Quantum vacuum state

Last updated

In quantum field theory, the quantum vacuum state (also called the quantum vacuum or vacuum state) is the quantum state with the lowest possible energy. Generally, it contains no physical particles. Zero-point field is sometimes used as a synonym for the vacuum state of an individual quantized field.

Contents

According to present-day understanding of what is called the vacuum state or the quantum vacuum, it is "by no means a simple empty space". [1] [2] According to quantum mechanics, the vacuum state is not truly empty but instead contains fleeting electromagnetic waves and particles that pop into and out of the quantum field. [3] [4] [5]

The QED vacuum of quantum electrodynamics (or QED) was the first vacuum of quantum field theory to be developed. QED originated in the 1930s, and in the late 1940s and early 1950s it was reformulated by Feynman, Tomonaga and Schwinger, who jointly received the Nobel prize for this work in 1965. [6] Today the electromagnetic interactions and the weak interactions are unified (at very high energies only) in the theory of the electroweak interaction.

The Standard Model is a generalization of the QED work to include all the known elementary particles and their interactions (except gravity). Quantum chromodynamics (or QCD) is the portion of the Standard Model that deals with strong interactions, and QCD vacuum is the vacuum of quantum chromodynamics. It is the object of study in the Large Hadron Collider and the Relativistic Heavy Ion Collider, and is related to the so-called vacuum structure of strong interactions. [7]

Non-zero expectation value

The video of an experiment showing vacuum fluctuations (in the red ring) amplified by spontaneous parametric down-conversion.

If the quantum field theory can be accurately described through perturbation theory, then the properties of the vacuum are analogous to the properties of the ground state of a quantum mechanical harmonic oscillator, or more accurately, the ground state of a measurement problem. In this case the vacuum expectation value (VEV) of any field operator vanishes. For quantum field theories in which perturbation theory breaks down at low energies (for example, Quantum chromodynamics or the BCS theory of superconductivity) field operators may have non-vanishing vacuum expectation values called condensates. In the Standard Model, the non-zero vacuum expectation value of the Higgs field, arising from spontaneous symmetry breaking, is the mechanism by which the other fields in the theory acquire mass.

Energy

The vacuum state is associated with a zero-point energy, and this zero-point energy (equivalent to the lowest possible energy state) has measurable effects. In the laboratory, it may be detected as the Casimir effect. In physical cosmology, the energy of the cosmological vacuum appears as the cosmological constant. In fact, the energy of a cubic centimeter of empty space has been calculated figuratively to be one trillionth of an erg (or 0.6 eV). [8] An outstanding requirement imposed on a potential Theory of Everything is that the energy of the quantum vacuum state must explain the physically observed cosmological constant.

Symmetry

For a relativistic field theory, the vacuum is Poincaré invariant, which follows from Wightman axioms but can be also proved directly without these axioms. [9] Poincaré invariance implies that only scalar combinations of field operators have non-vanishing VEV's. The VEV may break some of the internal symmetries of the Lagrangian of the field theory. In this case the vacuum has less symmetry than the theory allows, and one says that spontaneous symmetry breaking has occurred. See Higgs mechanism, standard model.

Non-linear permittivity

Quantum corrections to Maxwell's equations are expected to result in a tiny nonlinear electric polarization term in the vacuum, resulting in a field-dependent electrical permittivity ε deviating from the nominal value ε0 of vacuum permittivity. [10] These theoretical developments are described, for example, in Dittrich and Gies. [5] The theory of quantum electrodynamics predicts that the QED vacuum should exhibit a slight nonlinearity so that in the presence of a very strong electric field, the permitivity is increased by a tiny amount with respect to ε0. What's more, and what would be easier to observe (but still very difficult!), is that a strong electric field would modify the effective permeability of free space, becoming anisotropic with a value slightly below μ0 in the direction of the electric field and slightly exceeding μ0 in the perpendicular direction, thereby exhibiting birefringence for an electromagnetic wave travelling in a direction other than that of the electric field. The effect is similar to the Kerr effect but without matter being present. [11] This tiny nonlinearity can be interpreted in terms of virtual pair production [12] The required electric field is predicted to be enormous, about V/m, known as the Schwinger limit; the equivalent Kerr constant has been estimated, being about 1020 times smaller than the Kerr constant of water. Explanations for dichroism from particle physics, outside quantum electrodynamics, also have been proposed. [13] Experimentally measuring such an effect is very difficult, [14] and has not yet been successful.

