Casimir effect

Casimir force between two parallel plates in a vacuum.

The Casimir effect is an effect consisting in the mutual attraction of conducting uncharged bodies under the influence of quantum fluctuations in a vacuum . Most often we are talking about two parallel uncharged mirror surfaces located at close range, however, the Casimir effect exists for more complex geometries.

For optically anisotropic bodies, a Casimir torque, which depends on the mutual orientation of the main optical axes of these bodies, can also occur ^[1] .

The cause of the Casimir effect is the energy vibrations of the physical vacuum due to the constant birth and disappearance of virtual particles in it. The effect was predicted by the Dutch physicist Hendrik Casimir ( Hendrik Casimir , 1909-2000) in 1948 ^[2] , and later confirmed experimentally.

Content

The essence of the effect

According to quantum field theory , physical vacuum is not an absolute void. In it, pairs of virtual particles and antiparticles are constantly born and disappear - there are constant fluctuations (fluctuations) of the fields associated with these particles. In particular, oscillations of the electromagnetic field associated with photons occur. In a vacuum, virtual photons are born and disappear, corresponding to all wavelengths of the electromagnetic spectrum . However, in the space between closely spaced mirror surfaces, the situation is changing. At certain resonant lengths (an integer or half-integer number of times stacked between surfaces), electromagnetic waves are amplified. On all other lengths, which are longer, on the contrary, they are suppressed (that is, the birth of the corresponding virtual photons is suppressed). This is due to the fact that only standing waves can exist in the space between the plates, the amplitude of which on the plates is zero. As a result, the pressure of virtual photons from within on two surfaces is less than the pressure on them from outside , where the birth of photons is unlimited. The closer the surfaces are to each other, the shorter the wavelengths between them are in resonance and the more they will be suppressed. This state of vacuum in the literature is sometimes called the Casimir vacuum . As a result, the attractive force between the surfaces grows.

The phenomenon can be figuratively described as "negative pressure" when the vacuum is deprived of not only ordinary, but also parts of virtual particles, that is, "pumped everything out and a little more." The Scharnhorst effect is also associated with this phenomenon.

Analogy

A phenomenon similar to the Casimir effect was observed back in the 18th century by French sailors. When two ships swaying from side to side under conditions of strong waves , but weak winds , appeared at a distance of less than about 40 meters, as a result of the interference of waves in the space between the ships the waves ceased. The calm sea between the ships created less pressure than the waves from the outer sides of the ships. As a result, a force arose that tended to push the ships aboard. As a countermeasure, the navigation manual of the early 1800s recommended that both ships be sent along a boat with 10-20 sailors in order to push the ships. Due to this effect (among others), garbage islands form in the ocean today.

The effect also resembles the kinetic theory of Le Sage's gravity , consisting in the collision of bodies with each other under the pressure of certain hypothetical particles.

Casimir Strength

The force of gravity acting per unit area $F_{c}/A$ ${\ displaystyle F_ {c} / A}$ for two parallel ideal mirror surfaces in absolute vacuum is

{F_{c} \over A}={\hbar c\pi ^{2} \over 240d^{4}}

{\ displaystyle {F_ {c} \ over A} = {\ hbar c \ pi ^ {2} \ over 240d ^ {4}}}

,

Where

\hbar

{\ displaystyle \ hbar}

Is the reduced Planck constant ,

c

{\ displaystyle c}

- the speed of light in vacuum.

d

{\ displaystyle d}

- distance between surfaces.

This shows that the strength of Casimir is extremely small. The distance at which it begins to be noticeable is about a few micrometers . However, being inversely proportional to the 4th power of the distance, it grows very rapidly with a decrease in the latter. At distances of the order of 10 nm — hundreds of sizes of a typical atom — the pressure created by the Casimir effect is comparable to atmospheric pressure.

In the case of more complex geometry (for example, the interaction of a sphere and a plane or the interaction of more complex objects), the numerical value and the sign of the coefficient change ^[3] , so the Casimir force can be both attractive and repulsive.

