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On the physical basis of succussion
Homeopathy (2002) 91, 221–224 & 2002 The Faculty of Homeopathy PII: S1475-4916(02)00106-6, available online at www.idealibrary.com on
ORIGINAL PAPER
On the physical basis of succussion J-L Torres1* 1
lnstituto de Fı´sica y Matema´ticas, Universidad Michoacana, Morelia, Michoaca´n, Me´xico
It is argued that succussion drives the homeopathic tincture undergoing potentisation to a turbulent regime, where vortices continually form and disappear, ranging in size from the linear extent of the container to a minimum scale determined by viscosity and the rate of energy dissipation. Input mechanical energy cascades down this population of eddies and becomes available at the microscopic level to perform work (chemical, electrical, etc). A structure generated in the tincture would be rupted by vortices smaller than it, and this sets definite limits on the strength of succussion, so the power input leads to larger vortices than the structures one is trying to create and preserve through potentisation. An experimental procedure to test this proposal is suggested, based on Rayleigh scattering. Homeopathy (2002) 91, 221–224.
Keywords: succussion, turbulence, clathrate
Introduction Full understanding of potentisation and the origin and mechanism of the similitude principle will probably require new physical concepts, given the relative lack of success until now in the quest to understand these phenomena in microscopic terms. A plausible strategy is to look into novel results at the forefront of physical research for potentially useful tools in Homeopathy. However, well-known and even old results from physics are sometimes enough to understand homeopathic features that are described and often ‘explained’ in unnecessarily esoteric terms. In this note, I offer an explanation of succussion in terms of induced turbulence in the tincture undergoing potentisation, that allows transfer of the input mechanical energy all the way down to the molecular level, where it becomes available to perform chemical work. My approach is in the spirit of similar recent attempts to broaden the homeopathic perspective, based on concepts and methods from physics.1–3
Potentisation of homeopathic medicines involves gradual dilution accompanied by succussion at each step. I start from the premise that, whatever the changes brought about by potentisation (generation of stable clathrates or electric dipoles in water, etc.4,5), they occur at the molecular level and require input of energy, macroscopically supplied through mechanical agitation (succussion). A necessary condition to substantiate this assumption is that a mechanism exists to transfer energy from the macroscopic to the molecular scale. In fact, such a mechanism of energy transfer is available: in a turbulent regime, vortices of all sizes within a wide range continually form and disappear, and mechanical energy cascades from the largest all the way down to the microscopic level, where it can either be dissipated as heat due to viscosity, or become available to do work. The role of succussion is then to drive the homeopathic tincture to the turbulent state, by creating and maintaining the corresponding population of vortices.
Turbulence and Clathrates *Correspondence: Jose`-Leonel Torres, Instituto de Fı´sica y Matema´ticas, Universidad Michoacana, 58060 Morelia, Michoaca´n, Me`xico. E-mail: [email protected] Received 6 March 2002; revised 29 April 2002; accepted 20 May 2002
A turbulent state is one where the velocity at any point in a fluid varies with time both in magnitude and direction, in such a complicated way that it is best described as a random variable, thus allowing treat-
Physical basis of succussion J-L Torres
222
ment of this phenomenon in statistical terms. More pictorially, the fluid develops vortices of many sizes, with large eddies feeding smaller ones with solute or suspended material, energy and angular momentum, until a scale is reached where diffusion becomes dominant, beyond which heat is generated and chemical work may be performed at the molecular level (Figure 1). Persistence of this regime thus requires an external input of energy. More precisely,6 a pure number R LV=n (Reynolds number; ‘B’ denotes proportionality) can be formed with the linear size L of the container where motion takes place, the kinematic viscosity u of the fluid, and its average velocity difference V between two points separated a distance L; turbulence unfolds for large values of R, and fully developed turbulence formally occurs when R ! 1. In a steady state, the energy input at the largest vortices generates and sustains a fluctuating but statistically stable population of smaller ones, that feed in turn a population of yet smaller vortices, and so on; mechanical energy flows through such eddies all the way down to the smallest ones, with linear size, Z ðn3 =eÞ1=4 , where e is the rate of energy dissipation per unit mass and equals the rate of energy input in the steady state. For distances
Figure 1 Two-dimensional rendering of the vortex distribution in a turbulent regime. A fluctuating but statistically stable population of vortices is generated in a steady state, ranging in size from the linear dimension L of the container (in a confined environment) to the dissipation scale Z ðn3 =eÞ1=4 with u being the fluid kinematic viscosity and e the rate of energy dissipation per unit mass; below the scale Z diffusion becomes the dominant mechanism of energy transfer. Arrows show the direction of energy flow. Eddies at each level in the hierarchy are space-filling, and in a steady state, the same average energy flux traverses the system at all scales. Homeopathy
