Proposed mechanisms for homeopathy are physically impossible



Background  Homeopathy is a system of complementary and alternative medicine based on a belief that a malady can be treated by the administration of an extreme dilution of an agent thought to cause the physical signs of that malady. Homeopathy enjoys popular support from the general public and advocates of alternative medicine, but most large-scale clinical trials show no homeopathy to be no more effective than placebo treatment.

Objectives  To explore the chemical and physical plausibility of homeopathic treatments.

Methods  Homeopathic claims were put into a physical context and analysed using the laws of basic physics and chemistry.

Results  Through the laws of physics, homeopathic medicines appear to have zero chance of containing any biologically active component. Evidence from physical chemistry also rules out the plausibility of mechanisms such as water memory.

Conclusions  The proposed mechanisms of homeopathy are shown to be implausible when analysed from a physical and chemical perspective, and thus it is of no surprise that the biological effects of homeopathy cannot be measured in large-scale clinical trials.


Homeopathy is based on the ‘law of similars’ or ‘similia similibus curantur’, the philosophy of 18th century doctor Samuel Hahnemann. Hahnemann proposed that curative effects could be found by administering a substance thought to cause the same symptoms the patient complained of. Hahnemann also stated that the more diluted the active ingredient was, the more powerful the curative effect.1 It should be noted that this law of similars is in no way an empirical law of nature in the physical sense, but rather a concept conceived by Hahnemann who believed he had detected the phenomenon on himself.

Homeopathic treatments consist of an initial active ingredient thought to cause the same symptoms as the patient exhibits. These proposed causative agents are selected from books known as repertories, and are based on so-called provings where the effects of the active substance have been observed in healthy volunteers. Once a causative agent has been selected, the substance is diluted in water or alcohol and then shaken and struck against an elastic surface in a process called succussion. This process is repeated with even greater dilutions. The end product is referred to by homeopaths as a remedy.1

There have been numerous clinical trials investigating the efficacy of homeopathic medicine. Results of these trials demonstrate a clear trend; that is, homeopathic remedies perform no better than placebo. Meta-analyses of published trials have also shown no positive effect of homeopathy.1,2 The few studies that have suggested a weak beneficial effect have been of low quality.

Despite the lack of any clear benefit of homeopathy, public acceptance of homeopathy remains high. Further, several major medical schools have started actively teaching homeopathy under the banner of CAM. Several health providers, including the UK's NHS, also fund homeopathic treatments.

This article examines these claims from the perspective of physics and chemistry to ascertain, independently of clinical studies, whether homeopathy is a plausible treatment. To do so, we must begin by examining an integral part of the proposed mechanism of action – the dilutions.

Homeopathic dilutions and chemical limits

Homeopaths insist that the biological potency of any homeopathic remedy increases with dilution. This runs contrary to what is usually observed in nature, where higher doses trigger correspondingly higher reactions. The doses used in homeopathy are rather extreme; take, for instance, the centesimal scale (C scale) used by Hahnemann. As the name suggests, a 1C dilution is 1/100 the original concentration, which corresponds to 0.01 or 1% or 10−2 of the original concentration. For this article, we shall stick with scientific notation as the dilutions become rather difficult and unwieldy otherwise. Examples of other dilutions are shown in Table 11,3 with their respective dilution ratios.

Table 1.  Examples of homeopathic dilution ratios
DilutionDilution ratioExample
8C10−16Maximum allowable concentration of arsenic in US drinking water3
12C10−24Maximum dilution where is it possible a molecule from one mole of original substance potentially still exists
30C10−60Dilution advocated by Hahnemann for most preparations1
200C10−400Dilution of Oscillococcinum, a homeopathic flu remedy

An 8C concentration corresponds to one particle in 10 million billion. In a 12C dilution, there is a roughly 60% chance that one molecule of the original substance remains in the preparation. One mole of a substance contains Avogadro's number4 of molecules or atoms of that substance. This number is as follows:


A dilution of 12C is the same as a dilution of 1024; consequently, the number of molecules/atoms expected after such a dilution can be calculated explicitly by dividing this number by this dilution. Thus, the number of molecules/atoms remaining after such a dilution would have to be:


By definition, an atom or molecule is the smallest particle of a substance that retains the chemical and physical properties of that substance.5 Thus, one simply cannot talk of fractions of a molecule/atom as these are invariably integer values. For this reason, the number calculated above must be interpreted as a probability that one atom/molecule remains. This probability is roughly 0.6022, meaning there is a 60.22% chance that after a 12C dilution of a mole of a substance that there would be one molecule of that substance left.

