Casimir effect.

In 1999, some of my acquaintances were engaged in the production of nanometer-sized metal powders. Why it is necessary from a commercial point of view is not important here. Various technologies were used, one of them is the condensation of metal vapors under different conditions. This powder was then transported to another reactor for use. As you can imagine, the material is very unusual in terms of properties. The guys were mainly material scientists and chemists by education. And so they stumbled upon the fact that the overflow of this powder did not happen as it should have happened from the point of view of classical physics. The type of flow strongly depended on the conductivity of the powder, although they were all conductors, easily exchanging charges upon contact. They began to "pick", from their point of view, the effect was incomprehensible. They began to "whistle" all the friends, and it was my turn. I, too, could not figure out what kind of effect it was interfering with, but along the "chain" I passed them on to the physicists.

The casket opened simply - the Casimir effect. I will not rewrite Wikipedia's explanation of this effect. I'll just give him.

Http://ru.wikipedia.org/wiki/Kazimir_Effect

“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, placed at a close distance, but the Casimir effect also exists for more complex geometries. The reason for the Casimir effect is the energy oscillations of the physical vacuum due to the constant creation and disappearance of virtual particles in it. The effect was predicted by the Dutch physicist Hendrik Casimir (1909-2000) in 1948 and later confirmed experimentally.

The essence of the effect

According to quantum theory fields, the physical vacuum is not an absolute emptiness. In it, pairs of virtual particles and antiparticles are constantly born and disappear - constant fluctuations (fluctuations) of the fields associated with these particles occur. In particular, there are vibrations associated with photons electromagnetic field... 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 changes. At certain resonant lengths (an integer or half-integer number of times between surfaces), electromagnetic waves are amplified. At all other lengths, of which there are more, on the contrary, they are suppressed (that is, the production of the corresponding virtual photons is suppressed). As a result, the pressure of virtual photons from the inside on two surfaces turns out to be less than the pressure on them from the outside, where the production of photons is not limited by anything. The closer the surfaces are to each other, the shorter the wavelengths between them are in resonance and the longer they are suppressed. As a result, the force of attraction between the surfaces increases.

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

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 sign of the coefficient changes, so the Casimir force can be both an attractive force and a repulsive force. "

End of quote.

This case is notable for the fact that the behavior, it would seem, is purely mechanical system- metal powder, turned out to be tied to quantum effects and their one of the least understandable for many, as it seems to me, consequences - Virtual particles.

KAZIMIRA EFFECT, the general name for a wide range of phenomena caused by fluctuations of the vacuum state of a field (in particular, electromagnetic) in the presence of boundaries or changes in the geometry (topology) of space. The range of areas of physics in which the Casimir effect manifests itself is very wide - from statistical physics to physics elementary particles and cosmology.

For the first time the influence of quantum fluctuations of the electromagnetic field on the interaction of electrically neutral macroscopic bodies was predicted by the Dutch theoretical physicist H. Casimir (1948). He calculated that, due to quantum fluctuations of the field in the ground (vacuum) state, two plane-parallel, ideally conducting uncharged plates, separated in vacuum by a gap of width L, at absolute zero temperature should be attracted with a force F per unit area:

F = - 0,0065hc / L 4, (*)

where h is Planck's constant, c is the speed of light in vacuum. A more general formula for the force of attraction of two dielectric layers, taking into account the dependence of the dielectric constant on the frequency of the field, was obtained by E.M. Lifshitz in 1954. The Casimir force F is very small for distances exceeding a few micrometers, however, with decreasing distance, it rapidly grows and for L = 0.01 μm (about a hundred atomic dimensions) the effective negative pressure F reaches almost 1.3 × 10 6 Pa (13 atmospheres) ... Therefore, taking into account the Casimir forces is important when designing various electromechanical devices of micro- and nano-sizes. Sometimes the Casimir forces are considered as a manifestation of van der Waals forces of attraction at "large" (on an atomic scale) distances, when the delay of the electromagnetic interaction cannot be neglected.

