Chapter 4 Theory
4.1 The Descent from Orthodoxy into CAM
It is first necessary to establish some sort of ordering for my application of physics to CAM. In the 1970’s, my laboratory in Salford University was concerned with measurements of the dielectric properties of liquids. This was mostly on such substances as transformer insulation oils and related chemicals, but I also had a medical electronics activity in which we were applying dielectrics techniques to biomolecules. In an abstract for a conference in 1975, I wrote that I would discuss the effects of electric and magnetic fields on the dielectric properties of enzymes. Shortly before the conference, my student reminded me that we had not done any of the magnetic measurements which I had included in the Abstract for completeness. I replied that it would not take long because biomolecules were nonmagnetic and there should not be any magnetic effects but, we had better make certain. To our surprise, we found a reduction of about 40% in the permittivity and loss for humid enzymes in strong magnetic fields. Thus began the fall from orthodoxy.
This result was of immediate interest to Professor Herbert Froehlich at nearby Liverpool University. He told me that the crucial experiment would be to measure the magnetic susceptibility. We did this and found a diamagnetic susceptibility which was 10^{4} times higher than it should have been but which disappeared at a critical magnetic field strength. Diamagnetism can only arise from the equivalent of a shortcircuited loop carrying a current which does not decay. This implied the occurrence of some sort of superconductivity effect which must be concentrated in small superconductive regions associated with the lysozyme [1] .
This was our first evidence that we were dealing with coherence and longrange order. Froehlich was always careful to point out that superconductivity is a phenomenon of coherence and not directly of lowtemperature. If the enzymewater system could acquire the necessary coherence, it could have some of the properties of a lowtemperature superconductor although not necessarily the zero electrical resistance because the superconductivity might be restricted to isolated domains. A lowtemperature analogy for this would be droplets of superconducting mercury dispersed in liquid helium rather than some zero resistance mercury metal.
This result suggested the possibility of observing Josephson effects which would give rise to the emission of coherent electrical oscillations or to frequencyvoltage interactions determined by 2e/h (twice the electronic charge Ãƒâ€¢ Planck’s Constant {twice because pairedelectrons are involved}) ~ 500 MHz/ÂµV.
It is fundamental for any field effect that a certain volume of field is required to have enough field energy to overcome thermal disordering. We first assumed that this was solely associated with the lysozyme molecules although with hindsight, there were small but consistent magnetic field variations in the susceptibility of our pure water if the results for the quartz cells used are taken as an index of the experimental accuracy being achieved. At this time, there was no theoretical reason to expect coherence domains in water. This came with the quantum electrodynamics theory of Preparata and Del Giudice twenty years later (see Section 4.5).
4.2 Coherence
The “Classical Electromagnetic Field” describes physical states for which the phase is well defined but the number of particles (quanta) is undefined.
For a “Quantum Field” the uncertainty of the phase (DF) and the number of particles (DN) is determined by the Heisenberg Uncertainty Relation (? = h/2?)
(DF) (DN) > ? /2
Within a coherence domain the phase coherence increases as the number of particles in the domain is allowed to fluctuate. The more the uncertainty is taken up by fluctuation of the number of particles comprising a domain the more perfect is the coherence.
Figure 1
Coherence in frequency and phase.
In Figure 1, the phase coherence would be “Classical” if a very large number of clocks were involved, the actual number not being specified. It would be “Quantum” if the uncertainty in the phase and the number of clocks involved was determined by the Heisenberg Uncertainty Relation.
For a wave, the velocity with which it propagates equals its frequency multiplied by its wavelength as shown in Figure 9 of Chapter 3.
Within a coherent system, the range of the coherence (coherence length) becomes the constant quantity instead of the velocity. This makes frequency proportional to velocity apparently without restriction, so long as one remains within the coherence length. There can be many velocities each with a proportionate frequency; there can be as many frequencies as there are possible velocities. Frequency no longer has an absolute value, the system has become fractal in frequency.