Despite the fact that in the formula for the Casimir force there is no fine structure constant $\alpha$ ${\ displaystyle \ alpha}$ - the main characteristic of electromagnetic interaction, - this effect, however, has an electromagnetic origin. As shown in the note ^[4] , when the final conductivity of the plates is taken into account, a dependence on $\alpha$ ${\ displaystyle \ alpha}$ , and the standard expression for force appears in the limiting case $\alpha \gg mc/4\pi \hbar nd^{4}$ ${\ displaystyle \ alpha \ gg mc / 4 \ pi \ hbar nd ^ {4}}$ where $n$ ${\ displaystyle n}$ Is the electron density in the plate.

Graphene

The Casimir effect determines the interaction of any electrically neutral objects at small distances (of the order of a micron or less). In the case of realistic materials, the magnitude of the interaction is determined by the bulk properties of the material (dielectric constant in the case of dielectrics, conductivity for metals). However, calculations show that, for monoatomic graphene layers, the Casimir force can be relatively large, and observation of the effect can be experimentally available ^[5] ^[6] .

Discovery History

Hendrik Casimir worked at Philips Research Laboratories in the Netherlands, studying colloidal solutions, which are viscous substances with micron-sized particles. One of his colleagues, Theo Overbeek , discovered that the behavior of colloidal solutions was not quite consistent with existing theory, and asked Casimir to investigate this problem. Soon, Casimir came to the conclusion that deviations from the behavior predicted by the theory can be explained if the influence of vacuum fluctuations on intermolecular interactions is taken into account. This led him to the question of what effect fluctuations of vacuum can have on two parallel mirror surfaces, and led to the famous prediction of the existence of an attractive force between the latter.

Experimental Discovery

When Casimir made his prediction in 1948 , the imperfection of existing technologies and the extreme weakness of the effect itself made its experimental verification an extremely difficult task. One of the first experiments was conducted in 1958 by Marcus Spaarnay from the Philips center in Eindhoven . Spaarney concluded that his results "do not contradict the theoretical predictions of Casimir." In 1997, a series of much more accurate experiments began, in which the agreement was established between the observed results and the theory with an accuracy of more than 99%.

In 2011, a group of scientists from Chalmers University of Technology confirmed the Casimir dynamic effect . In the experiment, thanks to the modification of SQUID, the scientists got a kind of mirror, which under the influence of a magnetic field oscillated at a speed of about 5% of the light. This turned out to be enough to observe the dynamic Casimir effect: SQUID emitted a stream of microwave photons, and their frequency was equal to half the oscillation frequency of the “mirror”. Such an effect was predicted by quantum theory ^[7] ^[8] . At the moment ^{[ when?} ^] expected ^{[by whom?} ^] repetition of the experiment by any other group of scientists.

In 2012, a group of researchers from the University of Florida designed the first microcircuit to measure the Casimir force between an electrode and a silicon wafer 1.42 nm thick at room temperature. The device operates in automatic mode and is equipped with a drive that adjusts the distance between the plates from 1.92 nm to 260 nm, observing parallelism. The measurement results quite accurately coincide with the theoretically calculated values. This experiment shows that, at given distances, the Casimir force can be the main interaction force between the plates. ^[9] ^[10]

In 2015, it was possible to experimentally detect and measure the Casimir torque ^[11] .

Modern studies of the Casimir effect

Casimir effect for dielectrics
Casimir effect at nonzero temperature
connection of the Casimir effect and other effects or branches of physics (connection with geometric optics , decoherence , polymer physics )
Casimir dynamic effect
taking into account the Casimir effect in the development of highly sensitive MEMS devices.

Application

By 2018, the Russian-German group of physicists ( V.M. Mostepanenko , G.L. Klimchitskaya, V.M. Petrov and the group led by Theo Chudi from Darmstadt ) developed a theoretical and experimental scheme of a miniature quantum for laser beams on based on the Casimir effect, in which the Casimir force is balanced by the pressure of light ^[12] ^[13] .

Casimir effect in literature

The Casimir effect is described in some detail in Arthur Clark ’s science fiction book , “The Light of Other Days, ” where it is used to create two pair of wormholes in space-time, and transmit information through them.

