Quantum fluctuation

In the field of quantum physics, a quantum fluctuation is a temporary and random change in energy. These changes occur at specific points in space. They are also known as vacuum state fluctuations or vacuum fluctuations. This phenomenon happens because of the uncertainty principle. This principle was formulated by the scientist Werner Heisenberg. It describes how certain properties of the universe cannot be known perfectly at the same time. In this case, the principle relates the uncertainty in energy to the uncertainty in time.

The mechanism behind these fluctuations involves the fundamental fields of the universe. In quantum field theory, elementary particles are represented by these fields. For example, electric and magnetic fields represent the electromagnetic force, which is carried by photons. The W and Z fields carry the weak force. Additionally, gluon fields carry the strong force. Quantum fluctuations are minute random changes in the values of these specific fields. Because energy and time are linked by the uncertainty principle, pairs of virtual particles are continually created and annihilated in empty space. These virtual particles have an energy of ΔE and a lifetime shorter than Δt. While these particles are not directly detectable, their cumulative effects can be measured.

There are distinct ways to understand these fluctuations through different physical lenses. One way is to look at them as loop effects in Feynman diagrams. In quantum electrodynamics, for example, the electron self-energy diagram represents a quantum fluctuation in relation to the electron propagator. These loop diagrams can be mathematically problematic. They often introduce integrals over loop momentum that allow for contributions from arbitrarily large momenta. Another way to categorize fluctuations is by comparing quantum fluctuations to thermal fluctuations. While thermal fluctuations are controlled by temperature and the Boltzmann constant, quantum fluctuations are controlled by the Planck constant, or ℏ.

The history of discovering these effects is tied to major milestones in physics. One of the first observations providing evidence for vacuum fluctuations was the Lamb shift in hydrogen. Scientists also developed renormalization theory to address challenges caused by these fluctuations. Without quantum fluctuations, the "bare" mass and charge of elementary particles would be infinite. Renormalization theory explains that a cloud of virtual particles creates a shielding effect. This shielding is responsible for the finite mass and charge we observe in elementary particles.

The significance of these tiny events is found in the precise math of the universe. The uncertainty principle uses the Planck constant, where 1/2ℏ is approximately 5.27286 × 10⁻³⁵ J⋅s. This value helps define the relationship between energy and time. These fluctuations also lead to the Casimir effect. Even though these changes happen at a microscopic scale, they have massive implications. In July 2020, scientists reported that quantum vacuum fluctuations can influence macroscopic, human-scale objects. They achieved this by measuring correlations below the standard quantum limit. They looked at the position and momentum uncertainty of the mirrors in LIGO, which is a large-scale scientific tool.

Quantum fluctuations connect to broader concepts in field theory and measurement. A key distinction exists between relativistic and non-relativistic fields. For a relativistic Klein–Gordon field in a vacuum state, the probability of observing a configuration is determined by a specific mathematical propagator. In contrast, a non-relativistic field at a non-zero temperature follows a Gibbs probability density. This density is controlled by the temperature and the Boltzmann constant. Furthermore, the quantum vacuum state is Lorentz-invariant. This is a different property than the classical thermal state, which is not Lorentz-invariant. This highlights how the rules of the quantum world differ fundamentally from classical physics.