In quantum field theory, the quantum vacuum
state (also called the quantum vacuum or vacuum
state) 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". 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 1930s, and in the late 1940s and early
1950s 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-zero expectation value ==
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 measurement
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.
== 
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 (or 0.6 eV). 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.
== Symmetry ==
For a relativistic field theory, the vacuum
is Poincaré invariant, which follows from
Wightman axioms but can be also proved directly
without these axioms. 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.
== Electrical permittivity ==
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 yielded negative
results so far.
== Virtual particles ==
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, or variances,
based upon the Heisenberg energy-time uncertainty
principle:
Δ
E
Δ
t
≥
ℏ
,
{\displaystyle \Delta E\Delta t\geq \hbar
\ ,}
(with ΔE and Δt being the energy and time
variations respectively; ΔE is the accuracy
in the measurement of energy and Δt is the
time taken in the measurement, and ħ is the
Reduced Planck constant) 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. 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] = i ħ). 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.
== Physical nature of the quantum vacuum ==
According to Astrid Lambrecht (2002): "When
one empties out a space of all matter and
lowers the temperature to absolute zero, one
produces in a Gedankenexperiment [mental experiment]
the quantum vacuum state." According to Fowler
& Guggenheim (1939/1965), the third law of
thermodynamics may be precisely enunciated
as follows:
It is impossible by any procedure, no matter
how idealized, to reduce any assembly to the
absolute zero in a finite number of operations.
(See also.)
Photon-photon interaction can occur only through
interaction with the vacuum state of some
other field, for example through the Dirac
electron-positron vacuum field; this is associated
with the concept of vacuum polarization. According
to Milonni (1994): "... all quantum fields
have zero-point energies and vacuum fluctuations."
This means that there is a component of the
quantum vacuum respectively for each component
field (considered in the conceptual absence
of the other fields), such as the electromagnetic
field, the Dirac electron-positron field,
and so on. According to Milonni (1994), some
of the effects attributed to the vacuum electromagnetic
field can have several physical interpretations,
some more conventional than others. The Casimir
attraction between uncharged conductive plates
is often proposed as an example of an effect
of the vacuum electromagnetic field. Schwinger,
DeRaad, and Milton (1978) are cited by Milonni
(1994) as validly, though unconventionally,
explaining the Casimir effect with a model
in which "the vacuum is regarded as truly
a state with all physical properties equal
to zero." In this model, the observed phenomena
are explained as the effects of the electron
motions on the electromagnetic field, called
the source field effect. Milonni writes:
The basic idea here will be that the Casimir
force may be derived from the source fields
alone even in completely conventional QED,
... Milonni provides detailed argument that
the measurable physical effects usually attributed
to the vacuum electromagnetic field cannot
be explained by that field alone, but require
in addition a contribution from the self-energy
of the electrons, or their radiation reaction.
He writes: "The radiation reaction and the
vacuum fields are two aspects of the same
thing when it comes to physical interpretations
of various QED processes including the Lamb
shift, van der Waals forces, and Casimir effects.
This point of view is also stated by Jaffe
(2005): "The Casimir force can be calculated
without reference to vacuum fluctuations,
and like all other observable effects in QED,
it vanishes as the fine structure constant,
α, goes to zero."
== 
Notations ==
The vacuum state is written as
|
0
⟩
{\displaystyle |0\rangle }
or
|
⟩
{\displaystyle |\rangle }
. The vacuum expectation value (see also Expectation
value) of any field
ϕ
{\displaystyle \phi }
should be written as
⟨
0
|
ϕ
|
0
⟩
{\displaystyle \langle 0|\phi |0\rangle }
.
== See also ==
== 
References and notes ==
== 
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
Puthoff, H. E.; Little, S. R.; Ibison, M.
(2001). "Engineering the Zero-Point Field
and Polarizable Vacuum for Interstellar Flight".
arXiv:astro-ph/0107316.
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"
== External links ==
Energy into Matter
