## Introduction

In the UK, a vituperative debate has arisen over whether complementary and alternative medical (CAM) therapies should be included within the National Health Service.^{1} Homeopathy is arguably the most controversial form of CAM, not least because a highly publicised *Lancet* meta-analysis of clinical trials comparing homeopathy to allopathy dismissed the former as having no effects beyond placebo.^{2} This paper’s clear bias and methodological flaws,^{3-7} seemingly escaped most in the conventional medical community and the media,^{8} who are equally unaware of the many published fully peer-reviewed papers showing that homeopathy can indeed have effects beyond placebo.^{9-13} So, it is not surprising when twelve of the UK’s top medical scientists signed a letter to *The Times* calling for the cessation of CAM funding by the National Health Service (even though it is abundantly clear many conventional medical practitioners already avail themselves of adjunctive CAM therapies)^{14}, but also accusing homeopathy of being ‘an implausible treatment’.^{15}

The origin of this attitude is due in no small part to increasing demands that all therapeutic procedures be subjected to double-blind placebo-controlled trials (DBRCTs),^{16} according to the precepts of Evidence-Based Medicine (EBM).^{17,18} This could be considered hypocritical given that many of the drugs and procedures currently used in orthodox medicine have yet to be clinically confirmed by EBM.^{19} Apart from an almost inquisitorial overemphasis on the supremacy of one particular kind of evidence,^{18} the problem is how the meaning of the phrase ‘placebo effect’ is taken.

If in trials homeopathy works no better than a sugar pill, it is deemed ineffective. But the placebo effect has always been part of every doctor’s kitbag, and is enshrined in the Hippocratic Oath.^{14} Also homeopaths say their therapy encourages the body to heal itself, suggesting at the very least a more humane appreciation of the placebo effect.^{20}** **

But with none of the original material substance left, sceptics want to know how a highly diluted homeopathic remedy can exert any effect, let alone a therapeutic one.^{21} Clearly, homeopathy poses serious challenges to conventional bioscience’s dominant materialistic paradigm, and will continue to be regarded as delusional, cynical ‘quackery’, or at best the ‘placebo effect’.^{2} Yet, one of the most recent studies performed under the same Swiss-inspired** **Program of Evaluation of Complementary Medicine (PEK) that produced the flawed Lancet meta-analysis, found that the ‘*effectiveness of homeopathy can be supported by the clinical evidence’*.^{22}

It is this attitude that it *should* not work, therefore it cannot, which acts as one of the main hindrances to the integration of homeopathy into conventional medical practice. Another is many homeopaths’ distrust of anything to do with conventional science and medicine. Thus, for true integration to occur, homeopathy and conventional medicine will have to achieve some common ground.^{14}

## quantum theory, VITALISM, AND SYMPTOM EXPRESSION

*The similarity in discourse*

Conventional biomedicine is reductionist. This means sickness and disease are comprehended primarily in terms of pathological cellular biochemistry, as caused by external agents (viruses, bacteria, etc) or internal imbalances (e.g., genetic abnormalities). Treatment is therefore geared towards ‘fixing’ the problem by eradicating these causative disease factors, usually with powerfully toxic substances whose long-term side-effects can compromise the homeostatic immune system.

Homeopathy on the other hand, considers that ‘*In the healthy condition of man, the spiritual vital force…. retains all parts of the organism in admirable harmonious, vital operation as regards both sensations and functions….*‘^{23 }In other words, it is holistic. From conventional medicine’s reductionist view-point, the Vital Force (Vf) is treated with contempt because ‘*…it doesn’t have any identifiable source… obey any kind of (physical) law, it can’t be defined; it is simply postulated ad hoc to explain whatever effects or alleged effects need explaining: it can’t be pinned down or put to the question; its function is to provide the illusion of meaning without substance….it can’t be disproved because it is too amorphous and vague a concept.*‘^{24 }

However, complex systems are known to self-organise, are open, and possess a wholeness that cannot be attributed solely to any particular part or sub-system.^{25} Non-deterministically, the Vf might be an emergent property of billions of living cells, which generates an all-pervading field that by feedback so organises the totality’s elements, it reinforces itself. This field would not originate in any one cell or body part, and being the resultant of the whole organism, resists any dissipative entropic influence.^{ 26}

