This means that an electron, say, exists not as a point mass but rather as a "smear" of probability surrounding a point.
At each point in space, the electric field has a direction and a strength that can be measured if you put something there that can feel the effects of the field – an electron, say.
According to that weird theory, which, among other things, explains why our computers turn on every morning, there is an irreducible randomness at the microscopic heart of reality that leaves an elementary particle, an electron, say, in a sort of fog of being everywhere or anywhere, or being a wave or a particle, until some measurement fixes it in place.
"It is very efficient at generating electrons," said Prof Willner.
"But in [thorium's] case, the energy is so low that it causes the excitation of outer electrons," says Irwin.
"As a geochemist, I was surprised to see just how much 'machinery' the microbe builds to move electrons," says co-author Susan Brantley of Pennsylvania State University, University Park.
That's because it still requires a conventional accelerator to produce the electrons, says Michael Downer, a physicist at the University of Texas, Austin.
The states that are inaccessible to the particles of a particular kind, such as electrons say, can be taken as corresponding to just so much 'surplus structure'.
Particle physicists have long been able to measure the energies of single electrons, say by watching them crash into crystals that give off light in proportion to the electron's energy.
The main bottleneck that has prevented accurate electronic structure calculations from being applied to large molecules is the prohibitive scaling of computational cost with the number of electrons, say N, in a molecule.