As a consequence, effects can occur in many different parts of the electromagnetic spectrum all originating from the same source which might be chemical, biological or electromagnetic. It is this which links effects of frequencies characteristic of chemicals to technological frequencies and through to the frequencies of biological systems. It is also the reason why environmental frequencies can mimic a chemical exposure for hypersensitive patients carrying a toxic bodyload of a matching chemical. Table 1 shows the fractal frequencies generated by imprinting the optical spectrum from a mercury discharge lamp into water.
Table 1
Within a coherent system, external radiation will interact with an entire coherence domain or, not interact at all. It is the interaction and scattering of light by individual molecules which gives matter its refractive index. If radiation does not interact, it travels with the freespace velocity of light. If it does interact with an entire massive coherence domain, the velocity is greatly reduced. Coherence propagates by diffusion (like heat along the handle of a saucepan) and the soliton is a particular case of a metastable state which is described by a nonlinear diffusion equation. Coherence in water and metals appears to propagate by a diffusion process so solitons might be involved in this as well.
4.3 Lysozyme and Cells
We concentrated on lysozyme because its structure had recently been worked out by Professor D.C. Philips group at Oxford University. They advised us on experimental techniques for handling this material.
The reaction with lysozyme with the substrate Micrococcus lysodeikticus was shown to be affected by specific radiofrequencies [2] and its onset determined by a threshold magnetic field strength which corresponded to a single quantum of magnetic flux linking the cell as shown in Figure 2. This result distinguishes the enzyme chemistry of the sterile substrates from that in living cells which is of course the milieu within which homeopathy operates. Note that the lysozyme still had a constant activity as measured with sterile substrates, it is just that with live substrates the activity becomes magnetic flux quantum dependent. In general, with higher magnetic fields the effects did not increase continuously, instead they became periodic in respect of the number of magnetic flux quanta linking the cells.
Figure 2
This work on lysozyme continued over the next few years [3] ^{, [4] }. We did find voltage steps in conductivity measurements on thin films of lysozyme which interacted with the appropriate Josephson Effect frequency (~500 MHz/ÂµV).
Meanwhile, I was gradually acquiring the facilities for doing some basic cell biology in an electrical engineering laboratory where I had the necessary electrical measurement facilities. I also had set up a degree program in biomedical electronics from which I had graduate students skilled in both electrical and biological experimentation.
In one such case, dielectrophoretic techniques were used to make measurements on yeast cells exposed to a magnetic field strength and frequency which together satisfied the nuclear magnetic resonance (NMR) condition, an effect which arises from the quantised nature of nuclear angular momentum. Resonances for the ^{1}H, ^{31}P, ^{23}Na, ^{37}Cl, ^{39}K isotopes and for electron spin resonance were detected. Interactions in which live biological cells reacted to NMR conditions occurred in six different sets of experiments: dielectrophoresis; dielectric permittivity and loss; cell mean generation time; cell cycle modification (reduced cell size and increased cell number with no change in total cell mass); lysozymesubstrate reaction (stopped by protonNMR conditions); microwave induced cataracts in vitro in bovine eye lenses [5] ^{, [6] }.
This work involving quantum effects was in general not well received. It went against the paradigm that all biological effects of electromagnetic fields could be accounted for by “classical” physics. The NMR work gave rise to a cyclotron resonance theory which kept things within the “classical physics” paradigm. It was not until 1997 that I was invited to present the evidence for living systems being macroscopic quantum systems [7] in a lecture at the Frontier Sciences Department of Temple University, Philadelphia.
Work on the effects of lowfrequency magnetic fields using over 1000 cultures of Escherichia coli under carefully controlled conditions showed that the onset of effects on the mean generation time corresponded to a single quantum of magnetic flux linking the cross sectional area of the cell. Following on, very precise strengths of magnetic field were then found to affect the lac operon system of E. coli and again corresponded to magnetic flux quantum linkage with the cells. This took magnetic flux quantum effects right down to the level of a repressor protein binding to a specific site on the DNA.
The onset of magnetic field effects when a single flux quantum linked the crosssectional area of cells measured in the particular nutrients used, seems to be widespread as shown in Figure 3. Magnetic field effects only occurred with live cells.
