The infinitesimally low concentration of homeopathic preparations, which often lack even a single molecule of the diluted substance, has been the basis of questions about the effects of the preparations since the 19th century. Modern advocates of homeopathy have proposed a concept of "water memory", according to which water "remembers" the substances mixed in it, and transmits the effect of those substances when consumed. This concept is inconsistent with the current understanding of matter, and water memory has never been demonstrated to exist, in terms of any detectable effect, biological or otherwise.

James Randi and the 10:23 campaign groups have highlighted the lack of active ingredients in most homeopathic products by taking large 'overdoses'. None of the hundreds of demonstrators in the UK, Australia, New Zealand, Canada and the US were injured and "no one was cured of anything, either".Sam Jones, "Homeopathy protesters to take 'mass overdose' outside Boots", The Guardian, January 29, 2010

Outside of the alternative medicine community, scientists have long considered homeopathy a sham or a pseudoscience, and the mainstream medical community regards it as quackery. There is an overall absence of sound statistical evidence of therapeutic efficacy, which is consistent with the lack of any biologically plausible pharmacological agent or mechanism.

Abstract concepts within theoretical physics have been invoked to suggest explanations of how or why preparations might work, including quantum entanglement, quantum nonlocality, the theory of relativity and chaos theory. Contrariwise, quantum superposition has been invoked to explain why homeopathy does not work in double-blind trials. However, the explanations are offered by nonspecialists within the field, and often include speculations that are incorrect in their application of the concepts and not supported by actual experiments. Several of the key concepts of homeopathy conflict with fundamental concepts of physics and chemistry. The use of quantum entanglement to explain homeopathy's purported effects is "patent nonsense", as entanglement is a delicate state that rarely lasts longer than a fraction of a second. While entanglement may result in certain aspects of individual subatomic particles acquiring linked quantum states, this does not mean the particles will mirror or duplicate each other, nor cause health-improving transformations.

Plausibility

The proposed mechanisms for homeopathy are precluded from having any effect by the laws of physics and physical chemistry. The extreme dilutions used in homeopathic preparations usually leave not one molecule of the original substance in the final product.

A number of speculative mechanisms have been advanced to counter this, the most widely discussed being water memory, though this is now considered erroneous since short-range order in water only persists for about 1 picosecond. No evidence of stable clusters of water molecules was found when homeopathic preparations were studied using nuclear magnetic resonance, and many other physical experiments in homeopathy have been found to be of low methodological quality, which precludes any meaningful conclusion. Existence of a pharmacological effect in the absence of any true active ingredient is inconsistent with the law of mass action and the observed dose-response relationships characteristic of therapeutic drugs (whereas placebo effects are non-specific and unrelated to pharmacological activity).

Homeopaths contend that their methods produce a therapeutically active preparation, selectively including only the intended substance, though critics note that any water will have been in contact with millions of different substances throughout its history, and homeopaths have not been able to account for a reason why only the selected homeopathic substance would be a special case in their process. For comparison, ISO 3696:1987 defines a standard for water used in laboratory analysis; this allows for a contaminant level of ten parts per billion, 4C in homeopathic notation. This water may not be kept in glass as contaminants will leach out into the water.

Practitioners of homeopathy hold that higher dilutions―described as being of higher potency―produce stronger medicinal effects. This idea is also inconsistent with observed dose-response relationships, where effects are dependent on the concentration of the active ingredient in the body. This dose-response relationship has been confirmed in myriad experiments on organisms as diverse as nematodes, rats, and humans. Some homeopaths contend that the phenomenon of hormesis may support the idea of dilution increasing potency, but the dose-response relationship outside the zone of hormesis declines with dilution as normal, and nonlinear pharmacological effects do not provide any credible support for homeopathy.

Physicist Robert L. Park, former executive director of the American Physical Society, is quoted as saying: "since the least amount of a substance in a solution is one molecule, a 30C solution would have to have at least one molecule of the original substance dissolved in a minimum of 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 [or 1060] molecules of water. This would require a container more than 30,000,000,000 times the size of the Earth." Park is also quoted as saying that, "to expect to get even one molecule of the 'medicinal' substance allegedly present in 30X pills, it would be necessary to take some two billion of them, which would total about a thousand tons of lactose plus whatever impurities the lactose contained".

The laws of chemistry state that there is a limit to the dilution that can be made without losing the original substance altogether. This limit, which is related to the Avogadro constant, is roughly equal to homeopathic dilutions of 12C or 24X (1 part in 1024).For further discussion of homeopathic dilutions and the mathematics involved, see Homeopathic dilutions.

