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In quantum physics, a quantum fluctuation is the temporary change in the amount of energy in a point in space, arising from Werner Heisenberg
Werner Heisenberg

Werner Heisenberg was a German Theoretical physics who made foundational contributions to quantum mechanics and is best known for asserting the uncertainty principle of quantum theory....
's uncertainty principle
Uncertainty principle

In quantum physics, the Werner Heisenberg uncertainty principle states that certain physical quantities, like the position and momentum, cannot both have precise values at the same time....
.

According to one formulation of the principle, energy and time can be related by the relation



That means that conservation of energy
Conservation of energy

The law of conservation of energy states that the total amount of energy in an isolated system remains constant. A consequence of this law is that energy cannot be created or destroyed....
 can appear to be violated, but only for small times. This allows the creation of particle-antiparticle pairs of virtual particle
Virtual particle

In physics, a virtual particle is a particle that exists for a limited time and space, introducing uncertainty in their energy and momentum due to the Heisenberg Uncertainty Principle....
s. The effects of these particles are measurable, for example, in the effective charge of the electron, different from its "naked" charge.

In the modern view, energy
Energy

In physics, energy is a scalar physical quantity that describes the amount of Work_ that can be performed by a force. Energy is an attribute of objects and systems that is subject to a conservation law....
 is always conserved
Conservation law

In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves....
, but the eigenstates of the Hamiltonian
Hamiltonian (quantum mechanics)

In quantum mechanics, the Hamiltonian H is the observable corresponding to the total energy of the system. As with all observables, the Spectrum of the Hamiltonian is the set of possible outcomes when one measures the total energy of a system....
 (energy
Energy

In physics, energy is a scalar physical quantity that describes the amount of Work_ that can be performed by a force. Energy is an attribute of objects and systems that is subject to a conservation law....
 observable
Observable

In physics, particularly in quantum physics, a system observable is a property of the State that can be determined by some sequence of physical operational definition....
) are not the same as (e.g.the Hamiltonian doesn't commute with) the particle number operator
Particle number operator

In quantum mechanics, for systems where the total number of particles may not be preserved, the number operator is the observable that counts the number of particles....
s.

Quantum fluctuations may have been very important in the origin of the structure of the universe: according to the model of inflation
Cosmic inflation

In physical cosmology, cosmic inflation is the hypothesis that the wiktionary:nascent universe passed through a phase of exponential growth metric expansion of space was driven by a negative pressure vacuum energy density....
 the ones that existed when inflation began were amplified and formed the seed of all current observed structure.

Quantum fluctuations of a field
A reasonably odd distinction can be made between quantum fluctuations and thermal fluctuations
Temperature

In physics, temperature is a physical property of a Physical system that underlies the common notions of hot and cold; something that feels hotter generally has the greater temperature....
 of a quantum field
Quantum field theory

Quantum field theory or QFT provides a theoretical framework for constructing quantum mechanics models of systems classically described by field or of Many-body problem....
 (at least for a free field; for interacting fields, renormalization
Renormalization

In quantum field theory, the statistical mechanics of fields, and the theory of self-similarity geometric structures, renormalization refers to a collection of techniques used to take a continuum limit....
 complicates matters a lot).






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In quantum physics, a quantum fluctuation is the temporary change in the amount of energy in a point in space, arising from Werner Heisenberg
Werner Heisenberg

Werner Heisenberg was a German Theoretical physics who made foundational contributions to quantum mechanics and is best known for asserting the uncertainty principle of quantum theory....
's uncertainty principle
Uncertainty principle

In quantum physics, the Werner Heisenberg uncertainty principle states that certain physical quantities, like the position and momentum, cannot both have precise values at the same time....
.

According to one formulation of the principle, energy and time can be related by the relation



That means that conservation of energy
Conservation of energy

The law of conservation of energy states that the total amount of energy in an isolated system remains constant. A consequence of this law is that energy cannot be created or destroyed....
 can appear to be violated, but only for small times. This allows the creation of particle-antiparticle pairs of virtual particle
Virtual particle

In physics, a virtual particle is a particle that exists for a limited time and space, introducing uncertainty in their energy and momentum due to the Heisenberg Uncertainty Principle....
s. The effects of these particles are measurable, for example, in the effective charge of the electron, different from its "naked" charge.