Notes

↑ Barash, Yu.S., Ginzburg, V.L. Electromagnetic fluctuations in matter and molecular (van der Waals) forces between bodies, Usp . Fiz . Nauk , vol. 116, p. 5–40 (1975)
↑ Casimir HBG On the attraction between two perfectly conducting plates // Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen: journal. - 1948. - Vol. 51 . - P. 793-795 .
↑ Physical Encyclopedia, vol. 5. Stroboscopic devices - Brightness / Ch. ed. A.M. Prokhorov. Ed. Col.: A.M. Baldin, A.M. Bonch-Bruevich et al. - M.: Big Russian Encyclopedia, 1994, 1998. - 760 p. - ISBN 5-85270-101-7 , p. 644
↑ R. Jaffe - The Casimir Effect and the Quantum Vacuum
↑ Bordag M., Fialkovsky IV, Gitman DM, Vassilevich DV Casimir interaction between a perfect conductor and graphene described by the Dirac model (Eng.) // Physical Review B : journal. - 2009. - Vol. 80 . - P. 245406 . - DOI : 10.1103 / PhysRevB.80.245406 .
↑ Fialkovsky IV, Marachevskiy VN, Vassilevich DV Finite temperature Casimir effect for graphene (neopr.) . - 2011.
↑ Physicists first recorded the Casimir dynamic effect
↑ Article on the Casimir dynamic effect in the journal Nature
↑ First chip to measure Casimir strength
↑ Engineers Unveil First Casimir Chip That Exploits The Vacuum Energy | MIT Technology Review
↑ David AT Somers, Joseph L. Garrett, Kevin J. Palm & Jeremy N. Munday 19 Dec. 2018 Measurement of the Casimir torque // Nature , volume 564, pages 386–389 (2018)
↑ GL Klimchitskaya, VM Mostepanenko, VM Petrov, T. Tschudi. Optical Chopper Driven by the Casimir Force (Neopr.) // Phys. Rev. Applied. - 2018.- T. 10 , No. 1 . - S. 014010 . - DOI : 10.1103 / PhysRevApplied.10.014010 .
↑ KFU physicist together with a group of scientists developed a new device for optical communication systems , KFU Media Portal (February 26, 2019).

Literature

Mostepanenko V.M., Trunov N.N. Casimir effect and its applications. UFN , 1988, v. 156, no. 3, p. 385-426.
Mushroom A.A., Mamaev S.G., Mostepanenko V.M. Vacuum quantum effects in strong fields. - M .: Energoatomizdat, 1988.

Links

[1] Barash, Yu.S., Ginzburg, V.L. Electromagnetic fluctuations in matter and molecular (van der Waals) forces between bodies, Usp . Fiz . Nauk , vol. 116, p. 5–40 (1975)

[2] Casimir HBG On the attraction between two perfectly conducting plates // Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen: journal. - 1948. - Vol. 51 . - P. 793-795 .

[3] Physical Encyclopedia, vol. 5. Stroboscopic devices - Brightness / Ch. ed. A.M. Prokhorov. Ed. Col.: A.M. Baldin, A.M. Bonch-Bruevich et al. - M.: Big Russian Encyclopedia, 1994, 1998. - 760 p. - ISBN 5-85270-101-7 , p. 644

[Jaffe1-4] R. Jaffe - The Casimir Effect and the Quantum Vacuum

[BFGV-5] Bordag M., Fialkovsky IV, Gitman DM, Vassilevich DV Casimir interaction between a perfect conductor and graphene described by the Dirac model (Eng.) // Physical Review B : journal. - 2009. - Vol. 80 . - P. 245406 . - DOI : 10.1103 / PhysRevB.80.245406 .

[FMD-6] Fialkovsky IV, Marachevskiy VN, Vassilevich DV Finite temperature Casimir effect for graphene (neopr.) . - 2011.

[7] Physicists first recorded the Casimir dynamic effect

[8] Article on the Casimir dynamic effect in the journal Nature

[9] First chip to measure Casimir strength

[10] Engineers Unveil First Casimir Chip That Exploits The Vacuum Energy | MIT Technology Review

[11] David AT Somers, Joseph L. Garrett, Kevin J. Palm & Jeremy N. Munday 19 Dec. 2018 Measurement of the Casimir torque // Nature , volume 564, pages 386–389 (2018)

[12] GL Klimchitskaya, VM Mostepanenko, VM Petrov, T. Tschudi. Optical Chopper Driven by the Casimir Force (Neopr.) // Phys. Rev. Applied. - 2018.- T. 10 , No. 1 . - S. 014010 . - DOI : 10.1103 / PhysRevApplied.10.014010 .

[13] KFU physicist together with a group of scientists developed a new device for optical communication systems , KFU Media Portal (February 26, 2019).