat without federal aid, which President Vladimir V. Putin has been able to supply generously thanks to huge oil profits.

As in the gulf monarchies, such transfers have allowed the government to neutralize political opposition. But discontent is still on the rise, as evidenced by the occasional protests that have shaken Moscow since 2011. Even a temporary drop in oil prices would constrain Mr. Putin’s ability to pay off his enemies: experts at the Russian School of Economics predict that the country’s oil wealth fund, a stash of petrodollars reserved for times of need, would be depleted if prices fell to $60 a barrel for just one year.

If he’s unable to buy loyalty through patronage, Mr. Putin could turn to more pernicious methods like bullying neighbors and fanning the flames of nationalism. With outstanding border disputes and age-old rivals circling Russian territory, another conflict along the lines of the 2008 war against Georgia is not out of the question.

In the long run, of course, America would welcome a Russia that is more beholden to its people’s wishes than to fluctuations in energy markets. Washington should be under no illusions, however, that the transition to that point will be either smooth or linear, and it should prepare for turbulence along the way.

Many will argue that an energy-independent America could simply retreat into isolationism during such a period of turbulence. But American engagement abroad has never been purely about securing access to energy. The United States has benefited as much as any other country from the free exchange of goods, the safety of global sea lanes, the spread of democracy and the great-power stability that have characterized the entire post-World War II era. None of this could exist without the steadying hand of American power. Washington must make abundantly clear that it will continue to uphold this world order — irrespective of its own energy fortunes.

Americans should cheer the energy revolution. It will do wonders for the American economy, and the democratic politics it could encourage in the Middle East and Russia may ultimately serve American interests. But in the meantime, Washington should expect a world far less stable than the one it is used to — and, in turn, prepare to adopt an even more outward-looking foreign policy.