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The Casimir effect: A force from nothing
Abstract
WHAT happens if you take two mirrors and arrange them so that they are facing each other in empty space? Your first reaction might be "nothing at all". In fact, both mirrors are mutually attracted to each other by the simple presence of the vacuum. This startling phenomenon was first predicted in 1948 by the Dutch theoretical physicist Hendrik Casimir while he was working at Philips Research Laboratories in Eindhoven on – of all things – colloidal solutions (see box on page 30). The phenomenon is now dubbed the Casimir effect, while the force between the mirrors is known as the Casimir force.
... Contrarily, Casimir force experiments show significant charge is produced by otherwise neutral surfaces. In fact, the Casimir force measurements [4] that ostensibly verified the ZPE were swamped [5] by ESD, as the mirrors had to be kept neutral by first touching them together before each measurement was made. ...
... The Casimir force loaded the beam, and after time the beam contacted the electrode, the contact causing the fusion of the electrode along the full length of the protrusion. Since the Casimir induced contact pressure is estimated [5] to be very small, about 1 bar at 10 nm, it may be safely concluded that fusion induced by high pressure did not occur. What this means Is that charge is created in otherwise neutral surfaces separated by nanoscale gaps, i.e., the fusion in MEMS devices caused by ESD. ...
... Contrary to Casimir's notion of the ZPE, experiments [4][5][6][7][8][9][10][11] unequivocally show charge is created in the gap between otherwise neutral plates. Analogous to sphereplane Casimir experiments, charge is created [16] in vibrating AFMs. ...
Recent claims that the thermal Casimir force has been observed are questionable because of the significant charge created by the photoelectric effect from the conversion of thermal energy of atoms in gap surfaces to photons by quantum electrodynamics (QED).To obtain the thermal Casimir force, the unwanted electrostatic forces were removed by applying a servo-controlled compensating voltage to minimize the potential across the gap. Therefore, the measured forces is not the sought after thermal Casimir force, but rather the servo modified ubiquitous QED induced electrostatic force ever present in all Casimir experiments.
... With a previous body of work demonstrating the significance of noise (in interferometers) caused by vacuum fluctuations, it is somewhat surprising resistance exists in the OCT field accepting their relevance. It is even further surprising because vacuum fluctuations are of importance in other areas of optics, for example; being the source of spontaneous light emission, photons from spontaneous parametric down converted (SPDC) sources, and the Casmir effect [43][44][45][46]. They are even postulated to be the source of dark energy accelerating the entire universe, yet the general feelings is that they are too microscopic to be relevant to OCT imaging [47][48][49]. ...
... The energy and characteristics of the fluctuations depend on the modes that are present in the vacuum at any space-time point, as well as their interaction with non-vacuum modes [45,[48][49]. The frequencies of the vacuum energy is in general a function of the size and shape of the volume they are contained in (allowable modes), with the Casmir effect being a prime example, where not all vacuum frequencies are around between metal plates [45][46][47]. With OCT or any Michelson interferometer, vacuum fluctuations have their greatest impact from the energy fluctuations enter the detector port of the interferometer beam splitter. ...
... The first example is the influence of vacuum fluctuations in fiber versus free space OCT embodiments (where fluctuations are different). It is often envisioned that vacuum fluctuations in, for example, a closed space versus and open space, are the same [45,46]. But just examining the Casimir effect, as an example, illustrates why this is not the case. ...
Optical coherence tomography has become an important imaging technology in
cardiology and ophthalmology, with other applications under investigations.
Major advances in optical coherence tomography (OCT) imaging are likely to
occur through a quantum field approach to the technology. In this paper, which
is the first part in a series on the topic, the quantum basis of OCT first
order correlations is expressed in terms of full field quantization.
Specifically first order correlations are treated as the linear sum of single
photon interferences along indistinguishable paths. Photons and the
electromagnetic (EM) field are described in terms of quantum harmonic
oscillators. While the author feels the study of quantum second order
correlations will lead to greater paradigm shifts in the field, addressed in
part II, advances from the study of quantum first order correlations are given.
In particular, ranging errors are discussed (with remedies) from vacuum
fluctuations through the detector port, photon counting errors, and position
probability amplitude uncertainty. In addition, the principles of quantum field
theory and first order correlations are needed for studying second order
correlations in part II.
... But the force measured is likely to be electrostatic and not caused by the ZPE predicted by Casimir. In fact, the force measurements [4] that ostensibly verified the ZPE were swamped [5] by the electrostatic force, as the mirrors had to be kept neutral by first touching them together before each measurement was made. ...
... Conversely, a vacuum origin to the Casimir force would be indicated, if the Casimir force were confirmed in tests in a vacuum near absolute zero. But cryogenic [5] tests have never been performed, and therefore claims that the Casimir effect produces a force from the 'nothing' of the vacuum are speculative, and at the very least violate the conservation of EM energy. ...
... In MEMS, a doubly clamped gold coated beam [7] was found to cause permanent adhesion. But the Casimir induced contact pressure was estimated [5] to be very small, about 1 bar at 10 nm. Certainly, low contact pressure between neutral and otherwise chemically non-reactive surfaces is unlikely to cause permanent adhesion, and therefore it may be concluded that electric charge is somehow produced in otherwise neutral bodies separated by microscopic gaps, the permanent adhesion caused by ESD. ...
In the gap between plates, C asimir excluded electromagnetic (EM) waves having half-wavelengths longer than the gap. But this assumption violates the conservation of EM energy. If conserved, EM energy is required to be gained at the resonant frequency of the gap to compensate for the loss from the excluded long wavelength EM radiation. By neglecting the resonant EM gap radiation, Casimir found an attractive force between the plates. However, if Casimir would have included the resonant EM radiation, he would have shown the Casimir force does not exist.
... Where these virtual photons originate from is not explicitly stated. They could result from the tails of molecular potentials of matter nearby [3], but they could also originate from the zero-point fluctuations of fields within a perfect vacuum [4]. ...
... The anomalous external lateral forces resulting from the PFA calculations for partially metallized corrugation wavelengths depend upon the reality of a number of assumptions. First, zero point fields must originate from the vacuum of space itself, which most researchers believe is true because of the predictions of quantum mechanics [3,4,5,16]. It is not sufficient that the fields originate just from zero point fluctuations of the atoms and molecules of the bulk matter making up the plates. ...
Among the many interpretations as to the source of energy behind the Casimir effect there are two that stand out. In the first, the source is considered to come from the potential energy of atoms in the bulk matter making up the plates. In the second, the energy source is considered to be the zero-point fields in the vacuum of space between and around the plates. These interpretations are as old as the Casimir effect itself since they date back to two papers, one authored by Hendrik Casimir and the other coauthored with Dirk Polder, in 1948. It is believed that these two interpretations are equivalent. There are two commonly used approximations for calculating the forces on non-parallel plates that are based, either explicitly or implicitly on the assumption of these two energy sources. The proximity force approximation (PFA) can be implicitly premised upon the vacuum interpretation, the virtual photons in said vacuum producing a radiation pressure. On the other hand, the pair-wise summation (PWS) approximation is explicitly based upon the bulk matter interpretation. The putative equivalence between the two interpretations can be tested by actually calculating lateral and normal Casimir forces using the two approximations. The first set of plates to be calculated for normal forces will be parallel plates in order to obtain a scaling factor. Subsequently flat plates having sinusoidal corrugations with a conductor spanning the full wavelength will be calculated. Finally flat plates having sinusoidal corrugations with conductor spanning partially metallized corrugation wavelengths will be calculated. The results are that the two approximations produce results that are remarkably equivalent, save for scaling factors, for normal and lateral forces for plates having conductors spanning the full corrugation wavelength and for normal forces on plates with both full and partial corrugations wavelength conductors. However the sinusoidal corrugated plates with partial corrugation wavelength conductors produce lateral forces that are not only not equivalent between PFA and PWS, the PFA results produce anomalous external forces.
