Scientific Research

The Principle That Makes Homeopathy Scientifically Possible: The Whole is Greater than the Sum of its Parts

The Principle That Makes Homeopathy Scientifically Possible: The Whole is Greater than the Sum of its Parts


This paper examines the materialist, scientific view that homeopathy is necessarily contrary to all known laws of science, and shows it not to be the case. Recent theoretical advances contradict it. They indicate that systems involving correlations at both microscopic and macroscopic levels provide appropriate models. Materialism posits that no effect can occur without a material cause, failing to take into account the more abstract concept of information. It effectively holds that, for all systems, ‘The Whole is (only) Equal to the Sum of its Parts’. However, systems exhibiting correlations between subsystems possess hidden information, so that:

‘The Whole is Greater than the Sum of its Parts’

a principle for which a quantitative definition is given. The principle is well known and applies widely – for a system to be holistic, it must be true. To avoid violating scientific laws, theories of homeopathy must satisfy it – Holistic Medicine can only be described by appropriately holistic physics. By way of illustration, it is shown how the principle applies to the analysis of homeopathy itself, and to various theories of homeopathy.


It is often said that the possibility of physiological action of potentised homeopathic medicines is ruled out by modern science. Editors of top medical journals refuse to publish articles on them [1]; invited editorials say they “cannot possibly produce any effect” [2]; the debate does not conform to normal scientific standards [3,4]; “The medical and scientific community has generally dismissed homeopathy because of a lack of plausible mechanism”, and despite properties of complex systems [5]. There is every indication of an incipient scientific revolution [6].

Dylan Evans expresses the general misconception in his book, Placebo [7], as follows,”There is no place in our current scientific theories for any possible mechanism by which homeopathy might work.” Again, “either homeopathy is simply a placebo, or the whole of physics and chemistry as we know them are false.” Milgrom [8] quotes Ennis similarly: “if the findings of the pan-European experiment (Ennis) was part of, were repeated, the whole of physics and chemistry might have to be rewritten.”

In point of fact nothing could be further from the truth.  Recent advances indicate that the therapeutically active ingredient (TAI) of a homeopathic remedy has a quantum form connected to critical points. Torres [9], shows that critical points on networks provide suitable systems; Weingartner [10], that the TAI must obey scaling laws. In a heroic series of articles [11-15], Milgrom derives many known aspects of homeopathic medicine from his intuition that the TAI is a quantum wave function.

Recently, a new model of cellular regulation has been used to show how an ultra-diluted solution of a toxin can reactivate a physiological system, deactivated by the original toxin – a scientific derivation of the principle underlying homeopathy [16]. The new theory of cellular regulation uses a new physical concept, critical regulation, based on well-known work by Prigogine [17], who pointed out that critical instabilities necessarily occur in biological control systems.

The theory suggests that such instabilities can be dynamic attractors on which regulation becomes centered. The TAI is then identified as quantised critical point fluctuations since they can cause transitions in critically regulated systems. Significantly, there are reasons why such fluctuations can be activated by dilution and succussion – a theory emerges in agreement with the work of Torres [9] and Weingartner [10], consistent with Milgrom’s intuition [11-15].

That the work of four separate scientists, pursuing quite different lines of approach to the problem of the TAI should result in a single self-consistent theory suggests that a genuine scientific theory of homeopathy may soon be completed. It appears to be a quantum theory of cooperative phenomena at far-from-equilibrium critical instability points. The mere possibility of such a theory, however, raises important philosophical questions:

1. Why should the popular conception of what is and is not possible in science be so wide of the mark?

2. More specifically, what fundamental principle that science and scientists have taken for granted, is being so spectacularly violated?

