In

quantum field theoryQuantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...

, the

**vacuum state** (also called the

**vacuum**) is the

quantum state with the lowest possible

energyIn physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...

. 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

QCD vacuumThe QCD vacuum is the vacuum state of quantum chromodynamics . It is an example of a non-perturbative vacuum state, characterized by many non-vanishing condensates such as the gluon condensate or the quark condensate...

of

quantum chromodynamicsIn theoretical physics, quantum chromodynamics is a theory of the strong interaction , a fundamental force describing the interactions of the quarks and gluons making up hadrons . It is the study of the SU Yang–Mills theory of color-charged fermions...

is the object of study in the

Large Hadron ColliderThe Large Hadron Collider is the world's largest and highest-energy particle accelerator. It is expected to address some of the most fundamental questions of physics, advancing the understanding of the deepest laws of nature....

and the

Relativistic Heavy Ion ColliderThe Relativistic Heavy Ion Collider is one of two existing heavy-ion colliders, and the only spin-polarized proton collider in the world. It is located at Brookhaven National Laboratory in Upton, New York and operated by an international team of researchers...

, 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 theoryPerturbation theory comprises mathematical methods that are used to find an approximate solution to a problem which cannot be solved exactly, by starting from the exact solution of a related problem...

, then the properties of the vacuum are analogous to the properties of the

ground stateThe ground state of a quantum mechanical system is its lowest-energy state; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state...

of a quantum mechanical

harmonic oscillatorIn classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force, F, proportional to the displacement, x: \vec F = -k \vec x \, where k is a positive constant....

(or more accurately, the

ground stateThe ground state of a quantum mechanical system is its lowest-energy state; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state...

of a QM problem). In this case the

vacuum expectation valueIn quantum field theory the vacuum expectation value of an operator is its average, expected value in the vacuum. The vacuum expectation value of an operator O is usually denoted by \langle O\rangle...

(VEV) of any field operator vanishes. For quantum field theories in which

perturbation theoryPerturbation theory comprises mathematical methods that are used to find an approximate solution to a problem which cannot be solved exactly, by starting from the exact solution of a related problem...

breaks down at low energies (for example,

Quantum chromodynamicsIn theoretical physics, quantum chromodynamics is a theory of the strong interaction , a fundamental force describing the interactions of the quarks and gluons making up hadrons . It is the study of the SU Yang–Mills theory of color-charged fermions...

or the

BCS theoryBCS theory — proposed by Bardeen, Cooper, and Schrieffer in 1957 — is the first microscopic theory of superconductivity since its discovery in 1911. The theory describes superconductivity as a microscopic effect caused by a "condensation" of pairs of electrons into a boson-like state...

of

superconductivitySuperconductivity is a phenomenon of exactly zero electrical resistance occurring in certain materials below a characteristic temperature. It was discovered by Heike Kamerlingh Onnes on April 8, 1911 in Leiden. Like ferromagnetism and atomic spectral lines, superconductivity is a quantum...

) field operators may have non-vanishing

vacuum expectation valueIn quantum field theory the vacuum expectation value of an operator is its average, expected value in the vacuum. The vacuum expectation value of an operator O is usually denoted by \langle O\rangle...

s called condensates. In the

Standard ModelThe Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...

, the non-zero vacuum expectation value of the Higgs field, arising from

spontaneous symmetry breakingSpontaneous symmetry breaking is the process by which a system described in a theoretically symmetrical way ends up in an apparently asymmetric state....

, is the mechanism by which the other fields in the theory acquire mass.

## The energy of the vacuum state

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 energyZero-point energy is the lowest possible energy that a quantum mechanical physical system may have; it is the energy of its ground state. All quantum mechanical systems undergo fluctuations even in their ground state and have an associated zero-point energy, a consequence of their wave-like nature...

, and this zero-point energy has measurable effects. In the laboratory, it may be detected as the

Casimir effectIn quantum field theory, the Casimir effect and the Casimir–Polder force are physical forces arising from a quantized field. The typical example is of two uncharged metallic plates in a vacuum, like capacitors placed a few micrometers apart, without any external electromagnetic field...

. In

physical cosmologyPhysical cosmology, as a branch of astronomy, is the study of the largest-scale structures and dynamics of the universe and is concerned with fundamental questions about its formation and evolution. For most of human history, it was a branch of metaphysics and religion...

, the energy of the cosmological vacuum appears as the

cosmological constantIn physical cosmology, the cosmological constant was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe...

. In fact, the energy of a cubic centimeter of empty space has been calculated figuratively to be one trillionth of an

ergAn erg is the unit of energy and mechanical work in the centimetre-gram-second system of units, symbol "erg". Its name is derived from the Greek ergon, meaning "work"....

. An outstanding requirement imposed on a potential

Theory of EverythingA theory of everything is a putative theory of theoretical physics that fully explains and links together all known physical phenomena, and predicts the outcome of any experiment that could be carried out in principle....

is that the energy of the quantum vacuum state must explain the physically observed cosmological constant.

## The symmetry of the vacuum state

For a

relativisticThe theory of relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word relativity is sometimes used in reference to Galilean invariance....

field theory, the vacuum is Poincaré invariant. Poincaré invariance implies that only

scalarIn physics, a scalar is a simple physical quantity that is not changed by coordinate system rotations or translations , or by Lorentz transformations or space-time translations . This is in contrast to a vector...

combinations of field operators have non-vanishing

VEV'sIn quantum field theory the vacuum expectation value of an operator is its average, expected value in the vacuum. The vacuum expectation value of an operator O is usually denoted by \langle O\rangle...

