The Blackbody Radiation Spectrum Follows from Zero-Point Radiation and the Structure of Relativistic Spacetime in Classical Physics

The analysis of this article is entirely within classical physics. Any attempt to describe nature within classical physics requires the presence of Lorentz-invariant classical electromagnetic zero-point radiation so as to account for the Casimir forces between parallel conducting plates at low temperatures. Furthermore, conformal symmetry carries solutions of Maxwell's equations into solutions. In an inertial frame, conformal symmetry leaves zero-point radiation invariant and does not connect it to non-zero-temperature; time-dilating conformal transformations carry the Lorentz-invariant zero-point radiation spectrum into zero-point radiation and carry the thermal radiation spectrum at non-zero temperature into thermal radiation at a different non-zero-temperature. However, in a non-inertial frame, a time-dilating conformal transformation carries classical zero-point radiation into thermal radiation at a finite non-zero-temperature. By taking the no-acceleration limit, one can obtain the Planck radiation spectrum for blackbody radiation in an inertial frame from the thermal radiation spectrum in an accelerating frame. Here this connection between zero-point radiation and thermal radiation is illustrated for a scalar radiation field in a Rindler frame undergoing relativistic uniform proper acceleration through flat spacetime in two spacetime dimensions. The analysis indicates that the Planck radiation spectrum for thermal radiation follows from zero-point radiation and the structure of relativistic spacetime in classical physics.Comment: 21 page

The Energy Density in the Casimir Effect

We compute the expectations of the squares of the electric and magnetic fields in the vacuum region outside a half-space filled with a uniform dispersive dielectric. We find a positive energy density of the electromagnetic field which diverges at the interface despite the inclusion of dispersion in the calculation. We also investigate the mean squared fields and the energy density in the vacuum region between two parallel half-spaces. Of particular interest is the sign of the energy density. We find that the energy density is described by two terms: a negative position independent (Casimir) term, and a positive position dependent term with a minimum value at the center of the vacuum region. We argue that in some cases, including physically realizable ones, the negative term can dominate in a given region between the two half-spaces, so the overall energy density can be negative in this region.Comment: 16 pages, 4 figures; 3 references and some new material in Sect. 4.4 adde

On electrostatic and Casimir force measurements between conducting surfaces in a sphere-plane configuration

We report on measurements of forces acting between two conducting surfaces in a spherical-plane configuration in the 35 nm-1 micrometer separation range. The measurements are obtained by performing electrostatic calibrations followed by a residual analysis after subtracting the electrostatic-dependent component. We find in all runs optimal fitting of the calibrations for exponents smaller than the one predicted by electrostatics for an ideal sphere-plane geometry. We also find that the external bias potential necessary to minimize the electrostatic contribution depends on the sphere-plane distance. In spite of these anomalies, by implementing a parametrixation-dependent subtraction of the electrostatic contribution we have found evidence for short-distance attractive forces of magnitude comparable to the expected Casimir-Lifshitz force. We finally discuss the relevance of our findings in the more general context of Casimir-Lifshitz force measurements, with particular regard to the critical issues of the electrical and geometrical characterization of the involved surfaces.Comment: 22 pages, 15 figure

Casimir Effect, Achucarro-Ortiz Black Hole and the Cosmological Constant

We treat the two-dimensional Achucarro-Ortiz black hole (also known as (1+1) dilatonic black hole) as a Casimir-type system. The stress tensor of a massless scalar field satisfying Dirichlet boundary conditions on two one-dimensional "walls" ("Dirichlet walls") is explicitly calculated in three different vacua. Without employing known regularization techniques, the expression in each vacuum for the stress tensor is reached by using the Wald's axioms. Finally, within this asymptotically non-flat gravitational background, it is shown that the equilibrium of the configurations, obtained by setting Casimir force to zero, is controlled by the cosmological constant.Comment: 20 pages, LaTeX, minor corrections, comments and clarifications added, version to appear in Phys. Rev.