Virtual particles

The presence of virtual particles can be rigorously based upon the non-commutation of the quantized electromagnetic fields. Non-commutation means that although the average values of the fields vanish in a quantum vacuum, their variances do not. [15] The term "vacuum fluctuations" refers to the variance of the field strength in the minimal energy state, [16] and is described picturesquely as evidence of "virtual particles". [17] It is sometimes attempted to provide an intuitive picture of virtual particles, or variances, based upon the Heisenberg energy-time uncertainty principle:

(with ΔE and Δt being the energy and time variations respectively; ΔE is the accuracy in the measurement of energy and Δt is the time taken in the measurement, and ħ is the Reduced Planck constant) arguing along the lines that the short lifetime of virtual particles allows the "borrowing" of large energies from the vacuum and thus permits particle generation for short times. [18] Although the phenomenon of virtual particles is accepted, this interpretation of the energy-time uncertainty relation is not universal. [19] [20] One issue is the use of an uncertainty relation limiting measurement accuracy as though a time uncertainty Δt determines a "budget" for borrowing energy ΔE. Another issue is the meaning of "time" in this relation, because energy and time (unlike position q and momentum p, for example) do not satisfy a canonical commutation relation (such as [q, p] = iħ). [21] Various schemes have been advanced to construct an observable that has some kind of time interpretation, and yet does satisfy a canonical commutation relation with energy. [22] [23] The very many approaches to the energy-time uncertainty principle are a long and continuing subject. [23]

Physical nature of the quantum vacuum

According to Astrid Lambrecht (2002): "When one empties out a space of all matter and lowers the temperature to absolute zero, one produces in a Gedankenexperiment [thought experiment] the quantum vacuum state." [1] According to Fowler & Guggenheim (1939/1965), the third law of thermodynamics may be precisely enunciated as follows:

It is impossible by any procedure, no matter how idealized, to reduce any assembly to the absolute zero in a finite number of operations. [24] (See also. [25] [26] [27] )

Photon-photon interaction can occur only through interaction with the vacuum state of some other field, for example through the Dirac electron-positron vacuum field; this is associated with the concept of vacuum polarization. [28] According to Milonni (1994): "... all quantum fields have zero-point energies and vacuum fluctuations." [29] This means that there is a component of the quantum vacuum respectively for each component field (considered in the conceptual absence of the other fields), such as the electromagnetic field, the Dirac electron-positron field, and so on. According to Milonni (1994), some of the effects attributed to the vacuum electromagnetic field can have several physical interpretations, some more conventional than others. The Casimir attraction between uncharged conductive plates is often proposed as an example of an effect of the vacuum electromagnetic field. Schwinger, DeRaad, and Milton (1978) are cited by Milonni (1994) as validly, though unconventionally, explaining the Casimir effect with a model in which "the vacuum is regarded as truly a state with all physical properties equal to zero." [30] [31] In this model, the observed phenomena are explained as the effects of the electron motions on the electromagnetic field, called the source field effect. Milonni writes:

The basic idea here will be that the Casimir force may be derived from the source fields alone even in completely conventional QED, ... Milonni provides detailed argument that the measurable physical effects usually attributed to the vacuum electromagnetic field cannot be explained by that field alone, but require in addition a contribution from the self-energy of the electrons, or their radiation reaction. He writes: "The radiation reaction and the vacuum fields are two aspects of the same thing when it comes to physical interpretations of various QED processes including the Lamb shift, van der Waals forces, and Casimir effects." [32]

This point of view is also stated by Jaffe (2005): "The Casimir force can be calculated without reference to vacuum fluctuations, and like all other observable effects in QED, it vanishes as the fine structure constant, α, goes to zero." [33]

Notations

The vacuum state is written as or . The vacuum expectation value (see also Expectation value) of any field should be written as .

