Is empty space empty?

Two conducting plates a fraction of a micrometre apart restrict which field modes can exist between them. Fewer modes inside than outside means a pressure difference, pushing the plates together.

Predicted in 1948 and measured in 1997, between a flat plate and a curved surface, at separations between 0.6 and 6 micrometres; its author reported agreement with theory at the five per cent level, which a later review finds could hold only near one micrometre. Between two parallel plates, the arrangement Casimir described, it was measured in 2002 to fifteen per cent. The force is tiny and it is real, and at nanometre separations it is strong enough to move the parts of a micromachine.

In quantum field theory a particle is a quantum of excitation of a field that exists everywhere. On the theory, an accelerating observer sees a thermal bath of particles where an inertial observer sees vacuum.

Many take that to mean the number of particles is not an absolute, so that how many are in a region need not have an observer-independent answer. Others argue that the accelerating observer’s particles are not real, and philosophers of physics still dispute how much the effect shows.

Summing the zero-point energies of the fields gives a vacuum energy density. Gravity responds to energy, so that density should curve spacetime, and it corresponds to the cosmological constant that is measured from the expansion of the universe.

The measured value is smaller than the simplest estimate by something like 120 orders of magnitude. Even careful treatments leave a discrepancy of dozens of orders of magnitude.

This is not a small residual. Steven Weinberg called it a “veritable crisis”, and it has been open since the problem was recognised.

The standard statement of it is a 1989 review by Steven Weinberg, written before the acceleration of the expansion was discovered and before anyone knew the answer was small and not zero.

It works through the contributions to the vacuum energy from each part of the Standard Model, shows that they do not cancel for any reason anybody can find, and surveys the attempts to explain why the total is so much smaller than any of its parts.

The discovery of a small positive value nine years later made the problem harder rather than easier: a zero might have been explained by a symmetry, and a tiny non-zero number has to be explained by something that knows how tiny to be.

The Casimir effect is often presented as a direct demonstration of vacuum energy. It can also be derived as a force between the charges in the plates, mediated in a way that never mentions the vacuum.

The two calculations agree, so the measurement does not by itself settle which description is fundamental. That matters when the effect is used as evidence in arguments about the cosmological constant.