Everything about Vacuum State totally explained
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. The term "
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's "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 isn't truly empty but instead contains fleeting electromagnetic waves and particles that pop into and out of existence.
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
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 vacuum state appears as the
cosmological constant. An outstanding requirement imposed on a potential
Theory of Everything is that the energy of the 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 VEVs. 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, it's possible for the experimental electrical permittivity ε of the vacuum state to deviate from the defined scalar value ε
0 of the
electric constant due to quantum corrections to Maxwell's equations. These theoretical developments are described, for example, in Dittrich and Gies. In particular, the theory of
quantum electrodynamics predicts that vacuum should exhibit
nonlinear effects that will make it behave like a
birefringent material with ε slightly greater than ε
0 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
or
. The VEV of a field φ, which should be written as
, is usually condensed to
.
Virtual particles
The
uncertainty principle in the form
implies that in the vacuum one or more particles with energy ΔE above the vacuum may be created for a short time Δt. These
virtual particles are included in the definition of the vacuum.
References and notes
Further Information
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