Randell Mills, a Harvard University medic who also studied electrical engineering at Massachusetts Institute of Technology, claims to have built a prototype power source that generates up to 1,000 times more heat than conventional fuel. Independent scientists claim to have verified the experiments and Dr Mills says that his company, Blacklight Power, has tens of millions of dollars in investment lined up to bring the idea to market. And he claims to be just months away from unveiling his creation.

The problem is that according to the rules of quantum mechanics, the physics that governs the behaviour of atoms, the idea is theoretically impossible. "Physicists are quite conservative. It's not easy to convince them to change a theory that is accepted for 50 to 60 years. I don't think [Mills's] theory should be supported," said Jan Naudts, a theoretical physicist at the University of Antwerp.

What has much of the physics world up in arms is Dr Mills's claim that he has produced a new form of hydrogen, the simplest of all the atoms, with just a single proton circled by one electron. In his "hydrino", the electron sits a little closer to the proton than normal, and the formation of the new atoms from traditional hydrogen releases huge amounts of energy.

This is scientific heresy. According to quantum mechanics, electrons can only exist in an atom in strictly defined orbits, and the shortest distance allowed between the proton and electron in hydrogen is fixed. The two particles are simply not allowed to get any closer.

According to Dr Mills, there can be only one explanation: quantum mechanics must be wrong. "We've done a lot of testing. We've got 50 independent validation reports, we've got 65 peer-reviewed journal articles," he said. "We ran into this theoretical resistance and there are some vested interests here. People are very strong and fervent protectors of this [quantum] theory that they use."

Rick Maas, a chemist at the University of North Carolina at Asheville (UNC) who specialises in sustainable energy sources, was allowed unfettered access to Blacklight's laboratories this year. "We went in with a healthy amount of scepticism. While it would certainly be nice if this were true, in my position as head of a research institution, I really wouldn't want to make a mistake. The last thing I want is to be remembered as the person who derailed a lot of sustainable energy investment into something that wasn't real."

But Prof Maas and Randy Booker, a UNC physicist, left under no doubt about Dr Mill's claims. "All of us who are not quantum physicists are looking at Dr Mills's data and we find it very compelling," said Prof Maas. "Dr Booker and I have both put our professional reputations on the line as far as that goes."

Dr Mills's idea goes against almost a century of thinking. When scientists developed the theory of quantum mechanics they described a world where measuring the exact position or energy of a particle was impossible and where the laws of classical physics had no effect. The theory has been hailed as one of the 20th century's greatest achievements.

But it is an achievement Dr Mills thinks is flawed. He turned back to earlier classical physics to develop a theory which, unlike quantum mechanics, allows an electron to move much closer to the proton at the heart of a hydrogen atom and, in doing so, release the substantial amounts of energy he seeks to exploit. Dr Mills's theory, known as classical quantum mechanics and published in the journal Physics Essays in 2003, has been criticised most publicly by Andreas Rathke of the European Space Agency. In a damning critique published recently in the New Journal of Physics, he argued that Dr Mills's theory was the result of mathematical mistakes.

Dr Mills argues that there are plenty of flaws in Dr Rathke's critique. "His paper's riddled with mistakes. We've had other physicists contact him and say this is embarrassing to the journal and [Dr Rathke] won't respond," said Dr Mills.

While the theoretical tangle is unlikely to resolve itself soon, those wanting to exploit the technology are pushing ahead. "We would like to understand it from an academic standpoint and then we would like to be able to use the implications to actually produce energy products," said Prof Maas. "The companies that are lining up behind this are household names."

Dr Mills will not go into details of who is investing in his research but rumours suggest a range of US power companies. It is well known also that Nasa's institute of advanced concepts has funded research into finding a way of using Blacklight's technology to power rockets.

According to Prof Maas, the first product built with Blacklight's technology, which will be available in as little as four years, will be a household heater. As the technology is scaled up, he says, bigger furnaces will be able to boil water and turn turbines to produce electricity.

In a recent economic forecast, Prof Maas calculated that hydrino energy would cost around 1.2 cents (0.7p) per kilowatt hour. This compares to an average of 5 cents per kWh for coal and 6 cents for nuclear energy.

"If it's wrong, it will be proven wrong," said Kert Davies, research director of Greenpeace USA. "But if it's right, it is so important that all else falls away. It has the potential to solve our dependence on oil. Our stance is of cautious optimism."