In the modern view, energy
Energy

In physics, energy is a scalar physical quantity that describes the amount of Work_ that can be performed by a force. Energy is an attribute of objects and systems that is subject to a conservation law....
 is always conserved
Conservation law

In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves....
, but the eigenstates of the Hamiltonian
Hamiltonian (quantum mechanics)

In quantum mechanics, the Hamiltonian H is the observable corresponding to the total energy of the system. As with all observables, the Spectrum of the Hamiltonian is the set of possible outcomes when one measures the total energy of a system....
 (energy
Energy

In physics, energy is a scalar physical quantity that describes the amount of Work_ that can be performed by a force. Energy is an attribute of objects and systems that is subject to a conservation law....
 observable
Observable

In physics, particularly in quantum physics, a system observable is a property of the State that can be determined by some sequence of physical operational definition....
) are not the same as (e.g.the Hamiltonian doesn't commute with) the particle number operator
Particle number operator

In quantum mechanics, for systems where the total number of particles may not be preserved, the number operator is the observable that counts the number of particles....
s.

Quantum fluctuations may have been very important in the origin of the structure of the universe: according to the model of inflation
Cosmic inflation

In physical cosmology, cosmic inflation is the hypothesis that the wiktionary:nascent universe passed through a phase of exponential growth metric expansion of space was driven by a negative pressure vacuum energy density....
 the ones that existed when inflation began were amplified and formed the seed of all current observed structure.

Quantum fluctuations of a field


A reasonably odd distinction can be made between quantum fluctuations and thermal fluctuations
Temperature

In physics, temperature is a physical property of a Physical system that underlies the common notions of hot and cold; something that feels hotter generally has the greater temperature....
 of a quantum field
Quantum field theory

Quantum field theory or QFT provides a theoretical framework for constructing quantum mechanics models of systems classically described by field or of Many-body problem....
 (at least for a free field; for interacting fields, renormalization
Renormalization

In quantum field theory, the statistical mechanics of fields, and the theory of self-similarity geometric structures, renormalization refers to a collection of techniques used to take a continuum limit....
 complicates matters a lot). 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 in terms of its fourier transform to be

In contrast, for the classical Klein–Gordon field at non-zero temperature, the Gibbs probability density
Gibbs state

A Gibbs state in probability theory and statistical mechanics is an equilibrium probability distribution which remains invariant under future evolution of the system ....
 that we would observe a configuration at a time is

The amplitude of quantum fluctuations is controlled by the amplitude of Planck's constant
Planck constant

The Planck constant , also called Planck's constant, is a physical constant used to describe the sizes of quantum in quantum mechanics. It is named after Max Planck, one of the founders of quantum theory....
 , just as the amplitude of thermal fluctuations is controlled by . Note that the following three points are closely related:
(1) Planck's constant has units of action instead of units of energy,
(2) the quantum kernel is instead of (the quantum kernel is nonlocal from a classical heat kernel
Heat kernel

The heat kernel is* a fundamental solution to the heat equation.* a sum used in heat kernel regularization....
 viewpoint, but it is local in the sense that it does not allow signals to be transmitted),
(3) 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
Gibbs state

A Gibbs state in probability theory and statistical mechanics is an equilibrium probability distribution which remains invariant under future evolution of the system ....
 is not a Lorentz invariant initial condition).

We can construct a classical continuous random field
Field (physics)

In physics, a field is a physical quantity associated to each point of spacetime. A field can be classified as a scalar field, a vector field, or a tensor field, according to whether the value of the field at each point is a scalar , a vector , or, more generally, a tensor, respectively....
 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). Quantum effects that are consequences only of quantum fluctuations, not of subtleties of measurement incompatibility, can alternatively be modelled by classical continuous random fields.

See also


  • Casimir effect
    Casimir effect

    In physics, the Casimir effect and the Casimir-Polder force are physical force arising from a quantum field theory. The typical example is of two electric charge metallic plates in a vacuum, placed a few micrometers apart, without any external electromagnetic field....
  • Virtual particle
    Virtual particle

    In physics, a virtual particle is a particle that exists for a limited time and space, introducing uncertainty in their energy and momentum due to the Heisenberg Uncertainty Principle....
  • Quantum annealing
    Quantum annealing

    In mathematics and applications, quantum annealing is a general method for finding the global minimum of a given objective function over a given set of candidate solutions , by a process analogous to quantum fluctuations....