In this paper, we review research on homeopathy from four perspectives, focusing on reviews and some landmark studies. These perspectives are laboratory studies, clinical trials, observational studies, and theoretical work. In laboratory models, numerous effects and anomalies have been reported. However, no single model has been sufficiently widely replicated. Instead, researchers have focused on ever-new models and experiments, leaving the picture of scattered anomalies without coherence. Basic research, trying to elucidate a purported difference between homeopathic remedies and control solutions has also produced some encouraging results, but again, series of independent replications are missing. While there are nearly 200 reports on clinical trials, few series have been conducted for single conditions. Some of these series document clinically useful effects and differences against placebo and some series do not. Observational research into uncontrolled homeopathic practice documents consistently strong therapeutic effects and sustained satisfaction in patients. We suggest that this scattered picture has to do with the fourth line of research: lack of a good theory. Some of the extant theoretical models are reviewed, including placebo, water structure, silica contamination, energy models, and entanglement models. It emerges that local models, suggesting some change in structure in the solvent, are far from convincing. The nonlocal models proposed would predict that it is impossible to nail down homeopathic effects with direct experimental testing and this places homeopathy in a scientific dilemma. We close with some suggestions for potentially fruitful research.

Patients with a pressure gradient greater than 20 mm Hg should be good candidates for renal arterial dilatation, and use of the pressure guide wire will facilitate interventional decisions.

This paper discusses the nature of the active ingredient of homeopathic ultramolecular dilutions in terms of quantitative physics. First, the problem of the nature of an active ingredient in ultramolecular dilutions is analysed leading to the recognition of the necessity of characterizing the active ingredient as a non-local quality. Second, non-locality in quantum mechanics, which is used as a paradigm, is formally presented. Third, a generalization of quantum mechanics is considered, focussing on the consequences of weakening of the axioms. The formal treatment leads to the possible extension of the validity of quantum theory to macroscopic or even non-physical systems under certain circumstances with a while maintaining non-local behaviour. With respect to the survival of entanglement in such non-quantum systems a strong relationship between homeopathy and non-local behaviour can be envisaged. I describe how several authors apply this relationship. In conclusion, the paper reviews how quantum mechanics is closely related to information theory but why weak quantum theory and homeopathy have not hitherto been related in the same way.

The nature of the 'active ingredient', in homeopathic high dilutions is investigated. A model for every degree of dilution is introduced; within this the active ingredient can be dealt with in physical terms. In mathematical terms this model has features which correspond to the axioms of weak quantum theory. Features which are similar to entanglement in ordinary quantum theory are discussed in particular.

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