... Spaarnay [4] presumably verified he Casimir force in tests of flat mirrors. In a 2002 review, Lambrecht [5] reported that Spaarnay's tests were swamped by electrostatic force, the mirrors kept neutral by first touching them together before each measurement. ...
... In effect, Casimir What is being measured are electrostatic attractive and repulsive forces caused by the photoelectric effect from QED induced VUV radiation. Unlike stray charges that are removed by touching [5] of mirrors, the QED forces cannot be removed and heretofore have been erroneously interpreted as Casimir forces. ...
Casimir extended the short range van der Waals (vdW) force between atoms and molecules separated by a few angstroms to the attractive force between macroscopic bodies in a vacuum. However, recent experiments have suggested the Casimir force may be changed to repulsion by immersion in liquid bromobenzene. But this experiment not only falsely presupposes the Casimir force exists, but then extends that falsity to conclude the attractive Casimir force can be changed to repulsion. Indeed, the Casimir force is shown to not exist because Casimir did not conserve the electromagnetic (EM) radiation in the gap between the plates, for if he would have, Casimir would have found the frequency of the EM radiation increases as the gap decreases. At any instant during gap closure, conservation proceeds by the frequency up-conversion of EM radiation to the EM confinement frequency of the gap by quantum electrodynamics (QED). Hence, the force measured in the experiment has nothing to do with Casimir, but rather is electrostatic caused by the charging of the structures by the photoelectric effect from vacuum ultraviolet (VUV) radiation produced as the gap is decreased below 0.1 microns. The usual attractive force between gold and silicon structures in a vacuum is changed to repulsion upon immersion in bromobenzene because t he latter is an electron scavenger that alters the charge distribution.
... Vacuum fluctuations are also responsible for microscopic effects in particle physics such as the Lamb Shift and the Cassimir Effect [13]. Indeed, the Cassimir Effect can be either attractive or repulsive, depending on the geometrical configuration of the equipment [14] [15]. Repulsive gravity on a microscopic scale might therefore have a mechanical origin in vacuum fluctuations. ...
... where m 1 is the proton, ν 1 is its Compton frequency (equal to ν p ), r 0 is the electron's Bohr radius, n 0 is the electron's principal quantum number, r is any radius that is a multiple of r 0 , and R U is the radius of the universe. It's worth noting that one of the factors comprising R U is the unit of electrical resistance associated with the Quantum Hall Effect as defined by (14). The proton's electromagnetic radius emerges from these relations when n 0 = 1: ...
The Stoney scale, its characteristics and theoretical tendencies are argued to be consistent with Einstein's theory of gravitational ether and with the Stochastic Electrodynamic theory of vacuum-induced gravity. The Stoney scale is shown to be unique in that it posits the non-equivalence of gravitational and inertial mass in an electromagnetic setting. Several large number coincidences provide an interesting background to this study, which includes Dirac's hypothesis, a rationalization of the squared elementary charge, and a derivation of Boltzmann's Constant from the Stoney length.
... UE to the quantum fluctuations of the vacuum field, the Casimir force exists between neutral objects [1]- [10]. Especially for nanoscale electromechanical system devices, this effect could be significant. ...
... 49.4 modes/MHz(1) where V is the volume of the RC, f is the frequency (we use the center frequency of 900 MHz) and 0 = 3 × 10 8 / is the light speed in free space. In the simulated frequency range, theEmulating the Casimir Effect in a Reverberation Chamber: A Preliminary Numerical Simulation Qian Xu, Member, IEEE, Chun Ren, Tianyuan Jia and Yi Hunag, Senior Member IEEE D The simulated model. ...
A full-wave simulation is adopted in a reverberation chamber to emulate the Casimir effect. Typical electric and magnetic field distributions between two parallel plates are presented. Simulation results show that significant different modes exist inside and outside the parallel plates. The probability density function and the cumulative distribution function of the E-field and H-field are also presented.
... This effect systematically occurs in any absorbing anisotropic media, but it may be especially relevant for materials with a strong anisotropy. To prove the existence of such forces, we have solved the boundary value problem in the TM-waves approximation that ignores the hybrid nature of the waves supported by the slab for the considered anisotropy, if k y ≠ 0. The presence of these drag forces which can be referred to as "the driving force from nothing" 34 can play an important role in the manipulation of nanoparticles close to a surface. Frequency, THz Radiative forces, N F x F z F g Figure 6. ...
We predict the existence of lateral drag forces near the flat surface of an absorbing slab made of an anisotropic material. The forces originate from the fluctuations of the electromagnetic field, when the anisotropy axis of the material forms a certain angle with the surface. In this situation, the spatial spectra of the fluctuating electromagnetic fields becomes asymmetric, different for positive and negative transverse wave vectors components. Differently from the case of van der Waals interactions in which the forward-backward symmetry is broken due to the particle movement, in our case the lateral motion results merely from the anisotropy of the slab. This new effect, of particular significance in hyperbolic materials, could be used for the manipulation of nanoparticles.
... Whereas the p r (0, x) (main component of radial pressure) at least for these mentioned values, σ(x = 0) < 0.235, are negative. The closest known real representative of such exotic matter is a region of pseudo-negative pressure density produced by the Casimir effect [14][15][16][17]. Therefore the negative mass can be described by this model, quartic potential, the advantage which distinguishes this model from quadratic and exponential scalar potential. ...
In this paper, we will study some properties of oscillaton, spherically symmetric object made of a real time-dependent scalar field, Using a self- interaction quartic scalar potential instead of a quadratic or exponential ones discussed in previous works. Since the oscillatons can be regarded as models for astrophysical objects which play the role of dark matter, there- fore investigation of their properties has more importance place in present time of physics; research. Therefore we investigate the properties of these objects by Solving the system of differential equations obtained from the Einstein Klein Gordon (EKG) equations and will show their importance as new candidates for the role of dark matter in the galactic scales.
... The quantum nature of Casimir effect can be understood by the zero-point fluctuation of the quantum field which has to satisfy boundary conditions. This force has been measured and is a striking example of an effect captured formally by second quantization [2]. However, the treatment of boundary conditions in these calculations has led to some controversy. ...
In this work we reexamine the Casimir effect in which the vacuum expectation value of quantum fields is calculated over a so-called Krein space. This method has already been successfully applied to study Casimir effect on non-trivial topologies and also the covariance problem in the massless minimally coupled scalar field in de Sitter space-time. It is shown that within this method, no infinite term appears in the computation of the vacuum expectation value of energy-momentum tensor. We investigate the behavior of the Krein quantization for a scalar field in a box satisfying the Dirichlet boundary condition. We show that one can recover the usual theory with the exception that the vacuum energy of the free theory is zero.
... [3,4] and compared with the prediction by the proximity-force approximation (PFA) [5,6], which is supposedly valid when the characteristic curvature radii of the objects are large in relation to their intersurface separation [7]. Recent advances in nanotechnology making experimental measurements more accessible and accurate [8] have promoted a renewed interest in the Casimir effect and its dependence on the geometry of the device and the properties of the constituent material. The Casimir-Lifshitz forces have become a classical topic in quantum field theory, condensed matter physics, nano-optics, and atomic physics, also acting upon the correct functioning of microelectromechanical systems [9]. ...
We analyze both the attractive and repulsive Casimir-Lifshitz forces recently reported in experimental investigations. By using a kinetic approach, we obtain the Casimir forces from the power absorbed by the materials. We consider collective material excitations through a set of relaxation times distributed in frequency according to a log-normal function. A generalized expression for these forces for arbitrary values of temperature is obtained. We compare our results with experimental measurements and conclude that the model goes beyond the proximity-force approximation.
