Homeopathy – How It Works and How It Is Done

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 non-magnetic 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 Fröhlich 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 10⁴ 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 short-circuited 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 long-range order.  Fröhlich was always careful to point out that superconductivity is a phenomenon of coherence and not directly of low-temperature. If the enzyme-water system could acquire the necessary coherence, it could have some of the properties of a low-temperature superconductor although not necessarily the zero electrical resistance because the superconductivity might be restricted to isolated domains. A low-temperature 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 frequency-voltage interactions determined by  2e/h (twice the electronic charge ÷ Planck’s Constant  {twice because  paired-electrons are involved}) ~  500 MHz/µV.

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  (ħ = h/2π)

(DF) (DN) > ħ /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 body-load 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 free-space 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 non-linear 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 radio-frequencies [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/µV).

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 ¹H, ³¹P, ²³Na, ³⁷Cl, ³⁹K 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); lysozyme-substrate reaction (stopped by proton-NMR 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 low-frequency 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 cross-sectional 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 cross-sections 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 radio-frequency oscillations in the ranges 50-80 MHz, 7-9 MHz and 0.1-1 MHz from synchronously dividing yeast cells around the time of cyto-kinesis. 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 de-ionised 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

Radio-frequency emissions from yeast cells at cyto-kinesis

Current-voltage 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 37°C (T = 310K) the thermal energy kT = 4.28×10^-21 joules (k = Boltzmann’s Constant). If a cluster of n photons of frequency  ν 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 ν ≥ kT

(where h = Planck’s Constant   ) or

                                                              n ν  ≥  6.5 ×10¹²  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 ν for the classical concept of phase to be meaningful, then

                                          Δn . (h ν) . Δt  ≥  h/2π

or                                              Δn . ν . Δt ≥  1/2π

If the system involves random photons in a continuum of time, so that a Poisson Distribution is applicable then   

Δn  = √ ( < n >  ).

But, if the photons are coherent,            Δn  =  < n > 

The spectral line width  Δν  will be the reciprocal of the coherence time Δt   so, for:

Random photons                             Δν/ ν   ≤    2π / √ n

Coherent photons                            Δν/ ν   ≤    2π / n

If  ν = 8.5 MHz, then for:

Random photons                             Δν       ≤    61 kHz

Coherent photons                            Δν       ≤    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 cyto-kinesis 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 δ (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 20°C  and  ν = 50 kHz  give for:

Random photons                             Δν       ≤    28 Hz

Coherent photons                            Δν       ≤    2.6 mHz

Clearly  there is no change in the dielectric properties at  ± 20Hz or ±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 10⁷.

Figure 5

Dielectric measurements on water imprinted with 50 kHz

4.4       Coherence and Fröhlich

All the above involved the close cooperation and theoretical input from Professor Fröhlich 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 Fest-Schrift to celebrate the Centenary of his birth.

Fröhlich 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 long-range phase correlations in respect of biological order.  He combined the ideas of high frequencies and collective or cooperative behaviour with ideas of long-range phase correlation and coherence and applied them to biological systems. The subsequent development of his ideas and the work of his world-wide circle of collaborators are contained in the two “Green Books” which he edited [10] ^{, [11]} .

By 1967, Fröhlich had already recognised the importance of coherent modes of oscillation in non-linear systems and long-range phase correlations in respect of biological order with absorption defining the range of these phase correlations. He showed that a non-linear 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 Fröhlich 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 non-equilibrium 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 wave-like interference which is characteristic of quantum mechanics and quantum systems. The involvement of the magnetic vector potential (A-field) is implicit in wave equations and this will be introduced later.

Fröhlich 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 long-range quantum mechanical phase correlations in biological systems. This had been suggested to him by  Per-Olov Löwdin.

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 free-space 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  long-range quantum mechanical phase correlations resembling the low-temperature condensation of a gas obeying Bose statistics.

Scully et al. [12] may have removed the restriction that Fröhlich’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  Fröhlich’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 heats-of-mixing [13] and the informational content of dilute solutions, homeopathic potencies and frequency imprints. 

In her introduction to “Cooperative Phenomena”, Fanchon  Fröhlich [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.

Fröhlich  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 – non-trivial 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 - Lotka-Volterra 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 Fröhlich did not reach was hinted at in the second “Green Book” where Del Giudice et al. discussed the properties of filaments of coherence¹¹ .

Fröhlich had predicted that  long-range 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. Fröhlich  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  Fröhlich 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 non-vanishing temperature, the confinement of the internal EM field into filaments, low intensity coherent electromagnetic emission from living matter, magnetic flux quantization and Josephson-like 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 photo-absorption 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 ultra-violet 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 long-range-order 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. Fröhlich’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 vapour-like 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. Fröhlich 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 13-decades 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  52.92µm  diameter at ambient temperature,  or  47.40 µm at  -18ºC  and 62.22 µm at  +80 ºC.

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 µm, this would correspond to a ‘pearl-chain’ of three 52.92 µm domains (159 µm  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 strengths⁵ . 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 × 10⁸ 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 = m₀  n e n / 2a

where  m₀ 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 /  m₀  e  g

The water  erasure threshold is 375 nT giving the radius of a coherence domain a = 26.46 µm (52.92 µm diameter).  This makes  n = 6.29´10¹²  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 µm radius, 5.52´ 10¹⁵ 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 80ºC enabled imprinting to continue as far as 986 imprints. However, on cooling all these imprints self-erased.

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

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 proton-NMR 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]   Fröhlich 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 inter-conversion. 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 first-order 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 Schrödinger 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

·        Spectral power density (watts per cycle of bandwidth)  =  joules.

·        Water absorption band approximately 2 × 10¹⁰ to 10¹⁴ Hz.

·        Dielectric dispersions (Hz):

water relaxation (γ)  ~10¹⁰, proteins (β₁₎ ~ 10⁶,  Maxwell-Wagner (β) ~10⁴, ions & membranes  (α) ~10¹.