Saturday, July 25, 2015

26 Notes for WWI research: Louis Sheehan


26  Notes for WWI research: Louis Sheehan



The writer has just come from visiting a group of a dozen British and American military hospitals in one French town, with from one to four thousand patients in each, where at this moment the trains are arriving in almost a steady stream, bearing the wounded from the front in the great drive in Flanders. He has stood by the operating tables and passed down those long, unending rows of cots. Some of these tragic hospital wards are filled with men, every one of whom is blinded for life by poison gas or shrapnel. They, like all the other wounded, are brave and cheerful, but it will take great courage to maintain this cheer, groping a long lifetime in the dark. One man counted 151 trains of twenty cars each, or 3,000 carriages, filled with German wounded passing back in a steady stream through Belgium. Behind all the active fronts these train loads of wounded are daily bearing their burden of suffering humanity. The cities and towns of Europe are filled with limping or crippled or wounded men today.
Opposite the writer at the ship's table sat a young man with the lower part of his face carried away. His chin and jaw were gone, yet he must live on for a lifetime deformed. Another young fellow had spent seven long weary months in training. The moment his regiment reached the front it was ordered immediately into action. He sprang to the top of the trench, but never got over it. He fell back wounded. Within three days he was back in England again, but with only one leg. Seven months of training, five minutes in action, then crippled for life! The writer saw one young fellow whose face was left contorted by shrapnel, which had carried away one eye and the bridge of his nose. He was a quiet, earnest Christian. He said, "Of course, they cannot send me back again into the line or compel me to go with only one eye, but I am going just the same. I am going to give all that I have left to the country and the cause." [4]
Hear that young soldier of France, Alfred Casalis, a brilliant student of philosophy and theology, a Student Volunteer for the African mission field, as he writes home to his father and mother at the age of nineteen: "I volunteered of course. I know with an unalterable knowledge and with an unconquerable confidence that the foundation of my faith is unshakeable, it rests upon the Rock. I shall fight with a good conscience and without fear (I hope), certainly without hate. I feel myself filled with an illimitable hope. You can have no idea of the peace in which I live. On the march I sing inwardly. I listen to the music that is slumbering inside me. The Master's call is always ringing loudly in my ears. I am not afraid of death. I have made the sacrifice of my life. I know that to die is to begin to live." And the last sentence of the unfinished letter written before the charge in which he fell, "The attack cannot but succeed. There will be some wounded, some killed, but we shall go forward and far—" In the other pocket of his coat, at the end of his will were the words, "'I have fought the good fight, I have finished my course, I have kept the faith.' And I would that all my friends, all those who are every moment with me, and whose hearts beat with mine, should repeat the word of our hope, 'Because I live, ye shall live also.'" [5]
Professor Gilbert Murray, of Oxford, writes thus of the sacrifice of the men for us: "As for me personally, there is one thought that is always with me—the thought that other men are dying for me, better men, younger, with more hope in their lives, many of whom I have taught and loved. The orthodox Christian will be familiar with the thought of One who loved you dying for you. I would like to say that now I seem to be familiar with the feeling that something innocent, something great, something that loved me, is dying, and is dying daily for me. That is the sort of community we now are—a community in which one man dies for his brother."
Yes, these boys are making the great sacrifice for us. With 5,000,000 who have already been killed, with 10,000,000 of our own sons enrolled. as subject to their call to the colors when needed, with hundreds of American army camps at home and in France already crowded with men, what sacrifice can we make for them? How can we surround their lives with the best influences of home, that they may come back to us even better men than when they went away?
We have seen the terrible ordeal to which they will be subjected at the front, the temptations to which they are exposed in France, in the training schools, and the base camps; we have seen something of the havoc which demoralizing forces have already wrought in other armies in the camps of the prodigals, and we have seen the deadly dangers and perils, both physical and moral, which the soldier must face. We have spoken of the enormous sums voted to carry on a great war of destruction. Is there not a yet more urgent need that we should supply the great constructive forces for fortifying the physical and moral manhood of our nation? Two organizations have been recognized by our own and the other allied governments in the war zone—the one bearing the symbol of the red cross for the wounded, and the other the red triangle for the fighting men.
The nation has already generously responded to the needs of the wounded even before the first battle was fought, giving more in one week than any other nation in a year for the same purpose. And not a dollar too much has been given for this great cause. But we shall soon have several millions of fighting men under arms. What are we to do for these men? We have already seen that they present a threefold need. There is the physical need of these millions who will soon be training, fighting, and suffering. Only the men at the front know what it really is. There are the mental and social requirements of men who must have recreation, healthy amusement and occupation. There is also the moral and spiritual need of men who will face the greatest temptations of their lives, when they will be farthest from the help of home and friends, while old standards seem to be submerged or swept away "for the period of the war."
We have already seen that the building that bears the red triangle of the Y M C A at the front is at once the soldier's club, his home, his church where his own denomination holds its services, his school, his place of rest, his recreation center, his bank and postoffice where he writes his letters, his friend in need that stands by him at the last and meets his relatives who are called to his bedside in the hospital. If there is anything which safeguards the physical, social, and moral health of the men who are dying for us, can we do less than provide it for them? While billions are being spent for destruction, must we not at least invest an infinitesimal fraction of one per cent of our expenditure, in construction, in that which is the greatest asset of any nation—its moral manhood? Can we not provide a home away from home for our own sons and the other boys with them whose parents may be too poor to do so?
Here is a unique contribution which America can also make to her hard pressed allies who have been exhausted by three terrible years of fighting. Britain has already set us a wonderful example and will not need our help. But there is France to which we owe so much and whose war weary soldiers sorely need just such centers for recreation and rebuilding. General Petain, the Commander in Chief, and the French authorities have asked for the help of our Movement in their camps. General Pershing, after surveying the field, has declared that the greatest service which America can immediately render France, even before our own men can reach the trenches in large numbers, is to extend the welfare work of the Y M C A to the entire French Army. Can we do less than this for the nation that gave all that Washington asked in our own hour of crisis? Then there is Italy, with all her deep need and great possibilities. What can we do to minister to the wants of her great army?
Posted by at No comments:

Sunday, July 19, 2015

c26 . 2

The heights!  -- Louis Sheehan

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 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; in applied physics, it is significant in some aspects of emergingmicrotechnologies 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] illustrate the Casimir force.

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
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. Since only differences in energy are physically measurable (with the notable exception of gravitation, which remains beyond the scope of quantum field theory), this infinity may be considered a feature of the mathematics rather than of the physics. This argument is the underpinning of the theory of renormalization. Dealing with infinite quantities in this way was a cause of widespread unease among quantum field theorists before the development in the 1970s of the renormalization group, a mathematical formalism for scale transformations that provides a natural basis for the process.
When the scope of the physics is widened to include gravity, the interpretation of this formally infinite quantity remains problematic. There is currently no compelling explanation as to why it should not result in acosmological constant that is many orders of magnitude larger than observed.[15] However, since we do not yet have any fully coherent quantum theory of gravity, there is likewise no compelling reason as to why it should.[16]

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 approaching infinity limit," and that "The Casimir force is simply the (relativistic, retarded) van der Waals force between the metal plates."[17]

Coupled ground-state energy[edit]

Finally, a third way of understanding Casimir forces has been suggested, based on canonical macroscopic quantum electrodynamics. In this interpretation, there exists a ground (vacuum) state of the coupledsystem of matter and fields, which determines the ground-state properties of the electromagnetic field, giving rise to a force. The Casimir force is fundamentally a property of the coupled system of matter and fields, in which the interaction between the plates is mediated by the zero-point fields. In more traditional interpretations, however, the emphasis has fallen either on the electromagnetic field or the fluctuating material in the plates.[18]