... As micromechanical devices enter the sub-micron regime, fluctuation-induced electromagnetic forces such as van der Waals or Casimir forces become increasingly important, leading for example to unwanted "stiction" between moving parts [174][175][176][177]. Unlike their classical analogue, these interactions have their origins in the quantum and thermal fluctuation of charges in bodies [5,9,176,[178][179][180][181][182][183][184][185][186][187][188][189][190][191][192][193][194] and hence persist even in the absence of external inputs. The volumetric and broadband character of these fluctuations and their usually small nature makes design, calculations, and measurements of these forces significantly more challenging than their classical counterparts, although they can reach atmospheric pressures at nanometric separations. ...
Whether intentionally introduced to exert control over particles and
macroscopic objects, such as for trapping or cooling, or whether arising from
the quantum and thermal fluctuations of charges in otherwise neutral bodies,
leading to unwanted stiction between nearby mechanical parts, electromagnetic
interactions play a fundamental role in many naturally occurring processes and
technologies. In this review, we survey recent progress in the understanding
and experimental observation of optomechanical and quantum-fluctuation forces.
Although both of these effects arise from exchange of electromagnetic momentum,
their dramatically different origins, involving either real or virtual photons,
lead to different physical manifestations and design principles. Specifically,
we describe recent predictions and measurements of attractive and repulsive
optomechanical forces, based on the bonding and antibonding interactions of
evanescent waves, as well as predictions of modified and even repulsive Casimir
forces between nanostructured bodies. Finally, we discuss the potential impact
and interplay of these forces in emerging experimental regimes of
micromechanical devices.
... The decision of mentioning Casimir effect (Casimir, 1948) (Lambrecht, 2002)like force similar gravity was not a simple job. In actual scientifically literature this phenomenon appears between two parallel plates close enough (1-few micro-meters) mirrors with perfect surfaces and reflection in vacuum (null temperature). ...
In the time of formulation, the substantial nature of gravity, the real physical condition resulting from the presence of an electromagnetic field; the authors of this article used examples from their profession field which led them to formulate this present theory. This new theory of gravity gives very easy and simple reasonable answers several micro- and macro electro-potential, magnetic and gravitational phenomena. In the following material you will be presented some important examples which are often hard or over complicated topics when explained by academic scientists. Under section A, the reader will find examples from the Nano-(atomic) field: including laser tweezing (Wu, 2017), 2nd order nonlinear (Wegener, 2005), Josephson junction, Casimir effect, and Boise Einstein condensate. The macro EM-gravity phenomena will be written in section B which will include: the beginning of Planet formation from the Sun, the macro EM-gravity phenomena examples and reasonable explication to Earth tides, tsunamis, and Isostasy; distribution of gravity field onto surface of Earth.
... This, apparently foolish, conclusion has consequences of paramount importance in Physics, in particular in the theory of the renormalization and allows the possibility of providing a meaning for divergent integrals in quantum electrodynamics, like those emerging in the study of the Casimir effect, which is a manifestation of forces of genuine quantum nature [10]. ...
... The all-round non-zero universal energy density contained in the generators of the lowest group of symmetry tends to be in balance with all other densities whose generators belong to diverse groups of higher symmet ry. The physical character of vacuu m manifests itself in a variety of ways, most notably in Casimir effects[22][23][24], double-slit experiments[25]including the Aharanov-Bohm effect[26]as well as in propagation of light, perihelion precession, geodetic and frame dragging effects, galactic lensing and rotation[18,19,20,27], and eventually also in anomalous acceleration[28,29]. The co-propagating γγ * pair is an open action, i.e., a boson that sums up to a spin-2 force carrier. ...
Electron, proton and neutron are described in terms of energy densities on least-action paths to show that their charges, magnetic mo ments and masses are man ifestations of quantized geodesics. According to this geometric under-standing of matter, the mass of a part icle depends on how much the particle-associated curved path projects onto the straight paths of the universal surrounding energy density. The reference density of free space is embodied by the most elementary actions, the photons in propagation on their least-time paths. The vacuum density with rando m distribution of photon phases displays no electromagnetic field, yet the propagation of its force carriers will level off density differences. This manifests itself as gravitation. Transformations fro m one particle to another, for examp le oscillations, are described according to Noether's theorem as changes from one action to another. This physical portrayal of quantized nature, where every entity comprises mu ltip les of the most elementary action, parallels the atomistic tenet.
... Since its discovery over 50 years ago [2] the Casimir effect has been the subject of much research. Recently the effect has been measured in different situations [1] and, as a result, there is renewed interest in calculating the Casimir effect between different shaped boundaries [9]. A particularly elegant approximation based on geometric optics has been suggested by Jaffe and Scardicchio [7] and they have shown that between a sphere and a plane this approximation appears to work well. ...
The first two authors have developed a technique which uses the complex geometry of the space of oriented affine lines in R3 to describe the reflection of rays off a surface. This can be viewed as a parametric approach to geometric optics which has many possible applications. Recently, Jaffe and Scardicchio have developed a geometric optics approximation to the Casimir effect and the main purpose of this paper is to show that the quantities involved can be easily computed by this complex formalism. To illustrate this, we determine explicitly and in closed form the geometric optics approximation of the Casimir force between two non-parallel plates. By making one of the plates finite, we regularize the divergence that is caused by the intersection of the planes. In the parallel plate limit, we prove that our expression reduces to Casimir's original result.
... But interest in the phenomenon has blossomed in recent years. Experimental physicists have realized that the Casimir force affects the working of micromachined devices, while advances in instrumentation have enabled the force to be measured with ever-greater accuracy [1]. ...
Vacuum fluctuations have observable consequences, like the Casimir force between two plates in vacuum. There now exists good agreement between theory and experimental measurements of this force. The role of the Casimir effect in diverse fields such as Quantum Field Theory, Condensed Matter Physics and Atomic Physics etc is discussed. A brief description of current applications to nanotechnology and nanomechanical devices is also given.
... Unexpectedly, the results of their experiments turned out to contradict the quantum mechanical theory of charge fluctuations developed by Y. Aulin Casimir-Lifshitz Forces May 2009 University of Groningen 2 London in the 1930s. At separations beyond a few nanometers the strength of interaction was decreased faster than it was expected234. Overbeek suggested that this difference was due to the finite speed of light, i.e. the retardation effects, but because of the lack of theoretical knowledge needed to tackle the problem he asked theoretical physicist Hendrik Casimir to investigate it. ...
Current review paper is focused on theoretical and experimental research in the area of Casimir-Lifshitz forces, the topic which "most researchers try to avoid rather than study" and the force "which is so weak it is almost undetectable". An overview of Lifshitz theory for van der Waals/Casimir interactions has been given, as well as some results of it provided. The experimental difficulties while trying to precisely measure this kind of forces are mentioned and discussed. Particular attention is paid to the repulsive forces because of their chance to be utilized in novel nanoscale devices. The following types of repulsion are considered: in liquids, due to the geometrical effects, and in systems with metamaterials. Finally, potential applications are discussed, namely: gecko effect, quantum levitation, reduction of friction, elimination of stiction in NEMS/MEMS, etc.
... The force between the two perfect parallel planes is known as the Casimir force which is attractive in nature. The force is proportional to the crosssection area of the two planes and increases 16 times as distance between the plane decreases half [5]. Here, this is same as gravity formula derived in cause of gravity [2]. ...
It should be agreed that all objects like planets, stars etc. float in the full vacuum universe. It should also be agreed that atmosphere possessed by these objects is due to gravity and the atmosphere is in the open system full vacuum universe. Here, air molecules always try to escape in full vacuum universe against gravity to have uniformity in the universe. Means it is balanced between gravity and full vacuum universe. It is in science textbooks that the Earth’s atmosphere exerts pressure. But, to have pressure in the system, it must be isolated by boundary and its value is same at any point within. Here, Earth’s atmospheric air neither uniformly distributed nor in a closed system. It is known that gravity is holding each air molecule towards the Earth. On surface, air has high-density molecules and as further go away molecules density decreases. This density difference is balanced between gravity and full vacuum universe. This paper uncovers the misconception regarding Earth’s atmosphere exerts pressure due to its air molecules vertical column mass. To prove the argument, the manometer experiment is visited. In this experiment author makes the effort to raise mercury filled tube up against gravity above pot level then inverts it. Here, mercury level drops because of gravity which creates a vacuum in the top of the tube. This causes reduced surface energy inside wall of the tube. To be in the equilibrium state with outer tube wall, inner wall surface tries to suck in all direction that holds mercury up against gravity that means tube mercury weight is balanced by vacuum and that is demonstrated.
