Via Ben Goldacre's MiniBlog, “homeopath adopts victim posture,” I found a posting which links to “Towards a New Model of the Homeopathic Process Based on Quantum Field Theory” by Lionel R. Milgrom, Forschende Komplementärmedizin **13** (3) 174-183 (2006). This was blogged at the time but I missed it. It's worth picking up on it again now though, especially as I've managed to read the full text without chewing my own foot off.

From the summary:

“Disease manifestation by the Vital Force (Vf) could be an event similar to spontaneous symmetry breaking in QFT: the curative remedy acting to restore the broken symmetry of the Vf field. Entanglement between patient, practitioner, and remedy might be representable as Feynman-like diagrams.”

I'll start by pointing out how short the decoherence time is in a complicated system like a human. Tegmark [Phys. Rev. E **61** (4) 4194-4206 (2000)] estimates 0.0000000000001 s at most: he says,

“We find that the decoherence time scales (∼10

^{-13}—10^{-20}s) are typically much shorter than the relevant dynamical time scales (∼10^{-3}—10^{-1}s), both for regular neuron firing and for kinklike polarization excitations in microtubules. This conclusion disagrees with suggestions by Penrose and others that the brain acts as a quantum computer, and that quantum coherence is related to consciousness in a fundamental way.”

Those who do believe that the brain is a quantum computer [for example, Hagan *et. al.* Phys. Rev. E **65** 061901 (2002)] calculate a decoherence time more like 0.0001 s, which is a milliard times longer, but still somewhat shorter than a homeopathic consultation. Anyway, the whole idea of a “Vital force” is based on naïve biological intuition, and biology has come on quite a long way in the past couple of hundred years or so.

So, following the introduction there's a section on quantum field theory, which “draw[s] heavily for exposition on the writings of" (i.e. is copied out of the books of) Dr John Gribbon (sic.) and Prof. Sunny Y. Auyung (sic.).” The former is a popular science book on quantum field theory, the latter “presents a philosophical analysis of QFT.” He spells these two authors' names incorrectly, though not always.

He writes,

“In classical physics, fields, e.g., electromagnetic and gravitational, are imagined as attached to and emanating from sources... However in quantum physics, fields are intrinsic and irreducible parts of a relativistic 4-D space-time continuum. And because of the concept of wave-particle duality, this means that ripples in a field may also be described in terms of force-carrying particles, known as bosons, which are exchanged between other quantum entities called fermions. This is known as the

first quantisation.”

Wrong: first quantization means that we treat our particles as quantum objects moving in classical potentials. Fermions are particles with half-integer spin, and their statistics means that there can only be one fermion in any given state - therefore, fermions make solid matter.

He continues,

“This idea can be taken further by describing matter particles (e.g., electrons) in terms of waves, which are ripples in another kind of field depending on the type of particle. Thus the particles themselves may also be described in terms of field quanta, and this has been called the second quantisation.”

Second quantization is where the classical potential is replaced by the exchange of virtual bosons. In the case of the electromagnetic field these are photons.

A bit later, he is talking about symmetry breaking and the Higgs field but he appears to garble this with the concept of zero-point energy slightly. And then,

“The Higgs field is what is called a scalar field, which means that it is the same everywhere, hence extremely hard to detect.”

A classical scalar field is just something which can be described by a single numerical value for each point in space. (The pressure of the earth's atmosphere, for example, is a scalar field, while the wind makes a vector field.) In Quantum field theory a scalar field is one whose force-carrying bosons have zero spin - so it's true that the Higgs field certainly would be one of these, and the Higgs field would also have the same vacuum expectation value everywhere.

He then goes on to talk about Feynman diagrams without, of course, any references to Feynman's scientific publications but rather to his popular science account. At least by not misspelling Feynman's name he avoids a five point penalty.

The next section is entitled “Quantum Field Theory as a Metaphor for the Homeopathic Process.” This is a trick which Sokal & Bricmont flagged - there's a “strong” interpretation of this paper which says that homeopathy works by quantum entanglement, but when someone points out that this is nonsense he can claim the “weak” interpretation where it's only a metaphor, albeit one which is used to confuse and impress the audience rather than enlighten them. In any case there are references all over the place to something called “Weak Quantum Theory” - Harald Atmanspacher, Hartmann Römer, and Harald Walach. “Weak Quantum Theory: Complementarity and Entanglement in Physics and Beyond.” Found. Phys. **32** (3) 379-406 (2002). The last of these three authors also turns up here and here, by the way. I can't mine all of this rich seam alone, read for yourself if you are able. (There are some comments at the JREF forum.)

