Problems with the Newton-Schr\"odinger Equations

We examine the origin of the Newton-Schr\"odinger equations (NSEs) that play an important role in alternative quantum theories (AQT), macroscopic quantum mechanics and gravity-induced decoherence. We show that NSEs for individual particles do not follow from general relativity (GR) plus quantum field theory (QFT). Contrary to what is commonly assumed, the NSEs are not the weak-field (WF), non-relativistic (NR) limit of the semi-classical Einstein equation (SCE) (this nomenclature is preferred over the `M\/oller-Rosenfeld equation') based on GR+QFT. The wave-function in the NSEs makes sense only as that for a mean field describing a system of $N$ particles as $N \rightarrow \infty$, not that of a single or finite many particles. From GR+QFT the gravitational self-interaction leads to mass renormalization, not to a non-linear term in the evolution equations of some AQTs. The WF-NR limit of the gravitational interaction in GR+QFT involves no dynamics. To see the contrast, we give a derivation of the equation (i) governing the many-body wave function from GR+QFT and (ii) for the non-relativistic limit of quantum electrodynamics (QED). They have the same structure, being linear, and very different from NSEs. Adding to this our earlier consideration that for gravitational decoherence the master equations based on GR+QFT lead to decoherence in the energy basis and not in the position basis, despite some AQTs desiring it for the `collapse of the wave function', we conclude that the origins and consequences of NSEs are very different, and should be clearly demarcated from those of the SCE equation, the only legitimate representative of semiclassical gravity, based on GR+QFT.Comment: 18 pages. Invited paper for the Focus Issue on 'Gravitational quantum physics' in New Journal of Physic

Ant-colony-based multiuser detection for multifunctional-antenna-array-assisted MC DS-CDMA systems

A novel Ant Colony Optimization (ACO) based Multi-User Detector (MUD) is designed for the synchronous Multi-Functional Antenna Array (MFAA) assisted Multi-Carrier Direct-Sequence Code-Division Multiple-Access (MC DS-CDMA) uplink (UL), which supports both receiver diversity and receiver beamforming. The ACO-based MUD aims for achieving a bit-error-rate (BER) performance approaching that of the optimum maximum likelihood (ML) MUD, without carrying out an exhaustive search of the entire MC DS-CDMA search space constituted by all possible combinations of the received multi-user vectors. We will demonstrate that regardless of the number of the subcarriers or of the MFAA configuration, the system employing the proposed ACO based MUD is capable of supporting 32 users with the aid of 31-chip Gold codes used as the T-domain spreading sequence without any significant performance degradation compared to the single-user system. As a further benefit, the number of floating point operations per second (FLOPS) imposed by the proposed ACO-based MUD is a factor of 108 lower than that of the ML MUD. We will also show that at a given increase of the complexity, the MFAA will allow the ACO based MUD to achieve a higher SNR gain than the Single-Input Single-Output (SISO) MC DS-CDMA system. Index Terms—Ant Colony Optimization, Multi-User Detector, Multi-Functional Antenna Array, Multi-Carrier Direct-Sequence Code-Division Multiple-Access, Uplink, Near-Maximum Likelihood Detection

Low-latitude boundary layer clouds as seen by CALIPSO

The distribution of low-level cloud in the tropical belt is investigated using 6 months of Level 2 retrievals from Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) at 333 m and 1 km horizontal resolutions. Regional patterns of tropical clouds emerge from the data, matching expectations from existing observations. The advantage of the lidar is highlighted by the distribution of cloud-top height, revealing the preponderance of low-level clouds over the tropical oceans. Over land, cloud top is more uniformly distributed under the influence of diurnal variation. The integrated cloud-top distribution suggests tropical, marine low-cloud amount around 25-30%; a merged CALIPSO-CloudSat product has a similar cloud-top distribution and includes a complementary estimate of cloud fraction based on the lidar detections. The low-cloud distribution is similar to that found in fields of shallow cumulus observed during the Rain in Cumulus Over the Ocean (RICO) field study. The similarity is enhanced by sampling near the RICO site or sampling large-scale conditions similar to those during RICO. This finding shows how satellite observations can help to generalize findings from detailed field observations

The Apparent Fractal Conjecture

This short communication advances the hypothesis that the observed fractal structure of large-scale distribution of galaxies is due to a geometrical effect, which arises when observational quantities relevant for the characterization of a cosmological fractal structure are calculated along the past light cone. If this hypothesis proves, even partially, correct, most, if not all, objections raised against fractals in cosmology may be solved. For instance, under this view the standard cosmology has zero average density, as predicted by an infinite fractal structure, with, at the same time, the cosmological principle remaining valid. The theoretical results which suggest this conjecture are reviewed, as well as possible ways of checking its validity.Comment: 6 pages, LaTeX. Text unchanged. Two references corrected. Contributed paper presented at the "South Africa Relativistic Cosmology Conference in Honour of George F. R. Ellis 60th Birthday"; University of Cape Town, February 1-5, 199