Casimir effect From Wikipedia, the free encyclopedia Casimir forces on parallel plates Casimir forces on parallel plates File:Water wave analogue of Casimir effect.ogv A water wave analogue of the Casimir effect. Two parallel plates are submerged into colored water contained in a sonicator. When the sonicator is turned on, waves are excited imitating vacuum fluctuations; as a result, the plates attract to each other. In quantum field theory, the Casimir effect and the Casimir–Polder force are physical forces arising from a quantized field. They are named after the Dutch physicist Hendrik Casimir. The typical example is of two uncharged metallic plates in a vacuum, placed a few nanometers apart. In a classical description, the lack of an external field also means that there is no field between the plates, and no force would be measured between them.[1] When this field is instead studied using the QED vacuum of quantum electrodynamics, it is seen that the plates do affect the virtual photons which constitute the field, and generate a net force[2]—either an attraction or a repulsion depending on the specific arrangement of the two plates. Although the Casimir effect can be expressed in terms of virtual particles interacting with the objects, it is best described and more easily calculated in terms of the zero-point energy of a quantized field in the intervening space between the objects. This force has been measured, and is a striking example of an effect captured formally by second quantization.[3][4] However, the treatment of boundary conditions in these calculations has led to some controversy. In fact "Casimir's original goal was to compute the van der Waals force between polarizable molecules" of the metallic plates. Thus it can be interpreted without any reference to the zero-point energy (vacuum energy) of quantum fields.[5] Dutch physicists Hendrik B. G. Casimir and Dirk Polder at Philips Research Labs proposed the existence of a force between two polarizable atoms and between such an atom and a conducting plate in 1947, and, after a conversation with Niels Bohr who suggested it had something to do with zero-point energy, Casimir alone formulated the theory predicting a force between neutral conducting plates in 1948; the former is called the Casimir–Polder force while the latter is the Casimir effect in the narrow sense. Predictions of the force were later extended to finite-conductivity metals and dielectrics by Lifshitz and his students, and recent calculations have considered more general geometries. It was not until 1997, however, that a direct experiment, by S. Lamoreaux, described above, quantitatively measured the force (to within 15% of the value predicted by the theory),[6] although previous work [e.g. van Blockland and Overbeek (1978)] had observed the force qualitatively, and indirect validation of the predicted Casimir energy had been made by measuring the thickness of liquid helium films by Sabisky and Anderson in 1972. Subsequent experiments approach an accuracy of a few percent. Because the strength of the force falls off rapidly with distance, it is measurable only when the distance between the objects is extremely small. On a submicron scale, this force becomes so strong that it becomes the dominant force between uncharged conductors. In fact, at separations of 10 nm—about 100 times the typical size of an atom—the Casimir effect produces the equivalent of about 1 atmosphere of pressure (the precise value depending on surface geometry and other factors).[7] In modern theoretical physics, the Casimir effect plays an important role in the chiral bag model of the nucleon; and in applied physics, it is significant in some aspects of emerging microtechnologies and nanotechnologies.[8] Any medium supporting oscillations has an analogue of the Casimir effect. For example, beads on a string[9][10] as well as plates submerged in noisy water[11] or gas[12] exhibit the Casimir force. Contents [hide] 1 Overview 2 Possible causes 2.1 Vacuum energy 2.2 Relativistic van der Waals force 3 Effects 4 Derivation of Casimir effect assuming zeta-regularization 4.1 More recent theory 5 Measurement 6 Regularisation 7 Generalities 8 Dynamical Casimir effect 8.1 Analogies 9 Repulsive forces 10 Applications 11 See also 12 References 13 Further reading 13.1 Introductory readings 13.2 Papers, books and lectures 13.3 Temperature dependence 14 External links Overview[edit] The Casimir effect can be understood by the idea that the presence of conducting metals and dielectrics alters the vacuum expectation value of the energy of the second quantized electromagnetic field.[13][14] Since the value of this energy depends on the shapes and positions of the conductors and dielectrics, the Casimir effect manifests itself as a force between such objects. Possible causes[edit] Vacuum energy[edit] Quantum field theory Feynmann Diagram Gluon Radiation.svg Feynman diagram History Background[show] Symmetries[show] Tools[show] Equations[show] Standard Model[show] Incomplete theories[show] Scientists[show] v t e Main article: Vacuum energy The causes of the Casimir effect are described by quantum field theory, which states that all of the various fundamental fields, such as the electromagnetic field, must be quantized at each and every point in space. In a simplified view, a "field" in physics may be envisioned as if space were filled with interconnected vibrating balls and springs, and the strength of the field can be visualized as the displacement of a ball from its rest position. Vibrations in this field propagate and are governed by the appropriate wave equation for the particular field in question. The second quantization of quantum field theory requires that each such ball-spring combination be quantized, that is, that the strength of the field be quantized at each point in space. At the most basic level, the field at each point in space is a simple harmonic oscillator, and its quantization places a quantum harmonic oscillator at each point. Excitations of the field correspond to the elementary particles of particle physics. However, even the vacuum has a vastly complex structure, so all calculations of quantum field theory must be made in relation to this model of the vacuum. The vacuum has, implicitly, all of the properties that a particle may have: spin, or polarization in the case of light, energy, and so on. On average, most of these properties cancel out: the vacuum is, after all, "empty" in this sense. One important exception is the vacuum energy or the vacuum expectation value of the energy. The quantization of a simple harmonic oscillator states that the lowest possible energy or zero-point energy that such an oscillator may have is {E} = \begin{matrix} \frac{1}{2} \end{matrix} \hbar \omega \ . Summing over all possible oscillators at all points in space gives an infinite quantity. To remove this infinity, one may argue that only differences in energy are physically measurable; this argument is the underpinning of the theory of renormalization.[citation needed] In all practical calculations, this is how the infinity is always handled.[citation needed] In a wider systematic sense however, renormalization isn't a mathematically harmonious method for the removal of this infinity, and it presents a challenge in the search for a Theory of Everything. Currently there is no compelling explanation for why this infinity should be treated as essentially zero; a non-zero value is essentially the cosmological constant[citation needed] and any large value causes trouble in cosmology. Relativistic van der Waals force[edit] Alternatively, a 2005 paper by Robert Jaffe of MIT states that "Casimir effects can be formulated and Casimir forces can be computed without reference to zero-point energies. They are relativistic, quantum forces between charges and currents. The Casimir force (per unit area) between parallel plates vanishes as alpha, the fine structure constant, goes to zero, and the standard result, which appears to be independent of alpha, corresponds to the alpha → infinity limit," and that "The Casimir force is simply the (relativistic, retarded) van der Waals force between the metal plates."[15] Effects[edit] Casimir's observation was that the second-quantized quantum electromagnetic field, in the presence of bulk bodies such as metals or dielectrics, must obey the same boundary conditions that the classical electromagnetic field must obey. In particular, this affects the calculation of the vacuum energy in the presence of a conductor or dielectric. Consider, for example, the calculation of the vacuum expectation value of the electromagnetic field inside a metal cavity, such as, for example, a radar cavity or a microwave waveguide. In this case, the correct way to find the zero-point energy of the field is to sum the energies of the standing waves of the cavity. To each and every possible standing wave corresponds an energy; say the energy of the nth standing wave is E_n. The vacuum expectation value of the energy of the electromagnetic field in the cavity is then