The first experiments to check the Casimir and Lifshitz formulas, staged in the 1950s, qualitatively confirmed the presence of an attractive force between flat and spherical quartz surfaces (I. I. Abrikosov, B. V. Deryagin) and between flat metal plates (M. Sparnai , Netherlands). It was possible to significantly increase the accuracy and reliability of measurements of small forces (up to 10-12 N) and distances (in the range of 0.1-6 microns) only in the late 1990s thanks to the emergence of new tools and technologies, such as an atomic force microscope and microelectromechanical systems. The best achieved accuracy is around 1%. Satisfactory agreement was obtained between theory and experiment, although some details (for example, the dependence of the forces on temperature at distances exceeding several microns) require clarification. The real force of interaction essentially depends on the material and properties of the surfaces, so that even for good conductors (gold, copper), its value may differ from the value calculated by the formula (*) by tens of percent.

In 1959, I.E.Dzyaloshinsky, E.M. Lifshits, and L.P. Pitaevsky predicted the possibility of the appearance of a repulsive force in layered structures with different dielectric constants. Subsequently, many other models and geometric configurations were found that allow such a force, for example, with a combination of an ideal conductor and a magnet or various structures of metamaterials (artificial media with a negative refractive index). However, there is still no experimental confirmation of the theoretical results, although this issue is relevant in connection with the development of micro- and nanoelectromechanical devices.

The Casimir effect plays an important role in cosmology due to the fact that, within the framework of quantum field theory, a nonzero vacuum energy density arises at zero temperature. This is of great importance for solving the problem of the cosmological constant and is associated with the inflationary model of the Universe. The Casimir effect is very important in the physics of hadrons: when calculating their properties, the Casimir energy of quark and gluon fields must be taken into account. The Casimir effect is taken into account in supersymmetric field theories and models of the Kaluza - Klein type theory when analyzing the mechanisms of spontaneous compactification of additional spatial dimensions.

If the surfaces bounding the field move or their properties depend on time, then one speaks of a nonstationary (or dynamic) Casimir effect, a bright manifestation of which could be the production of photons from a vacuum due to the motion of the boundaries of electrically neutral macroscopic bodies. This effect has not yet been discovered, since the predicted number of photons produced is proportional to the square of the ratio of the characteristic speed of movement to the speed of light, that is, it is very small. However, this number can be increased by many orders of magnitude due to quantum interference if the boundary is forced to oscillate with sufficient amplitude and a period close to half the oscillation period of the selected electromagnetic field mode, using the effect of parametric resonance. Such an experiment is realistic for frequencies in the range of several gigahertz.

Lit .: Barash Yu.S. Van der Waals forces. M., 1988; Mostepanenko VM, Trunov NN Casimir effect and its applications. M., 1990; Bordag M., Mohideen U., Mostepanenko V. M. New developments in the Casimir effect // Physics Reports. 2001. Vol. 353. No. 1-3.

Casimir effect

The Casimir effect: power from nothing

Astrid Lambrecht

translation by S.

The force of attraction between two surfaces in a vacuum, first predicted by Hendrik Casimir more than 50 years ago, can affect almost everything from microdevices to theories of the Universe.

However, very few of the experiments measuring the Casimir force used the original configuration of the planes as parallel mirrors. This is due to the fact that they must be kept parallel throughout the entire experiment, which is very difficult. It is much easier to bring the sphere close enough to the mirror, since the distance between objects used in the formula to calculate the force, in this case, is simply the distance between the nearest points. The only drawback of using a sphere and a flat mirror is that the calculations of the Casimir force in this case are not as accurate as in the case of two parallel mirrors. In particular, it is assumed that the force contributions between the sphere and the plate are completely independent at each point. And this is true only if the radius of the sphere is much greater than the distance between the sphere and the plate.

And only quite recently was an experiment carried out that completely repeats the Casimir system of two flat, parallel mirrors. It was conducted by Gianni Carugno, Roberto Onofrio with collaborators from the University of Padova in Italy. They measured the force between a hard chrome plate and the flat surface of a bracket made of the same material, which were spaced 0.5-3 microns apart (G Bressi et al. 2002 Phys. Rev. Lett. 88 041804). According to their measurements, the Casimir force agrees with the theoretical prediction by 75%. Such a relatively large error is associated with technical difficulties in the implementation of the experiment.

