Homeopathy is a system of “alternative medicine” (i.e. not medicine) developed in 1796 by Samuel Hahnemann, based on the doctrine of “similia similibus curentur,” or “like cures like” – a claim that he apparently pulled directly out of the aether, since it has absolutely no basis in current understandings of physics, chemistry, or biology. It is thought that he extrapolated this idea from Paracelsus, a sixteenth-century pioneer of pharmacology, who claimed that “what makes a man ill also cures him,” based on his readings of Hippocrates (the namesake of the Hippocratic Oath which medical practitioners swear by), who in 400 BC is noted to have prescribed a small dose of mandrake root to treat mania, knowing that it produced mania in larger doses. We should stop here to note that this doctrine is absolutely not the same principal as the basis for vaccinations (which inoculate your immune system to fight off infections by exposing it to inert samples of a disease), and the two should not be conflated; although coincidentally, Edward Jenner did discover the smallpox vaccine the same year that Hahnemann invented homeopathy. But as far we are aware, they did not consult.
Homeopathy teaches that diseases can be treated by homeopathic preparations (called “homeopathics” or “remedies”), which are prepared using a process called homeopathic dilution, in which a given substance is repeatedly diluted in alcohol or distilled water, each time with the container being struck against some sort of elastic material. The dilutions are conducted using a “centesimal scale,” diluting each mixture by a factor of 100 at each stage – thus, a 2C dilution is diluted twice, with the final product containing one part of the original substance per 10,000 parts of mixture. The greatest dilution at which even a single molecule of the original substance might possibly remain is 12C; Hahnemann advocated a dilution of 30C for most purposes, believing that lower doses made a mixture more, not less, potent.
Modern homeopaths have proposed several solutions to the discrepancies with modern science which have developed in the two centuries since its invention, the most prominent of which is the phenomenon of “water memory,” which suggests that water molecules “remember” the substance they’re mixed with, and transmit the physiological effects of those substances when consumed. This is, of course, inconsistent with current understandings of physical chemistry and how matter works in general –several pharmacological studies on homeopathic remedies using nuclear magnetic resonance have failed to show any stable clusters of water molecules, and no scientific studies have ever demonstrated credible evidence of the phenomenon in any other contexts.
Other abstract, theoretical concepts such as chaos theory as well as quantum entanglement and superposition have been proposed to explain homeopathy’s mechanism of action. However, these explanations are rife with speculation and incorrect applications – for example, the use of quantum entanglement to explain homeopathy’s effects has been described by experts in the field as “patent nonsense” and “pseudoscientific technobabble,” who note that entanglement states rarely last for longer than a fraction of a second, and merely result in linked subatomic particles acquiring identical quantum states (e.g. spin factor, velocity, etc.), rather than mirroring each-other’s physical properties.
In clinical trials, no homeopathic preparation has ever been unambiguously shown to be any more effective than a placebo. Studies which do report positive results often stuffer from poor methodology such as low sample sizes, selection and publication bias (journals tend to prefer to publish positive rather than null results, even if they’re questionable), and poor study design and reporting, and preclude any meaningful conclusions since their results cannot be replicated. Systematic reviews and meta-analysis, which compile data from existing studies, all support the conclusion that homeopathy is ineffective as either a treatment or preventative measure. However if you’re interested in homeopathy, why not go try to find the water for it with your dowsing rods.