Vacuum fluctuations appear as
virtual particles, which are always created in particle–antiparticle pairs.[4] Since they are created spontaneously without a source of energy, vacuum fluctuations and virtual particles are said to violate the
conservation of energy. The disposition of this energy gap is not well-understood; some physicists believe that the energy is transferred to or from the macroscopic environment in the course of the measurement process, while others believe that the observable energy is only conserved "on average".[5][6] No experiment has been confirmed as definitive evidence of violations of the conservation of energy principle in quantum mechanics, but that doesn't rule out that some newer experiments, as proposed, may find evidence of violations of the conservation of energy principle in quantum mechanics.[6]
The
uncertainty principle states the uncertainty in
energy and
time can be related by[7], where 1/2ħ ≈ 5.27286×10−35 Js. This means[citation needed] that pairs of virtual particles with energy and lifetime shorter than are continually created and annihilated in empty space. Although the particles are not directly detectable, the cumulative effects of these particles are measurable. For example, without quantum fluctuations, the
"bare" mass and charge of elementary particles would be infinite; from
renormalization theory the shielding effect of the cloud of virtual particles is responsible for the finite mass and charge of elementary particles.
Another consequence is the
Casimir effect. One of the first observations which was evidence for vacuum fluctuations was the
Lamb shift in hydrogen. In July 2020, scientists reported that quantum vacuum fluctuations can influence the motion of macroscopic, human-scale objects by measuring correlations below the
standard quantum limit between the position/momentum uncertainty of the mirrors of
LIGO and the photon number/phase uncertainty of light that they reflect.[8][9][10]
Field fluctuations
In
quantum field theory, fields undergo quantum fluctuations. A reasonably clear distinction can be made between quantum fluctuations and
thermal fluctuations of a
quantum field (at least for a free field; for interacting fields,
renormalization substantially complicates matters). An illustration of this distinction can be seen by considering quantum and classical Klein–Gordon fields:[11] For the
quantized Klein–Gordon field in the
vacuum state, we can calculate the probability density that we would observe a configuration at a time t in terms of its
Fourier transform to be
These probability distributions illustrate that every possible configuration of the field is possible, with the amplitude of quantum fluctuations controlled by
Planck's constant, just as the amplitude of thermal fluctuations is controlled by , where kB is
Boltzmann's constant. Note that the following three points are closely related:
Planck's constant has units of
action (joule-seconds) instead of units of energy (joules),
the quantum kernel is instead of (the quantum kernel is nonlocal from a classical
heat kernel viewpoint, but it is local in the sense that it does not allow signals to be transmitted),[citation needed]
the quantum vacuum state is
Lorentz-invariant (although not manifestly in the above), whereas the classical thermal state is not (the classical dynamics is Lorentz-invariant, but the Gibbs probability density is not a Lorentz-invariant initial condition).
A
classical continuous random field can be constructed that has the same probability density as the quantum vacuum state, so that the principal difference from quantum field theory is the measurement theory (
measurement in quantum theory is different from measurement for a classical continuous random field, in that classical measurements are always mutually compatible – in quantum-mechanical terms they always commute).