They say that everyone who finally gets it about climate change has an “Oh, shit” moment–an instant when the full scientific implications become clear and they suddenly realize what a horrifically dangerous situation humanity has created for itself. Listening to the speeches, groundbreaking in their way, that President Obama and Chinese President Hu Jintao delivered September 22 at the UN Summit on Climate Change, I was reminded of my most recent “Oh, shit” moment.

It came in July, courtesy of the chief climate adviser to the German government. Hans Joachim Schellnhuber, chair of an advisory council known by its German acronym, WBGU, is a physicist whose specialty, fittingly, is chaos theory. Speaking to an invitation-only conference at New Mexico’s Santa Fe Institute, Schellnhuber divulged the findings of a study so new he had not yet briefed Chancellor Angela Merkel about it. The study has now been published. If its conclusions are correct–and Schellnhuber ranks among the world’s half-dozen most eminent climate scientists–it has monumental implications for the pivotal meeting in December in Copenhagen, where world leaders will try to agree on reversing global warming.

Schellnhuber and his WBGU colleagues go a giant step beyond the findings of the Intergovernmental Panel on Climate Change, the UN body whose scientific reports are constrained because the world’s governments must approve their contents. The IPCC says that rich industrial countries must cut emissions 25 to 40 percent by 2020 (from 1990 levels) if the world is to have a fair chance of avoiding catastrophic climate change. By contrast, the WBGU study says the United States must cut emissions 100 percent by 2020–i.e., quit carbon entirely within ten years. Germany, Italy and other industrial nations must do the same by 2025 to 2030. China only has until 2035, and the world as a whole must be carbon-free by 2050. The study adds that big polluters can delay their day of reckoning by “buying” emissions rights from developing countries, a step the study estimates would extend some countries’ deadlines by a decade or so.

Needless to say, this timetable is light-years more demanding than what the world’s major governments are talking about in the run-up to Copenhagen. The European Union has pledged 20 percent reductions by 2020, which it will increase to 30 percent if others–like the United States–do the same. Japan’s new prime minister likewise has promised 25 percent reductions by 2020 if others do the same. Obama didn’t mention a number, but the Waxman-Markey bill, which he supports, would deliver less than 5 percent reductions by 2020. Obama’s silence–doubtless a function of the fact that Republicans are implacably opposed to serious emissions cuts–allowed Hu to claim the higher ground at the UN. Hu went further than any Chinese leader has before, pledging to curb greenhouse gas emissions growth by a “notable margin” by 2020. Obama dropped his own bombshell, however, urging that all G-20 governments phase out subsidies for fossil fuels. “The time we have to reverse this tide is running out,” Obama declared. Alas, the WBGU study suggests that our time is in fact all but gone.

Obama, like other G-8 leaders, agreed in July to limit the global temperature rise to 2 degrees Celsius (3.6 degrees Fahrenheit) above the preindustrial level at which human civilization developed. Schellnhuber, addressing the Santa Fe conference, joked that the G-8 leaders had agreed to the 2C limit “probably because they don’t know what it means.” In fact, even the “brutal” timeline of the WBGU study, Schellnhuber cautioned, would not guarantee staying within the 2C target. It would merely give humanity a two-out-of-three chance of doing so–“worse odds than Russian roulette,” he wryly noted. “But it is the best we can do.” To have a three-out-of-four chance, countries would have to quit carbon even sooner. Likewise, we could decide to wait another decade or so to halt all greenhouse emissions, but this lowers the odds of hitting the 2C target to fifty-fifty. “And what kind of precautionary principle is that?” Schellnhuber asked.

There is a fundamental political assumption underlying the WBGU study: that the right to emit greenhouse gases is shared equally by all people on earth. Known in diplomatic circles as “the per capita principle,” this approach has long been insisted upon by China and most other developing countries and thus is seen as essential to an agreement in Copenhagen, though among G-8 leaders only Merkel has endorsed it. The WBGU study applies the per capita principle to the world population of 7 billion people and arrives at an annual emissions quota of 2.7 tons of carbon dioxide per person. That’s harsh news for Americans, who emit 20 tons per person annually, and it explains why the US deadline is the most imminent. But China won’t welcome this news either. Its combination of high annual emissions and huge population gives it a deadline only a few years later than Europe’s and Japan’s.

“I myself was terrified when I saw these numbers,” Schellnhuber said. He urges governments to agree in Copenhagen to launch “a Green Apollo Project.” Like John Kennedy’s pledge to land a man on the moon in ten years, a global Green Apollo Project would aim to put leading economies on a trajectory of zero carbon emissions within ten years. Combined with carbon trading with low-emissions countries, Schellnhuber says, such a “wartime mobilization” might still save us from the worst impacts of climate change. The alternative is more and more “Oh, shit” moments for all of us.