In the quantum theory of a particular physical system, the lowest energy attainable is higher than the minimum energy of the system predicted by the classical Newtonian theory. This difference in energy is called “zero point” energy.

For example, in the classical theory of the hydrogen atom, the electron orbiting the proton would gradually lose an infinite amount of energy in the form of electromagnetic radiation and fall onto the proton. In the classical theory, the hydrogen atom would therefore be the size of a single proton, or roughly 10^{-15} m. In the real world, the hydrogen atom is way bigger, with a size of about 10^{-10} m. The quantum theory, which gives a very good description of the properties of the hydrogen atom, only allows the electron to lose a finite amount of energy until it reaches an energy 13.6 eV below that of the ionised hydrogen atom. But no more. The zero point energy in that case is infinite. We also find that the electromagnetic zero point energy of empty space is infinite, or at least extremely large if we assume that there is a minimum wavelength (the Planck length) for electromagnetic radiation. But it is no cause for alarm, since in electromagnetism only energy differences matter, and not their absolute value. The zero point energy cancels out of the calculations.

This is different in Einstein’s theory of gravitation, in that the absolute value of the density of matter determines the curvature of space-time. Einstein’s celebrated equation E = mc^{2} states that mass and energy are equivalent. Hence the very large (essentially infinite) zero point energy predicted by the quantum theory should be equivalent to a very large mass density that in turn would produce some enormous gravitational fields, which are not observed.

The development of a quantum theory of gravity is an important and yet unsolved problem that is occupying some of the best minds in theoretical physics.

Fortunately, the solution of problems caused by gravity is a lot easier in Photoshop. In the photograph above, I appear to float in zero gravity in my flat. A problem I was able to solve in relatively little time. Thank you Adobe!