Scientific tests run by both the BBC's Horizon and ABC's 20/20 programmes were unable to differentiate homeopathic dilutions from water, even when using tests suggested by homeopaths themselves. (transcript).

In May 2018, the German skeptical organization GWUP issued an invitation to individuals and groups to respond to its challenge "to identify homeopathic preparations in high potency and to give a detailed description on how this can be achieved reproducibly." The first participant to correctly identify selected homeopathic preparations under an agreed-upon protocol will receive €50,000.

Efficacy

No individual homeopathic preparation has been unambiguously shown by research to be different from placebo. The methodological quality of the primary research was generally low, with such problems as weaknesses in study design and reporting, small sample size, and selection bias. Since better quality trials have become available, the evidence for efficacy of homeopathy preparations has diminished; the highest-quality trials indicate that the preparations themselves exert no intrinsic effect. A review conducted in 2010 of all the pertinent studies of "best evidence" produced by the Cochrane Collaboration concluded that "the most reliable evidence – that produced by Cochrane reviews – fails to demonstrate that homeopathic medicines have effects beyond placebo."

Government level reviews Government-level reviews have been conducted in recent years by Switzerland (2005), the United Kingdom (2009), Australia (2015) and the European Academies' Science Advisory Council (2017).

The Swiss programme for the evaluation of complementary medicine (PEK) resulted in the peer-reviewed Shang publication (see Systematic reviews and meta-analyses of efficacy) and a controversial competing analysis by homeopaths and advocates led by Gudrun Bornhöft and Peter Matthiessen, which has misleadingly been presented as a Swiss government report by homeopathy proponents, a claim that has been repudiated by the Swiss Federal Office of Public Health. The Swiss Government terminated reimbursement, though it was subsequently reinstated after a political campaign and referendum for a further six-year trial period.

The United Kingdom's House of Commons Science and Technology Committee sought written evidence and submissions from concerned parties, timeshighereducation.co.ukEvidence check: Homeopathy , House of Commons Science and Technology Committee, October 20, 2009, parliament.uk and, following a review of all submissions, concluded that there was no compelling evidence of effect other than placebo and recommended that the Medicines and Healthcare products Regulatory Agency (MHRA) should not allow homeopathic product labels to make medical claims, that homeopathic products should no longer be licensed by the MHRA, as they are not medicines, and that further clinical trials of homeopathy could not be justified.UK Parliamentary Committee Science and Technology Committee – "Evidence Check 2: Homeopathy" They recommended that funding of homeopathic hospitals should not continue, and NHS doctors should not refer patients to homeopaths.Evidence Check 2: Homeopathy, Fourth Report of Session 2009–10, House of Commons Science and Technology Committee, October 20, 2009, parliament.uk By February 2011 only one-third of primary care trusts still funded homeopathy and by 2012 no British universities offered homeopathy courses. In July 2017, as part of a plan to save £200m a year by preventing the "misuse of scarce" funding, the NHS announced that it would no longer provide homeopathic medicines. A legal appeal by the British Homeopathic Association against the decision was rejected in June 2018.

The Australian National Health and Medical Research Council completed a comprehensive review of the effectiveness of homeopathic preparations in 2015, in which it concluded that "there were no health conditions for which there was reliable evidence that homeopathy was effective. No good-quality, well-designed studies with enough participants for a meaningful result reported either that homeopathy caused greater health improvements than placebo, or caused health improvements equal to those of another treatment."

On September 20, 2017, the European Academies' Science Advisory Council (EASAC) published its official analysis and conclusion on the use of homeopathic products, finding a lack of evidence that homeopathic products are effective, and raising concerns about quality control.

Publication bias and other methodological problems

The fact that individual randomized controlled trials have given positive results is not in contradiction with an overall lack of statistical evidence of efficacy. A small proportion of randomized controlled trials inevitably provide false-positive outcomes due to the play of chance: a statistically significant positive outcome is commonly adjudicated when the probability of it being due to chance rather than a real effect is no more than 5%―a level at which about 1 in 20 tests can be expected to show a positive result in the absence of any therapeutic effect. Furthermore, trials of low methodological quality (i.e. ones that have been inappropriately designed, conducted or reported) are prone to give misleading results. In a systematic review of the methodological quality of randomized trials in three branches of alternative medicine, Linde et al. highlighted major weaknesses in the homeopathy sector, including poor randomization. A separate 2001 systematic review that assessed the quality of clinical trials of homeopathy found that such trials were generally of lower quality than trials of conventional medicine.