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
\langle E \rangle = \frac{1}{2} \sum_n E_n
with the sum running over all possible values of n enumerating the standing waves. The factor of 1/2 corresponds to the fact that the zero-point energies are being summed (it is the same 1/2 as appears in the equation E=\hbar \omega/2). Written in this way, this sum is clearly divergent; however, it can be used to create finite expressions.
In particular, one may ask how the zero-point energy depends on the shape s of the cavity. Each energy level E_n depends on the shape, and so one should write E_n(s) for the energy level, and \langle E(s) \rangle for the vacuum expectation value. At this point comes an important observation: the force at point p on the wall of the cavity is equal to the change in the vacuum energy if the shape s of the wall is perturbed a little bit, say by \delta s, at point p. That is, one has
F(p) = - \left. \frac{\delta \langle E(s) \rangle} {\delta s} \right\vert_p.\,
This value is finite in many practical calculations.[19]
Attraction between the plates can be easily understood by focusing on the one-dimensional situation. Suppose that a moveable conductive plate is positioned at a short distance a from one of two widely separated plates (distance L apart). With a << L, the states within the slot of width a are highly constrained so that the energy E of any one mode is widely separated from that of the next. This is not the case in open region L, where there is a large number (about L/a) of states with energy evenly spaced between E and the next mode in the narrow slot---in other words, all slightly larger than E. Now on shortening a by da(< 0), the mode in the slot shrinks in wavelength and therefore increases in energy proportional to -da/a, whereas all the outside L/a states lengthen and correspondingly lower energy proportional to da/L (note the denominator). The net change is slightly negative, because all the L/a modes' energies are slightly larger than the single mode in the slot.

Derivation of Casimir effect assuming zeta-regularization[edit]

  • See Wikiversity for an elementary calculation in one dimension.
In the original calculation done by Casimir, he considered the space between a pair of conducting metal plates at distance a apart. In this case, the standing waves are particularly easy to calculate, because the transverse component of the electric field and the normal component of the magnetic field must vanish on the surface of a conductor. Assuming the parallel plates lie in the xy-plane, the standing waves are
\psi_n(x,y,z;t) = e^{-i\omega_nt} e^{ik_xx+ik_yy} \sin \left(k_n z \right)
where \psi stands for the electric component of the electromagnetic field, and, for brevity, the polarization and the magnetic components are ignored here. Here, k_x and k_y are the wave vectors in directions parallel to the plates, and
k_n = \frac{n\pi}{a}
is the wave-vector perpendicular to the plates. Here, n is an integer, resulting from the requirement that ψ vanish on the metal plates. The frequency of this wave is
\omega_n = c \sqrt{{k_x}^2 + {k_y}^2 + \frac{n^2\pi^2}{a^2}}
where c is the speed of light. The vacuum energy is then the sum over all possible excitation modes. Since the area of the plates is large, we may sum by integrating over two of the dimensions in k-space. The assumption of periodic boundary conditions yields,
\langle E \rangle = \frac{\hbar}{2} \cdot 2 \int \frac{A dk_x dk_y}{(2\pi)^2} \sum_{n=1}^\infty \omega_n
where A is the area of the metal plates, and a factor of 2 is introduced for the two possible polarizations of the wave. This expression is clearly infinite, and to proceed with the calculation, it is convenient to introduce a regulator (discussed in greater detail below). The regulator will serve to make the expression finite, and in the end will be removed. The zeta-regulated version of the energy per unit-area of the plate is
\frac{\langle E(s) \rangle}{A} = \hbar \int \frac{dk_x dk_y}{(2\pi)^2} \sum_{n=1}^\infty \omega_n \vert \omega_n\vert^{-s}.
In the end, the limit s\to 0 is to be taken. Here s is just a complex number, not to be confused with the shape discussed previously. This integral/sum is finite for s real and larger than 3. The sum has a pole at s = 3, but may be analytically continued to s = 0, where the expression is finite. The above expression simplifies to:
\frac{\langle E(s) \rangle}{A} = \frac{\hbar c^{1-s}}{4\pi^2} \sum_n \int_0^\infty 2\pi qdq \left \vert q^2 + \frac{\pi^2 n^2}{a^2} \right\vert^{(1-s)/2},
where polar coordinates q^2 = k_x^2+k_y^2 were introduced to turn the double integral into a single integral. The q in front is the Jacobian, and the 2\pi comes from the angular integration. The integral converges if Re[s] > 3, resulting in
\frac{\langle E(s) \rangle}{A} = -\frac {\hbar c^{1-s} \pi^{2-s}}{2a^{3-s}} \frac{1}{3-s} \sum_n \vert n\vert ^{3-s}.
The sum diverges at s in the neighborhood of zero, but if the damping of large-frequency excitations corresponding to analytic continuation of the Riemann zeta function to s = 0 is assumed to make sense physically in some way, then one has
\frac{\langle E \rangle}{A} = \lim_{s\to 0} \frac{\langle E(s) \rangle}{A} = -\frac {\hbar c \pi^{2}}{6a^{3}} \zeta (-3).
But \zeta(-3)=1/120 and so one obtains
\frac{\langle E \rangle}{A} = \frac {-\hbar c \pi^{2}}{3 \cdot 240 a^{3}}.
The analytic continuation has evidently lost an additive positive infinity, somehow exactly accounting for the zero-point energy (not included above) outside the slot between the plates, but which changes upon plate movement within a closed system. The Casimir force per unit area F_c / A for idealized, perfectly conducting plates with vacuum between them is
{F_c \over A} = - \frac{d}{da} \frac{\langle E \rangle}{A} = -\frac {\hbar c \pi^2} {240 a^4}
where
\hbar (hbar, ħ) is the reduced Planck constant,
c is the speed of light,
a is the distance between the two plates
The force is negative, indicating that the force is attractive: by moving the two plates closer together, the energy is lowered. The presence of \hbar shows that the Casimir force per unit area F_c / A is very small, and that furthermore, the force is inherently of quantum-mechanical origin.
NOTE: In Casimir's original derivation [2], a moveable conductive plate is positioned at a short distance a from one of two widely separated plates (distance L apart). The 0-point energy on both sides of the plate is considered. Instead of the above ad hoc analytic continuation assumption, non-convergent sums and integrals are computed using Euler–Maclaurin summation with a regularizing function (e.g., exponential regularization) not so anomalous as \vert\omega_n\vert^{-s} in the above.[20]