More accurate calculations

The problem in studying the Casimir effect is that ordinary mirrors are not perfectly smooth and flat, as Heinrich Casimir considered. In particular, conventional mirrors do not reflect perfectly at all wavelengths. On some, they reflect well - even almost perfectly, while on others - poorly. In addition, all mirrors become transparent at very high frequencies. Thus, when calculating the Casimir force, it is necessary to take into account the frequency-dependent reflections from the mirrors. This problem was considered by Evgeny Lifshits in the 1950s, then by Julian Schwinge and many others.

It turned out that the measured Casimir force between ordinary metal mirrors located at a distance of 0.1 microns is only half of that predicted by the theory for ideal mirrors. If this disagreement is not taken into account when comparing experimental data with theory, one can incorrectly conclude that this disagreement is caused by the existence of a new force. Astrid Lambrecht and his colleague Serge Reynaud performed their calculations for the actual behavior of mirrors, taking into account the physical properties of metals. They concluded that in the simplest model, the mirrors behave "normally" at distances exceeding 0.5 microns.

Another problem that arises in calculating the theoretical value of the Casimir force is the fact that the experiment, in principle, cannot be carried out at absolute zero - which was assumed in the Casimir calculations - but is carried out at room temperature. Because of this, thermal fluctuations have to be taken into account as well. They can create their own radiation pressure and thereby increase the effect of the Casimir force. For example, the Casimir force acting between flat mirrors spaced 7 microns apart at room temperature is twice as large as at absolute zero. Fortunately, thermal fluctuations at room temperature are important only at distances greater than one micron; at smaller distances, the fluctuation wavelength is too large to completely fit into the potential well at least once.

Although the effect of temperature on the Casimir force has not yet been studied in detail, it must be taken into account at distances exceeding one micron. Many researchers have grappled with this problem, including Lifshitz and Schwinger in the 1950s. It was recently reviewed by Michael Bordag of the University of Leipzig, Bo Sernelius of Linköping University in Sweden, Galina Klimchitskaya and Vladimir Mostapenko of the University of Paraiba in Brazil, and the group Astrid Lambrecht in Paris. The dependence of the Casimir force on temperature was some time ago a topic of heated discussion in the scientific community. True, many contradictions have already been resolved, but they stimulated experiments to determine the dependence of the Casimir force on temperature.

The third and final problem in calculating the Casimir force is the fact that real mirrors are not perfectly smooth. The vast majority of mirrors are made by covering the base with a thin metal film; in this case, the "sputtering" technology is used. In this case, the film thickness fluctuates by 50 nm. This accuracy is invisible to the naked eye, but affects the measured value of the Casimir force, which is very sensitive to distance.

Mohideen and his team (California), using deformed surfaces, recently showed that such surfaces also experience a "lateral" Casimir force, which acts not in a perpendicular, but in a parallel direction with respect to the mirror. For experiments, they prepared special mirrors, the surfaces of which were sinusoidally curved. Then they moved the mirrors so that the peak of one of the mirrors passed sequentially through the peaks and "lows" of the second mirror. It was found that the lateral Casimir force changes sinusoidally with the phase difference between the two "waves". The magnitude of the force turned out to be 10 times less than it would have been in the case of "normal" mirrors spaced at the same distance. The lateral force also owes its nature to vacuum fluctuations.

Mehran Kadar with staff from Massachusetts Institute of Technology calculated the theoretical value of the force between two perfectly reflecting wavy mirrors, while Mohiden and colleagues recalculated it for metal mirrors and found good agreement between theory and experiment. Casimir lateral force can have other consequences for microdevices as well.

New physics?

The Casimir effect can also play a role in accurate measurements of force in the microworld on micro- and nanometer scales. Newton's law has been tested many times in the macrocosm, for example, when studying the motion of planets. But no one has yet been able to test it at micron distances with good accuracy. Such tests are very important because there are many theories that combine all four interactions, and these theories predict the existence of new forces acting on these scales. Thus, any discrepancy between experiment and theory can be interpreted as the existence of new forces. In any case, measurements will put new constraints on existing theories.