At dilutions greater than 12C, there is no chance that even a single atom or molecule would remain if one mole of a substance had originally been used. Using less than one mole of active ingredient would not escape the problem either, as it would take even less than a 12C dilution to remove any of the allegedly active ingredients. Hahnemann often employed a 30C dilution1 and most over-the-counter homeopathic preparations are at this dilution. But this presents a physical problem; a 30C dilution is one in 1060– this is a massive dilution, and hard to visualise. It would be akin to having one particle in one million billion billion billion billion billion billion particles. If the diluting medium was water, and the mass of a single water molecule is:


then in order to have a 30C dilution of just one molecule/atom of the active ingredient it would require 1060 water molecules with a combined mass of:


This is literally a stellar mass – by comparison, the mass of the Sun, the largest body in our solar system,6 is:


This means that the mass of water required for a 30C dilution would be over 15 000 times the mass of the Sun. This ‘container’ problem does not stop there, however. The density of water is known, and as density is given by the ratio of mass to volume, it is possible to calculate the volume of water this dilution would require, which is:


If this volume of water was arranged into a sphere similar to the Sun, it would be possible to calculate its radius, and hence, its size relative to the Sun by rearranging the formula for the volume of a sphere. This yields:


This value is almost 28 times greater than the radius of the Sun, coming within 1% of the largest star in the universe yet discovered.7 As this obviously outlandish situation has never occurred and indeed never could, it is safe to conclude that there is no possible way a homeopathic solution could be diluted to 30C and still retain any active ingredient on Earth or indeed this solar system. This is illustrated in Figure 1.

Figure 1.

Relative size of Sun and Earth to a hypothetical 30C dilution. The Sun is approximately 110 times the radius of the Earth. The hypothetical dilution would have a radius almost 3100 times that of earth, rendering it much bigger than the Sun. For dilutions above this, the situation is even more drastic. Thus, it is unreasonable to expect that even one molecule of active ingredient could be present in such extreme dilutions. Key: inline image Earth; inline imageSun; inline image30C dilution.

Even if the entire mass of the earth was composed of water, this would mean the maximum possible dilution was roughly one in two times 1050, which corresponds to 25.15C. This situation would still be impossible to achieve.

Homeopathic solutions go far beyond these concentrations, despite the obvious absurdity of doing so. It is estimated that there are roughly 1080 particles in our universe. This rather neatly corresponds to a 40C dilution; meaning that even if one could overcome massive practical barriers, no dilution containing even a single molecule of active ingredient would be possible at dilutions greater than 40C. Despite this glaring physical problem, many homeopathic solutions are sold in much greater dilutions than this. For example, Oscilloccinum is a homeopathic flu remedy made from duck liver and sold in 200C dilutions; far beyond the 40C theoretical upper limit for the universe. By a similar analysis it can be shown that a 200C dilution would require 10320 universes of water just to have one molecule of active ingredient.8 Indeed, the sheer scale of these dilutions frequently appears in criticisms of homeopathy. Thus, it is impossible that any molecule of the active ingredient could actually appear in a homeopathic remedy above dilutions of 12C.

The structure of water and the water memory conjecture

The physics of the prior section effectively preclude the existence of even a single molecule of any biologically active ingredient in all but the lowest potency or weakest dilution preparations. When Hahnemann proposed this, he could have perhaps been forgiven for this; the existence of atoms was not proposed and proven until almost a hundred years later,9 so it may have seemed plausible that there would be no limits to how much one could dilute a substance and still have elements remaining. However, improved understanding of scientific and medical realities in the 21st century mean that modern physicians and medical scientists should not take a position so clearly divorced from reality. Modern homeopaths concede that there is no biological agent present in dilutions above 12C, yet continue to maintain that their treatments are plausible.

A common claim by the homeopathic community is that water has the ability to somehow ‘remember’ what it has been in contact with. This proposed retention is called water memory. Water is indeed a unique molecule with some strange properties, and it is worth examining this conjecture. Water molecules are formed from two hydrogen atoms and one oxygen atom, yielding the common chemical nomenclature H20. The hydrogen atom and oxygen atoms share their electrons, yet they exert different ‘pulls’ on the electron cloud. This results in areas of uneven positive (+ ∂) and negative (– ∂) attraction. The attraction between water molecules is called a polar covalent bond.10Figure 2a shows the electrical affinity of a water molecule and Figure 2b shows how the water molecule forms electrical bonds with other such molecules.