More recent theory[edit]

Casimir's analysis of idealized metal plates was generalized to arbitrary dielectric and realistic metal plates by Lifshitz and his students.[21][22] Using this approach, complications of the bounding surfaces, such as the modifications to the Casimir force due to finite conductivity, can be calculated numerically using the tabulated complex dielectric functions of the bounding materials. Lifshitz' theory for two metal plates reduces to Casimir's idealized 1/a4 force law for large separations a much greater than the skin depth of the metal, and conversely reduces to the 1/a3 force law of the London dispersion force (with a coefficient called aHamaker constant) for small a, with a more complicated dependence on a for intermediate separations determined by the dispersion of the materials.[23]
Lifshitz' result was subsequently generalized to arbitrary multilayer planar geometries as well as to anisotropic and magnetic materials, but for several decades the calculation of Casimir forces for non-planar geometries remained limited to a few idealized cases admitting analytical solutions.[24] For example, the force in the experimental sphere–plate geometry was computed with an approximation (due to Derjaguin) that the sphere radius R is much larger than the separation a, in which case the nearby surfaces are nearly parallel and the parallel-plate result can be adapted to obtain an approximate R/a3 force (neglecting both skin-depth and higher-order curvature effects).[24][25] However, in the 2000s a number of authors developed and demonstrated a variety of numerical techniques, in many cases adapted from classicalcomputational electromagnetics, that are capable of accurately calculating Casimir forces for arbitrary geometries and materials, from simple finite-size effects of finite plates to more complicated phenomena arising for patterned surfaces or objects of various shapes.[24][26]

Measurement[edit]

One of the first experimental tests was conducted by Marcus Sparnaay at Philips in Eindhoven (Netherlands), in 1958, in a delicate and difficult experiment with parallel plates, obtaining results not in contradiction with the Casimir theory,[27][28] but with large experimental errors. Some of the experimental details as well as some background information on how Casimir, Polder and Sparnaay arrived at this point[29] are highlighted in a 2007 interview with Marcus Sparnaay.
The Casimir effect was measured more accurately in 1997 by Steve K. Lamoreaux of Los Alamos National Laboratory,[30] and by Umar Mohideen and Anushree Roy of the University of California, Riverside.[31] In practice, rather than using two parallel plates, which would require phenomenally accurate alignment to ensure they were parallel, the experiments use one plate that is flat and another plate that is a part of asphere with a large radius.
In 2001, a group (Giacomo Bressi, Gianni Carugno, Roberto Onofrio and Giuseppe Ruoso) at the University of Padua (Italy) finally succeeded in measuring the Casimir force between parallel plates usingmicroresonators.[32]

Regularisation[edit]