Jens Gundlach and colleagues from Washington, for example, used a torsional pendulum to determine the gravitational force between two test masses separated by 10 mm to 220 microns. Their measurements confirmed that Newtonian gravity acts on these scales, and the Casimir force dominates at much smaller distances. Meanwhile, Joshua Long, John Price and colleagues at the University of Colorado, along with Ephraim Fischbach and his collaborators at Purdue University, have tried to eliminate the Casimir effect on submillimeter gravity tests by more rigorous selection of materials used in the experiment.

This article provides only a brief overview of many experimental and theoretical studies of the Casimir effect. Of course, there are many equally exciting experiments out there. Many scientific groups, for example, are studying what will happen if the interaction between mirrors does not involve an electromagnetic field, which is carried by massless bosons, but the fields of massive fermions, such as quarks or neutrinos. Other teams, meanwhile, are studying the Casimir effect for cases with other topologies, such as Mobius strip and toroidal objects.

But, despite all the efforts made by researchers, there are still many unresolved problems associated with the Casimir effect. In particular, the seemingly simple question of the Casimir force in a single hollow sphere is still burning. I’m not even sure whether this force will be attractive or repulsive. Heinrich Casimir himself pondered this problem in 1953 when he was looking for a stable model of the electron.

M Bordag, U Mohideen and V M Mostepanenko 2001 New developments in the Casimir effect Phys. Rep. 353 1

H B Chan et al. 2001 Nonlinear micromechanical Casimir oscillator Phys. Rev. Lett. 87 211801

F Chen and U Mohideen 2002 Demonstration of the lateral Casimir force Phys. Rev. Lett. 88 101801

C Genet, A Lambrecht and S Reynaud 2000 Temperature dependence of the Casimir force between metallic mirrors Phys. Rev. A 62 012110

S K Lamoreaux 1997 Demonstration of the Casimir force in the 0.6 to 6 micrometer range Phys. Rev. Lett. 78 5

K A Milton 2001 The Casimir Effect: Physical Manifestations of Zero-point Energy(World Scientific, Singapore)

Power from Empty Space: the Casimir Effect

• 1958 - Indirect experiment: Sparnai used parallel plates to get visual manifestations of the Casimir effect, but with many experimental errors;
• 1972 - indirect experiment: Sabiski and Anderson measured the thickness of helium films, indirectly confirming the Casimir effect;
• 1978 - indirect experiment: von Black and Overbeek observed force qualitatively;
• 1997 - direct experiment: Lamoreau, Mohidine and Roy qualitatively measured strength within 15% of the value predicted by theory;
• 2001 - Direct experiment: Scientists at the University of Padi used microcavities to detect this effect between parallel plates.

It has become apparent over the years that using two parallel plates to detect this force requires incredible precision when it comes to alignment. One of the plates was replaced by a spherical plate with a very large radius.

The dynamic Casimir effect took longer to verify. It was predicted in the 1970s and experimentally confirmed in May 2011 by scientists from Technological University Chalmers in Gothenburg, Sweden. Scientists have generated microwave photons in the vacuum of a superconducting microwave resonator. To achieve the effect of a moving plate, the scientists used a modified SQUID (Superconducting Quantum Interference Device) to adjust the distance between the plates. The results are still pending scientific examination, but if they are confirmed, this will be the first experimental confirmation dynamic Casimir effect.

From nanometers to space travel

How, then, can we switch from the force that moves the nanoplates to space travel at near-light speeds? The dynamic Casimir effect can be used to create an engine for spaceship by getting energy directly from the vacuum. Although the idea is quite ambitious, one young Egyptian has already patented it.

Another theory, which stems from the Casimir effect, is that the wormhole is due to a lack of mass between the two plates. In theory, this could lead to faster-than-light travel, although this is speculative and in general theory.

Fortunately, new experiments are being carried out, technologies are improving, and it may well be that the use of the Casimir effect in practice is not far off. In particular, it can be useful in nanotechnology - in silicon circuitry and Casimir oscillators.