Thermodynamical aspects of the Casimir force between real metals at nonzero temperature

We investigate the thermodynamical aspects of the Casimir effect in the case of plane parallel plates made of real metals. The thermal corrections to the Casimir force between real metals were recently computed by several authors using different approaches based on the Lifshitz formula with diverse results. Both the Drude and plasma models were used to describe a real metal. We calculate the entropy density of photons between metallic plates as a function of the surface separation and temperature. Some of these approaches are demonstrated to lead to negative values of entropy and to nonzero entropy at zero temperature depending on the parameters of the system. The conclusion is that these approaches are in contradiction with the third law of thermodynamics and must be rejected. It is shown that the plasma dielectric function in combination with the unmodified Lifshitz formula is in perfect agreement with the general principles of thermodynamics. As to the Drude dielectric function, the modification of the zero-frequency term of the Lifshitz formula is outlined that not to violate the laws of thermodynamics.Comment: 8pages, 4 figures; Phys. Rev. A, to appea

Charge and Spin Effects in Mesoscopic Josephson Junctions

We consider the charge and spin effects in low dimensional superconducting weak links. The first part of the review deals with the effects of electron-electron interaction in Superconductor/Luttinger liquid/Superconductor junctions. The experimental realization of this mesoscopic hybrid system can be the individual single wall carbon nanotube that bridges the gap between two bulk superconductors. The dc Josephson current through a Luttinger liquid in the limits of perfectly and poorly transmitting junctions is evaluated. The relationship between the Josephson effect in a long SNS junction and the Casimir effect is discussed. In the second part of the paper we review the recent results concerning the influence of the Zeeman and Rashba interactions on the thermodynamical properties of ballistic S/QW/S junction fabricated in two dimensional electron gas. It is shown that in magnetically controlled junction there are conditions for resonant Cooper pair transition which results in giant supercurrent through a tunnel junction and a giant magnetic response of a multichannel SNS junction. The supercurrent induced by the joint action of the Zeeman and Rashba interactions in 1D quantum wires connected to bulk superconductors is predicted.Comment: 36 pages, 8 figures; minor changes in reference

Normal and Lateral Casimir Forces between Deformed Plates

The Casimir force between macroscopic bodies depends strongly on their shape and orientation. To study this geometry dependence in the case of two deformed metal plates, we use a path integral quantization of the electromagnetic field which properly treats the many-body nature of the interaction, going beyond the commonly used pairwise summation (PWS) of van der Waals forces. For arbitrary deformations we provide an analytical result for the deformation induced change in Casimir energy, which is exact to second order in the deformation amplitude. For the specific case of sinusoidally corrugated plates, we calculate both the normal and the lateral Casimir forces. The deformation induced change in the Casimir interaction of a flat and a corrugated plate shows an interesting crossover as a function of the ratio of the mean platedistance H to the corrugation length \lambda: For \lambda \ll H we find a slower decay \sim H^{-4}, compared to the H^{-5} behavior predicted by PWS which we show to be valid only for \lambda \gg H. The amplitude of the lateral force between two corrugated plates which are out of registry is shown to have a maximum at an optimal wavelength of \lambda \approx 2.5 H. With increasing H/\lambda \gtrsim 0.3 the PWS approach becomes a progressively worse description of the lateral force due to many-body effects. These results may be of relevance for the design and operation of novel microelectromechanical systems (MEMS) and other nanoscale devices.Comment: 20 pages, 5 figure

ACTRIS ACSM intercomparison – Part 2: Intercomparison of ME-2 organic source apportionment results from 15 individual, co-located aerosol mass spectrometers

Chemically resolved atmospheric aerosol data sets from the largest intercomparison of the Aerodyne aerosol chemical speciation monitors (ACSMs) performed to date were collected at the French atmospheric supersite SIRTA. In total 13 quadrupole ACSMs (Q-ACSM) from the European ACTRIS ACSM network, one time-of-flight ACSM (ToF-ACSM), and one high-resolution ToF aerosol mass spectrometer (AMS) were operated in parallel for about 3 weeks in November and December~2013. Part 1 of this study reports on the accuracy and precision of the instruments for all the measured species. In this work we report on the intercomparison of organic components and the results from factor analysis source apportionment by positive matrix factorisation (PMF) utilising the multilinear engine 2 (ME-2). Except for the organic contribution of mass-to-charge ratio m/z 44 to the total organics (f44), which varied by factors between 0.6 and 1.3 compared to the mean, the peaks in the organic mass spectra were similar among instruments. The m/z 44 differences in the spectra resulted in a variable f44 in the source profiles extracted by ME-2, but had only a minor influence on the extracted mass contributions of the sources. The presented source apportionment yielded four factors for all 15 instruments: hydrocarbon-like organic aerosol (HOA), cooking-related organic aerosol (COA), biomass burning-related organic aerosol (BBOA) and secondary oxygenated organic aerosol (OOA). ME-2 boundary conditions (profile constraints) were optimised individually by means of correlation to external data in order to achieve equivalent / comparable solutions for all ACSM instruments and the results are discussed together with the investigation of the influence of alternative anchors (reference profiles). A comparison of the ME-2 source apportionment output of all 15 instruments resulted in relative standard deviations (SD) from the mean between 13.7 and 22.7 % of the source's average mass contribution depending on the factors (HOA: 14.3 ± 2.2 %, COA: 15.0 ± 3.4 %, OOA: 41.5 ± 5.7 %, BBOA: 29.3 ± 5.0 %). Factors which tend to be subject to minor factor mixing (in this case COA) have higher relative uncertainties than factors which are recognised more readily like the OOA. Averaged over all factors and instruments the relative first SD from the mean of a source extracted with ME-2 was 17.2 %.JRC.H.2-Air and Climat

