The development of classical physics was based on the idealization that space can be thought of, as being absolutely empty. This classical idealization could not be maintained, not even as a limiting case. Indeed, the advent of the quantum theory has deeply changed our idea of empty space by obliging us to conceive vacuum as filled with quantum fluctuations of electromagnetic field. In quantum theory, vacuum becomes a well defined notion. Vacuum is permanently filled with electro-magnetic field fluctuations and it corresponds to the field state where the energy of field fluctuations is minimal. This prevents us from using this energy to build up perpetual motions violating the laws of thermodynamics.
However, this leads to a serious problem which can be named vacuum catastrophe in analogy to
ultraviolet catastrophe, the latter being solved by Planck in 1900 for blackbody radiation. When the total energy of quantum vacuum is calculated by adding the energies of all field modes in the vacuum state, an infinite value is obtained. The problem can be formally solved introducing a high frequency cut-off. Although, the problem persists for any value of the cut-off which preserves the laws of quantum theory at the energies where they are well tested. In fact, the calculated vacuum energy density is tremendously larger than the mean vacuum energy observed in the world around us through gravitational phenomena.
Vacuum energy should as any energy in general relativity contribute to the gravitational field. Supposing the universe to be filled with vacuum fluctuations, they should therefore produce for example an effect on planetary motion. As a consequence, astrophysical and cosmological observations can be used to impose an upper bound for the vacuum energy density. The limiting value which can be deduced in this manner is many orders of magnitude smaller than the theoretical prediction using a reasonable cut-off frequency. The discrepancy is such that it is sometimes called the largest discrepancy ever observed in physics This problem is know as the cosmological constant problem because of its obvious connection with the introduction of a cosmological constant in Einstein's gravitation equations. It has remained unsolved during the twentieth century despite considerable efforts for proposing solutions.
In the same period that a self-consistent quantum theory was built up, London provided a quantum interpretation of the interaction forces between neutral atoms or molecules, which were known since the work of Van der Waals. Van der Waals forces are important for a great number of phenomena. They play a crucial role in biology, in adhesion processes or in the chemistry of colloids, where the van der Waals attraction between colloids determines the stability properties. While studying this subject, Overbeek observed a disagreement between the London theory and his measurements.
Noticing that the London theory is based on instantaneous interactions, he asks his colleague Henrik Casimir to study the influence of a finite speed of light on the Van der Waals force. With Dirk Polder, Casimir provided a
complete expression of the Van der Waals force taking into account retarded interaction due to the finite field propagation velocity. Very quickly, Casimir realized that his results could be interpreted by starting from the concept of vacuum fluctuations. Expanding his analysis, Casimir observed that vacuum fluctuations should also produce observable physical effects on macroscopic mirrors; thus predicting for the first time a macroscopic mechanical effect of vacuum fluctuations.