Such a holistic view of the Vf bares phenomenological comparison with certain conclusions derived from quantum physics.^{27, 28 }Thus, the Vf is thought not to be directly ascertainable: it is observed indirectly through the symptoms it produces.^{23} Similarly in quantum theory, the *wave function* (a multi-dimensional mathematical descriptor of a quantum system’s state) may only be inferred from the effects it produces in our reality.^{28, 29} This is through no fault in observation but depends more on the multi-dimensional mathematical language used in describing wave functions.^{30} As a result, trying to visualise a quantum state in our usual 3-D terms^{31, 32} leads to loss of information: one reason why entanglement in quantum theory seems so paradoxical.^{ 28}

Entanglement in a quantum system occurs if its seemingly separate parts are so holistically matched, measurement of one part of the system *instantaneously* (i.e., not limited by the speed of light and therefore without classical signal transmission) provides information about all its other parts, regardless of their separation in space and time*, or their size*.^{33} This last point addresses naÃ¯ve criticisms^{34} often levelled at those who use quantum theory to explain the therapeutic effects of homeopathy/CAMs.^{35-43}

In addition, more modern interpretations of quantum theory resolve such paradoxes as entanglement by taking the quantum state of a system not as an objective ‘thing-in-itself’, separate from us, but as *a subjective representation of what we can know about it*.^{44-49} Thus, apart from predicting a quantum system’s evolution in time, the wave function is also telling us something about the *irreducible* *relationship* *between the observer and the observed quantum system*. Also, a generalised form of quantum theory has recently been formulated called Weak Quantum Theory (WQT),^{50} which develops the idea of ‘macro-entanglement’ and uses it to explain not only phenomenological problems arising out of information theory and psychology,^{50} but also the therapeutic process in homeopathy^{35-37} and CAMs.^{41} The subsequent development of this idea^{51} leads to ways of considering macro-entanglement that explains significant correlations found between the brain functions of spatially separated pairs of human subjects.^{52, 53}

In this context, Walach^{54, 55} and others^{56} have demonstrated clear correlations between remedy and placebo groups during double blind homeopathic provings; observations which are difficult to account for other than in terms of macro-entanglement between the two groups.^{36, 57} While purely physical entanglement between macroscopic objects seems unlikely, *generalisation of* *the concept could be used to help explain certain observed correlations in human relationships*. Although a sufficient but not a necessary condition for applying entanglement ideas to the problem of how homeopathy might work, it leads to a ** metaphorical** use of concepts with an otherwise unique meaning in physics.

^{57, 58 }It should be stressed that this use of quantum mathematics has yet to be rigorously proven.

^{ }

*The Vital Force as a quantum entity *

Based on the discourse similarity between the Vital Force and a quantum entity’s wave function, i.e., it is only inferable from the symptoms it produces,^{23,28} a new metaphor imagines the Vf as a quantised precessing gyroscope.^{59} This means the Vf’s spinning ‘flywheel’ slows discreetly, so that precession about an imaginary* *vertical axis also changes by fixed amounts. Quantised precession (i.e., a hypothetical ‘angular momentum’ vector Vf rotates in the x-*i*y plane: figure 1) arises by initially defining ‘Vf shift operators’, similar to the angular momentum shift operators from the physics of

Figure 1. Schematic of the Vf gyroscope: a real gyroscope in 3-D space precesses around the z-axis sweeping out gradually increasing ‘orbits’ in the x-y plane. The metaphorical Vf gyroscope precesses in fixed quantised ‘orbits’ as shown and the y and z axes are complex. Symptoms are observed along the real x axis.

electrons in atoms.^{60} Vf shift operators were derived from complementary combinations^{30} of primary and secondary symptoms, experienced by the patient; observed by the practitioner.^{59} Thus, ‘diseases’ and ‘remedies’ are simply factors that increase or decrease the Vf’s strength by quantised amounts.