In order to be able to perform calculations in the general case, it is convenient to introduce a regulator in the summations. This is an artificial device, used to make the sums finite so that they can be more easily manipulated, followed by the taking of a limit so as to remove the regulator.
The heat kernel or exponentially regulated sum is
\langle E(t) \rangle = \frac{1}{2} \sum_n \hbar |\omega_n| \exp (-t|\omega_n|)
where the limit t\to 0^+ is taken in the end. The divergence of the sum is typically manifested as
\langle E(t) \rangle = \frac{C}{t^3} + \textrm{finite}\,
for three-dimensional cavities. The infinite part of the sum is associated with the bulk constant C which does not depend on the shape of the cavity. The interesting part of the sum is the finite part, which is shape-dependent. The Gaussian regulator
\langle E(t) \rangle = \frac{1}{2} \sum_n \hbar |\omega_n| \exp (-t^2|\omega_n|^2)
is better suited to numerical calculations because of its superior convergence properties, but is more difficult to use in theoretical calculations. Other, suitably smooth, regulators may be used as well. The zeta function regulator
\langle E(s) \rangle = \frac{1}{2} \sum_n \hbar |\omega_n| |\omega_n|^{-s}
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[edit]

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, inconfiguration 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.

Dynamical Casimir effect[edit]

The dynamical Casimir effect is the production of particles and energy from an accelerated moving mirror. This reaction was predicted by certain numerical solutions to quantum mechanics equations made in the 1970s.[33] In May 2011 an announcement was made by researchers at the Chalmers University of Technology, in Gothenburg, Sweden, of the detection of the dynamical Casimir effect. In their experiment, microwave photons were generated out of the vacuum in a superconducting microwave resonator. These researchers used a modified SQUID to change the effective length of the resonator in time, mimicking a mirror moving at the required relativistic velocity. If confirmed this would be the first experimental verification of the dynamical Casimir effect.[34] [35]

Analogies[edit]

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-antiparticlepair, the other particle having been captured by the black hole).[citation needed]
Constructed within the framework of quantum field theory in curved spacetime, the dynamical Casimir effect has been used to better understand acceleration radiation such as the Unruh effect.[citation needed]

Dynamical Casimir effect and the Big Bang[edit]

From a Scalar field model of the Big Bang the Geometric phase is used in a paper by O'Brien "Dynamical Casimir effect and the Big Bang"[36] to relate the Hartle-Hawking State, Guth's and Linde's Inflationary Model and Baryon asymmetry into a single model.
Using the premise of the Feynman–Stueckelberg interpretation that antiparticles travel backwards in time to reflect off the infinite potential boundary of the Scalar field. The Scalar field undergoes a Dynamical Casimir effect during an adiabatic transition, this adiabatic transition is cyclic and satisfies the requirement of a cyclic adiabatic process - where the revolution in the paper's title refers to this cycle. This provides a mechanism for matter-antimatter asymmetry and the formation of real on-mass matter, and all takes place as the universe inflates (Guth & Linde mechanism) from Euclidean geometry to a Minkowski spacetimesatisfying the Hartle-Hawking State.

Repulsive forces[edit]

There are few instances wherein the Casimir effect can give rise to repulsive forces between uncharged objects. Evgeny Lifshitz showed (theoretically) that in certain circumstances (most commonly involving liquids), repulsive forces can arise.[37] This has sparked interest in applications of the Casimir effect toward the development of levitating devices. An experimental demonstration of the Casimir-based repulsion predicted by Lifshitz was recently carried out by Munday et al.[38] Other scientists have also suggested the use of gain media to achieve a similar levitation effect,[39] though this is controversial because these materials seem to violate fundamental causality constraints and the requirement of thermodynamic equilibrium (Kramers-Kronig relations). Casimir and Casimir-Polder repulsion can in fact occur for sufficiently anisotropic electrical bodies; for a review of the issues involved with repulsion see Milton et al.[40]

Applications[edit]