... It may be possible to test this experimentally using the Casimir effect. For parallel conducting plates, this force is always attractive [55]. Actualization of non-entangled versus entangled quantum variables between the plates constructing spacetime between the plates, so increasing the distance between the plates might be detectable as a weakening of the Casimir effect upon actualization of the entangled, but not the non-entangled variables. ...
I take non-locality to be the Michelson–Morley experiment of the early 21st century, assume its universal validity, and try to derive its consequences. Spacetime, with its locality, cannot be fundamental, but must somehow be emergent from entangled coherent quantum variables and their behaviors. There are, then, two immediate consequences: (i). if we start with non-locality, we need not explain non-locality. We must instead explain an emergence of locality and spacetime. (ii). There can be no emergence of spacetime without matter. These propositions flatly contradict General Relativity, which is foundationally local, can be formulated without matter, and in which there is no “emergence” of spacetime. If these be true, then quantum gravity cannot be a minor alteration of General Relativity but must demand its deep reformulation. This will almost inevitably lead to: matter not only curves spacetime, but “creates” spacetime. We will see independent grounds for the assertion that matter both curves and creates spacetime that may invite a new union of quantum gravity and General Relativity. This quantum creation of spacetime consists of: (i) fully non-local entangled coherent quantum variables. (ii) The onset of locality via decoherence. (iii) A metric in Hilbert space among entangled quantum variables by the sub-additive von Neumann entropy between pairs of variables. (iv) Mapping from metric distances in Hilbert space to metric distances in classical spacetime by episodic actualization events. (v) Discrete spacetime is the relations among these discrete actualization events. (vi) “Now” is the shared moment of actualization of one among the entangled variables when the amplitudes of the remaining entangled variables change instantaneously. (vii) The discrete, successive, episodic, irreversible actualization events constitute a quantum arrow of time. (viii) The arrow of time history of these events is recorded in the very structure of the spacetime constructed. (ix) Actual Time is a succession of two or more actual events. The theory inevitably yields a UV cutoff of a new type. The cutoff is a phase transition between continuous spacetime before the transition and discontinuous spacetime beyond the phase transition. This quantum creation of spacetime modifies General Relativity and may account for Dark Energy, Dark Matter, and the possible elimination of the singularities of General Relativity. Relations to Causal Set Theory, faithful Lorentzian manifolds, and past and future light cones joined at “Actual Now” are discussed. Possible observational and experimental tests based on: (i). the existence of Sub- Planckian photons, (ii). knee and ankle discontinuities in the high-energy gamma ray spectrum, and (iii). possible experiments to detect a creation of spacetime in the Casimir system are discussed. A quantum actualization enhancement of repulsive Casimir effect would be anti-gravitational and of possible practical use. The ideas and concepts discussed here are not yet a theory, but at most the start of a framework that may be useful.
... Furthermore, several experimental results within the theoretical framework of quantum theory supports the compressible fluid model of the physical universe, and equilibrium theory. For instance, it is generally accepted that vacuum, once thought of as static and free of energy per classical theory, is a highly dynamical environment, endowed with energy, as manifested in several experimental results, including the Casimir effect [24][25]. Said model of vacuum, supports the assertion the physical universe is a non-discrete compressible fluid in its entirety, with different specific energy densities at different locations. This publication redefines quantum theory in the context of equilibrium theory, thereby "freeing" Schrödinger's longitudinal wave of the constraints of existence in time/spacetime and space dimensions, and enabling the realization that the entire physical universe (including its's constituents) is a quantum dynamical system. ...
Recent mathematical evidence suggest that the structure and evolution (dynamics) of gravitational objects (for example, astrophysical disks) can be describe using the wave equation in the form of the Schrödinger equation; thus suggesting an underlining symmetry between large scales and subatomic/atomic scales of the physical universe. However, the current widely accepted underlining theoretical physics frameworks at said scales of the physical universe are incompatible. This publication propose that the philosophical assumptions concerning time in quantum theory and general relativity, as constituting the major barrier in reconciling the two discordant frameworks. In both quantum theory and general relativity, time (spacetime) is presumed to be a dimension in which events in the physical universe occur. This publication propose a novel philosophical approach and theoretical framework, which redefines time, and resolves the discordancy between quantum theory and general relativity. The suggestive idea is proposed that the concept time should be separated into two distinct concepts, namely physical time and non-physical time. Physical time is a measure of changes in the location of a demarcated (non-discrete) physical structure (for example a clock), within a “non-discrete compressible fluid” physical universe, that is an enclosed structure (a closed ball), which neither exist in time (spacetime) nor space dimensions. Consequently, physical time and length are one and the same, as both measure the magnitude of change in location within the compressible fluid system. Furthermore, vacuum (space) and matter, along with all other components of the physical universe are manifestations of differential “specific energy” densities within the non-discrete compressible fluid system. Non-physical time is a means by which human consciousness/society order non-physical structures (for example economic growth) within the human consciousness. The nature and dynamics of demarcated physical structures (for example, objects) within the “enclosed” non-discrete compressible fluid system is mediated by energy exchange, restricted to supersymmetric partners termed, “bosons” and “fermions”, which are fundamental demarcated structures. Consequently, the nature and dynamics of demarcated physical structures (for example, particles, objects) within the non-discrete compressible fluid system is termed an “emergent equilibrium state”, and is accurately model one dimensionally (a line segment in the closed ball) as a longitudinal wave and analyzed using the wave equation and perturbation theory methods in a novel theoretical framework, termed, “equilibrium theory”.
... The effects of vacuum energy can be experimentally observed in various phenomena such as spontaneous emission [25], the Casimir effect [26] and the Lamb shift [27]. These effects are thought to influence the behaviour of the Universe on cosmological scales, which thus gives rise to the problem of the energy required for the accelerating expansion of space containing the zero-point field of light; in other words, the amount of energy required is an absolutely huge value compared to the localised atomic based value of vacuum energy. ...
In following on from the preceding papers [1-13], this paper presents the case for the disparity between vacuum energy [14] and the associated metric expansion of space energy requirements. A solution is provided to this problem while correctly deriving the value for the Lamb shift radiation as evidence for vacuum energy marrying up correctly with a newly proposed large scale cosmological model, such in the context of a revised understanding of the redshift effect and associated scaling system for the Planck constant [13]. The process of proof presented here is by taking a close look at the theory behind the metric expansion of space, those calculations, and any of those associated assumptions of theory and modelling of time and space in those calculations and observations that could lead to the cosmological constant problem, and thus determine in fact why the value for the proposed energy of space needs to be so disproportionate compared to the known vacuum energy value. Above all, this paper shall present proof for vacuum energy in a steady-state reality, such by using the fundamental basis of the phi-quantum wave-function scaling system in deriving the temperature value of the CMBR and Boltzmann constant, and finally proof for the precession of the perihelion of Mercury which is demonstrated to be directed related to the vacuum energy of space and CMBR.
... It may be possible to test this experimentally using the Casimir Effect. For parallel conducting plates this force is always attractive [47]. Actualization of non-entangled versus entangled quantum variables between the plates might be detectable as a weakening of the Casimir effect upon actualization of the entangled, but not the non-entangled variables. ...
