Casimir effect Totally Explained

Everything about Casimir Effect totally explained

In physics, the Casimir effect and the Casimir-Polder force are physical forces arising from a quantized field. The typical example is of two uncharged metallic plates in a vacuum, placed a few micrometers apart, without any external electromagnetic field. In a classical description, the lack of an external field also means that there's no field between the plates, and no force would be measured between them. When this field is instead studied using quantum mechanics, it's seen that the plates do affect the virtual photons which constitute the field, and generate a net force—either an attraction or a repulsion depending on the specific arrangement of the two plates. This force has been measured, and is a striking example of an effect purely due to second quantization. (However, the treatment of boundary conditions in these calculations has led to some controversy.) Dutch physicists Hendrik B. G. Casimir and Dirk Polder first proposed the existence of the force and formulated an experiment to detect it in 1948 while participating in research at Philips Research Labs. The classic form of the experiment, described above, successfully demonstrated the force to within 15% of the value predicted by the theory.
Because the strength of the force falls off rapidly with distance, it's only measurable when the distance between the objects is extremely small. On a submicrometre 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 1 atmosphere of pressure (101.3 kPa).
Although the Casimir effect can be expressed in terms of virtual particles interacting with the objects, it's best described and more easily calculated in terms of the zero-point energy of a quantized field in the intervening space between the objects. In modern theoretical physics, the Casimir effect plays an important role in the chiral bag model of the nucleon; and in applied physics, it's becoming increasingly important in the development of the ever-smaller, miniaturised components of emerging microtechnologies and nanotechnologies.

Overview

The Casimir effect can be understood by the idea that the presence of conducting metals and dielectrics alter the vacuum expectation value of the energy of the second quantized electromagnetic field. 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.

Vacuum energy

The Casimir effect is an outcome of 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. Canonically, 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. 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, all 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 ť

is completely unsuited for numerical calculations, but is quite useful in theoretical calculations. In particular, divergences show up as poles in the complex s plane, with the bulk divergence at s=4. This sum may be analytically continued past this pole, to obtain a finite part at s=0.
Not every cavity configuration necessarily leads to a finite part (the lack of a pole at s=0) or shape-independent infinite parts. In this case, it should be understood that additional physics has to be taken into account. In particular, at extremely large frequencies (above the plasma frequency), metals become transparent to photons (such as x-rays), and dielectrics show a frequency-dependent cutoff as well. This frequency dependence acts as a natural regulator. There are a variety of bulk effects in solid state physics, mathematically very similar to the Casimir effect, where the cutoff frequency comes into explicit play to keep expressions finite. (These are discussed in greater detail in Landau and Lifshitz, "Theory of Continuous Media".)

Generalities

The Casimir effect can also be computed using the mathematical mechanisms of functional integrals of quantum field theory, although such calculations are considerably more abstract, and thus difficult to comprehend. In addition, they can be carried out only for the simplest of geometries. However, the formalism of quantum field theory makes it clear that the vacuum expectation value summations are in a certain sense summations over so-called "virtual particles".
More interesting is the understanding that the sums over the energies of standing waves should be formally understood as sums over the eigenvalues of a Hamiltonian. This allows atomic and molecular effects, such as the van der Waals force, to be understood as a variation on the theme of the Casimir effect. Thus one considers the Hamiltonian of a system as a function of the arrangement of objects, such as atoms, in configuration space. The change in the zero-point energy as a function of changes of the configuration can be understood to result in forces acting between the objects.
In the chiral bag model of the nucleon, the Casimir energy plays an important role in showing the mass of the nucleon is independent of the bag radius. In addition, the spectral asymmetry is interpreted as a non-zero vacuum expectation value of the baryon number, cancelling the topological winding number of the pion field surrounding the nucleon.

Casimir effect and wormholes

Exotic matter with negative energy density is required to stabilize a wormhole. Morris, Thorne and Yurtsever pointed out that the quantum mechanics of the Casimir effect can be used to produce a locally mass-negative region of space-time, and suggested that negative effect could be used to stabilize a wormhole to allow faster than light travel.

Analogies

A similar analysis can be used to explain Hawking radiation that causes the slow "evaporation" of black holes (although this is generally visualized as the escape of one particle from a virtual particle-antiparticle pair, the other particle having been captured by the black hole).

Reversal

Through the use of a perfect lens (one with the ability to focus an image with resolution unrestricted by the wavelength of light) with a negative refractive index, the effect can be reversed, causing small objects to be repelled rather than attracted. However, because of the scale at which the effect applies, its applications are most likely to be found in nanotechnology. According to Professor Ulf Leonhardt and Dr Thomas Philbin of the University's School of Physics & Astronomy, it's theoretically possible to levitate objects as big as humans, but scientists are a long way off developing the technology for such feats.

Applications

It has been suggested that the Casimir forces have application in nanotechnology, in particular silicon integrated circuit technology based micro- and nanoelectromechanical systems, and so-called Casimir oscillators.

Popular culture

In relation to science fiction, although the nature of the effect hasn't been revealed yet, during an orientation video of the TV series Lost, a Dharma Initiative doctor states that the island exhibits a "natural Casimir effect." This may explain why the Island exhibits strange temporal qualities like time displacement from the rest of the world.

Further Information

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