# Is the Casimir effect possible

## Casimir effect

Illustration of the calculation of the Casimir force on two parallel plates under the assumption of hypothetical vacuum fluctuations. This picture does not illustrate the Van der Waals interaction, which is the real cause of the force.

The Casimir effect The quantum field theory is a quantum physical effect that causes a force to act on two parallel, conductive plates in a vacuum, which presses both together. The effect was predicted in 1948 by Hendrik Casimir and named after him. In 1956 there was experimental confirmation by Boris Wladimirowitsch Derjagin, I. I. Abrikosowa and Evgeni Michailowitsch Lifschitz in the Soviet Union and in 1958 by Marcus Sparnaay from the Philips research laboratories in Eindhoven.

Scientists are investigating the possibilities of using the Casimir effect in the field of nanotechnology for microsystems.

### Van der Waals force

The Casimir force, like the Van der Waals and Casimir Polder forces, belongs to the dispersion interactions. In the following, the Casimir force is explained with the help of virtual particles and their fluctuations in a vacuum (vacuum fluctuation). Vacuum fluctuations arise when one derives the zero point energy from Planck's radiation formula, which is also called vacuum energy. Due to the uncertainty relation between time and energy, vacuum fluctuations must arise in limited spaces. Therefore, the Casimir force is often seen as evidence of vacuum energy and vacuum fluctuations. In the limiting case of thin media, however, the Casimir effect can also be understood as a sum of the van der Waals force between the individual atoms of the two conductive plates. This was pointed out by Robert L. Jaffe in 2005. In 2012 this was confirmed by Joseph Cugnon.

### Simplified representation

Joseph Cugnon reports in an article how Casimir came up with his simplified calculation. Calculating van der Waals forces between bodies is very difficult. When Casimir had found an unexpectedly simple formula for the van der Waals force between an atom and a conductive plate, for example, he doubted whether it could be correct. He then followed advice from Niels Bohr: “Why not calculate the effect by determining the difference in the zero point energies of the electromagnetic field?” He then calculated the forces between two atoms and between an atom and a conductive plate. Eventually he realized that the calculation is even easier for two conductive plates, and he finally published this result.

So the van der Waals force between conductive plates can be more easily calculated if it is assumed that the vacuum is a space full of virtual particles called vacuum fluctuations. Such particles can be assigned a de Broglie wavelength. The distance between the two plates must correspond to a multiple of half the wavelength of the virtual particles. Outside the plates, however, there are all possible wavelengths. There is an unlimited, continuous spectrum. This includes the states that are allowed to occur within the plates as well as those that are not possible between the plates due to the boundary conditions.

Outside the plates there is a continuum of virtual particles, while inside the plates only a discrete number of particles can arise, namely those that meet the boundary conditions of the opposing plates. This results in a “photon pressure” from the outside onto the plates.

### Calculation using the simplified calculation method

For this purpose, virtual particles are assumed that are generated from the vacuum for a short time due to the energy uncertainty. These can be any impulse outside of the two plates

assume (i.e. have a continuous spectrum) with

They have a discrete pulse spectrum between the two plates. This is due to the boundary conditions that your equations of motion on the plates must satisfy. This discrete spectrum of impulses can be understood as standing waves between the two plates. Certain states of virtual particles that can be assumed from outside are therefore prohibited between the plates. However, all permitted virtual particles are reflected on the plates. Push from the outside more (Allowed) virtual particles than in the space between the plates, and a pressure difference arises. This Casimir "print" acts as a force on the plates of the respective area and squeezes them together. For perfectly conductive plates in a vacuum it is:

with the sizes

According to this formula, a distance of 190 nm results in a pressure of 1 Pa, at 11 nm one reaches 100 kPa (1 bar).

Quantitative measurements were taken by Steve Lamoreaux (Seattle, 1997) as well as Umar Mohideen and Anushree Roy (Riverside, 1998).

In 2009, Alexej Weber from the University of Heidelberg and Holger Gies from the University of Jena showed that the Casimir effect shows different properties when plates are tilted against each other; for example, it increases with a higher surface temperature.

The Casimir effect was also researched in NASA's Breakthrough Propulsion Physics Project. Since 2008 DARPA has been running a research program that Casimir Effect Enhancement program.

### Reverse Casimir effect

There are special cases in which the Casimir effect Repulsiveforces between (unloaded) objects. This had already been predicted by Yevgeny M. Lifschitz in 1956. The repulsive forces should most easily occur in liquids. After suitable metamaterials were available, the effect was again predicted by Eyal Buks and Michael L. Roukes in 2002. In 2007, physicists led by Ulf Leonhardt from the University of St Andrews theoretically predicted that with the help of metamaterial with a negative refractive index it would be possible to reverse the Casimir effect, i.e. one rejection to achieve the plates. this will reverser or repulsive Casimir effect or also Quantum levitation called.

A experimental Demonstration of the repulsion predicted by Lifschitz due to the reversal of the Casimir effect was provided by Munday et al. Carried out in 2009, which also referred to the effect as quantum levitation.

Other scientists have suggested the use of laser-active media to achieve a similar levitation effect, although this is controversial as these materials appear to violate basic causality and thermodynamic equilibrium requirements (Kramers-Kronig relationships). Casimir and Casimir-Polder repulsion can actually occur with sufficiently anisotropic electrical bodies. For an overview of the problems associated with rejection, see Milton et al. For more on the controllable repulsive Casimir effect, see Qing-Dong Jiang et al. (2019).

### Dynamic Casimir effect

As early as 1970, physicist Gerald T. Moore derived from quantum field theory that virtual particles that are in a vacuum can become real when they are reflected by a mirror that moves almost at the speed of light. This effect was later also called the dynamic Casimir effect. The experimental physicist Per Delsing and colleagues from the University of Gothenburg were able to prove this in 2011.

### Casimir torque

In addition to the Casimir force between parallel plates, there is also a Casimir torque. This was proven in 2018 by the twisting of liquid crystals. The acting torques were in the order of magnitude of a few billionths of a newton meter.

### literature

• William M. R. Simpson, et al .: Forces of the quantum vacuum - an introduction to Casimir physics. World Scientific, New Jersey 2015, ISBN 978-981-4632-90-4.
• Vladimir M. Mostepanenko, et al .: The Casimir effect and its applications. Clarendon Press, Oxford 1997, ISBN 0-19-853998-3.
Based on an article in: Wikipedia.de
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