I take non-locality to be the Michaelson Morley experiment of the early 21st Century, assume its universal validity, and try to derive its consequences. Spacetime, with its locality, cannot be fundamental, but must be emergent from entangled coherent quantum variables and their behaviors. Two immediate consequences are: i. If we start with non-locality, we need not explain non-locality. We must instead explain an emergence of locality and spacetime. ii. There can be no emergence of spacetime without matter. These propositions flatly contradict General Relativity, which is foundationaly local, can be formulated without matter, and where there is no "emergence" of spacetime. If true, then quantum gravity cannot be a minor alteration of General Relativity, but must demand its deep reformulation. This will lead to: Matter not only deforms spacetime, but "creates" spacetime. This quantum creation of spacetime consists in: i. Fully non-local entangled coherent quantum variables. ii. The onset of locality via decoherence. iii. A metric in Hilbert Space among entangled quantum variables by the sub-additive von Neumann Entropy between pairs of variables. iv. Mapping from metric distances in Hilbert Space to metric distances in classical spacetime by episodic actualization events. v. Discrete spacetime is the relations among these discrete actualization events. vi. "Now" is the shared moment of actualization of one among the entangled variables when the amplitudes of the remaining entangled variables change instantaneously. vii. The discrete, successive, episodic, irreversible actualization events constitute a quantum arrow of time. viii. The arrow of time history of these events is recorded in the very structure of the spacetime constructed. ix. Actual Time is a succession of two or more actual events.
... Furthermore, experimental results within the theoretical framework of quantum theory supports the nondiscrete compressible fluid model of the physical universe, and equilibrium theory. For instance, it is generally accepted that vacuum, once thought of as static and free of energy per classical theory, is a highly dynamical environment, endowed with energy, as manifested in several experimental results, including the Casimir effect [27][28]. Said model of vacuum, supports the assertion the physical universe is a non-discrete compressible fluid in its entirety, with different specific energy densities at different locations. This publication redefines quantum theory in the context of equilibrium theory, thereby "freeing" Schrödinger's wave of the constraints of existence in time/spacetime and space dimensions, and enabling the realization that the entire physical universe (including it's constituents) is a quantum dynamical system. ...
... The key point of this effect is the boundary condition in a way that the zero-point energy of any relativistic field might be by boundary conditions. By the means of the quantized vacuum, the virtual particle-antiparticle pair can be created from vacuum and annihilated back to vacuum [1][2][3][4][5][6][7][8][9][10]. ...
We apply the AdS/CFT correspondence in considering the Casimir energy and some non-local entanglement measures in the non-relativistic backgrounds for general dynamical exponent z with and without hyperscaling violation exponent 𝜃. In such background, we use holographic methods and compute the mutual information and tripartite information. We also consider the monogamy of holographic mutual information in the Schrödinger-type geometry and by numerical analysis we show that this quantity is monogamous.
... Casimir's prediction was subsequently confirmed in several experiments in the following decades [1] in what became a striking example of an effect captured by the second quantization. This force even becomes the dominant force between uncharged conductors for plates separations of ~10 nm or less [6]. Figure 1: The walls of the cavity impose boundary conditions on the field modes; only modes with nodes at the locations of the boundaries can be sustained within the cavity [7]. ...
The Casimir effect is a physical force attributed to a disturbance in the vacuum state of the electromagnetic field, predicted by the Dutch physicist Hendrik Casimir in 1948. While Casimir effect can be understood by the notion that the presence of conducting metals and dielectrics alters the vacuum state expectation value of the energy of the second quantized electromagnetic field, explanations of the phenomenon are not uniformly consistent among theorists. The Casimir force has been described, on the one hand, as an effect resulting from the alteration of the zero-point electromagnetic energy due to the boundaries condition. According to this explanation Casimir force is a property of the vacuum and can be regarded as an evidence for the existence of vacuum fluctuations. On the other hand, the Casimir Effect has also been described as a force originating from the forces between charged particles which can be computed without reference to zero-point energies. According to this explanation the Casimir force is simply the (relativistic, retarded Van der Waals force between the metal plates and the phenomenon offers no evidence that the zero-point energies are real. In this article we will review several interpretation and derivation approaches to the Casimir Effect and compare it with the modern on Macroscopic Quantum Electro-Dynamics (MQED). In addition, we address the Dynamic Casimir Effect (DCE), which predicts the production of particles and energy out of the vacuum state of the electromagnetic field in case the mirrors are accelerated towards each other.
... According to Heisenberg's uncertainty principles in quantum mechanics, this field cannot be still and is continuously bubbling and fluctuating in a very complicated way considered as quantum vacuum fluctuations (Shalyt-Margolin, 2016). Computer simulations are being used to understand these forces which can be measured using theorems such as the Casimir effect which in actuality demonstrates nothingness (Nguyen 2003;Lambrecht 2002). Though quantum vacuum is the simplest and fundamental thing in the universe, studying this involves inherent complications. ...
Because of its superior information processing capability, previous authors have proposed that phase conjugation holography offers a feasible mechanism to explain various aspects of human perception. These previous models focused on the relationship between the perceived image of an object and the actual object with little attention to the anatomical location of the phase-conjugation mirror. The present article proposes that phase-conjugation mirrors exist in the brain as 3D networks of organic molecules previously observed to exhibit phase-conjugation behavior. In particular rhodopsin photoreceptor molecules are proposed to form extra-retinal, deep brain networks which function as phase-conjugation mirrors which are distributed throughout the brain. Furthermore, such networks are proposed to convert endogenous biophotons into virtual holograms which function to store cognitive information in the brain. Such a system offers a new functional definition of the mind.
... Furthermore, experimental results within the theoretical framework of quantum theory supports the nondiscrete compressible fluid model of the physical universe, and equilibrium theory. For instance, it is generally accepted that vacuum, once thought of as static and free of energy per classical theory, is a highly dynamical environment, endowed with energy, as manifested in several experimental results, including the Casimir effect [27][28]. Said model of vacuum, supports the assertion the physical universe is a non-discrete compressible fluid in its entirety, with different specific energy densities at different locations. This publication redefines quantum theory in the context of equilibrium theory, thereby "freeing" Schrödinger's wave of the constraints of existence in time/spacetime and space dimensions, and enabling the realization that the entire physical universe (including its constituents) is a quantum dynamical system. ...
Recent mathematical evidence suggests that the structure and dynamics of gravitational objects can be described using the wave equation in the form of the Schrödinger equation; thus suggesting an underlining symmetry across large and subatomic/atomic scales of the physical universe. However, the current accepted theoretical frameworks across said scales of the physical universe are incompatible. This publication proposes that the philosophical assumptions concerning the concept time in quantum theory and general relativity, as constituting the major barrier in reconciling the two discordant frameworks. In both quantum theory and general relativity, time is presumed to be a dimension, in which events occur, with the time dimension interpreted as asymmetric. This publication proposes a novel theoretical framework, which redefines time, and resolves the discordancy between quantum theory and gravitation. Most important, this publication reconciles human-associated interactions with the fundamental forces and quantum theory. In this publication, the suggestive idea is proposed that the concept time in the physical universe (termed, physical time) should be defined as the measure of the magnitude of change in the location of a demarcated physical structure (for example, a clock) within a non-discrete compressible fluid physical universe, which is an enclosed structure (a closed ball). Consequently, physical time and length are not just related, but are in fact one and the same, as both measure the magnitude of change in location within the non-discrete compressible fluid. Matter and vacuum, along with all other constituents of the physical universe are manifestations of differential "specific energy" densities, due to compressions and rarefactions within the non-discrete compressible fluid. Demarcation (detection, interaction, or wavefunction collapse) and analysis of the dynamics of said demarcated physical structures within the non-discrete compressible fluid system is governed by the framework of the Wheeler-Feynman-Cramer-Mead transactional (quantum handshake) theory, wherein energy exchange is restricted to supersymmetric partner-wavefunctions termed, "bosons" and "fermions" (which are fundamental demarcated structures) resulting in the manifestation of the "quantum" phenomena. Consequently, the nature and dynamics/interactions of demarcated physical structures (for example, particles, clocks, rulers, humans, planets) within the non-discrete compressible fluid system is termed an emergent equilibrium state, and is accurately model one-dimensionally as a longitudinal wave (compression wave) and analyzed using the wave equation and perturbation theory methods in a novel theoretical framework, termed, "equilibrium theory".