See also

References and notes

  1. 1 2 Astrid Lambrecht (2002). Hartmut Figger; Dieter Meschede; Claus Zimmermann (eds.). Observing mechanical dissipation in the quantum vacuum: an experimental challenge; in Laser physics at the limits. Berlin/New York: Springer. p. 197. ISBN   978-3-540-42418-5.
  2. Christopher Ray (1991). Time, space and philosophy. London/New York: Routledge. Chapter 10, p. 205. ISBN   978-0-415-03221-6.
  3. AIP Physics News Update,1996
  4. Physical Review Focus Dec. 1998
  5. 1 2 Walter Dittrich & Gies H (2000). Probing the quantum vacuum: perturbative effective action approach. Berlin: Springer. ISBN   978-3-540-67428-3.
  6. For an historical discussion, see for example Ari Ben-Menaḥem, ed. (2009). "Quantum electrodynamics (QED)". Historical Encyclopedia of Natural and Mathematical Sciences. 1 (5th ed.). Springer. pp. 4892 ff. ISBN   978-3-540-68831-0. For the Nobel prize details and the Nobel lectures by these authors see "The Nobel Prize in Physics 1965". Nobelprize.org. Retrieved 2012-02-06.
  7. Jean Letessier; Johann Rafelski (2002). Hadrons and Quark-Gluon Plasma. Cambridge University Press. p. 37 ff. ISBN   978-0-521-38536-7.
  8. Sean Carroll, Sr Research Associate - Physics, California Institute of Technology, June 22, 2006 C-SPAN broadcast of Cosmology at Yearly Kos Science Panel, Part 1
  9. Bednorz, Adam (November 2013). "Relativistic invariance of the vacuum". The European Physical Journal C. 73 (12): 2654. arXiv: 1209.0209 . Bibcode:2013EPJC...73.2654B. doi:10.1140/epjc/s10052-013-2654-9. S2CID   39308527.
  10. David Delphenich (2006). "Nonlinear Electrodynamics and QED". arXiv: hep-th/0610088 .
  11. Mourou, G. A., T. Tajima, and S. V. Bulanov, Optics in the relativistic regime; § XI Nonlinear QED, Reviews of Modern Physics vol. 78 (no. 2), 309-371 (2006) pdf file.
  12. Klein, James J. and B. P. Nigam, Birefringence of the vacuum, Physical Review vol. 135, p. B1279-B1280 (1964).
  13. Holger Gies; Joerg Jaeckel; Andreas Ringwald (2006). "Polarized Light Propagating in a Magnetic Field as a Probe of Millicharged Fermions". Physical Review Letters. 97 (14): 140402. arXiv: hep-ph/0607118 . Bibcode:2006PhRvL..97n0402G. doi:10.1103/PhysRevLett.97.140402. PMID   17155223. S2CID   43654455.
  14. Davis; Joseph Harris; Gammon; Smolyaninov; Kyuman Cho (2007). "Experimental Challenges Involved in Searches for Axion-Like Particles and Nonlinear Quantum Electrodynamic Effects by Sensitive Optical Techniques". arXiv: 0704.0748 [hep-th].
  15. Myron Wyn Evans; Stanisław Kielich (1994). Modern nonlinear optics, Volume 85, Part 3. John Wiley & Sons. p. 462. ISBN   978-0-471-57548-1. For all field states that have classical analog the field quadrature variances are also greater than or equal to this commutator.
  16. David Nikolaevich Klyshko (1988). Photons and nonlinear optics. Taylor & Francis. p. 126. ISBN   978-2-88124-669-2.
  17. Milton K. Munitz (1990). Cosmic Understanding: Philosophy and Science of the Universe. Princeton University Press. p. 132. ISBN   978-0-691-02059-4. The spontaneous, temporary emergence of particles from vacuum is called a "vacuum fluctuation".
  18. For an example, see P. C. W. Davies (1982). The accidental universe . Cambridge University Press. pp.  106. ISBN   978-0-521-28692-3.
  19. A vaguer description is provided by Jonathan Allday (2002). Quarks, leptons and the big bang (2nd ed.). CRC Press. pp. 224 ff. ISBN   978-0-7503-0806-9. The interaction will last for a certain duration Δt. This implies that the amplitude for the total energy involved in the interaction is spread over a range of energies ΔE.
  20. This "borrowing" idea has led to proposals for using the zero-point energy of vacuum as an infinite reservoir and a variety of "camps" about this interpretation. See, for example, Moray B. King (2001). Quest for zero point energy: engineering principles for 'free energy' inventions. Adventures Unlimited Press. pp. 124 ff. ISBN   978-0-932813-94-7.
  21. Quantities satisfying a canonical commutation rule are said to be noncompatible observables, by which is meant that they can both be measured simultaneously only with limited precision. See Kiyosi Itô (1993). "§ 351 (XX.23) C: Canonical commutation relations". Encyclopedic dictionary of mathematics (2nd ed.). MIT Press. p. 1303. ISBN   978-0-262-59020-4.
  22. Paul Busch; Marian Grabowski; Pekka J. Lahti (1995). "§III.4: Energy and time". Operational quantum physics . Springer. pp.  77 ff. ISBN   978-3-540-59358-4.
  23. 1 2 For a review, see Paul Busch (2008). "Chapter 3: The Time–Energy Uncertainty Relation". In J.G. Muga; R. Sala Mayato; Í.L. Egusquiza (eds.). Time in Quantum Mechanics. Lecture Notes in Physics. 734 (2nd ed.). Springer. pp. 73–105. arXiv: quant-ph/0105049 . Bibcode:2002tqm..conf...69B. doi:10.1007/978-3-540-73473-4_3. ISBN   978-3-540-73472-7. S2CID   14119708.
  24. Fowler, R., Guggenheim, E.A. (1965). Statistical Thermodynamics. A Version of Statistical Mechanics for Students of Physics and Chemistry, reprinted with corrections, Cambridge University Press, London, page 224.
  25. Partington, J.R. (1949). An Advanced Treatise on Physical Chemistry, volume 1, Fundamental Principles. The Properties of Gases, Longmans, Green and Co., London, page 220.
  26. Wilks, J. (1971). The Third Law of Thermodynamics, Chapter 6 in Thermodynamics, volume 1, ed. W. Jost, of H. Eyring, D. Henderson, W. Jost, Physical Chemistry. An Advanced Treatise, Academic Press, New York, page 477.
  27. Bailyn, M. (1994). A Survey of Thermodynamics, American Institute of Physics, New York, ISBN   0-88318-797-3, page 342.
  28. Jauch, J.M., Rohrlich, F. (1955/1980). The Theory of Photons and Electrons. The Relativistic Quantum Field Theory of Charged Particles with Spin One-half, second expanded edition, Springer-Verlag, New York, ISBN   0-387-07295-0, pages 287–288.
  29. Milonni, P.W. (1994). The Quantum Vacuum. An Introduction to Quantum Electrodynamics, Academic Press, Inc., Boston, ISBN   0-12-498080-5, page xv.
  30. Milonni, P.W. (1994). The Quantum Vacuum. An Introduction to Quantum Electrodynamics, Academic Press, Inc., Boston, ISBN   0-12-498080-5, page 239.
  31. Schwinger, J.; DeRaad, L.L.; Milton, K.A. (1978). "Casimir effect in dielectrics". Annals of Physics. 115 (1): 1–23. Bibcode:1978AnPhy.115....1S. doi:10.1016/0003-4916(78)90172-0.
  32. Milonni, P.W. (1994). The Quantum Vacuum. An Introduction to Quantum Electrodynamics, Academic Press, Inc., Boston, ISBN   0-12-498080-5, page 418.
  33. Jaffe, R.L. (2005). Casimir effect and the quantum vacuum, Phys. Rev. D72: 021301(R), http://1–5.cua.mit.edu/8.422_s07/jaffe2005_casimir.pdf%5B%5D