So anyway, his summary of quantum field theory contains quite a few mistakes: He gets “first quantisation” and “second quantisation” the wrong way round, he seems to confuse zero-point energy and the Higgs field slightly, he states that “the Higgs field is what is called a scalar field, which means that it is the same everywhere,” which is not what “scalar field” actually means, and he misspells the names of the authors (John Gribbin and Sunny Auyang) whose books he is getting this from.

He introduces the “Mexican-hat potential” and then modifies it as if “different energy states of the Vital Force, Vf” correspond to different states of ill health and the state in the centre (where the symmetry is unbroken) represents health. It's not obvious what he thinks the x-axis of his graph is - he then takes a picture which he previous used in the paper I'm going to get to in a minute (which once did useful service as a schematic representation of localized and delocalized electrons in a crystalline conductor but has already been ruined by changing it to be about localized and delocalized energy states of the Vital force) and bungs in his new potential as if a state of chronic ill health moved a person a little bit to one side.

Greater (and more tractable) abuses of quantum theory seem to take place in “Patient-Practitioner-Remedy (PPR) Entanglement, Part 7: A Gyroscopic Metaphor for the Vital Force and Its Use to Illustrate Some of the Empirical Laws of Homeopathy” by Lionel R. Milgrom, Forschende Komplementärmedizin **11** (4) 212-223 (2004).

“It can be argued that homeopathy might be better ‘explained’ within the conventional scientific paradigm... if it were to draw on certain of the more modern ideas and concepts that have been developed within the physical sciences, particularly physics...”

Well you should start by drawing on some *biology*. And if you want to draw on “modern ideas” you could also learn that taking the square of a complex number [ *z*^{2}=(*x+iy*)^{2}=*x*^{2}+2*ixy*-*y*^{2} ] isn't the same as taking its modulus squared [ |*z*^{2}=|*x+iy*|^{2}=(*x+iy*)×(*x-iy*)=z.z^{*}=*x*^{2}-*y*^{2} ]. But anyway, most of the actual quantum mechanics seems to have been copied out accurately in this paper even if he gets the units of Planck's constant wrong; he writes Js^{-1}, not Js. Given that he's going to spend the whole paper talking about angular momentum he'd have been better off by defining *ħ=h/2π* anyway.

The main body of this paper is the gyroscope metaphor for the Vital force. He notices that the faster a gyroscope spins, the slower it precesses if it's not standing vertically (and therefore has gravity trying to pull it into a horizontal position) and he decides that this is the same as having a strong Vital force resisting the effects of “dis-ease” (sic.). He goes through (i.e. copies out) a derivation ending up with simple harmonic motion and then tries to use this to “predict” (i.e. postdict) some “empirical laws of homeopathy” (as if such things exist) although he keeps needing to fudge it. (And I don't find any actual testable, falsifiable *pre*dictions yet.)

Arnst-Schulz Law as refined by Koetschau: “Every drug has a stimulating effect in a small dose, while larger doses inhibit, and much larger doses kill” - the figure given here is much better than the one in the paper, but it's still not accurate and doesn't show exactly the things which Milgrom tries to show.

Koetschau's refinement says that small doses have a stimulating effect, moderate doses at first stimulate and then depress and then the patient returns to normal, and that large doses cause a large stimulation followed by a depression large enough that it leads to death. Milgrom has at hand an equation which says that the Vital force oscillates sinusoidally, and although he's talking about the time dependence of effect now there's no point at which he puts time into his equation. His independent variable is “S_{2}” and his wavenumber is “k_{2}”; on previous pages he defined “k_{2}Σσ_{2}” as “the totality of secondary symptoms,” apparently, and then S_{2} is the integral (over what variable, is not specified) of Σσ_{2} with the k_{2} not in it anymore - “Σσ_{2} represents the totality of secondard symptoms exhibited by Vf. However, just as the pixels of a television screen are integrated by the brain into an image, which is more that the sum of its pixelated parts, so ∫Σσ_{2} represents the overall image of an individual's Vf, integrated over and out of the sum of the secondary symptoms presented to the practitioner.” So following this hand-waving he ends up with Vf=Ae^{ik2S2}+Be^{-ik2S2} which, if anything (and it's a big if), describes the *shape* of the wavefunction, and it doesn't change with time because it's a stationary state (i.e. an energy eigenstate); to understand what happens to his Vital force gyroscope under the influence of a “drug” he'd actually need time-dependent peturbation theory - I look forward to seeing this in a future paper. So his attempt to apply this to the variation of effects with time is already kind of knackered and I can't help feeling that I'm trying far too hard to find meaning in it all when there really isn't any, and his misuse of concepts, formalism and terminology is sapping my will to live - he appears to plot a line with an imaginary gradient, calls a system which has a large negative response to a positive stimulus “over-damped” (you actually need feedback for that to happen - an overdamped system would just slowly return to equilibrium) and magically has his sinusoidal oscillation stop after exactly one cycle. As an exercise for the reader, set yourself up a damped harmonic oscillator (in a spreadsheet or something) and work out what really happens in the case of small, medium and large offsets at time zero.