3. Which scientific theories violate the principle? Is it valid or invalid?

4. If it is invalid, what correct principle can replace it?

5. How do the new theories conform to the new principle?


Answers indicated by the proposed theory of homeopathy [16], derive from the anomalous physics it entails. It uses unusual properties of physical systems: critical points where matter is unstable [18,9], such as occur in regulatory systems of living organisms [17]; that critical instability fluctuations obey scaling laws [19,10]; that in far-from-thermodynamic-equilibrium systems, instability fluctuations can induce phase transitions [20]; and the highly anomalous nature of the quantum fields of chemical instability fluctuations in the physiology [11-16,21-22], which thus have the power to induce observable phase transitions[1].

All these elements of the theory possess properties contradicting common sense materialist science. Materialism posits the idea that all effect requires a material cause: without matter or energy, there can be no cause and effect. To the materialist, if all matter is removed, and a vacuum created, no effects can result from that lack of matter – it can have no action. Quantum theory and quantum field theory, however, are well-known to violate the mechanical materialist outlook; critical instabilities do so because they produce long range correlations so that different elements of the system are no longer independent of each other – independence of parts is a general supposition of the materialist perspective (see (2) below).

First consider quantum systems: the necessity of material causes seems true in the macroscopic world, and remains true in the early quantum theories of Bohr, Heisenberg and Schroedinger, but it is not true in quantum theories of complex systems, because of the correlations pointed out by Einstein [23]. Nor is it true of quantum fields. In quantum field theory, the vacuum state itself is regarded as an infinite superposition of the ‘bare vacuum’ together with all possible ‘vacuum fluctuations’, consisting of all possible transitions from vacuum to vacuum with a virtual something in between. Virtual transitions, including vacuum fluctuations, virtual though they may be, are well recognized to produce real effects in matter and energy around them. They result in the famous Lamb Shift, in which two quantum states of the Hydrogen atom of otherwise equal energy are shifted relative to each other. If virtual transitions become correlated with similar virtual transitions in neighbouring systems in the environment, further energy shifts take place. Van Der Waals forces between non-polar chemical molecules, and the Casimir Effect, in which two parallel, uncharged conducting plates exert a measurable attractive force on each other, both arise in this way. The lowering of energies increases when such systems are closer to each other, giving rise to the forces between them[2].  In the Casimir effect, the cause may be visualised: tiny fluctuations in electrical polarisation in each plate spontaneously become correlated because this lowers their energy. The mechanics is clearly identical to quantum theory’s use of correlated virtual transitions, as outlined above, since quantum transitions are required to produce the tiny polarisations in each plate, and correspondingly virtual transitions to produce fluctuating polarisations.

In the case of the quantum vacuum, spontaneous emission of quanta from any system, such as light from an atom in a light bulb, can be considered an effect of the vacuum and its fluctuations. This is seen most clearly from the theory of lasers. A state of n photons stimulates photon emission multiplying its probability by a factor of (n + 1). The extra 1 in the (n + 1) means that when no photons of the field are present, the vacuum state still has a stimulating effect. ‘Spontaneous emission’ can be attributed to stimulation by a residual potential in the vacuum state – its fluctuations, consisting of virtual, vacuum to vacuum, transitions.

If all this is known and understood, what is the problem with homeopathy?

If a quantum nothing, the quantum vacuum, can create effects by inducing transitions, why shouldn’t homeopathic remedies, similar kinds of nothing, in the form an ultra diluted solutions, also create effects inducing transitions in the physiology? The answer according to the new theory [16] is that they do, but the problem with accepting this possibility is two fold: first, the naïve materialism of popular scientific outlook, and second,  the difficulty of seeing chemical systems in quantum terms. In fact, the new theories [11-16] adopt the latter perspective, but the first may still blind a person from seeing it.

The problem lies in the apparent objectivity of what is being diluted. We think matter is ‘real’ because we can reach out and touch it, we can see it, taste it and smell it, all in a self-consistent way. We know matter is made of atoms, and therefore tend to think about them in exactly the same way, despite the fact that as scientists, we know equally well that they can only be adequately described by quantum theory with all its anomalies compared to the classical physics of the macroscopic world. We still tend to think of atoms as little, real, objects of the kind we see on the table in front of us – which they are not. As quantum entities they are not objectively real [24]. They have very different properties, and behave in surprisingly different ways. Naïve materialism fails to take this into account.

