Einstein Hubble on Vacuum Energy

Crisis meeting today, at lunch time, at the CERN cafeteria. The Einstein-Hubble scientific steering board, composed of Einstein, Hubble and Planck, was having lunch on a superb Tablecloth with assorted Provence Place Mats and Provence Napkins. Tastefull Provencal meals were being served in a bright Provencal Tableware when Planck raised the idea that Vacuum might not be as empty as one would thought but, instead, was filled with Vacuum Energy or 'Black Energy'.

As Planck explained, Vacuum energy is an underlying background energy that exists in space even when devoid of matter (known as free space). The vacuum energy results in the existence of most (if not all) of the fundamental forces - and thus in all effects involving these forces, too. It is observed in various experiments (like the spontaneous emission of light or gamma radiation, the Casimir effect, Van-Der Waals bonds, the Lamb shift, etc); and it is thought (but not yet demonstrated) to have consequences for the behavior of the Universe on cosmological scales.

Quantum field theory states that all of the various fundamental fields, such as the electromagnetic field, must be quantized at each and every point in space. In a naïve sense, a field in physics may be envisioned as if space were filled with interconnected vibrating balls and springs, and the strength of the field can be visualized as the displacement of a ball from its rest position. Vibrations in this field propagate and are governed by the appropriate wave equation for the particular field in question. The second quantization of quantum field theory requires that each such ball-spring combination be quantized, that is, that the strength of the field be quantized at each point in space. Canonically, the field at each point in space is a simple harmonic oscillator, and its quantization places a quantum harmonic oscillator at each point. Excitations of the field correspond to the elementary particles of particle physics. However, even the vacuum has a vastly complex structure. All calculations of quantum field theory must be made in relation to this model of the vacuum.
The vacuum has, implicitly, all of the properties that a particle may have: spin, or polarization in the case of light, energy, and so on. On average, all of these properties cancel out: the vacuum is after all, "empty" in this sense. One important exception is the vacuum energy or the vacuum expectation value of the energy. The quantization of a simple harmonic oscillator states that the lowest possible energy or zero-point energy that such an oscillator may have is
Summing over all possible oscillators at all points in space gives an infinite quantity. To remove this infinity, one may argue that only differences in energy are physically measurable, much as the concept of potential energy has been treated in classical mechanics for centuries. This argument is the underpinning of the theory of renormalization. In all practical calculations, this is how the infinity is always handled.
Vacuum energy can also be thought of in terms of virtual particles (also known as vacuum fluctuations) which are created and destroyed out of the vacuum. These particles are always created out of the vacuum in particle-antiparticle pairs, which shortly annihilate each-other and disappear. However, these particles and antiparticles may interact with others before disappearing, a process which can be mapped using Feynman diagrams. It is these fundamental interactions which give rise to all physical forces. Note that this method of computing vacuum energy is mathematically completely equivalent to having a quantum harmonic oscillator at each point, and therefore suffers the same renormalization problems.
Additional contributions to the vacuum energy come from spontaneous symmetry breaking in quantum field theory.

Needless to say that Einstein and Hubble were a bit excited by the fascinating implications of the Vacuum Energy. This, however, is left for the next issue of Extreme Science, the newsletter of the Einstein-Hubble scientific association. Coming soon!