Figure 3
Threshold magnetic field vs. reciprocal of cell crosssections showing fit to line of slope equal the quantum of magnetic flux.
This was about the state of work and level of understanding in my laboratory in 1982 when I received the letter from Dr. Jean Monro asking for help with her electromagnetically hypersensitive patients already described in Chapter 2. This only involved myself, my students’ research continued uninterrupted.
The following year, we were able to demonstrate the emission of radiofrequency oscillations in the ranges 5080 MHz, 79 MHz and 0.11 MHz from synchronously dividing yeast cells around the time of cytokinesis. These experiments were carried out in an electrically screened laboratory using a spectrum analyser. The cells were collected between point electrodes by dielectrophoresis from a highly deionised isotonic suspension and kept in total darkness. The oscillations appeared for a few minutes after one mean generation time. The bandwidth decreased to a minimum and then increased again as the signal disappeared into the noise, the maximum amplitudes were a few tenths of a microvolt. A typical sequence made at 1 minute intervals is shown in Figure 4.
Figure 4
Radiofrequency emissions from yeast cells at cytokinesis
Currentvoltage measurements on an aliquot were made at the same time. These showed the appearance of Josephson Effect voltage steps simultaneously with these oscillations. The narrowest bandwidth observed was 50 Hz in 8.5 MHz [8] . Professor Sydney Webb calculated that a frequency 8 MHz was consistent with the rate constant for ATP hydrolysis so we were probably seeing the result of the cells’ demands for energy at the instant of cell division.
For a system at temperature 37Â°C (T = 310K) the thermal energy kT = 4.28Ãƒâ€”10^{21 }joules (k = Boltzmann’s Constant). If a cluster of n photons of frequency ? occurs within the coherence time of the system, then for the energy change of emission or absorption to be greater than the thermal energy
n h ? ? kT
(where h = Planck’s Constant ) or
n ? ? 6.5 Ãƒâ€”10^{12 } Hz . Quanta
If the Heisenberg Uncertainty Principle is applied to such a system having a lifetime t and there is a sufficient average number of photons < n > of frequency ? for the classical concept of phase to be meaningful, then
?n . (h ?) . ?t ? h/2?
or ?n . ? . ?t ? 1/2?
If the system involves random photons in a continuum of time, so that a Poisson Distribution is applicable then
?n = ? ( < n > ).
But, if the photons are coherent, ?n = < n >
The spectral line width ?? will be the reciprocal of the coherence time ?t so, for:
Random photons ??/ ? ? 2? / ? n
Coherent photons ??/ ? ? 2? / n
If ? = 8.5 MHz, then for:
Random photons ?? ? 61 kHz
Coherent photons ?? ? 70 Hz
The 70 Hz assumes that the signal equalled thermal noise, in practice it was somewhat greater so, 50 Hz is consistent with the yeast oscillations at cytokinesis being due to the quantum fluctuations of coherent photons at 8.5 MHz.
Dielectric measurements on a water imprint are shown in Figure 5. There were decreases in the capacitance (dielectric constant) and the tan ? (dielectric loss) from the initial values only at the imprinted 50 kHz and 10 Hz on either side. This was the limit of frequency resolution from the best available oscillator. The above equations for 20Â°C and ? = 50 kHz give for:
Random photons ?? ? 28 Hz
Coherent photons ?? ? 2.6 mHz
Clearly there is no change in the dielectric properties at Â± 20Hz or Â±30 Hz relative to the 50 kHz which at least excludes the involvement of random photons in a water frequency imprint. To measure the bandwidth of a water imprint would require an oscillator with a resolution of better than 2 parts in 10^{7}.
Figure 5
Dielectric measurements on water imprinted with 50 kHz
4.4 Coherence and Froehlich
All the above involved the close cooperation and theoretical input from Professor Froehlich whose work on the physics of coherent oscillations in active biological systems was but one of his major contributions to four distinct areas of physics. I have summarised his interpretation of biology through theoretical physics [9] in the FestSchrift to celebrate the Centenary of his birth.