When a chemical solution is diluted, we tend to think that it can only have properties we would ascribe to its component molecules as if they behaved the same as little billiard balls, or tiny versions of the ball and stick models we make to represent their internal structure. The idea that some hidden, latent property of atoms and molecules might manifest, simply because they have undergone a special process of dilution, does not occur to the materialist. To put it most simply, the materialist subscribes to a simplistic principle: ‘The whole is equal to the sum of its parts’ – get rid of all the parts, and, ‘Voila!’, there can be no effects.

The ability of the quantum vacuum to induce transitions totally contradicts the materialist outlook, however. No longer is it true that nothing cannot have an effect. No longer can we say with King Lear, ‘Nothing will come of nothing’ [25]. The particular ‘Nothing’ consisting of the vacuum can exert a causative effect. If it can be shown that a ‘quantum nothing’ similar to the vacuum state of the electromagnetic field, but originating in dilution of chemical molecules, can produce changes in the physiology, a scientific theory of homeopathy would have been constructed consistent with what we already know about quantum theory.


‘The whole is equal to the sum of the parts’, is not universally valid. A deeper, more spiritual, principle holds. The old principle breaks down for correlated systems. Cooperative phenomena at phase transitions, such as are utilized in the new theory of homeopathy [16], and stimulated emission of light in lasers, are both due to correlations, which represent an internal ordering of a system’s subsystems. They have information value, but no inherent material energy – they are the domain of the information theorist, rather than the materialist. Nowadays, this is seen as the very nature of quantum physics, for as Stapp emphasises, ‘Information is the currency of quantum theory’ [26].

Correlations’ internal ordering have observable consequences that cannot be predicted from gross knowledge of the system’s composition alone. If it is asked, ‘Why are observations on two such systems different?’ the matter energy content cannot explain it. The information contained in the abstract correlations is outside the materialist domain. Knowledge of the parts is not sufficient to predict all possible observations on the whole system – there is more information I (w) stored in the whole (w) than the sum Si of all the information I(pi) in each of the parts pi :

I(w) >  Si I(pi)   (1)

Such a system is said to be a whole more than the sum of its parts. In contrast classical systems conforming to the materialist idea that the whole is only equal to the sum of its parts satisfy:

I(w) =  Si I(pi)   (2)

The inequality (1) thus offers a quantitative definition, and criterion for the validity in any given system, of a different principle:

The Whole is Greater than the Sum of its Parts

This principle is widely known, and applied in many ways, not just to physical or scientific concepts such as systems. In the humanities where internal ordering principles, balancing interrelationships and harmonies, have central importance, it is a fundamental concept. It is not just at work in the nothing of a quantum vacuum, in human situations it is important because a mere nothing – an idea, information – can motivate everything.

In King Lear, the whole drama emerges from Lear’s reaction to Cordelia’s ‘Nothing’! Shakespeare is in effect illustrating the deep principle whereby the Void is the origin and source of all things, an idea embodied in modern quantum cosmology by the ‘inflationary process’. Conclusive observational evidence now exists for this process [27], which initiates the Big Bang from an unstable pre-physical potentiality – physics shows conclusively that the origin of the universe as a whole is governed by the new principle, not the materialist one.