Further reading

Related Research Articles

In physics, the fundamental interactions, also known as fundamental forces, are the interactions that do not appear to be reducible to more basic interactions. There are four fundamental interactions known to exist: the gravitational and electromagnetic interactions, which produce significant long-range forces whose effects can be seen directly in everyday life, and the strong and weak interactions, which produce forces at minuscule, subatomic distances and govern nuclear interactions. Some scientists hypothesize that a fifth force might exist, but these hypotheses remain speculative.

Quantum field theory Theoretical framework combining classical field theory, special relativity, and quantum mechanics

In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and in condensed matter physics to construct models of quasiparticles.

Quantum electrodynamics Relativistic quantum field theory of electromagnetism

In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved. QED mathematically describes all phenomena involving electrically charged particles interacting by means of exchange of photons and represents the quantum counterpart of classical electromagnetism giving a complete account of matter and light interaction.

Zero-point energy Lowest possible energy of a quantum system or field

Zero-point energy (ZPE) is the lowest possible energy that a quantum mechanical system may have. Unlike in classical mechanics, quantum systems constantly fluctuate in their lowest energy state as described by the Heisenberg uncertainty principle. As well as atoms and molecules, the empty space of the vacuum has these properties. According to quantum field theory, the universe can be thought of not as isolated particles but continuous fluctuating fields: matter fields, whose quanta are fermions, and force fields, whose quanta are bosons. All these fields have zero-point energy. These fluctuating zero-point fields lead to a kind of reintroduction of an aether in physics, since some systems can detect the existence of this energy; however, this aether cannot be thought of as a physical medium if it is to be Lorentz invariant such that there is no contradiction with Einstein's theory of special relativity.

In physics, a virtual particle is a transient quantum fluctuation that exhibits some of the characteristics of an ordinary particle, while having its existence limited by the uncertainty principle. The concept of virtual particles arises in perturbation theory of quantum field theory where interactions between ordinary particles are described in terms of exchanges of virtual particles. A process involving virtual particles can be described by a schematic representation known as a Feynman diagram, in which virtual particles are represented by internal lines.