Figure 2.

(a) The electrical affinity of oxygen atoms and hydrogen atoms in a water molecule. (b) Hydrogen bonds between five such water molecules, based on the electrical attraction between the uneven charges.

The resulting bond is called a hydrogen bond, and it can be viewed as the magnet-like attraction between water molecules. It is quite a weak bond compared to other chemical bonds, and can be easily broken, but it gives rise to interesting phenomena such as surface tension where water molecules on the ‘outside’ of the bond group have fewer neighbours and thus greater attraction to the inner molecules, making the surface of the water harder to break.

If water has memory, then the hydrogen bonds would have to be able to persist long after the molecules that caused their rearrangement were diluted out of the solution. Essentially, for this proposed mechanism to work water must be able to maintain bonds in the absence of the original agent and this bond must be long lived. There have been many physical investigations to ascertain how long water can hold the memory of a bond, and these have shown the time to be exceptionally short and difficult to measure, with results no more than fractions of a nano-second (10−9 s). The most convincing experiments were conducted by Cowan et al.11 using infra-red spectroscopy in multiple dimensions. Cowan et al.11 performed ultra-precise measurements on liquid water and found that water is highly efficient at redistributing its bond with a ‘memory’ of less than 50 femtoseconds or 5 × 10−14 s.

Thus, the proposed mechanism of water memory is not only at odds with modern physical chemistry, it is also refuted by experimental data; this indicates that the mechanism of water memory is highly implausible.

Water memory Nature controversy

Despite the implausibility of water memory, there was considerable debate on this subject in the late 1980s when French immunologist Jacques Benveniste submitted a paper to the journal Nature, which stated human antibodies still produced histamine when exposed to anti-immunoglobulin E that had been diluted up to 60C.12 This ran contrary to several known laws and raised the suspicions of physicist editor John Maddox. Despite this, the paper was allowed to run on the condition that it would be independently examined. Benveniste did not propose a mechanism of action at that time.

An independent team consisting of Nature editor John Maddox, Nobel Laureate in chemistry and fraud investigator Walter Stewart and magician/sceptic James Randi performed the investigation and found that the results had been an artefact caused by observer bias; the team stated ‘that experimental data have been uncritically assessed and their imperfections inadequately reported.’13

Attempts by other independent laboratories to replicate Benveniste's findings also ended in failure,14–16 and questions were raised about two of Benveniste's original team who were funded by French homeopathic giant Boiron. The 1987 paper in Nature is considered an example of pathological science by the scientific community; yet, to this day, it is still quoted by homeopaths to support their belief.

Electromagnetic signals from diluted bacteria

In 2009, Nobel Prize winning virologist Luc Montagnier claimed to be able to find electromagnetic signals from bacterial deoxyribonucleic acid (DNA) in extreme dilutions.17 While not specifically mentioning homeopathy, many homeopathic institutions (such as the Society of Homeopaths in the UK) cite this as evidence rendering homeopathy plausible.

From a physical and technical perspective, this work is suspect. A systematic drawing of the apparatus used by Montagnier et al. in this controversial paper is shown in Figure 3. It should be noted that this system was derived by Benveniste who claimed he could use it to send homeopathic signals down telephone lines.18

Figure 3.

Montagnier et al.'s proposed set up for measuring electromagnetic signals from diluted bacteria.

The system purports to record electromagnetic signals from the vial and carry them from the conducting wire to the amplifier where the signal is increased and read by a computer. The 2009 paper claimed to find small readings from highly diluted preparations, but this is not surprising – the coil is not electrically insulated in a Faraday cage19 or similar method, which means no background signals are screened out. Background noise is ubiquitous, and any detection system should be screened to avoid this. As this was not the case in the experiment, the amplifier was essentially increasing the noise, raising serious questions about what was being measured.