It has been suggested that the Casimir forces have application in nanotechnology,[41] in particular silicon integrated circuit technology based micro- and nanoelectromechanical systems, silicon array propulsion for space drives, and so-called Casimir oscillators.[42]
Because the Casimir effect shows that quantum field theory allows the energy density in certain regions of space to be negative relative to the ordinary vacuum energy, and it has been shown theoretically that quantum field theory allows states where the energy can be arbitrarily negative at a given point,[43] Many physicists such as Stephen Hawking,[44] Kip Thorne,[45] and others[46][47][48] therefore argue that such effects might make it possible to stabilize a traversable wormhole. Similar suggestions have been made for the Alcubierre Drive.
On 4 June 2013 it was reported[49] that a conglomerate of scientists from Hong Kong University of Science and Technology, University of Florida, Harvard University, Massachusetts Institute of Technology, andOak Ridge National Laboratory have for the first time demonstrated a compact integrated silicon chip that can measure the Casimir force.[50]

See also[edit]

Portal iconPhysics portal

References[edit]

  1. Jump up^ Cyriaque Genet, Francesco Intravaia, Astrid Lambrecht and Serge Reynaud (2004) "Electromagnetic vacuum fluctuations, Casimir and Van der Waals forces"
  2. Jump up^ The Force of Empty Space, Physical Review Focus, 3 December 1998
  3. Jump up^ A. Lambrecht, The Casimir effect: a force from nothing, Physics World, September 2002.
  4. Jump up^ American Institute of Physics News Note 1996
  5. Jump up^ Jaffe, R. (2005). "Casimir effect and the quantum vacuum".Physical Review D 72 (2): 021301. arXiv:hep-th/0503158.Bibcode:2005PhRvD..72b1301J.doi:10.1103/PhysRevD.72.021301.
  6. Jump up^ Photo of ball attracted to a plate by Casimir effect
  7. Jump up^ "The Casimir effect: a force from nothing". physicsworld.com. 1 September 2002. Retrieved 17 July 2009.
  8. Jump up^ Astrid Lambrecht,Serge Reynaud and Cyriaque Genet" Casimir In The Nanoworld"
  9. Jump up^ Griffiths, D. J.; Ho, E. (2001). "Classical Casimir effect for beads on a string". American Journal of Physics 69 (11): 1173.doi:10.1119/1.1396620. edit
  10. Jump up^ Cooke, J. H. (1998). "Casimir force on a loaded string". American Journal of Physics 66 (7): 569–561. doi:10.1119/1.18907. edit
  11. Jump up^ Denardo, B. C.; Puda, J. J.; Larraza, A. S. (2009). "A water wave analog of the Casimir effect". American Journal of Physics 77 (12): 1095. doi:10.1119/1.3211416. edit
  12. Jump up^ Larraza, A. S.; Denardo, B. (1998). "An acoustic Casimir effect".Physics Letters A 248 (2–4): 151. doi:10.1016/S0375-9601(98)00652-5. edit
  13. Jump up^ E. L. Losada" Functional Approach to the Fermionic Casimir Effect"
  14. Jump up^ Michael Bordag, Galina Leonidovna Klimchitskaya, Umar Mohideen (2009). "Chapter I; §3: Field quantization and vacuum energy in the presence of boundaries". Advances in the Casimir effect. Oxford University Press. pp. 33 ff. ISBN 0-19-923874-X.
  15. Jump up^ SE Rugh, H Zinkernagel; Zinkernagel (2002). "The quantum vacuum and the cosmological constant problem". Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 33 (4): 663–705. doi:10.1016/S1355-2198(02)00033-3.
  16. Jump up^ Bianchi, Eugenio; Rovelli, Carlo (2010). "Why all these prejudices against a constant?". arXiv:1002.3966 [astro-ph.CO].