ACTRIS ACSM intercomparison – Part 1: Reproducibility of concentration and fragment results from 13 individual Quadrupole Aerosol Chemical Speciation Monitors (Q-ACSM) and consistency with co-located instruments

As part of the European ACTRIS project, the first large Quadrupole Aerosol Chemical Speciation Monitor (Q-ACSM) intercomparison study was conducted in the region of Paris for 3 weeks during the late-fall – early-winter period (November–December 2013). The first week was dedicated to the tuning and calibration of each instrument, whereas the second and third were dedicated to side-by-side comparison in ambient conditions with co-located instruments providing independent information on submicron aerosol optical, physical, and chemical properties. Near real-time measurements of the major chemical species (organic matter, sulfate, nitrate, ammonium, and chloride) in the non-refractory submicron aerosols (NR-PM1) were obtained here from 13 Q-ACSM. The results show that these instruments can produce highly comparable and robust measurements of the NR-PM1 total mass and its major components. Taking the median of the 13 Q-ACSM as a reference for this study, strong correlations (r2 > 0.9) were observed systematically for each individual Q-ACSM across all chemical families except for chloride for which three Q-ACSMs showing weak correlations partly due to the very low concentrations during the study. Reproducibility expanded uncertainties of Q-ACSM concentration measurements were determined using appropriate methodologies defined by the International Standard Organization (ISO 17025, 1999) and were found to be 9, 15, 19, 28, and 36 % for NR-PM1, nitrate, organic matter, sulfate, and ammonium, respectively. However, discrepancies were observed in the relative concentrations of the constituent mass fragments for each chemical component. In particular, significant differences were observed for the organic fragment at mass-to-charge ratio 44, which is a key parameter describing the oxidation state of organic aerosol. Following this first major intercomparison exercise of a large number of Q-ACSMs, detailed intercomparison results are presented, along with a discussion of some recommendations about best calibration practices, standardized data processing, and data treatment.JRC.H.2-Air and Climat

The effect of improvisational music therapy on the treatment of depression: protocol for a randomised controlled trial

Background. Music therapy is frequently offered to individuals suffering from depression. Despite the lack of research into the effects of music therapy on this population, anecdotal evidence suggests that the results are rather promising. The aim of this study is to examine whether improvisational, psychodynamically orientated music therapy in an individual setting helps reduce symptoms of depression and improve other health-related outcomes. In particular, attention will be given to mediator agents, such as musical expression and interaction in the sessions, as well as to the explanatory potential of EEG recordings in investigating emotion related music perception of individuals with depression. Methods. 85 adults (18–50 years of age) with depression (ICD-10: F 32 or F33) will be randomly assigned to an experimental or a control condition. All participants will receive standard care, but the experimental group will be offered biweekly sessions of improvisational music therapy over a period of 3 months. A blind assessor will measure outcomes before testing, after 3 months, and after 6 months. Discussion. This study aims to fill a gap in knowledge as to whether active (improvisational) music therapy applied to people with depression improves their condition. For the first time in this context, the mediating processes, such as changes in musical expression and interaction during the course of therapy, will be objectively investigated, and it is expected that the results will provide new insights into these processes. Furthermore, the findings are expected to reveal whether music related emotional experiences, as measured by EEG, can be utilized in assessing a depressive client's improvement in the therapy. The size and the comprehensiveness of the study are sufficient for generalizing its findings to clinical practice as well as to further music therapy research. Trial registration. ISRCTN84185937peerReviewe