The authors also do not make any mention of the amplitude of the signal, mentioning only that it was very small and could only be detected after being filtered with a band pass filter. The authors make some passing reference to the noise generated by the power source ‘which was found to be necessary for the induction of the resonance signals from the specific nano structures.’17 They also noted that the effects disappeared when they reduced the noise, and concluded that the effect needs noise to work rather than the more obvious solution that the effect is the result of noise. In practice, all measurements are affected by noise, and this is a great problem when signals are small. To determine the amount of noise, signal and electrical engineers employ the signal-to-noise ratio (SNR). This is defined in linear terms or, if preferred, in decibels, as follows:


This measurement becomes extremely important when measuring small signals, such as the ones Montagnier and colleagues reported observing.17 A linear SNR of one or less, for example, would indicate that the noise was respectively the same as or less than the signal measured, rendering the results meaningless. Low SNR values indicate the data are practically useless. There are various tools and methods for analysing and quantifying SNR to investigate whether the results obtained are useful or not, but Montagnier et al. made no reference or indeed any analysis of error despite mentioning the signal was extremely small. The lack of quantification raises serious questions about the nature of the signals recorded and seems to be an extreme oversight.

The experiment lacked even basic calibration or screening. More worrying is that the journal that carried it, Interdisciplinary Sciences – Computational Life Sciences, is a journal Montagnier set up and is editor of. The paper was received, revised and accepted for publication within 3 days, a suspiciously fast turnaround time. This, coupled with the lack of quantification, suggests serious flaws were overlooked in the peer-review and publishing processes.

In any case, a deeper reading shows that several of the paper's claims, even if verified, were actively at odds with the claims of homeopathy. Homeopathy claims that higher dilutions lead to higher potency, whereas Montagnier et al. claimed the effects were seen at some dilutions and vanished at higher dilutions.17 This is the opposite of what homeopathy predicts. Secondly, the authors claim that there were still particles of DNA present in the diluted solution, again at odds with general homeopathic convention. Indeed, for the dilutions about the 12C limits, this statement is at odds with modern chemistry as well.

To date, no experiments have replicated these findings, indicating that the paper shares the pathological problem found in Benveniste's famous work. This work is therefore suspect and, even if its findings did stand, they would offer little support for homeopathy.

Miasma and vitalism

Vitalism is the school of thought that the functioning of living organisms cannot be explained solely by bio-chemical reactions, and can instead be explained by some ‘vital force’. Homeopathy is deeply rooted in the vitalistic tradition, maintaining that illness is caused by a disturbance in the body's vital force. Hahnemann called these agents miasmas, a ‘peculiar morbid derangement of [the] vital force’, and claimed they were the root cause of all diseases and disorders.20

However, this concept is easily refutable by modern medicine. Koch's postulates,21 which were first published in 1890, used clearly established protocols to evaluate whether a micro-organism is responsible for a given condition. Improved understanding of how illness originates has essentially rendered the miasma theory of disease obsolete. The germ theory of disease22 also offers a testable hypothesis for the origins of illness, whereas the miasma conjecture offers a mystical untestable explanation. Despite the fact that miasma is an out-dated notion that has effectively been debunked with the advent of microbiology, it continues to form a central tenant of homeopathy.

Regardless of whether vitalism has a place in medicine, the miasma theory of disease has effectively been disproven and, by extension, its inclusion in homeopathic theory is not well founded.


Many clinical trials investigating the efficacy of homeopathy have failed to show any benefit of the therapy beyond a placebo effect. Patients who receive benefit from homeopathy may do so because of the non-specific effects of the therapeutic encounter.23 The proposed mechanisms of homeopathy have been shown in this paper to be impossible.

Despite this, some proponents claim that scientific criticism of homeopathy is ignorant and unnecessary as it is ‘grounded on assumptions differing from the traditional scientific ones’;24 but this is an incredibly dishonest and self-insulating position. Homeopathy fails on both a clinical and a theoretical level, and one cannot insulate it from criticism by dismissing investigation. The problem is not the scientific method or evidence-based practice – it is that homeopathy has been shown to have zero efficacy and, as this work establishes, there is no reason it should. Indeed, there is a level of hypocrisy when proponents of homeopathy dismiss the scientific method, yet claim to have scientific studies only when it verifies their belief. Introducing questionable epistemological objections should be seen as no more than weak rhetoric to hold an untenable position.

To summarise, homeopathy suffers from the doubly fatal flaw of not being supported by clinical evidence and not being physically plausible. Because of this, the author suggests that promoting homeopathy as a valid therapy would be highly questionable in a clinical environment.

Conflict of interest  None declared.


The author would like to thank Professor Edzard Ernst of Exeter University, UK, for his insight and editorial assistance, and Dr Kevin Carney of Dublin City University, Ireland, for his expertise in signal-to-noise ratios.

David Robert Grimes, PhD, BSc, Oak Farm house, Milverton, Skerries, County Dublin, Dublin n/a, Ireland.