In quantum field theory, the quantum vacuum state (also called the quantum vacuum or vacuum state) is the state with the lowest possible energy. Usually, it does not contain any physical particles. However, the quantum vacuum is not completely empty. Instead, it has brief flashes of electromagnetic waves and particles that appear and disappear in the quantum field.
The QED vacuum, part of quantum electrodynamics (QED), was the first vacuum state in quantum field theory to be developed. QED began in the 1930s. In the late 1940s and early 1950s, it was revised by Feynman, Tomonaga, and Schwinger. These scientists shared the Nobel Prize in 1965 for this work. Today, electromagnetic interactions and weak interactions are unified only at very high energies in the theory of the electroweak interaction.
The Standard Model is an expansion of QED ideas to include all known elementary particles and their interactions, except for gravity. Quantum chromodynamics (QCD) is the part of the Standard Model that explains strong interactions. The QCD vacuum is the vacuum state in quantum chromodynamics. Scientists study this vacuum in experiments at the Large Hadron Collider and the Relativistic Heavy Ion Collider. It is connected to the structure of the vacuum in strong interactions.
Non-zero expectation value
If quantum field theory can be accurately described using perturbation theory, then the properties of the vacuum are similar to the lowest energy state of a quantum mechanical harmonic oscillator, or more precisely, the ground state of a measurement problem. In this case, the average value of any field operator in the vacuum is zero. However, in quantum field theories where perturbation theory is not effective at low energies (such as Quantum Chromodynamics or the BCS theory of superconductivity), field operators can have non-zero average values in the vacuum due to a process called spontaneous symmetry breaking. In the Standard Model, the Higgs field gains a non-zero average value when the electroweak symmetry is broken, which helps explain the masses of other particles.
Energy
The vacuum state is connected to zero-point energy, which is the lowest possible energy state. This energy can be measured in experiments, such as the Casimir effect observed in laboratories. In physical cosmology, the energy of the cosmological vacuum is known as the cosmological constant. The energy found in a cubic centimeter of empty space has been calculated to be about one trillionth of an erg (or 0.6 eV). A key requirement for a potential Theory of Everything is that the energy of the quantum vacuum state must account for the cosmological constant observed in the universe.
Symmetry
In a relativistic field theory, the vacuum remains unchanged under Poincaré transformations, a property that comes from the Wightman axioms but can also be shown directly without these axioms. This invariance means that only combinations of field operators that are scalars (unchanged under rotations and translations) can have non-zero average values in the vacuum. The vacuum may also break some internal symmetries present in the theory's equations. When this happens, the vacuum has fewer symmetries than the theory allows, and this situation is called spontaneous symmetry breaking.
Non-linear permittivity
Quantum corrections to Maxwell's equations suggest that the vacuum may have a very small nonlinear response to electric fields, changing how it allows electric fields to pass through. These ideas are discussed in works by scientists such as Dittrich and Gies. According to quantum electrodynamics (QED), the vacuum should show a slight nonlinearity, meaning that a very strong electric field would cause the vacuum's permittivity to increase slightly compared to its usual value, ε₀. It is also possible that a strong electric field could change the vacuum's permeability, making it anisotropic. In this case, the permeability might be slightly less than μ₀ in the direction of the electric field and slightly greater than μ₀ in directions perpendicular to it. When an electromagnetic wave travels in a direction not aligned with the electric field, the vacuum may exhibit birefringence, a phenomenon similar to the Kerr effect but without the presence of matter. This tiny nonlinearity can be explained by the temporary creation of virtual particle pairs. A specific electric field strength, called the Schwinger limit, is predicted to be about 1.32 × 10¹⁸ volts per meter, where these nonlinear effects become noticeable. The related Kerr constant is estimated to be about 10 times smaller than that of water. Other theories from particle physics have also been proposed to explain dichroism, but experiments to measure these effects remain challenging and have not yet been successful.
Virtual particles
Virtual particles exist because the electromagnetic fields in quantum physics do not follow a specific order rule. This means that while the average strength of these fields is zero in a vacuum, their variations are not. The term "vacuum fluctuations" describes these variations in the field strength when the system is in its lowest energy state. This phenomenon is sometimes explained using the Heisenberg energy-time uncertainty principle, which states that the product of energy uncertainty (ΔE) and time uncertainty (Δt) is always greater than or equal to half of the reduced Planck constant (ℏ/2). This principle suggests that the short lifetime of virtual particles allows the temporary use of large amounts of energy from the vacuum, enabling their brief existence. However, not all scientists agree on how the energy-time uncertainty principle explains this phenomenon. One issue is the interpretation of time in the principle, as energy and time do not follow the same rules as position and momentum, which do have a specific relationship. Scientists continue to explore different ways to define time in a way that connects with energy through a clear mathematical rule. Research into the energy-time uncertainty principle remains an ongoing and complex topic in physics.
Physical nature of the quantum vacuum
According to Astrid Lambrecht (2002): "When all matter is removed from a space and the temperature is lowered to absolute zero, a quantum vacuum state is created in a thought experiment." According to Fowler & Guggenheim (1939/1965), the third law of thermodynamics can be clearly stated as:
It is impossible to reach absolute zero through any process, no matter how perfect, in a limited number of steps. (See also.)
Photon-photon interaction happens only when photons interact with the vacuum state of another field, such as the Dirac electron-positron vacuum field. This is connected to the idea of vacuum polarization. According to Milonni (1994): "All quantum fields have zero-point energy and vacuum fluctuations." This means that each field, such as the electromagnetic field or the Dirac electron-positron field, has a component of the quantum vacuum (when other fields are not considered). According to Milonni (1994), some effects linked to the vacuum electromagnetic field can be explained in different ways, some more traditional than others. The Casimir attraction between uncharged conductive plates is often given as an example of an effect caused by the vacuum electromagnetic field. Schwinger, DeRaad, and Milton (1978) are cited by Milonni (1994) as correctly, though less traditionally, explaining the Casimir effect using a model where "the vacuum is considered as a state with all physical properties equal to zero." In this model, observed effects are explained as the result of electron motion on the electromagnetic field, called the source field effect. Milonni writes:
The main idea here is that the Casimir force can be calculated using only the source fields in conventional quantum electrodynamics (QED), … Milonni provides detailed arguments that the physical effects usually linked to the vacuum electromagnetic field cannot be explained by that field alone. They also require a contribution from the self-energy of electrons or their radiation reaction. He writes: "The radiation reaction and the vacuum fields are two sides of the same concept when explaining physical processes in QED, including the Lamb shift, van der Waals forces, and Casimir effects."
This idea is also stated by Jaffe (2005): "The Casimir force can be calculated without considering vacuum fluctuations, and like all other observable effects in QED, it disappears as the fine structure constant, α, approaches zero."