... According to Heisenberg's uncertainty principles in quantum mechanics, this field cannot be still and is continuously bubbling and fluctuating in a very complicated way considered as quantum vacuum fluctuations (Shalyt-Margolin, 2016). Computer simulations are being used to understand these forces which can be measured using theorems such as the Casimir effect which in actuality demonstrates nothingness (Nguyen 2003;Lambrecht 2002). Though quantum vacuum is the simplest and fundamental thing in the universe, studying this involves inherent complications. ...
A 'field' according to quantum pilot-wave theory (Bush 2015) and quantum field theory (QFT) (Griffiths 2009) when applied to the working of the universe is a fluid that is spread across the universe with a value taken in that space which can change in time. New observations in the fields of quantum fluid mechanics, artificial intelligence (AI) and deep learning in machines are providing us novel insights into how quantum processing, memory creation and storage work using the laws that governs the quantum world and quantum field theories. Such an understanding can be extrapolated to the workings of the mind to see if similar processes underlie the functioning of living systems. This paper hypothesizes that the construct of the mind is the resultant of chaotic system of interacting subatomic fields driven by force fields that intersperse with the quantum vacuum; a mechanism which has not yet been fully understood. We propose that this integrated phenomenon also gives rise to the subtle mechanisms that help in the formation of memories and also the structures which store these memories as reservoirs. The future of our evolution is the mind which evolves in these boundless intermingling quantum fields and their force fields within the quantum vacuum. With computers getting intelligent we are instantaneously but naively evolving our minds, and in the future, working together with these intelligent machines will augment it further. In fact, the design and working of these AI systems are resultant of the proof of the intelligence of conscious mind. This way the working of mind is always superior to those of the artificial systems that emerge from it.
We predict the existence of lateral drag forces near the flat surface of an absorbing slab of an anisotropic material. The forces originate from the fluctuations of the electromagnetic field, when the anisotropy axis of the material forms a certain angle with the surface. In this situation, the spatial spectra of the fluctuating electromagnetic fields becomes asymmetric, different for positive and negative transverse wave vectors components. Differently from the case of van der Waals interactions in which the forward-backward symmetry is broken due to the particle movement or in quantum noncontact friction where it is caused by the mutual motion of the bodies, in our case the lateral motion results merely from the anisotropy of the slab. This new effect, of particular significance in hyperbolic materials, could be used for the manipulation of nanoparticles.
The Casimir force exerted on a gold dipolar nanoparticle by a finite-thickness slab of the natural hyperbolic material namely, the ortorhombic crystalline modification of boron nitride, is investigated. The main contribution to the force originates from the TM-polarized waves, for frequencies at which the parallel and perpendicular components of the dielectric tensor reach minimal values. These frequencies differ from those corresponding to the Lorentzian resonances for the permittivity components. We show that when the slab is made of an isotropic epsilon-near-zero absorbing material the force on the nanoparticle is larger than that induced by a hyperbolic material, for similar values of the characteristic parameters. This fact makes these materials optimal in the use of Casimir’s forces for nanotechnology applications.
A "Big Bang" creation event which begins as a subatomic singularity leads to the question: where did the singularity come from? As detailed here, the evidence indicates that this (observable) "universe" recycles itself by expanding outward and collapsing back into a singularity which explodes outward again. The cosmos, however, may be infinite, and consist of innumerable "universes" all of which eventually collapse into a singularity which then mushrooms outward giving rise to new universes (including our own) and thus explaining why our universe behaves and is organized contrary to Big Bang theory. These theories of cyclic, oscillating universes and of repeated episodes of expansion, contraction, and colliding universes, have failed to generate widespread support, and are based on the beliefs that: A) this universe is expanding-when, it may already be accelerating toward a collapse-and that B) a singularity explodes outward. Quantum physics and relativity, however, predict that a singularity-which has shrunk to smaller than a Planck Length (1.61619926 x 10-33 cm), will blow an imploding hole through the fabric of the space-time quantum continuum, forming an Einstein-Rosen bridge and creating a mirror universe on the other side. The mirror of a positive-matter universe, is an antimatter universe. If cycles of creation alternate from antimatter to matter, and if a collapsing/imploding antimatter universe gave birth to our own, there is no violation of the second law of thermodynamics, entropy ceases to be a limiting factor, and the conservation laws of energy and mass are maintained. As predicted by Einstein's theory of relativity, and when coupled with quantum physics, it appears we may be dwelling in a Mirror Universe which formed from the remnants of a collapsing antimatter universe which upon shrinking to a singularity smaller than a Planck length, blew a hole in the quantum continuum thereby leading to the creation of this universe on the other side. Further, our Mirror Universe is not be expanding, but already collapsing and accelerating to its doom. If so, this collapse may account for the clumping and formation of great galactic walls separated by vast voids, colliding galaxies, and phenomenon attributed to the purely hypothetical "dark energy" which may not exist at all.
We explore how the entropic notion of depletion forces between spheres, introduced by Asakura and Oosawa, can be extended to depletion torques that affect the orientations of colloidal particles having complex shapes. In prior experimental work, systems of microscale plate-like particles in the presence of a nanoscale depletion agent have been shown to form polymer-like columnar chains; restoring depletion torques act to align lithographically-structured platelets within a chain orientationally about the chain’s axis. We consider depletion torques corresponding to parallel, face-to-face, near-contact pair interactions for complex-shaped, plate-like, prismatic lithographic particles in colloidal dispersions containing a spherical nanoscale depletion agent. We calculate depletion torques for a wide variety of such particles, including rotationally symmetric, asymmetric, achiral, chiral, and elongated particles. Moreover, we determine depletion torques between two non-parallel proximate square platelets connected by a lossless hinge along a common edge. Our investigations show that depletion torques can be tailored through lithographic or synthetic design of specific geometrical features in the shapes of particles.
The electromagnetic vacuum is known to have energy. It has been recently
argued that the quantum vacuum can possess momentum, that adds up to the
momentum of matter. This ``Casimir momentum'' is closely related to the Casimir
effect, in which case energy is exchanged. In previous theory it was treated
semi-classically. We present a non-relativistic quantum theory for the linear
momentum of electromagnetic zero-point fluctuations, considering an harmonic
oscillator subject to crossed, quasi-static magnetic and electric and coupled
to the quantum vacuum. We derive a contribution of the quantum vacuum to the
linear pseudo-momentum and give a new estimate for the achievable speed. Our
analysis show that the effect exists and that it is finite.
Using the measured optical response and surface roughness topography as inputs, we perform realistic calculations of the combined effect of Casimir and electrostatic forces on the actuation dynamics of micro-electromechanical systems (MEMS). In contrast with the expectations, roughness can influence MEMS dynamics even at distances between bodies significantly larger than the root-mean-square roughness. This effect is associated with statistically rare high asperities that can be locally close to the point of contact. It is found that, even though surface roughness appears to have a detrimental effect on the availability of stable equilibria, it ensures that those equilibria can be reached more easily than in the case of flat surfaces. Hence our findings play a principal role for the stability of microdevices such as vibration sensors, switches, and other related MEM architectures operating at distances below 100 nm.
Micro electromechanical systems (MEMS) and mechanical effects of quantum fluctuations become strongly related. MEMS have allowed the production of important experimental results such as quantitative measurements of the Casimir force at the micro- and nanoscales. MEMS are used to probe these effects because they are sensitive to them and engineers will certainly have to increasingly consider the effects of quantum and thermal fluctuations in the design of MEMS that are used as actuators and sensors. These effects on MEMS are controlled by the electron–photon coupling. These questions are then coupled to new fields of research, such as photonics and plasmonics.
