Homeopathy occupies a curious position in modern healthcare—widely used, legally sold, yet fundamentally at odds with established chemistry and physics. Founded by Samuel Hahnemann in the late 18th century, it rests on two core principles: similia similibus curentur (like cures like) and the law of infinitesimals, which holds that diluting a substance increases its therapeutic potency.

These principles predate our understanding of atoms, molecules, and Avogadro's number. When Hahnemann developed his theories, scientists didn't yet know that matter was composed of countable particles. Today, we can calculate precisely what happens during serial dilution—and the mathematics reveals a fundamental problem that no amount of clinical enthusiasm can resolve.

This isn't about dismissing patients' experiences or questioning practitioners' sincerity. It's about examining whether homeopathy's proposed mechanism can possibly work as described. When we apply basic chemistry to homeopathic dilutions, we encounter not a minor technical difficulty but a complete implausibility that any serious evaluation must address.

Homeopathic remedies are prepared through serial dilution—typically using a 1:100 ratio (called 'C' potencies) or 1:10 ratio ('X' or 'D' potencies). A 6C preparation means the original substance has been diluted 1:100 six times, yielding a final concentration of one part in 10¹². This might still contain some molecules of the original substance. But homeopaths don't stop there.

Common homeopathic preparations include 30C (standard for many remedies) and 200C (considered more potent). A 30C dilution means one part original substance in 10⁶⁰ parts water. To grasp this number: there are approximately 10⁸⁰ atoms in the observable universe. At 30C dilution, you would need a container of water larger than the known universe to have reasonable odds of finding a single molecule of the original substance.

The critical threshold is Avogadro's number—approximately 6 × 10²³. This tells us how many molecules exist in a mole of any substance. Beyond about 12C dilution, the probability of even one original molecule remaining drops below 50%. At 13C, it's roughly 3%. At 15C, you're looking at one chance in a million. Most homeopathic remedies on pharmacy shelves are prepared at 30C or higher.

This isn't a philosophical objection or a matter of interpretation. It's arithmetic. The pills and drops sold as homeopathic remedies, prepared according to classical homeopathic principles, are chemically indistinguishable from their carrier substances—typically sugar pills or water-alcohol solutions. Whatever effect they produce cannot be attributed to the original substance, because that substance is simply not present.

Takeaway

At standard homeopathic dilutions of 30C, you would need more water than exists in the observable universe to statistically expect a single molecule of the original substance—these preparations are chemically identical to plain water or sugar.

Faced with the dilution problem, some homeopathy proponents invoke 'water memory'—the idea that water retains a therapeutic imprint of substances previously dissolved in it. This hypothesis gained brief notoriety in 1988 when Jacques Benveniste published a paper in Nature claiming that highly diluted antibody solutions could trigger cellular responses. The journal took the unusual step of publishing the paper with an editorial reservation and subsequently sent investigators, including a magician, to observe replication attempts.

The attempted replications failed. Benveniste's results could not be reproduced under blinded conditions. Multiple subsequent studies have examined whether water structure changes in ways that could encode molecular information. The consistent finding: water's hydrogen bonding networks rearrange on timescales of femtoseconds to picoseconds—trillionths of a second. Any 'memory' would be erased almost instantaneously, certainly long before a remedy reaches a patient.

More recent proposals have invoked nanoparticles, quantum entanglement, or electromagnetic signatures. Each faces its own scientific difficulties. Nanoparticle studies have been criticised for contamination and methodology problems. Quantum effects decohere rapidly in warm, wet biological systems. Electromagnetic theories lack proposed mechanisms for how such signals would survive dilution, storage, and ingestion to produce specific therapeutic effects.

The burden here falls on homeopathy's proponents. Extraordinary claims—that water can store therapeutic information despite all we know about molecular physics—require extraordinary evidence. What's been offered so far consists of disputed studies, unreplicated findings, and theoretical proposals that conflict with established physics. The mechanism remains not just unproven but scientifically implausible given current knowledge.

Takeaway

Water's molecular structure reorganises trillionths of a second after any disturbance; proposed 'memory' mechanisms conflict with established physics and have failed replication under controlled conditions.

Clinical trials of homeopathy present a consistent pattern that researchers have documented across multiple systematic reviews and meta-analyses. Studies with methodological weaknesses—small sample sizes, inadequate blinding, high risk of bias—tend to show positive results. As trial quality improves, effects shrink toward zero. The most rigorous trials find homeopathy indistinguishable from placebo.

A 2005 Lancet meta-analysis by Shang and colleagues compared 110 homeopathy trials against 110 matched conventional medicine trials. When restricted to the largest, highest-quality studies, homeopathy showed no effects beyond placebo while conventional treatments maintained significant effects. A 2015 report by Australia's National Health and Medical Research Council systematically evaluated evidence across 68 conditions and found no reliable evidence that homeopathy was effective for any of them.

Critics of these analyses sometimes argue that homeopathy requires individualised treatment and cannot be fairly tested in randomised trials. Yet when individualised homeopathy has been subjected to rigorous testing—comparing outcomes when patients receive their prescribed remedy versus an identical-looking placebo—results remain negative. The 2015 Cochrane review of homeopathy for attention deficit hyperactivity disorder, for example, found no evidence of effectiveness.

This pattern—positive results in weak studies, null results in strong studies—is precisely what we would expect if homeopathy's effects are due to placebo response, regression to the mean, natural disease course, and biases introduced by poor methodology. It's also consistent with the fundamental implausibility: treatments containing no active ingredient would not be expected to show specific pharmacological effects, and they don't.

Takeaway

The inverse relationship between trial quality and positive results for homeopathy suggests the apparent effects arise from methodological weaknesses rather than genuine therapeutic action.

Homeopathy faces a convergence of problems that distinguish it from genuinely uncertain areas of medicine. The basic chemistry is clear: standard preparations contain no active molecules. Proposed mechanisms contradict established physics. And clinical evidence follows the characteristic pattern of treatments that don't work—positive results only in studies designed poorly enough to allow bias and noise to masquerade as effect.

None of this means patients don't feel better after homeopathic treatment. Placebo effects, therapeutic relationships, regression to the mean, and natural recovery all produce genuine subjective improvement. But attributing that improvement to remedies that are chemically inert requires ignoring what we know about molecules, water, and rigorous evidence evaluation.

For healthcare decisions, the practical conclusion is straightforward: resources—time, money, hope—directed toward homeopathy are resources diverted from approaches with plausible mechanisms and demonstrated effectiveness. Understanding why homeopathy cannot work as proposed isn't closed-mindedness; it's the application of basic scientific literacy to health choices.