Froehlich had already considered biological problems in relation to theoretical physics in the 1930’s. War intervened and he could not develop these ideas until in 1967, at a conference in Versailles, he considered longrange phase correlations in respect of biological order. He combined the ideas of high frequencies and collective or cooperative behaviour with ideas of longrange phase correlation and coherence and applied them to biological systems. The subsequent development of his ideas and the work of his worldwide circle of collaborators are contained in the two “Green Books” which he edited [10] ^{, [11] }.
By 1967, Froehlich had already recognised the importance of coherent modes of oscillation in nonlinear systems and longrange phase correlations in respect of biological order with absorption defining the range of these phase correlations. He showed that a nonlinear interaction will channel energy into coherent modes and that the excitation of organs to their correct frequency could be achieved by energy pumping from metabolic sources. He further showed that within a coherent system, the range of the forces of interaction greatly increased at resonance.
In 1969 Froehlich considered the possibility of quantization on a macroscopic scale giving rise to a new kind of order based on the concept of phase correlations in nonequilibrium systems which are stable but cannot be described in terms of a static or spatial order and further how this might be applied to biological systems. He continued by noting that quantum mechanics treats the dynamic behaviour of any system in terms of a state vector or wave function which for a single particle is essentially the de Broglie wave. An essential feature of quantum mechanics is that the state vectors of two (or more) states can be superimposed linearly to form a combined state the probability of which depends on the difference of the phases of its components. This is an expression of the wavelike interference which is characteristic of quantum mechanics and quantum systems. The involvement of the magnetic vector potential (Afield) is implicit in wave equations and this will be introduced later.
Froehlich then discussed how a definite phase correlation could persist over long distances in spite of thermal agitation citing as examples: low temperature superconductivity phenomena and the laser. He remarked that it is not the state function but a much simpler quantity a macroscopic wave function which persists after thermal averaging. He then felt. tempted to postulate the existence of longrange quantum mechanical phase correlations in biological systems. This had been suggested to him by PerOlov Loewdin.
The strongly polar dielectric character of biological objects suggested the existence of longitudinal oscillations with internal deformations providing additional stabilization but which would be lost at too high cell concentrations. Longitudinal modes of oscillation are supported within matter but do not travel into freespace so there would not be any energy loss by radiation. He showed quite generally that if energy is supplied to such longitudinal modes of oscillation above a certain mean rate then a steady state would evolve with a strongly excited single frequency. The energy would be stored in a highly ordered way involving longrange quantum mechanical phase correlations resembling the lowtemperature condensation of a gas obeying Bose statistics.
Scully et al. [12] may have removed the restriction that Froehlich’s systems had to be pumped with energy from metabolic sources. Here, the addition of a quantum coherence term to the classical Carnot Heat Engine cycle provides a new parameter (information) which can be varied so as to increase the radiation temperature and enable work to be extracted from a single heat bath. If this concept is applicable to Froehlich’s systems they could become their own heat bath and pump themselves. This may also relate to the work of Professor Elia on the thermodynamics of heatsofmixing [13] and the informational content of dilute solutions, homeopathic potencies and frequency imprints.
In her introduction to “Cooperative Phenomena”, Fanchon Froehlich [14] writes that, “It would be highly interesting, to attempt to impose the necessary oscillations by external means in the hope of influencing biological developments”. The excitation of living systems to their correct frequency is an implied aim of homeopathic remedies.
Froehlich published his second “Green Book” in 1988 and in his introduction entitled, “Theoretical Physics and Biology” he covered the theory of:
1. Active Biological Systems – stable but far from equilibrium – nontrivial order – extraordinary dielectric properties.
2. Coherent Excitations – single mode – metastable highly polar ferroelectric state – limit cycles – Davydov solitons as a particular case of a metastable state.
3. Deterministic Chaos – something which happens when two very different metastable states occur with equal probability. It leads to lack of experimental reproducibility and effects which only appear in the standard deviations, not in the mean values.