All the Maths have been scrambled during uploading of the .docx version, I have tried but cannot repair this and have uploaded a .pdf version which, contains the equations (recommended). The .docx contains visual evidences in the form of video and audio, and I refer the reader to those for this aspect of the research. (Apologise for any inconvenience caused). This research revolves around an exploration of the internuclear 're' field involving active 'warp-cores', the results relate to the Harmonics Oscillation Chart, ZPE, Luminous and Dark Energy, Mirror Point Energy (MPE), and other. The research utilises warp-cores as the mechanism for exploring the internuclear exchange, in an attempt to advance warp-core design and understanding. The paper has been re-uploaded due to previous upload errors with that effecting the maths, here the focus is upon supporting the research with maths and visual evidencing.
In diesem Kapitel werden einige Anwendungen der Dirac-Gleichung betrachtet. Es wird unter anderem die Spin-Bahn-Wechselwirkung
im Zusammenhang mit dem nichtrelativistischen Grenzfall der Dirac-Gleichung in der 1/c2-Näherung hergeleitet und anschließend die Feinstruktur von H-Atomen studiert. Weiterhin wird die Streuung von Elektronen
und Positronen in äußerem elektromagnetischen Feld unter Verwendung der kausalen Greenschen Funktion betrachtet. Der Wirkungsquerschnitt
für die Streuung von relativistischen Elektronen (die Mott-Formel) wird ausführlich hergeleitet. In den Aufgaben am Ende des
Kapitels findet man auch einige Anwendungen zur Klein-Gordon-Gleichung. Die meisten Aufgabenstellungen zur Klein-Gordon-Gleichung
können auch auf die Dirac-Gleichung erweitert werden.
Quantum optics combines classical electrodynamics with quantum mechanics to describe how light interacts with material on the nanoscale, and many of the tricks and techniques used in nanophotonics can be extended to this quantum realm. Specifically, quantum vacuum fluctuations of electromagnetic fields experience boundary conditions that can be tailored by the nanoscopic geometry and dielectric properties of the involved materials. These quantum fluctuations give rise to a plethora of phenomena ranging from spontaneous emission to the Casimir effect, which can all be controlled and manipulated by changing the boundary conditions for the fields. Here, we focus on several recent developments in modifying the Casimir effect and related phenomena, including the generation of torques and repulsive forces, creation of photons from vacuum, modified chemistry, and engineered material functionality, as well as future directions and applications for nanotechnology.
Chemisch strukturierte Substrate haben zunehmend an Bedeutung gewonnen seit es möglich ist, Oberflächen im Bereich von Mikrometern und darunter zu strukturieren. Auf diesen kleinen Skalen wird die Wechselwirkung der Flüssigkeiten mit dem Substrat wichtig und eine chemische Strukturierung der Substrate verursacht eine reiche Grenzflächenstruktur, die von den molekularen
Details des lokalen Kraftfeldes anhängt. Konzentriert man sich jedoch auf das Gebiet um den kritischen Punkt eines Phasenübergangs zweiter Ordnung, werden die molekularen Details unbedeutend und das System zeigt ein universelles Verhalten, das durch kritische Exponenten, nicht-universelle Amplituden und universelle Skalenfunktionen beschrieben wird.
Systeme mit kritischen Punkten werden bezüglich ihres Bulk-Verhaltens klassifiziert und Universalitätsklassen zugeordnet. Bei Systemen, die durch ein Substrat oder eine freie Oberfläche begrenzt werden, spalten die Universalitätsklassen in Oberflächen-Universalitätsklassen bezüglich des kritischen Verhaltens an der Oberfläche auf. Physikalisch unterschiedliche Systeme können zur selben Universalitätsklasse gehören: einkomponentige Flüssigkeiten in der Nähe ihres kritischen Punktes zwischen Flüssigkeit und Gas gehören ebenso wie binäre Flüssigkeitsmischungen nahe ihres kritischen Punktes der Entmischung - die in dieser Arbeit betrachtet werden - und uniaxiale Ferromagnete nahe der Curie-Temperatur zur Ising-Universalitätsklasse. Die Universalitätsklassen werden durch die Reichweite der Wechselwirkung, die räumliche Dimension des Systems und die Dimension des Ordnungsparameters bestimmt.
Für eine binäre Flüssigkeitsmischung lässt sich der Ordnungsparameter, der den Grad der Ordnung im System beschreibt, entweder als Differenz der Konzentrationen der beiden Flüssigkeiten oder als Konzentration einer der Flüssigkeiten minus ihrer Konzentration am kritischen Entmischungspunkt definieren.
Das Thema dieser Arbeit sind die kritischen Phänomene, die auftreten, wenn eine binäre Flüssigkeitsmischung, die sich in der Umgebung ihres kritischen Entmischungspunktes befindet, mit einem topologisch flachen, chemisch strukturierten Substrat in Kontakt gebracht wird. Dabei verursacht der chemische Kontrast unterschiedliche lokale Präferenzen für die beiden Spezies der binären Flüssigkeitsmischung.
In der vorliegenden Arbeit werden drei verschiedene Typen von chemisch strukturierten Substraten betrachtet: eine chemische Stufe (wichtig für das Verständnis von lokalen Eigenschaften einer Flüssigkeit an der Grenze von chemischen Streifen), ein einzelner chemischer Streifen (das einfachste chemische Muster auf einer Oberfläche) und ein periodisches Streifenmuster (als Beispiel für die Adsorption an heterogenen Oberflächen).
Die Ordnungsparameterprofile und ihre Temperaturabhängigkeit sind durch universelle Skalenfunktionen gegeben, die im Rahmen der Mean-Field-Theorie berechnet werden. Die Skalenfunktionen und der Einfluss der chemischen Streifen werden in der Arbeit eingehend untersucht.
Wird eine Flüssigkeit, die von zwei Substraten eingeschlossen wird, in die Nähe ihres kritischen Punkts gebracht, entsteht aufgrund der Randbedingungen, die das Spektrum der kritischen Fluktuationen des Ordnungsparameters einschränken, eine auf die Substrate wirkende effektive Kraft ("kritische Casimir-Kraft").
In dieser Arbeit werden die singulären Beiträge der effektiven Kraft untersucht, die auf chemisch inhomogene Substrate wirken, welche binäre Flüssigkeitsmischungen begrenzen.
Es werden vier grundlegende Konfigurationen zweier geometrisch flachen, parallelen Substrate mit periodischen chemischen Mustern aus Streifen mit positiven und Streifen mit negativen Oberflächenfeldern betrachtet: zwei Substrate mit den gleichen Streifenmustern (d.h. ein positiver Streifen liegt gegenüber einem positiven Streifen), zwei Substrate mit entgegengesetzten
Streifenmustern (d.h. ein positiver Streifen liegt gegenüber einem negativen Streifen), ein strukturiertes und ein homogenes Substrat und abschließend zwei Substrate mit den gleichen Streifenmustern, die aber gegeneinander verschoben sind (d.h. ein positiver Streifen liegt teilweise einem positiven und teilweise einem negativen Streifen gegenüber).
Das universelle Verhalten der Ordnungsparameterprofile und der effektiven Kräfte, die auf die Substrate wirken, wird durch universelle Skalenfunktionen beschrieben. Die Skalenfunktionen der Ordnungsparameterprofile werden im Rahmen der Mean-Field-Theorie numerisch berechnet und daraus mittels des Stress-Tensors die Kräfte zwischen den Substraten abgeleitet. Die Abhängigkeit der Skalenfunktionen der Kräfte von der Distanz zwischen den Substraten, von den Streifenbreiten und - im Fall des verschobenen Streifenmusters - von der relativen Verschiebung wird untersucht. Es werden verallgemeinerte Casimir-Amplituden definiert und ihre Abhängigkeit von der chemischen Strukturierung der Substrate betrachtet.