  17. Jump up^ R.L.Jaffe (2005). "The Casimir Effect and the Quantum Vacuum".arXiv:hep-th/0503158v1.
  18. Jump up^ Simpson, W.M.R. (2014). "Ontological aspects of the Casimir effect". Studies in History and Philosophy of Science Part B 48: 84–88. doi:10.1016/j.shpsb.2014.08.001.
  19. Jump up^ For a brief summary, see the introduction in Passante, R.; Spagnolo, S. (2007). "Casimir-Polder interatomic potential between two atoms at finite temperature and in the presence of boundary conditions". Physical Review A 76 (4): 042112. arXiv:0708.2240.Bibcode:2007PhRvA..76d2112P.doi:10.1103/PhysRevA.76.042112.
  20. Jump up^ Ruggiero, Zimerman, and Villani, "Application of Analytic Regularization to the Casimir Forces " Revista Brasileira de Física, Vol. 7, Nº 3, 1977;http://www.sbfisica.org.br/bjp/download/v07/v07a43.pdf
  21. Jump up^ Dzyaloshinskii, I E; Lifshitz, E M; Pitaevskii, Lev P (1961). "GENERAL THEORY OF VAN DER WAALS' FORCES". Soviet Physics Uspekhi 4 (2): 153. Bibcode:1961SvPhU...4..153D.doi:10.1070/PU1961v004n02ABEH003330.
  22. Jump up^ Dzyaloshinskii, I E; Kats, E I (2004). "Casimir forces in modulated systems". Journal of Physics: Condensed Matter 16 (32): 5659.arXiv:cond-mat/0408348. Bibcode:2004JPCM...16.5659D.doi:10.1088/0953-8984/16/32/003.
  23. Jump up^ V. A. Parsegian, Van der Waals Forces: A Handbook for Biologists, Chemists, Engineers, and Physicists (Cambridge Univ. Press, 2006).
  24. ^ Jump up to:a b c Rodriguez, A. W.; Capasso, F.; Johnson, Steven G. (2011). "The Casimir effect in microstructured geometries". Nature Photonics5 (4): 211–221. Bibcode:2011NaPho...5..211R.doi:10.1038/nphoton.2011.39. Review article.
  25. Jump up^ B. V. Derjaguin, I. I. Abrikosova, and E. M. Lifshitz, Quarterly Reviews, Chemical Society, vol. 10, 295–329 (1956).
  26. Jump up^ Reid, M. T. H.; White, J.; Johnson, S. G. (2011). "Computation of Casimir interactions between arbitrary three-dimensional objects with arbitrary material properties". Physical Review A 84 (1): 010503(R).arXiv:1010.5539. Bibcode:2011PhRvA..84a0503R.doi:10.1103/PhysRevA.84.010503.
  27. Jump up^ Sparnaay, M. J. (1957). "Attractive Forces between Flat Plates".Nature 180 (4581): 334. Bibcode:1957Natur.180..334S.doi:10.1038/180334b0.
  28. Jump up^ Sparnaay, M (1958). "Measurements of attractive forces between flat plates". Physica 24 (6–10): 751. Bibcode:1958Phy....24..751S.doi:10.1016/S0031-8914(58)80090-7.
  29. Jump up^ Movie
  30. Jump up^ Lamoreaux, S. K. (1997). "Demonstration of the Casimir Force in the 0.6 to 6 μm Range". Physical Review Letters 78: 5.Bibcode:1997PhRvL..78....5L. doi:10.1103/PhysRevLett.78.5.
  31. Jump up^ Mohideen, U.; Roy, Anushree (1998). "Precision Measurement of the Casimir Force from 0.1 to 0.9 µm". Physical Review Letters 81(21): 4549. arXiv:physics/9805038.Bibcode:1998PhRvL..81.4549M.doi:10.1103/PhysRevLett.81.4549.
  32. Jump up^ Bressi, G.; Carugno, G.; Onofrio, R.; Ruoso, G. (2002). "Measurement of the Casimir Force between Parallel Metallic Surfaces". Physical Review Letters 88 (4): 041804. arXiv:quant-ph/0203002. Bibcode:2002PhRvL..88d1804B.doi:10.1103/PhysRevLett.88.041804. PMID 11801108.
  33. Jump up^ Fulling, S. A.; Davies, P. C. W. (1976). "Radiation from a Moving Mirror in Two Dimensional Space-Time: Conformal Anomaly".Proceedings of the Royal Society A 348 (1654): 393.Bibcode:1976RSPSA.348..393F. doi:10.1098/rspa.1976.0045.
  34. Jump up^ "First Observation of the Dynamical Casimir Effect". Technology Review.
