"Eventually solar will become so large that there will be consequences everywhere," Parker and Chang said. This remarkable overthrow of everything we take for granted in world energy politics may occur within "the better part of a decade".
If the hypothesis is broadly correct, solar will slowly squeeze the revenues of petro-rentier regimes in Russia, Venezuela and Saudi Arabia, among others. Many already need oil prices near $100 a barrel to cover welfare budgets. They will have to find a new business model.
The Saudis are themselves betting on solar, investing more than $100bn in 41GW of capacity, enough to cover 30pc of their power needs by 2030. That will mean more crude - other things being equal - washing into a deflating global energy market.
Clean Energy Trends says new solar installations overtook wind worldwide last year, with an extra 36.5 gigawatts. China accounted for a third. Wind is still ahead with 2.5 times old capacity but the "solar sorpasso" will be reached in 2021 as photovoltaic costs keep falling.
The US National Renewable Energy Laboratory says scientists can now capture 31.1pc of the sun's energy with a 111V Solar cell, the latest world record. This will find its way briskly into routine use. Wind cannot keep pace. It is static by comparison.
A McKinsey study said the average cost of installed solar power in the US has dropped to $2.59 from $6 a watt in 2010. It expects this to fall to $2.30 next year and to $1.60 by 2020. This will put US solar within "striking distance" of coal and gas.
It is hard to keep up with the cascade of new research papers, so many brimming with optimism. The University of Buffalo has developed a nanoscale microchip able to capture a "rainbow" of wavelengths and absorb far more light. An Oxford team is pioneering use of perovskite, an abundant material that is cheaper than silicon and produces 40mc more voltage.
One by one, the seemingly intractable obstacles are being conquered. Israel's Ecoppia has just begun using robots to clean the panels of its Ketura Sun park in the Negev desert without the use of water. It is beautifully simple. Soft microfibres sweep away 99pc of the dust each night with the help of airflows.
Prof Michael Aziz at Harvard University is developing a flow-battery that promises to cut the cost of energy storage by two-thirds below the latest vanadium batteries. He said technology gives us a "fighting chance" to overcome the curse of intermittency from wind and solar power, which spike and die in bursts. "I foresee a future where we can vastly cut down on fossil fuel use."
Even thermal solar is coming of age, driven for now by use of molten salts to store heat. California opened the world's biggest solar thermal park in February in the Mojave desert - the Ivanpah project, co-owned by Google - able to produce power for 100,000 homes by reflecting sunlight from 170,000 mirrors on to boilers that generate electricity from steam. Ivanpah still relies on subsidies but a new SunPower project in Chile will go naked, selling into the spot market.
Deutsche Bank says there are already 19 regional markets around the world that have achieved "grid parity", meaning that photovoltaic solar panels can match or undercut local electricity prices without subsidy: California, Chile, Australia, Turkey, Israel, Germany, Japan, Italy, Spain and Greece for residential power; Mexico and China for industrial power.
This will spread as battery storage costs keep dropping, a spin-off from electric car ventures. Sanford Bernstein's report says it may not be long before home energy storage is cheap enough to lure households away from the grid en masse across the world, spelling "disaster" for some utilities.
Solar competes directly. Each year it supplies a bigger chunk of peak power needs in the middle of the day, when air conditioners and factories are both at full throttle. "Demand during what was one of the most profitable times of the day disappears," the report says.
Michael Liebreich from Bloomberg New Energy Finance says we can already discern the moment of "peak fossil fuels" around 2030, the tipping point when the world starts using less coal, oil and gas in absolute terms.
This is a remarkable twist of history. Six years ago we faced an oil shock with crude trading at $148. The rise of "Chindia" and the sudden inclusion of 2bn consumers into the world economy seemed to be taxing resources to breaking point.
For Germany it is a bitter-sweet vindication. The country sank euros 100bn into feed-in tariffs or in solar companies that blazed the trail, did us all a favour and went bankrupt. They have the world's biggest solar infrastructure but latecomers get it much cheaper.
For Britain it offers hope of reprieve after 20 years of energy drift, yet also raises a quandry: should the country lock into more nuclear power with strike-prices fixed for 35 years? Should it spend pounds 100bn on off-shore wind when imported LNG might well be cheaper in the future?
For the world, it portends a once-in-a-century upset of the geostrategic order.
Sheikh Yamani, the veteran Saudi oil minister, saw the writing on the wall long ago.
"Thirty years from now there will be a huge amount of oil - and no buyers. The Stone Age came to an end, not because we had a lack of stones,'' he told The Daily Telegraph in 2000.