. The

VEVIn quantum field theory the vacuum expectation value of an operator is its average, expected value in the vacuum. The vacuum expectation value of an operator O is usually denoted by \langle O\rangle...

may break some of the internal symmetries of the

LagrangianThe Lagrangian, L, of a dynamical system is a function that summarizes the dynamics of the system. It is named after Joseph Louis Lagrange. The concept of a Lagrangian was originally introduced in a reformulation of classical mechanics by Irish mathematician William Rowan Hamilton known as...

of the field theory. In this case the vacuum has less symmetry than the theory allows, and one says that

*spontaneous symmetry breaking*Spontaneous symmetry breaking is the process by which a system described in a theoretically symmetrical way ends up in an apparently asymmetric state....

has occurred. See

Higgs mechanismIn particle physics, the Higgs mechanism is the process in which gauge bosons in a gauge theory can acquire non-vanishing masses through absorption of Nambu-Goldstone bosons arising in spontaneous symmetry breaking....

,

standard modelThe Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...

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 ε

_{0} of the

electric constantThe physical constant ε0, commonly called the vacuum permittivity, permittivity of free space or electric constant is an ideal, physical constant, which is the value of the absolute dielectric permittivity of classical vacuum...

. These theoretical developments are described, for example, in Dittrich and Gies. In particular, the theory of

quantum electrodynamicsQuantum electrodynamics is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved...

predicts that the vacuum should exhibit

nonlinear effectsNonlinear optics is the branch of optics that describes the behavior of light in nonlinear media, that is, media in which the dielectric polarization P responds nonlinearly to the electric field E of the light...

that will make it behave like a birefringent material with ε slightly greater than ε

_{0} for extremely strong electric fields. Explanations for

dichroismDichroism has two related but distinct meanings in optics. A dichroic material is either one which causes visible light to be split up into distinct beams of different wavelengths , or one in which light rays having different polarizations are absorbed by different amounts.The original meaning of...

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

or

. The VEV of a field φ, which should be written as

, is usually condensed to

.

## Virtual particles

The

uncertainty principleIn quantum mechanics, the Heisenberg uncertainty principle states a fundamental limit on the accuracy with which certain pairs of physical properties of a particle, such as position and momentum, can be simultaneously known...

in the form

implies that from the vacuum a particle pair with energy ΔE above the vacuum may undergo spontaneous creation for a short time Δt. These

*virtual particles* are included in the definition of the vacuum.

## See also

- Vacuum energy
Vacuum energy is an underlying background energy that exists in space even when the space is devoid of matter . The concept of vacuum energy has been deduced from the concept of virtual particles, which is itself derived from the energy-time uncertainty principle...

- Virtual particle
In physics, a virtual particle is a particle that exists for a limited time and space. The energy and momentum of a virtual particle are uncertain according to the uncertainty principle...

- Pair production
Pair production refers to the creation of an elementary particle and its antiparticle, usually from a photon . For example an electron and its antiparticle, the positron, may be created...

- Vacuum polarization
In quantum field theory, and specifically quantum electrodynamics, vacuum polarization describes a process in which a background electromagnetic field produces virtual electron–positron pairs that change the distribution of charges and currents that generated the original electromagnetic...

- Vacuum
In everyday usage, vacuum is a volume of space that is essentially empty of matter, such that its gaseous pressure is much less than atmospheric pressure. The word comes from the Latin term for "empty". A perfect vacuum would be one with no particles in it at all, which is impossible to achieve in...

- QCD vacuum
The QCD vacuum is the vacuum state of quantum chromodynamics . It is an example of a non-perturbative vacuum state, characterized by many non-vanishing condensates such as the gluon condensate or the quark condensate...

- Squeezed coherent state
- False vacuum
In quantum field theory, a false vacuum is a metastable sector of space that appears to be a perturbative vacuum, but is unstable due to instanton effects that may tunnel to a lower energy state. This tunneling can be caused by quantum fluctuations or the creation of high-energy particles...

- Casimir effect
In quantum field theory, the Casimir effect and the Casimir–Polder force are physical forces arising from a quantized field. The typical example is of two uncharged metallic plates in a vacuum, like capacitors placed a few micrometers apart, without any external electromagnetic field...

- Van der Waals force
In physical chemistry, the van der Waals force , named after Dutch scientist Johannes Diderik van der Waals, is the sum of the attractive or repulsive forces between molecules other than those due to covalent bonds or to the electrostatic interaction of ions with one another or with neutral...

- Free space
- Scharnhorst effect
The Scharnhorst effect is a hypothetical phenomenon in which light signals travel faster than c between two closely spaced conducting plates. It was predicted by Klaus Scharnhorst of the Humboldt University of Berlin, Germany, and Gabriel Barton of the University of Sussex in Brighton, England...

- Energy into Matter

## Further reading

- Free pdf copy of The Structured Vacuum - thinking about nothing by Johann Rafelski
Johann Rafelski is a German-American theoretical physicist and author. He is Professor of Physics at The University of Arizona in Tucson, guest scientist at CERN , and has been LMU-Excellent Guest Professor at the Ludwig Maximilian University of Munich in Munich, Germany.Rafelski’s current...

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"