Saturday, June 23, 2007

The Quantum Vacuum

There's much talk in the popular physics literature about the 'quantum vacuum'. Fluctuations of the vacuum purportedly give rise to observable effects such as the Lamb shift in the energy levels of a Hydrogen atom, or the Casimir effect, an attractive force between closely-separated parallel conducting plates. However, the popular literature tends to speak only of the vacuum, and neglects to explain that:

(i) Each different theory tends to have its own notion of the vacuum, and

(ii) Each different field within a fixed theory has a vacuum associated with it.

So, for example, quantum field theory and general relativity have different concepts of the vacuum, and within quantum field theory, there is the vacuum state of the electromagnetic field, there is the vacuum state of the electron field, and there is the vacuum state of the interacting electron-electromagnetic field, and they are all distinct.

Nevertheless, the various vacua of all the fields in the standard model of particle physics (an application of quantum field theory) add up to give a vacuum energy density which is many orders of magnitude greater than the upper bound placed upon the vacuum energy of empty space ('dark energy') by cosmological observations. This is the 'cosmological constant problem', superbly analysed by Rugh and Zinkernagel in 2001. The accelerating expansion of the universe can be explained by some sort of vacuum energy, but not that predicted by quantum field theory.

Rugh and Zinkernagel suggest that the existence of the quantum vacuum has not actually been demonstrated. And, indeed, the fact that the purported vacuum fluctuations do not contribute to the 'scattering amplitudes' (i.e., the probabilities of various outcomes of a collision) between, say, photons and electrons, requires an explanation from those who believe in the reality of the quantum vacuum. Rugh and Zinkernagel also propose that there may be some false beliefs about the assumed relation between quantum field theory in curved space-time and general relativity.

However, another possibility, that provided by supersymmetry, seems most intriguing. There are two types of elementary particles: bosons and fermions. Supersymmetry postulates that each type of boson with which we are currently familiar, has a supersymmetric fermionic partner, and each type of fermion with which we are currently familiar, has a supersymmetric bosonic partner. So, for example, the photon (a boson) has a supersymmetric partner called the photino (a fermion). The idea is that at some time in the universe's early history, the higher energy levels were such that each supersymmetric boson-fermion pair were merely different states of the same type of elementary particle. As the energy levels dropped, supersymmetric symmetry breaking took place, and, as a consequence, the particles with which we are currently familiar, interact very rarely with their supersymmetric partners. These weakly-interacting supersymmetric particles provide a nice candidate to explain the existence of dark matter in astronomy and cosmology. Moreover, as Rugh and Zinkernagel point out "In a supersymmetric theory the fermion and boson contributions to the vacuum energy would cancel to an exact zero (they are equally large and have opposite sign), so if we lived in a world in which each particle had a superpartner, we would understand why the vacuum energy vanishes." Sadly, supersymmetric symmetry breaking seems to produce a non-zero energy density which exceeds that required to explain dark energy. Perhaps we need to combine supersymmetry with a refined understanding of the link between quantum field theory and general relativity. Food for thought...

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