4. Macro and Micro Physics – the relations between them.
5. Resonance Interactions between two harmonic oscillators.
6. Periodic Reactions – LotkaVolterra oscillations in complex systems such as enzyme reactions.
7. Quantization of Magnetic flux – a completely general property of the magnetic field.
8. Multicomponent Systems and the Cancer Problem – cessation of control by a healthy excited mode and the transition from order to disorder (disease).
9. Coherent Excitations as Interpreters of Biological Features – coherent excitations and the resulting interactions between excited cells.
4.5 Coherence in Water – Del Giudice and Preparata
One theoretical concept that Froehlich did not reach was hinted at in the second “Green Book” where Del Giudice et al. discussed the properties of filaments of coherence^{11 }.
Froehlich had predicted that longrange phase correlations in respect of biological order would persist over long distances in spite of thermal agitation. He assumed that the range would be limited by an absorption process and assumed that coulomb interactions would suffice. Del Giudice and Preparata considered that coulomb interactions would be screened by ion motion and that exchange of radiation between water molecule resonances could generate the necessary force. Froehlich did not appreciate the possibility of coherence as a fundamental property of the ground state of water.
Del Giudice et al.^{11} remarked that, “….the basic proposal of Froehlich that density of electric polarization was the “order parameter” relevant for biological systems led them to a scheme for living systems with a finite size related to a nonvanishing temperature, the confinement of the internal EM field into filaments, low intensity coherent electromagnetic emission from living matter, magnetic flux quantization and Josephsonlike effects, solitons on molecular chains and water electrets”.
In 1995, Arani, Del Giudice and Preparata [15] showed through quantum electrodynamics (QED) theory that water had coherence as a fundamental property in its ground state arising from the exchange of radiation at the natural photoabsorption resonances of the water molecule. This coherence was confined to domains of size determined by the coherence length which was twice the wavelength of the spectral line involved. The 12.06 eV spectral line in the far ultraviolet and close to the ionisation potential of water was used for the calculations. It should be the first to form a coherence domain when water vapour condensed to the liquid phase. They were able to show that a permanent coherence can become established in water and give rise to a longrangeorder within domains 75 nm in size (Figure 6). This coherence is in the unexcited or ground energy state of water. It is a fundamental property of liquid water and unlike the laser, no energy pumping is required to establish coherence. Froehlich’s model needed a supply of metabolic energy and as such is applicable to active biological systems as he describes.
Figure 6
Using QED theory they showed that water at 300 K was a mixture comprising 28% coherent water in 75 nm domains interspersed with the remaining 72% as incoherent or vapourlike water. It is the coherent water that has the “memory” properties. The incoherent water is responsible for its normal thermodynamic properties. This theory was the first to give the experimentally determined values for many of the physical properties of water including: critical volume; boiling temperature; latent heat of vaporisation; specific heat; the specific heat and compressibility anomaly at 230K; the density anomaly at freezing point and the low frequency dielectric constant for water. Froehlich had applied the Kirkwood formula to this but only got a value of 63 for the static dielectric constant of water compared with the experimental value of 78.
4.6 “Water Memory”
I have recently summarised the various effects in water of clinical and scientific relevance [16] . During attempts to measure frequency imprints in water by instrumentation and in work with electrically hypersensitive patients and with homeopathic potencies, it was found that a water imprint or a homeopathic potency would be erased if the geomagnetic field was shielded by placing it in a closed steel box [17] . The threshold magnetic field for erasure is ~1% of the geomagnetic field and is independent of an imprinted frequency over at least the 13decades from 10^{4} Hz to 10^{+9} Hz.
If erasure of an imprint occurs when thermal energy exceeds the magnetic energy, this would occur for a spherical domain of 52.92Âµm diameter at ambient temperature, or 47.40 Âµm at 18ÂºC and 62.22 Âµm at +80 ÂºC.