Wave-particle duality is one of the many strange phenomena observed in the quantum world that desperately requires a new theory. Such a theory is proposed herein through a metaphysical approach based on the Qur’an and the principles of Islamic science, supplemented by philosophical rational arguments. Interpreting relevant Qur’anic verses, together with the pairing concept and the one-to-one correspondence principle, manages to facilitate some detailed explanations regarding the wave-particle duality of an electron. Scientific analysis indicates an electron can consist of both a unit electrical charge and a permanent magnet, which all reflects on its wave-particle duality behaviour as per experimental observations. Though physicists are currently only considering the existence of the induced magnetic field, the presence of which is due to the spin of the electron, the new theory postulates that a permanent magnetic field is additionally present. Furthermore, the electrical charge and the permanent magnetism could be considered as potential energy, which is also believed to be possibly the zero point energy that has been observed to exist, but has yet to be properly explained. Based on this new theory, a mathematical equation has been derived to calculate the postulated potential energy of an electron. Islamic science in this case appears to have demonstrated its significance in proposing a new perspective in the exploration of the mysterious quantum world.
There is no "universal now." The distinctions between past present and future are illusions. As predicted by Einstein's field equations space-time may be a circle such that the future leads to the present and then the past which leads to the future, thereby creating multiple futures and pasts and which allows information from the future to effect the present. Causes may cause themselves. Coupled with evidence from entanglement where choices made in the future effect measurements made in the present and theoretical tachyons which travel at superluminal speeds from the future to the present and then the past, this may account for precognition, deja vu, and premonitions. In quantum mechanics, where reality and the quantum continuum are a unity, time is also a unity such that the future present past are a continuum which are linked and the same could be said of consciousness which exists in the future and in the present and past. If considered as a "world line" and in space-like instead of time-like intervals, then consciousness from birth to death would be linked as a basic unity extending not in time but in space and the same could be said of time. Time-space and consciousness are also linked and interact via the wave function and as demonstrated by entanglement and the Uncertainty Principle. Evidence from space-time contraction, atomic clocks and the twin paradox as functions of gravity and acceleration also demonstrate that the future already exists before it is experienced by consciousness in the present. Likewise, under conditions of accelerated consciousness (such as in reaction to terror) and dream states where various brain structures are in a heightened state of activity, space-time may also contract, such that time may slow down and consciousness may be given glimpses of the future in advance of other conscious minds thereby providing again for experiences such as precognition, premonitions, and deja vu. Closed time curves, conscious time, relative time, dream time, and quantum time are also discussed.
The influence of Casimir and van der Waals forces on the instability of vibratory micro and nano-bridge gyroscopes with proof mass attached to its midpoint is studied. The gyroscope subjected to the base rotation, Casimir and van der Waals attractions is actuated and detected by electrostatic methods. The system has two coupled bending motions actuated by the electrostatic and Coriolis forces. First a system of nonlinear equations for the flexural-flexural deflection of beam gyroscopes is derived using the extended Hamilton's principle. In modeling, the nonlinearities due to mid-plane stretching, electrostatic forces, including fringing field, Casimir and van der Waals attractions, are considered. The method of homotopy perturbation is used to solve the equations of equilibrium, with the solution validated by numerical methods. In addition, the effect of nondimensional parameters on the instability and deflection of the gyroscope is investigated. The data presented can be used in the design of vibratory micro/nano gyroscopes.
Oxides of non-magnetic cations exhibit elusive signs of weak temperature-independent ferromagnetism. The effect is associated with surface defects, but it defies conventional explanation. Possible hypotheses are a spin-split defect impurity band, or giant orbital paramagnetism related to zero-point vacuum fluctuations.
Quantum mechanics teaches us that vacuum is not empty. Rather, it contains all kinds of virtual particles. The energy of such particles is called zero point energy. If two surfaces come in close proximity of each other, they will create a difference between the zero point energies in between them and on the outside. Consequently the surfaces will be pushed toward each other. This phenomenon is known as the Casimir effect. It has turned out to be a generalization of the more familiar van der Waals force.
Present technology has only recently enabled us to measure the Casimir force directly. Part of this thesis is about a complication that arises in such measurements: a real surface does not have a nice, smooth shape, but it is often rough. Surface roughness influences the Casimir force mainly at relatively short distances of one ten millionth meter or less. This influence is predominantly determined by statistically rare high asperities in the surfaces. This thesis introduces a model that reproduces measurements of the Casimir force between rough surfaces.
The Casimir force is unavoidable: the existence of virtual particles cannot be shut down in any way. The smaller the distance between the surfaces, the larger the Casimir force. Hence at short distances it is of interest for technology of micro electromechanical systems (MEMS), such as micro switches or accelerometers. The Casmir force has a considerable influence on the motion of MEMS components at short distances. Surface roughness turns out to make this motion more predictable.
This chapter contains sections titled: Introduction Basic Concepts Modeling Techniques Discussion and Prospects Summary
Casimir assumed the electromagnetic (EM) radiation in the gap between plates was the zero point energy (ZPE). Irrespective of whether the ZPE exists, Casimir did not conserve ZPE in the gap as required by EM confinement. Conservation requires constancy of ZPE as the gap increases or decreases, and therefore the gradient of the ZPE with respect to the gap vanishes and the Casimir force does not exist. In contrast, the existence of blackbody (BB) radiation given by the thermal kT energy of surface atoms is without question. Under EM confinement, conservation proceeds by the quantum electrodynamics (QED) up-conversion of low-frequency thermal kT energy of surface atoms in Casimir's plates to the EM confinement frequency of the gap, typically at frequencies beyond the vacuum ultraviolet (VUV). In radiationless recombination, the excitons produce an attractive force if the positive hole of an exciton is created in one plate and an electron in the other. B ut excitons cannot span typical gaps between Casimir's plates, and therefore recombination proceeds by the emission of QED photons. In a vacuum, the QED photons by the photoelectric effect charge the plates equally and a net attractive force between the plates is not produced. However, the QED photons produce EM energy density in the gap that unlike EM energy is not constant, but increases as the gap decreases. Hence, the attractive force measured in Casimir experiments is the BB force produced as the gradient of the EM energy density in the gap interacts with the polarity of surface atoms is equal and opposite across the plates. Immersing the surfaces in the electron scavenger bromobenzene produces a repulsive BB force because unlike the vacuum the electrons removed from the plates by the QED photons in bromobenzene are scavenged leaving both plates with net positive charge.
The lateral Casimir force between a sinusoidally corrugated gold coated plate and large sphere was measured for surface separations between 0.2 to 0.3 microm using an atomic force microscope. The measured force shows the required periodicity corresponding to the corrugations. It also exhibits the necessary inverse fourth power distance dependence. The obtained results are shown to be in good agreement with a complete theory taking into account the imperfectness of the boundary metal. This demonstration opens new opportunities for the use of the Casimir effect for lateral translation in microelectromechanical systems.
The vacuum stress between closely spaced conducting surfaces, due to the modification of the zero-point fluctuations of the electromagnetic field,has been conclusively demonstrated. The measurement employed an electromechanical system based on a torsion pendulum. Agreement with theory at the level of 5% is obtained. {copyright} {ital 1996} {ital The American Physical Society}
The Casimir force between uncharged metallic surfaces originates from quantum-mechanical zero-point fluctuations of the electromagnetic field. We demonstrate that this quantum electrodynamical effect has a profound influence on the oscillatory behavior of microstructures when surfaces are in close proximity (< or =100 nm). Frequency shifts, hysteretic behavior, and bistability caused by the Casimir force are observed in the frequency response of a periodically driven micromachined torsional oscillator.
We calculate the Casimir force and free energy for plane metallic mirrors at non-zero temperature. Numerical evaluations are given with temperature and conductivity effects treated simultaneously. The results are compared with the approximation where both effects are treated independently and the corrections simply multiplied. The deviation between the exact and approximated results takes the form of a temperature dependent function for which an analytical expression is given. The knowledge of this function allows simple and accurate estimations at the % level. Comment: 8 pages, 4 figures, uses RevTeX