A Vf ‘wave function’, ?_{Vf}, then relates Vf quantised precessional motion solely to observed secondary symptoms, S_{2}, (i.e., ?_{Vf} = A(e^{i}^{k}2^{S}2 + e^{–ik}2^{S}2)),^{59} and used to illustrate some of homeopathy’s empirical ‘laws’, e.g., bi-phasal action of remedies,^{61} and resonance effects among remedy provers and associates.^{62} A therapeutic analogue of the time-dependent Schroedinger equation^{60} was derived, and used to investigate the practitioner’s effect on the patient’s Vf during therapeutic PPR entanglement.^{63} Manipulating the Vf wave function further allowed remedies and diseases to be understood as ‘torques’ that respectively accelerate or brake the speed of rotation of the Vf gyroscope’s ‘flywheel’.^{64} Thus, if gyroscopic precession is a metaphor for Vf symptom expression, then eradication of symptoms by the remedy corresponds to an accelerating ‘remedial’ torque on the Vf ‘flywheel’, slowing precession.

*Metaphorical motion in imaginary spaces*

Precession of the Vf ‘gyroscope’ occurs in a mathematically complex plane. This means that only the x axis in Figures 1 and 2 is real: the y and z axes are complex.^{30} The ‘orbits’ represent different Vf states: the larger the precessional trajectory of the vector Vf, the greater the strength of Vf symptom expression. However, as with any quantum entity (e.g., an electron in an atom), transitions between the different states represented by these trajectories may be thought to occur instantaneously not gradually.

real axis along which symptoms are expressed

**Figure 2. View of the Vf gyroscope in Figure 1, looking down the imaginary iz axis. **

It follows that when the Vf ‘gyroscope’ is not precessing (i.e., its axis of rotation is co-linear with the complex z-axis), it is not producing symptoms, i.e., **S _{2} = 0**. Consequently, the larger the ‘orbit’ of Vf precession, the greater the degree of observed symptom expression along the real x axis (representing our four space-time dimensions are conflated into one) in figures 1 and 2. Thus, by precessing in a 3-D complex space defined by one real and two complex axes, the Vf may be imagined as a 6-D (i.e., four real plus two complex dimensions) rotating entity, precessing when disturbed, and producing observable effects in our reality experienced as symptoms. In future better mathematical treatments of these ideas might be realised using the multi-dimensional algebras of spinors

^{65}and Lie groups.

^{66}

*The effect of the similar homeopathic remedy*

In previous papers,^{59, 63, 64} wave functions were derived for the vital force and the curative homeopathic remedy. These were:-

**? _{Vf} = A(e^{i}^{k}**

**2**

^{S}**2**

**+ e**

^{–ik}**2**

^{S}**2**

**) = 2Acosk**, and

_{2}S_{2}**? _{Rx} = e**

^{–ik}**2**

^{?S}**2**,

where *i* = ?-1, **S**** _{2 }**is the totality of secondary symptoms, and

**?S**

**is the change in secondary symptoms wrought by the curative remedy. The constant**

_{2}**A**relates to the intensity of the wave form, which in turn relates to the strength of symptom expression by the Vf, and so to the sizes of precessional ‘orbits’ shown in figures 1 and 2. The constant

**k**relates to the energy and ‘moment of inertia’ of the Vf ‘gyroscope’, and expresses the ‘frequency’ of the Vf wave function

_{2}**?**. But this constant also appears in the wave function of the curative remedy,

_{Vf}**?**and relates to the remedy’s ability to bring about this change in secondary symptom expression, by increasing the energy and ‘moment of inertia’ of the Vf.

_{Rx}The previous paper^{64} also made the point about the ‘torque-like’ action on the Vf of remedies and diseases; the remedy as an accelerating ‘torque’, and the disease as a braking ‘torque’. Thus, disease can be represented as the remedy’s mirror image, or mathematically, its complex conjugate,^{30} i.e.

**? _{Dx} = ?_{Rx}**

^{*}**= e**

^{i}

^{k}**2**

^{?S}**2**

Consequently, just as **k _{2}** relates to both the potency of the homeopathic remedy and its power to cure by providing an accelerating torque, it also expresses the power of the disease over the Vf as a braking torque. Therefore, the curative remedy at the correct potency exactly cancels out the disease, i.e.,

**? _{Dx }**X

**?**

_{Rx}= e

^{i}

^{k}**2**

^{?S}**2**

**X**

**e**

^{–ik}**2**

^{?S}**2**

**= e**

^{0}**= 1**.