Imprinting a frequency into water affects the natural water resonances so if this model is correct, these must also resonate with the coherence domains. The 62 cm^{1 }difference between a pair of water laser lines corresponds to a wavelength of 161 Âµm, this would correspond to a ‘pearlchain’ of three 52.92 Âµm domains (159 Âµm with present accuracy). If one water resonance can couple to a domain, fractality will couple others to it.
We had shown in 1983 that living systems can respond to magnetic resonance (NMR) conditions, even at geomagnetic field strengths^{5 }. Therefore, a frequency might be retained in water if proton precession becomes coherently synchronised to an applied alternating magnetic vector potential and then these coherent protons can generate their own internal magnetic field such as to satisfy proton NMR conditions. Such a process should be stable unless the domain is thermally broken up by removing the stabilising geomagnetic field.
The proton NMR condition gives the precession frequency n
n = g B/2p
where g is the gyromagnetic ratio 2.675 Ãƒâ€” 10^{8} rad T^{1} s^{1}, B is the magnetic field and n is in Hz.
The magnetic field B at the centre of a magnetic dipole from a rotating charge is
B = m_{0} n e n / 2a
where m_{0} is the permeability of free space, n is the number of charges e involved, n is frequency (Hz) and a is the radius of the orbit. Whence, the number of charges n required is independent of frequency and
n = 4p a / m_{0} e g?
The water erasure threshold is 375 nT giving the radius of a coherence domain a = 26.46 Âµm (52.92 Âµm diameter). This makes n = 6.29Â´10^{12} which is the number of proton charges required to generate a magnetic field to satisfy NMR conditions. With two protons available for coherent synchronisation from each water molecule within sphere of 26.46 Âµm radius, 5.52Â´ 10^{15} protons should be available for taking up frequency imprints. Thus, there should be enough protons for 878 frequencies to be imprinted.
To test this prediction, water was imprinted successively with a sequence of frequencies increased in 10 Hz steps. From the above, there should have been enough protons in a domain to imprint 878 distinct frequencies. After 965 frequencies had been imprinted, no further imprinting was possible. At higher temperatures the domains should be larger hence more protons should be available for imprinting. Heating this already saturation imprinted water to 80ÂºC enabled imprinting to continue as far as 986 imprints. However, on cooling all these imprints selferased.
The pH of water measures the availability of protons. It was found that whereas 1 ml of water at pH 5 would accept 935 frequency imprints, at pH 9 it would only accept 77. Figure 7 shows that the number of frequency imprints possible depends on the pH and the available volume.
Figure 7
The number of frequencies that can be imprinted into typical tablets, pills and pillules used in homeopathy are given in Table 2. This sets a fundamental limit as to how far the process of potentisation can be taken
Table 2
Frequency Information Capacity
Maximum number of distinct frequency imprints
Small pillule (1 mm diameter) 
446 imprints 
Large pillule (3.5 mm diameter) 
395 imprints 
Tablet (6 mm diameter) 
584 imprints 
Water (pH 7) 
~1000 imprint/ml~1 imprint/Âµl 
The chart recording in Figure 8 shows that the pH of a solution of sodium hydroxide at pH 8.01 increased to pH 8.05 at memory saturation which occurred after 377 separate frequencies had been imprinted. Erasure returned the pH to the initial value.
An increase in pH corresponds to the removal of H+ ions. The change in pH confirms that the number of protons involved in pH change per frequency imprint is equal to the number needed to generate the local magnetic field to satisfy protonNMR conditions independently of the imprinted frequency. Thus, imprinting a frequency into water creates proton coherence which stores that frequency.
Figure 8
Changes of pH on imprinting frequencies and reversibly on erasure
(Chart speed: 10min/div)
Conclusion
In his paper, “Quantum Mechanical Concepts in Biology” [18] Froehlich got it exactly right even in his first words, “Quantum Mechanics – Biology”. He considered quantum mechanical concepts on a macroscopic scale with superconductivity a consequence of coherence – not of low temperature, of magnetic flux always being quantised and the possibility of the Josephson effect giving a frequency to voltage interconversion. The involvement of the magnetic vector potential is implicit in the wave equations which it enters like the chemical potential although he did not specifically discuss the possibility of living systems being sensitive to it.
