Vacuum state

Quantum field theory
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In quantum field theory, the vacuum state (also called the vacuum) is the quantum state with the lowest possible energy. Generally, it contains no physical particles. Zero-point field is sometimes used as a synonym for the vacuum state of an individual quantized field.

According to present-day understanding of what is called the vacuum state or the quantum vacuum, it is "by no means a simple empty space", and again: "it is a mistake to think of any physical vacuum as some absolutely empty void." According to quantum mechanics, the vacuum state is not truly empty but instead contains fleeting electromagnetic waves and particles that pop into and out of existence.

The QED vacuum of quantum electrodynamics (or QED) was the first vacuum of quantum field theory to be developed. QED originated in the 1930's, and in the late 1940's and early 1950's it was reformulated by Feynman, Tomonaga and Schwinger, who jointly received the Nobel prize for this work in 1965. Today the electromagnetic interactions and the weak interactions are unified in the theory of the electroweak interaction.

The Standard Model is a generalization of the QED work to include all the known elementary particles and their interactions (except gravity). Quantum chromodynamics is the portion of the Standard Model that deals with strong interactions, and QCD vacuum is the vacuum of quantum chromodynamics. It is the object of study in the Large Hadron Collider and the Relativistic Heavy Ion Collider, and is related to the so-called vacuum structure of strong interactions.

Non-vanishing vacuum state

If the quantum field theory can be accurately described through perturbation theory, then the properties of the vacuum are analogous to the properties of the ground state of a quantum mechanical harmonic oscillator (or more accurately, the ground state of a QM problem). In this case the vacuum expectation value (VEV) of any field operator vanishes. For quantum field theories in which perturbation theory breaks down at low energies (for example, Quantum chromodynamics or the BCS theory of superconductivity) field operators may have non-vanishing vacuum expectation values called condensates. In the Standard Model, the non-zero vacuum expectation value of the Higgs field, arising from spontaneous symmetry breaking, is the mechanism by which the other fields in the theory acquire mass.

The energy of the vacuum state

Main article: Vacuum energy

In many situations, the vacuum state can be defined to have zero energy, although the actual situation is considerably more subtle. The vacuum state is associated with a zero-point energy, and this zero-point energy has measurable effects. In the laboratory, it may be detected as the Casimir effect. In physical cosmology, the energy of the cosmological vacuum appears as the cosmological constant. In fact, the energy of a cubic centimeter of empty space has been calculated figuratively to be one trillionth of an erg. An outstanding requirement imposed on a potential Theory of Everything is that the energy of the quantum vacuum state must explain the physically observed cosmological constant.

The symmetry of the vacuum state

For a relativistic field theory, the vacuum is Poincaré invariant. Poincaré invariance implies that only scalar combinations of field operators have non-vanishing VEV's. The VEV may break some of the internal symmetries of the Lagrangian of the field theory. In this case the vacuum has less symmetry than the theory allows, and one says that spontaneous symmetry breaking has occurred. See Higgs mechanism, standard model and Woit.

Electrical permittivity of vacuum state

In principle, quantum corrections to Maxwell's equations can cause the experimental electrical permittivity ε of the vacuum state to deviate from the defined scalar value ε₀ of the electric constant. These theoretical developments are described, for example, in Dittrich and Gies. In particular, the theory of quantum electrodynamics predicts that the QED vacuum should exhibit nonlinear effects that will make it behave like a birefringent material with ε slightly greater than ε₀ for extremely strong electric fields. Explanations for dichroism from particle physics, outside quantum electrodynamics, also have been proposed. Active attempts to measure such effects have been unsuccessful so far.

Notations

The vacuum state is written as $|0\rangle$ or $|\rangle$. The VEV of a field φ, which should be written as $\langle0|\phi|0\rangle$, is usually condensed to $\langle\phi\rangle$.

Virtual particles

Main article: Virtual particle

The presence of virtual particles can be rigorously based upon the non-commutation of the quantized electromagnetic fields. Non-commutation means that although the average values of the fields vanish in a quantum vacuum, their variances do not. The term "vacuum fluctuations" refers to the variance of the field strength in the minimal energy state, and is described picturesquely as evidence of "virtual particles".

It is sometimes attempted to provide an intuitive picture of virtual particles based upon the Heisenberg energy-time uncertainty principle:

$\Delta E \Delta t \ge \hbar \ ,$

(with ΔE and Δt energy and time variations, and ℏ the Planck constant divided by 2π) arguing along the lines that the short lifetime of virtual particles allows the "borrowing" of large energies from the vacuum and thus permits particle generation for short times.

Although the phenomenon of virtual particles is accepted, this interpretation of the energy-time uncertainty relation is not universal, however. One issue is the use of an uncertainty relation limiting measurement accuracy as though a time uncertainty Δt determines a "budget" for borrowing energy ΔE. Another issue is the meaning of "time" in this relation, because energy and time (unlike position q and momentum p, for example) do not satisfy a canonical commutation relation (such as [q, p ] = iℏ) . Various schemes have been advanced to construct an observable that has some kind of time interpretation, and yet does satisfy a canonical commutation relation with energy. The very many approaches to the energy-time uncertainty principle are a long and continuing subject.

See also

• Vacuum energy
• Virtual particle
• Pair production
• Vacuum polarization

• Vacuum
• QCD vacuum
• QED vacuum
• Squeezed coherent state
• False vacuum

• Casimir effect
• Van der Waals force
• Free space
• Scharnhorst effect
• Energy into Matter

Further reading

• Free pdf copy of The Structured Vacuum - thinking about nothing by Johann Rafelski and Berndt Muller (1985) ISBN 3-87144-889-3.
• M.E. Peskin and D.V. Schroeder, An introduction to Quantum Field Theory.
• H. Genz, Nothingness: The Science of Empty Space
• Maybe this should discuss Star Trek and/or Star Gate: Engineering the Zero-Point Field and Polarizable Vacuum for Interstellar Flight
• E. W. Davis, V. L. Teofilo, B. Haisch, H. E. Puthoff, L. J. Nickisch, A. Rueda and D. C. Cole(2006)"Review of Experimental Concepts for Studying the Quantum Vacuum Field"