Then there's a part where he copies a schematic diagram of the localized and delocalized electronic energy levels of a (1-dimensional) crystalline conductor out of a solid-state physics text book and then relabels “atomic nuclei regularly spaced within a lattice” as “individual Vf's of provers and their associates” and “electronic energy states” as “Vf energy states.” This is to somehow illustrate the concept that “there can be synchronous effects among provers and between provers and those closely related to them who are not otherwise involved in the proving.” - a clause inserted to excuse the placebo effect, I expect.

This is the same diagram, with different labels, as the one in the other paper where he's talking about disease as a broken symmetry or something. Also, there's a caveat at the end of the paper about the Vf being a nonphysical entity and needing its own therapeutic `state-space' a bit like a Hilbert space - something which he turns to in the other paper.

A more recent article is “Journeys in the country of the blind: Entanglement theory and the effects of blinding on trials of homeopathy and homeopathic provings” by Lionel R. Milgrom, Evidence-based Complementary and Alternative Medicine **4** (1) 7-16 (2007). It's rubbish on many levels, from misspelling the names of authors whose work he refers to (again) and getting the units of Planck's constant wrong (he writes Js^{-1}, not Js, again) to typographical errors in equations and the fundamental misconception that when a wavefunction collapses it becomes zero. It actually becomes an eigenstate of the operator which collapsed it, but it keeps on being a wavefunction. (See S. Dürr *et. al.* regarding the Double-Slit experiment, by the way.)

He freely exchanges terms like “metaphor,” “model,” and “analogy” when describing the relationship between quantum physics and homeopathy, such that it's not obvious how seriously anything should be taken. (Roughly, a *model* is usually considered to be a mathematical description of a physical system where the trick is to make it complicated enough that it reproduces the important physical phenomena but simple enough that we can still tell what's going on it in and therefore gain some Insight; a *metaphor* is a way of describing a complicated physical problem in normal language which we know isn't rigorous; and an *analogy* is a comparison between a familiar system and an unfamiliar one so that you get a head start understanding the unfamiliar one.) But it's nonsense to suggest that there really is quantum entanglement between humans in verum and control groups during a double-blind trial, and the metaphorical interpretation is equally useless if it doesn't help in understanding any real phenomenon. You certainly can't expect to use the physics of a metaphor (even if you understand it, which *he* doesn't) to bring new information to the physical thing it's supposed to be a metaphor for. It's like saying, “an electron feels a force,” and then wondering what other emotions it can experience.

And he writes, “... in order to comply with implicit assumptions inherent in the DBRCT methodology, homeopathic practioners are expected to engage in a highly questionable (and ultimately confusing) form of self-deception that would be utterly unthinkable in a real therapeutic situation.”

I just felt a dip in the world irony level.

It's idea that in a double-blind randomized controlled trial of homeopathic remedy versus placebo, where trials demonstrate that homeopathy works no better than a placebo, it's either because the homeopathic practitioners can't bring themselves to deceive their patients (subconcious self-deception obviously coming much more easily) or because the control group is entangled in some quantum-mechanical-but-not-really-resona

This paper also contains the pseudoscience buzzword "non-linear", because he wants to explain that the practitioner is both part of the entangled patient-practitioner-remedy wavefunction and part of the homeopathic operator which operates on that wavefunction to produce the change in symptoms. This *would* be nonsense *if* it actually meant anything.

Why bother? Well, this is apparently The Principle That Makes Homeopathy Scientifically Possible: “In a heroic series of articles [11, 12, 13, 14, 15], Milgrom derives many known aspects of homeopathic medicine from his intuition that the TAI [therapeutically active ingredient] is a quantum wave function.” Note: “*is* a quantum wave function” not “behaves like” or “can be imagined to share some of the spooky properties of” or such like.

So there really are people out there who actually think this is going to make homeopathy scientifically respectable. I'm not really expecting to make the blindest bit of difference but *somebody* has to read this stuff and point out that it's nonsense.

*Edit:* how could I have forgotten this?