In this Chapter, I have tried to show that living systems are sensitive to magnetic fields and photons at the single quantum level and that enzyme chemistry applied to living systems can differ significantly from regular chemistry even down to the DNA level. I have shown that cells can emit highly coherent oscillations at the time of cell division which are not present during the other parts of the cell cycle and which are coherent down to the level of quantum fluctuations. Dielectric measurements on a frequency imprint in water do not fit with random photons and therefore must also have coherence determined by quantum fluctuations and by implication so must all homeopathic potencies. The conclusion must be that Nature is working with a frequency precision of the order of parts per million.
A basic mechanism is postulated by which any frequency can be retained in water and which fits experiments with reasonable approximation. The indefinite retention of frequency imprints is needed by any theory of potentisation because of the observation that one of Hahnemann’s original potencies was still clinically provable 150 years after he had prepared it.
There is no point in doing clever mathematics if there in no firstorder theory that gives a reasonable fit to such numbers as can be obtained by experiment – the Bohr model of the atom (1913) had to come before the Schroedinger Equation (1926). Since Nature seems to be using frequencies in such an extremely precise manner that all the related chemical and physical parameters may well be involved with similar precision in living systems. The Table in the Appendix provides a useful chart for comparing the different ways in which frequency and energy have been considered by the different disciplines.
Appendix 1
Electromagnetic Radiation and Energy
Radiation 
Frequency Hz 
Wavelength m 
Wave Number cm^{1} 
Quantum Energy eV 
Chemical kJ/mole (kcal/mole) 
Thermal K 
Energy Joules 
Ionizing 
3 Ãƒâ€” 10^{15} 
100 nm 
100,000 
12.4 
1088 (260) 
130,000 
2Ãƒâ€”10^{18} 
Ultraviolet – visible 
10^{15} 
300 nm 
30,000 
3.7 
360 (86) 
43,000 
6Ãƒâ€”10^{19} 
Infrared 
10^{14} – 10^{13} 
3 Âµm – 30 Âµm 
3,000 – 300 
3.7Ãƒâ€”10^{1} 
36 (8.6) 
4,300 
6Ãƒâ€”10^{20} 
Submm 
10^{12} 
300 Âµm 
30 
3.7Ãƒâ€”10^{2} 
3.6 (0.86) 
430 
6Ãƒâ€”10^{21} 
Thermal 
7.5 Ãƒâ€” 10^{11} 
400 Âµm 
23 
2.5Ãƒâ€”10^{2} 
2.7 (0.65) 
300 (27Â°C) 
4Ãƒâ€”10^{21} 
mm 
10^{11} 
3 mm 
3 
3.7Ãƒâ€”10^{3} 
43 
6Ãƒâ€”10^{22} 

cm 
10^{10 } – 10^{9} 
3 cm – 30 cm 
4.3 

RF 
10^{8} – 10^{6} 
3 m – 300 m 

Audio 
10^{4} 10^{2} 
30 – 3,000 km 

Flicker 
10^{1} 
30,000 km 

Telluric 
10^{0} – 10^{3} 
â€¢ Spectral power density (watts per cycle of bandwidth) = joules.
â€¢ Water absorption band approximately 2 Ãƒâ€” 10^{10 }to 10^{14 }Hz.
â€¢ Dielectric dispersions (Hz):
water relaxation (?) ~10^{10}, proteins (?_{1)} ~ 10^{6}, MaxwellWagner (?) ~10^{4}, ions & membranes (?) ~10^{1}.
[1] Ahmed NAG, Calderwood JH, Froehlich H, Smith CW (1975) Evidence for collective magnetic effects in an enzyme: likelihood of room temperature superconductive regions. Phys. Lett. 53A:129130.
[2] Shaya SY, Smith CW (1977) The effects of magnetic and radiofrequency fields on the activity of lysozyme. Collect. Phenom. 2:215218.