It applies to all systems of thought summarized by Aldous Huxley in his Perennial Philosophy [28]. Wordsworth alludes to it at the climax of his autobiographical ‘Prelude’, his longest, and arguably his greatest, poem. Reflecting on a full-moon cloudscape seen from above during a night ascent of Mt Snowdon, he locates in the scene ‘the Imagination of the Whole‘ – the cosmic creative intelligence behind the whole creation – describing it as ‘the perfect image of a Mighty Mind, of One that feeds upon infinity‘ [29] – an experience of the total wholeness of all creation, greater than the sum of its parts, thus revealing the truly holistic nature of reality. He tells how this experience of wholeness in the totality brought the final strokes of growth of (the cosmic) Imagination in the poet’s own mind – a true and valid experience of enlightenment, and principle theme of the whole poem.

T.S. Eliot illustrates its role in writing and literature, at the climactic ending of Little Gidding, the final poem in Four Quartets: ‘every phrase and  sentence is right, (where every word is at home, taking its place to support the others … the complete consort dancing together)‘ [30]. Here, Eliot is also writing at a second, symbolic level, in which he uses ‘Word’ and ‘word’ consistently throughout his Quartets to represent the divine and individual soul. Incorporating the allusion to Shiva Nataraja, the passage’s symbolic meaning transmits an image of the wholeness of individual souls (words) rising to perfect wholeness in the divine, the ultimate basis of Wholeness and holism – once again, a realisation of enlightenment expressed in an image of the holistic nature of experience.

The principle’s use is becoming more widespread, it is taught in schools and colleges around the world as one of the 16 principles of the core curriculum of the world’s largest and most successful system of private education, Maharishi Mahesh Yogi’s Consciousness Based System of Education [31]. Sometimes in popular form, it is stated as: ‘A House is More than a Collection of Bricks’. Clearly a mere pile of bricks has little use compared to a house, or even a single wall, in both of which physical organisation creates potential uses and value. Organisation of what would otherwise be just a ‘pile of bricks’ both distinguishes it and makes it useful. Organisation results from information, and encodes it: once again inequality (1) holds. Such a role of spatial organisation in the uses of an object or system is one way the principle applies in classical physical science, and is of great significance, since it is the key to the relationship between structure and function – the way classical science begins to go beyond mere local causality. Similarly, the principle applies to any system with feedback, since the value of the whole is fed back to the parts, probably one reason why Cybernetics, Wiener’s work on regulation and control, made such a huge impact when it appeared [32].

In all these ways, the new principle is of fundamental significance, to the universe as a whole, and everything within it. It is only those systems that do not satisfy it to which materialism applies. However, such systems were the only ones considered in the first centuries of mathematical physics, up to the 1930’s, so a false simplicity, materialism, was assumed to hold universally. In reality, the universe possesses a far richer structure due to the existence of correlations, quantum ones vilified by Einstein [23], and others at a classical macroscopic level. Such internal correlations endow systems with additional, hidden information, which can be denoted by I(C) and the numerical value of which is given by,

I(C)  =  I(w) –  Si I(pi)   (3)

the difference between the information I(w) attributable to the whole system and the sum of the values I(pi) attributable to its subsystems, or parts.

At a macroscopic level correlations result from cooperative phenomena. They exist in all systems exhibiting phase transitions and critical instability points. At a microscopic level they exist in all multi-component quantum systems. This shows that the principle applies to all the theories proposed to explain homeopathy and referred to above [9-16].


We still may ask, how does the validity of the new principle help to explain homeopathy? The answer is: in quantum field theory additional information I(C) hidden in a correlated system can, under the right circumstances, itself take on a quantum field form, endowing it with dynamic organizing power. The new quantum field, the quantised fluctuation field, is like a harmonic of the original field. Because of the details of their mathematical form, quantised fluctuation fields behave very differently from usual quantum fields when diluted. Apparently they are still observably present, even when the field itself has been diluted to zero. They can produce observable transitions, but only in special kinds of detector consisting of systems about to undergo a phase transition near far-from-equilibrium critical instability points. In such a detector, organizing power is supplied by the quantised fluctuation field, but most, if not all, the required energy comes from the dissipative processes required to maintain the system far from equilibrium.

About the author

Alex Hankey

Alex Hankey

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