In addition, this paper^{64} proposed that the ‘torque-like’ therapeutic effect of the curative remedy could be understood as the rate of change of the patient’s vital force with symptoms, derived by differentiating the Vf wave function with respect to** S**** _{2}**, i.e.,

if **? _{Vf} = A(e^{i}^{k}**

**2**

^{S}**2**

**+ e**

^{–ik}**2**

^{S}**2**

**) = A(2cosk**, then

_{2}S_{2})**d?**

_{Vf}/dS_{2}= T = -2Ak_{2}sink_{2}S_{2}This led to some rudimentary insight into the torque-like action of the remedy was gained by graphically representing, **? _{Vf}**

_{ }(black curve),

**d?**(white curve), and their sum

_{Vf}/dS_{2}**?**, generating a series of diagrams representing how

_{Vf }+ d?_{Vf}/dS_{2}**?**

_{Vf}_{ }and

**d?**interact to produce

_{Vf}/dS_{2}**?**for different

_{Vf }+ d?_{Vf}/dS_{2}**k**values, three of which are shown below.

_{2 }

** a b c**

**Figure 3. **Plots of the Vital Force wave function, **?**_{Vf}** = 2Acosk _{2}S_{2}** (black curve),

**the remedial torque,**

d

d

**?**

_{Vf}**/dS**(white curve)

_{2}= -2Ak_{2}sink_{2}S_{2}**,**and the combination,

**?**

_{Vf}**+ d**

**?**

_{Vf}**/dS**(grey curve),

_{2}= 2Acosk_{2}S_{2}– 2Ak_{2}sink_{2}S_{2}**where**

**A**= 1, and (

**a**),

**k**= 0.5; (

_{2}**b**),

**k**= 1; and (

_{2}**c**),

**k**= 2. Note how as

_{2}**k**increases, so do the frequencies of the wave forms, and the grey curve peak amplitude and position with respect to the black and white curves: at low

_{2}**k**the grey curve is like the black curve, while at high

_{2}**k**the grey curve is more like the white curve

_{2}**(see reference 64).**

This analysis considers only the initial effect of the torque on Vf: it does not take into account how long the torque is applied, and what happens after its action ceases.

It is interesting to re-examine the wave function for the curative remedy which is given as:-^{63, 64}

?_{Rx} = e^{–ik}2^{?}^{S}2 1

Using Euler’s transformation,^{30} equation 1 may be rewritten in polar form as:-

?_{Rx} = cos k_{2}?S_{2} – *i*sin k_{2}?S_{2} 2

This shows that ?_{Rx} consists of real and imaginary parts. So it should be possible to contemplate remedy action in more than just physical terms, with the imaginary part of ?_{Rx} representing the remedy’s less physically tangible effects, e.g., perhaps on mental and emotional levels. Now, as k_{2} tends to 0 (i.e., at very low potency and the remedy becomes more material), the imaginary term,

– *i*sin k_{2}?S_{2} disappears, while the real cos k_{2}?S_{2} term tends to a maximum. So, as k_{2} approaches zero, ?_{Rx} » cos k_{2}?S_{2} and the remedy may be considered to act physically. At high k_{2}, the real term disappears and the imaginary term increases to a maximum so that ?_{Rx} = –*i*sin k_{2}?S_{2}. The remedy is now acting mainly non-physically (which does NOT mean it exerts no physical effect). This wave function depiction of the curative remedy, allows its action on the whole person to be followed.

## TOWARDS UNIFYING HOMEOPATHY AND CONVENTIONAL MEDICINE

*The periodicity of wave functions*

Depicting the Vf, remedy, and remedy torque as wave functions, implies a certain periodicity in their properties and behaviour. Such periodicity can indeed be exhibited by the Vital Force in its expression of symptoms; their strength varying according to periodic modalities, such as the time of day, etc.

