Vacuum energy is an underlying background energy that exists in space throughout the entire Universe. This behavior is codified in Heisenberg's energy–time uncertainty principle. Still, the exact effect of such fleeting bits of energy is difficult to quantify. The vacuum energy is a special case of zero-point energy that relates to the quantum vacuum.
The effects of vacuum energy can be experimentally observed in various phenomena such as spontaneous emission, the Casimir effect and the Lamb shift, and are thought to influence the behavior of the Universe on cosmological scales. Using the upper limit of the cosmological constant, the vacuum energy of free space has been estimated to be 10−9 joules (10−2 ergs) per cubic meter. However, in both quantum electrodynamics (QED) and stochastic electrodynamics (SED), consistency with the principle of Lorentz covariance and with the magnitude of the Planck constant suggest a much larger value of 10113 joules per cubic meter. This huge discrepancy is known as the cosmological constant problem.
Origin
Quantum field theory states that all fundamental fields, such as the electromagnetic field, must be quantized at each and every point in space.
A field in physics may be envisioned as if space were filled with
interconnected vibrating balls and springs, and the strength of the
field is like the displacement of a ball from its rest position. The
theory requires "vibrations" in, or more accurately changes in the
strength of, such a field to propagate as per the appropriate wave equation for the particular field in question. The second quantization
of quantum field theory requires that each such ball–spring combination
be quantized, that is, that the strength of the field be quantized at
each point in space. Canonically, if the field at each point in space is
a simple harmonic oscillator, its quantization places a quantum harmonic oscillator at each point. Excitations of the field correspond to the elementary particles of particle physics. Thus, according to the theory, even the vacuum
has a vastly complex structure and all calculations of quantum field
theory must be made in relation to this model of the vacuum.
The theory considers vacuum to implicitly have the same properties as a particle, such as spin or polarization in the case of light,
energy, and so on. According to the theory, most of these properties
cancel out on average leaving the vacuum empty in the literal sense of
the word. One important exception, however, is the vacuum energy or the vacuum expectation value of the energy. The quantization of a simple harmonic oscillator requires the lowest possible energy, or zero-point energy of such an oscillator to be:
Summing over all possible oscillators at all points in space
gives an infinite quantity. To remove this infinity, one may argue that
only differences in energy are physically measurable, much as the
concept of potential energy has been treated in classical mechanics for centuries. This argument is the underpinning of the theory of renormalization. In all practical calculations, this is how the infinity is handled.
Vacuum energy can also be thought of in terms of virtual particles
(also known as vacuum fluctuations) which are created and destroyed out
of the vacuum. These particles are always created out of the vacuum in
particle–antiparticle
pairs, which in most cases shortly annihilate each other and disappear.
However, these particles and antiparticles may interact with others
before disappearing, a process which can be mapped using Feynman diagrams. Note that this method of computing vacuum energy is mathematically equivalent to having a quantum harmonic oscillator at each point and, therefore, suffers the same renormalization problems.
Additional contributions to the vacuum energy come from spontaneous symmetry breaking in quantum field theory.
Implications
Vacuum energy has a number of consequences. In 1948, Dutch physicists Hendrik B. G. Casimir and Dirk Polder predicted the existence of a tiny attractive force between closely placed metal plates due to resonances in the vacuum energy in the space between them. This is now known as the Casimir effect
and has since been extensively experimentally verified. It is therefore
believed that the vacuum energy is "real" in the same sense that more
familiar conceptual objects such as electrons, magnetic fields, etc.,
are real. However, alternative explanations for the Casimir effect have
since been proposed.
Other predictions are harder to verify. Vacuum fluctuations are
always created as particle–antiparticle pairs. The creation of these
virtual particles near the event horizon of a black hole has been hypothesized by physicist Stephen Hawking to be a mechanism for the eventual "evaporation" of black holes.
If one of the pair is pulled into the black hole before this, then the
other particle becomes "real" and energy/mass is essentially radiated
into space from the black hole. This loss is cumulative and could result
in the black hole's disappearance over time. The time required is
dependent on the mass of the black hole (the equations indicate that the
smaller the black hole, the more rapidly it evaporates) but could be on
the order of 10100 years for large solar-mass black holes.
The vacuum energy also has important consequences for physical cosmology. General relativity predicts that energy is equivalent to mass, and therefore, if the vacuum energy is "really there", it should exert a gravitational force. Essentially, a non-zero vacuum energy is expected to contribute to the cosmological constant, which affects the expansion of the universe. In the special case of vacuum energy, general relativity stipulates that the gravitational field is proportional to ρ + 3p (where ρ is the mass–energy density, and p
is the pressure). Quantum theory of the vacuum further stipulates that
the pressure of the zero-state vacuum energy is always negative and
equal in magnitude to ρ. Thus, the total is ρ + 3p = ρ − 3ρ = −2ρ,
a negative value. If indeed the vacuum ground state has non-zero
energy, the calculation implies a repulsive gravitational field, giving
rise to acceleration of the expansion of the universe. However, the vacuum energy is mathematically infinite without renormalization,
which is based on the assumption that we can only measure energy in a
relative sense, which is not true if we can observe it indirectly via
the cosmological constant.
The existence of vacuum energy is also sometimes used as
theoretical justification for the possibility of free-energy machines.
It has been argued that due to the broken symmetry (in QED), free energy
does not violate conservation of energy, since the laws of
thermodynamics only apply to equilibrium systems. However, consensus
amongst physicists is that this is unknown as the nature of vacuum
energy remains an unsolved problem. In particular, the second law of thermodynamics is unaffected by the existence of vacuum energy. However, in Stochastic Electrodynamics,
the energy density is taken to be a classical random noise wave field
which consists of real electromagnetic noise waves propagating
isotropically in all directions. The energy in such a wave field would
seem to be accessible, e.g., with nothing more complicated than a directional coupler. The most obvious difficulty appears to be the spectral distribution of the energy, which compatibility with Lorentz invariance requires to take the form Kf3, where K is a constant and f denotes frequency.
It follows that the energy and momentum flux in this wave field only
becomes significant at extremely short wavelengths where directional
coupler technology is currently lacking.
History
In 1934, Georges Lemaître used an unusual perfect-fluidequation of state to interpret the cosmological constant as due to vacuum energy. In 1948, the Casimir effect provided an experimental method for a verification of the existence of vacuum energy; in 1955, however, Evgeny Lifshitz offered a different origin for the Casimir effect. In 1957, Lee and Yang proved the concepts of broken symmetry and parity violation, for which they won the Nobel prize. In 1973, Edward Tryon proposed the zero-energy universe hypothesis: that the Universe may be a large-scale quantum-mechanical vacuum fluctuation where positive mass–energy is balanced by negative gravitational potential energy.
During the 1980s, there were many attempts to relate the fields that
generate the vacuum energy to specific fields that were predicted by
attempts at a Grand unification theory
and to use observations of the Universe to confirm one or another
version. However, the exact nature of the particles (or fields) that
generate vacuum energy, with a density such as that required by
inflation theory, remains a mystery.