[3] Ahmed NAG, Smith CW, Calderwood JH, Froehlich H (1976) Electric and magnetic properties of lysozyme and other biomolecules. Collect. Phenom. 2:155166.
[4] Ahmed NAG, Smith CW (1978) Further investigations of anomalous effects in lysozyme. Collect. Phenom. 3:2533.
[5] JafaryAsl AH, Solanki SN, Aarholt E, Smith CW (1983) Dielectric measurements on live biological materials under magnetic resonance conditions. J. Biol. Phys. 11:1522.
[6] Aarholt E, Jaberansari J, JafaryAsl AH, Marsh PN and Smith CW. NMR conditions and biological systems. In: Marino AA (Ed.) Modern Bioelectricity. New York: Marcel Dekker, 75104, 1990.
[7] Smith C.W. Is a living system a macroscopic quantum system? Frontier Perspectives, 7(1), 915 (1998).
[8] Smith CW, JafaryAsl AH, Choy RYS, Monro JA. The Emission of Low Intensity Electromagnetic Radiation from Multiple Allergy Patients and other Biological Systems. In: JezowskaTrzebiatowska B, Kochel B, Slawinski J, Strek W (Eds.). Photon Emission from Biological Systems. Singapore: World Scientific, 110126, 1987.
[9] Smith CW (2006) Froehlich’s Interpretation of Biology through Theoretical Physics. In: Hyland GJ and Rowlands P (Eds.) Herbert Froehlich FRS: A physicist ahead of his time. Liverpool: University of Liverpool pp 91138.
[10] Froehlich, H. (1983) Coherence in Biology, in ‘Coherent Excitations in Biological Systems’, Froehlich, H. and Kremer, F. (Editors). Berlin: SpringerVerlag pp 15.
[11] Froehlich, H. (1988) Theoretical Physics and Biology, in Froehlich, H. (Editor) “Biological Coherence and Response to External Stimuli”. Berlin: SpringerVerlag pp 124.
[12] Scully, M.O. Zubairy, M.S. Agarwal, G.S. Walther, H. (2003) Extracting Work from a Single Heat Bath via Vanishing Quantum Coherence. Science 299, 862864.
[13] Elia, V. Niccoli, M. (1999) Thermodynamics of Extremely Diluted Aqueous Solutions. Ann NY Acad of Sci879, 241248.
[14] Froehlich, F. (1973) Life as a Collective Phenomenon,in ‘Cooperative Phenomena’, Haken, H. and Wagner, M. (Editors). Berlin: Springer Verlag, pp VIIXII.
[15] Arani,R. Bono, I. Del Giudice, E. Preparata, G. (1995) QED Coherence and the Thermodynamics of Water. Intl. J. of Mod. Phys.B, 9, 18131841.
[16] Smith CW. (2007) Water – its clinical and scientific depths. In: Emoto M, The Healing Power of Water. London: Hay House. Chap.3, pp. 7788.
[17] Using a steel shielded amplifier, it took us a long time to realise that we were trying to measure an erased specimen.
[18] Froehlich, H. (1969) Quantum Mechanical Concepts in Biology, in ‘Theoretical Physics & Biology’, Marois, M. (Editor). Amsterdam: NorthHolland, pp 1322.
Hello there Hpathy,
I am an independent science writer based in Vancouver, British Columbia, and I wanted to know if you had a current email address for Cyril W. Smith, or if you could ask him to get in touch with me. I wanted to ask him about his research with A.H. JafaryAsl from 1983 on the frequencies emitted by brewers’ yeast. Thought subsequent research did find MHz emissions in a different group of cells, the range they measured was said to have been due to feedbacks from their instruments (HÃ¶lzel 1990). Also, I wanted to know what the initials “A.H.” stand for in JafaryAsl’s name? And what was this person’s position or title at the time? Many thanks.
Paul H. LeMay
There is some great math here that I would like to get a look at but unfortunately the symbols got corrupted and I am seeing things like ” ?n . ? . ?t ? 1/2?” where there should be an equation.
Is there somewhere I can get a PDF version of this document with the readable equations?