Interestingly, there is some experimental evidence that biologically active substances at different serially diluted potencies will have periodic effects on their substrates. For example, Schiff reports alternating effects of different ultra-diluted potencies of anti-immunoglobuline E (aIgE) on the decoloursation of stained basophils, in most cases when the aIgE had been diluted and agitated beyond molecular existence:^{67} some potencies enhance decolourisation while others retard it. Schiff claims this as evidence for the water memory effect.

Accordingly, k_{2} values determine the periodicity of the Vf and remedy wave functions. As this constant is also associated with remedy potency (inversely proportional to material dose), it is interesting to investigate the possible effects of very low remedy k_{2} values on the periodicity of ?_{Rx}.

From the previous section, we know that at low k_{2} values, the remedy wave function approximates to ?_{Rx} » cos k_{2}?S_{2}. Now, the cosine function can be represented algebraically as the power series:-^{68}

cos x = 1 – x^{2}/2! + x^{4}/4! – x^{6}/6! +….(-1)^{n}x^{2n}/(2n)! 3

As x becomes very small, the values of the higher powers of x effectively vanish. Therefore, for small x, equation 3 approximates to :-

cos x » 1 – x^{2}/2! 4

Similarly, for small values of k_{2}, the remedy wave function, ?_{Rx} approximates to:-

?_{Rx} » 1 – [k_{2}?S_{2}]^{2}/2! 5

Equation 5 is no longer a periodic: it is now a parabolic function (see steep and shallow white curves in figure 4: the steepness is determined by the value of k_{2}).

Figure 4. Plots of the real part of equation 2 (?_{Rx} = cos k_{2}?S_{2}: k_{2} = 1; black curve: k_{2} = 0.075; shallow grey curve), and equation 5 (?_{Rx} » 1 – [k_{2}?S_{2}]^{2}/2!: k_{2} = 1; steep white curve: k_{2} = 0.075; shallow white curve).

Thus, for small values of **k _{2}**, the shallow grey (equation

**2**) and white (equation

**5**) curves in figure 4 are virtually indistinguishable. Only as

**k**grows does the difference between the grey and white curves become apparent. This theoretical finding may help illustrate essential differences between the homeopathic and the conventional medical approaches to the action of remedies.

_{2}*The effect of remedy potency*

Homeopathic philosophy maintains that a remedy becomes more potent the more it is diluted and succussed.^{69} This means that even at only moderate potencies (greater than 12c and 24x), homeopathic remedies possess little or no molecules of the original material substance, yet a remedy of higher potency should have a more profound effect on the Vf than one of lower potency.

The conventional medical approach to the action of remedies predicts otherwise: the less of the remedy’s material substance is actually present, the weaker its effect in curing the disease (in conventional medicine, the idea of an all-pervading Vital Force is considered moribund: its nearest equivalent is the homeostatic immune system). This could be represented in figure 4 by the grey curve, i.e., equation **5**. Its parabolic shape means it crosses the x axis only once, after which it never returns, regardless of the value of **k _{2}**. However, its response to a remedy at low

**k**(or potency, in this case in a material dose) approximates to the extended white curve in figure 4. Thus, the form of the remedy function

_{2}**?**shown in equation

_{Rx}**5**could be said to represent the predictions of conventional medicine concerning the effect of highly diluted remedies, i.e., that the weaker the drug dose in material terms, the less effect the drug has on the homeostatic immune system. However, the form of the remedy wave function

**?**in equations

_{Rx}**1**and

**2**represents the predictions of homeopathy, i.e., ultra-highly diluted remedies can still affect the Vital Force.

Dear Dr. Milgrom,

Many many thanks for this great article. You have nicely explained the VF with the help of Quantum Physics.Congratulate you for this article as it is great scientific evidence to the scientist in conventional medicine. I request you to send this article to Editorial Board of Lancet> Please ask them to disprove this explanation of Vital Force.Also send this article to scientific Board of United Kingdom and American Medical Board of Scientific Research In Clinical Medicine. At least they will try to give approval to Homeopathic Science and give serious look to its theory.I am Clinical Biochemist so it is little difficult for me to understand details.But I appreciate the way you have explained as a great Physicist.

Kind Regards,

Dr. N.V.Pai