Julian Schwinger American theoretical physicist

Julian Seymour Schwinger was a Nobel Prize winning American theoretical physicist. He is best known for his work on quantum electrodynamics (QED), in particular for developing a relativistically invariant perturbation theory, and for renormalizing QED to one loop order. Schwinger was a physics professor at several universities.

Renormalization Process of assuring meaningful mathematical results in quantum field theory and related disciplines

Renormalization is a collection of techniques in quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, that are used to treat infinities arising in calculated quantities by altering values of these quantities to compensate for effects of their self-interactions. But even if no infinities arose in loop diagrams in quantum field theory, it could be shown that it would be necessary to renormalize the mass and fields appearing in the original Lagrangian.

Vacuum energy is an underlying background energy that exists in space throughout the entire Universe. The vacuum energy is a special case of zero-point energy that relates to the quantum vacuum.

In theoretical physics and applied mathematics, a field equation is a partial differential equation which determines the dynamics of a physical field, specifically the time evolution and spatial distribution of the field. The solutions to the equation are mathematical functions which correspond directly to the field, as functions of time and space. Since the field equation is a partial differential equation, there are families of solutions which represent a variety of physical possibilities. Usually, there is not just a single equation, but a set of coupled equations which must be solved simultaneously. Field equations are not ordinary differential equations since a field depends on space and time, which requires at least two variables.


Stochastic electrodynamics (SED) is a variant of classical electrodynamics (CED) of theoretical physics. SED consists of a set of controversial theories that posit the existence of a classical Lorentz invariant radiation field having statistical properties similar to that of the electromagnetic zero-point field (ZPF) of quantum electrodynamics (QED).

History of quantum field theory

In particle physics, the history of quantum field theory starts with its creation by Paul Dirac, when he attempted to quantize the electromagnetic field in the late 1920s. Major advances in the theory were made in the 1940s and 1950s, and led to the introduction of renormalized quantum electrodynamics (QED). QED was so successful and accurately predictive that efforts were made to apply the same basic concepts for the other forces of nature. By the late 1970s, these efforts successfully utilized gauge theory in the strong nuclear force and weak nuclear force, producing the modern standard model of particle physics.

Asım Orhan Barut was a Turkish-American theoretical physicist.

The history of quantum mechanics is a fundamental part of the history of modern physics. Quantum mechanics' history, as it interlaces with the history of quantum chemistry, began essentially with a number of different scientific discoveries: the 1838 discovery of cathode rays by Michael Faraday; the 1859–60 winter statement of the black-body radiation problem by Gustav Kirchhoff; the 1877 suggestion by Ludwig Boltzmann that the energy states of a physical system could be discrete; the discovery of the photoelectric effect by Heinrich Hertz in 1887; and the 1900 quantum hypothesis by Max Planck that any energy-radiating atomic system can theoretically be divided into a number of discrete "energy elements" ε such that each of these energy elements is proportional to the frequency ν with which each of them individually radiate energy, as defined by the following formula:

PVLAS aims to carry out a test of quantum electrodynamics and possibly detect dark matter at the Department of Physics and National Institute of Nuclear Physics in Ferrara, Italy. It searches for vacuum polarization causing nonlinear optical behavior in magnetic fields. Experiments began in 2001 at the INFN Laboratory in Legnaro and continue today with new equipment.

Branches of physics

Physics is a scientific discipline that seeks to construct and experimentally test theories of the physical universe. These theories vary in their scope and can be organized into several distinct branches, which are outlined in this article.

Stochastic quantum mechanics is an interpretation of quantum mechanics.

Superfluid vacuum theory Theory of fundamental physics

Superfluid vacuum theory (SVT), sometimes known as the BEC vacuum theory, is an approach in theoretical physics and quantum mechanics where the fundamental physical vacuum is viewed as superfluid or as a Bose–Einstein condensate (BEC).

QED vacuum lowest-energy state

The QED vacuum is the field-theoretic vacuum of quantum electrodynamics. It is the lowest energy state of the electromagnetic field when the fields are quantized. When Planck's constant is hypothetically allowed to approach zero, QED vacuum is converted to classical vacuum, which is to say, the vacuum of classical electromagnetism.

Peter Walden Milonni is an American theoretical physicist who deals with quantum optics, laser physics, quantum electrodynamics and the Casimir effect.

<i>The Quantum Vacuum</i> 1993 physics textbook by Peter W. Milonni

The Quantum Vacuum: An Introduction to Quantum Electrodynamics is a physics textbook authored by Peter W. Milonni in 1993. The book provides a careful and thorough treatment of zero-point energy, spontaneous emission, the Casimir, van der Waals forces, Lamb shift and anomalous magnetic moment of the electron at a level of detail not found in other introductory texts to quantum electrodynamics.