  35. Jump up^ Wilson, C. M.; Johansson, G.; Pourkabirian, A.; Simoen, M.; Johansson, J. R.; Duty, T.; Nori, F.; Delsing, P. (2011). "Observation of the Dynamical Casimir Effect in a Superconducting Circuit". Nature479 (7373): 376–379. arXiv:1105.4714.Bibcode:2011Natur.479..376W. doi:10.1038/nature10561.PMID 22094697.
  36. Jump up^ J.C.O'Brien "[1]" (2014)
  37. Jump up^ Dzyaloshinskii, I.E.; Lifshitz, E.M.; Pitaevskii, L.P. (1961). "The general theory of van der Waals forces†". Advances in Physics 10(38): 165. Bibcode:1961AdPhy..10..165D.doi:10.1080/00018736100101281.
  38. Jump up^ Munday, J.N.; Capasso, F.; Parsegian, V.A. (2009). "Measured long-range repulsive Casimir-Lifshitz forces". Nature 457 (7226): 170–3. Bibcode:2009Natur.457..170M. doi:10.1038/nature07610.PMID 19129843.
  39. Jump up^ Highfield, Roger (6 August 2007). "Physicists have 'solved' mystery of levitation". The Daily Telegraph (London). Retrieved 28 April2010.
  40. Jump up^ Milton, K. A.; Abalo, E. K.; Parashar, Prachi; Pourtolami, Nima; Brevik, Iver; Ellingsen, Simen A. (2012). "Repulsive Casimir and Casimir-Polder Forces". J. Phys. A 45 (37): 4006.arXiv:1202.6415v2. Bibcode:2012JPhA...45K4006M.doi:10.1088/1751-8113/45/37/374006.
  41. Jump up^ Capasso, F.; Munday, J.N.; Iannuzzi, D.; Chan, H.B. (2007). "Casimir forces and quantum electrodynamical torques: physics and nanomechanics". IEEE Journal of Selected Topics in Quantum Electronics 13 (2): 400. doi:10.1109/JSTQE.2007.893082.
  42. Jump up^ Serry, F.M.; Walliser, D.; MacLay, G.J. (1995). "The anharmonic Casimir oscillator (ACO)-the Casimir effect in a model microelectromechanical system" (PDF). Journal of Microelectromechanical Systems 4 (4): 193.doi:10.1109/84.475546.
  43. Jump up^ Everett, Allen; Roman, Thomas (2012). Time Travel and Warp Drives. University of Chicago Press. p. 167. ISBN 0-226-22498-8.
  44. Jump up^ "Space and Time Warps". Hawking.org.uk. Retrieved 2010-11-11.
  45. Jump up^ Morris, Michael; Thorne, Kip; Yurtsever, Ulvi (1988). "Wormholes, Time Machines, and the Weak Energy Condition" (PDF). Physical Review Letters 61 (13): 1446–1449.Bibcode:1988PhRvL..61.1446M.doi:10.1103/PhysRevLett.61.1446. PMID 10038800.
  46. Jump up^ Sopova; Ford (2002). "The Energy Density in the Casimir Effect".Physical Review D 66 (4): 045026. arXiv:quant-ph/0204125.Bibcode:2002PhRvD..66d5026S.doi:10.1103/PhysRevD.66.045026.
  47. Jump up^ Ford; Roman (1995). "Averaged Energy Conditions and Quantum Inequalities". Physical Review D 51 (8): 4277–4286. arXiv:gr-qc/9410043. Bibcode:1995PhRvD..51.4277F.doi:10.1103/PhysRevD.51.4277.
  48. Jump up^ Olum (1998). "Superluminal travel requires negative energies".Physical Review Letters 81 (17): 3567–3570. arXiv:gr-qc/9805003.Bibcode:1998PhRvL..81.3567O.doi:10.1103/PhysRevLett.81.3567.
  49. Jump up^ "Chip harnesses mysterious Casimir effect force". 4 June 2013. Retrieved 4 June 2013.
  50. Jump up^ Zao, J.; Marcet, Z.; Rodriguez, A. W.; Reid, M. T. H.; McCauley, A. P.; Kravchenko, I. I.; Lu, T.; Bao, Y.; Johnson, S. G.; Chan, H. B. et al. (14 May 2013). "Casimir forces on a silicon micromechanical chip". Nature Communications 4: 1845. arXiv:1207.6163.Bibcode:2013NatCo...4E1845Z. doi:10.1038/ncomms2842.PMID 23673630. Retrieved 5 June 2013.

Further reading[edit]

Introductory readings[edit]

Papers, books and lectures[edit]

Temperature dependence[edit]

External links[edit]

Posted by at No comments:
Subscribe to: Posts (Atom)