smaller than Z (often called Kolmogorov’s dissipation scale), dissipation effects become dominant over the mechanical ones produced by vortices, and energy diffuses towards the molecular level, generating heat in the process (due to viscosity) and becoming available to do work, subject to the limitations imposed by the laws of thermodynamics. As the energy input e increases, the smallest vortices decrease in size and energy diffusion starts closer to the molecular level; the appearance of stable material features in the tincture with size DoZ thus becomes feasible (ie, structures able to ‘ride’ the existing vortices), as larger ones would be perturbed and possibly torn by the smallest eddies. One would naively expect that after a few dilution steps the viscosity of the tincture would become identical with that of the unperturbed solvent. However, the presence of newly generated clathrates might, in principle, affect the viscosity of the solvent, so u must also be monitored during potentisation, as the limiting scale Z for microscopic structures depends both on energy input and viscosity. Although the detailed relationship between clathrates and viscosity may be complicated, one would expect the effect to grow with clathrate density. Clathrate density in the steady state will depend on a balance condition involving their generation and decay rates; these are in turn related to prominent features of the potential energy profile for clathrates (Figure 2). Succussion thus emerges as an operation whose intensity and duration must be carefully tuned to generate and preserve the appropriate density of microscopic structures in each case. Apart from tincture viscosity, that also needs to be monitored throughout potentisation according to our argument, the relevant parameter turns out to be the rate of energy input e, which is determined by the intensity of succussion. The practical relevance of this constraint can be ascertained with some numerical estimates. We rewrite the above expression for Z more precisely as follows: Z ¼ Aðn3 =eÞ1=4 , with A a numerical coefficient of order unity.7 The condition Z 4 D to preserve structures with size D in the tincture implies e4u3/D4. This dependence of e on the fourth power of D enhances the role of the latter in determining succussion strength. For example, if the relevant clathrates are a few nanometres in diameter (D’ 107 cm), there is practically no upper limit on the input power during succussion (using u’102 cm2/s for the kinematic viscosity of water8). However, if there are clathrates, say, a few micrometres in diameter, e must be lower than about 1 W/g tincture. The presence of stable clathrates several hundred micrometers in size has been suggested in polar solvents like water, through the coherent coupling of its molecules to the quantised electromagnetic field,5,9,10 in the presence of some solute or impurity with an electric dipole moment. For a clathrate 100 mm across, our bound eoV3/D4 implies that succussion
Physical basis of succussion J-L Torres
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must supply less than 105 W/g tincture, so it must be extremely mild if the desired structures are to survive mechanical perturbation from the smallest vortices. One must add, however, that the existence of such large clathrates was proposed in the static limit, ie, neglecting their possible disruption from thermal effects at finite temperature, so the question of their stability remains open (cf. Figure 2 and observation (c) below).
Testing the hypothesis How can the proposal that the intensity of succussion determines the size of the largest structures in the tincture be tested in the laboratory? The obvious procedure is through spectroscopic analysis. Briefly, the experiment would consist of detecting clathrates up to a certain size that does not exceed the proposed limit D (u3/e)1/4 for a given power input from succussion, and repeating this test for several values of e. As we are only interested at this stage in the question of the presence of such clathrates, not in individual structural details, Rayleigh scattering should provide the necessary answers. The relevant formulas are those from Rayleigh’s argument for the blue colour of the sky.11 If there are N scatterers with comparable linear size D per unit volume in the tincture, and we irradiate the latter with plane waves of wavelength l D (in practice l\10D leads to a reasonably good approximation), and the radiation traverses a thickness x of the tincture, its intensity will decay as I(x)=I0eax, where I0 is the original intensity of the beam and a, the attenuation coefficient, is given by a = Ag2N/l4 with A a
numerical factor whose precise value is not relevant to our argument, and g the individual polarisability, ie, p=gE, where p is the polarisation induced in a scatterer by the electric field E from the radiation. The experimental procedure would be as follows. Start with a mechanised succussion process that allows precise measurement of the power input e. From this and the tincture viscosity u, calculate the limiting size D ’ (u3/e)1/4 for After reaching a steady-state succussion would be stopped, and the existing vortices allowed to disappear. The tincture is then irradiated with plane electromagnetic waves whose wavelengths fail in the interval lmin l lmax with lmin and lmax such that lmin D lmax, so the condition for Rayleigh scattering (l\10D) is fulfilled. The following measurements would be made:
The intensity I(l) of the beam in the forward
direction after traversing a fixed amount of tincture, for several values of l. If a significant density of structures with (maximum) size D is indeed present, a log–log plot of I(l) vs l will be well fitted by a straight line with slope 4 in the interval 10Dtl lmax, and it will deviate from this line in the interval lmin ltB10D, as Rayleigh scattering is replaced by Mie12 scattering (wavelength comparable with or smaller than linear size of individual scatterers). For a fixed wavelength l, vary the length x of the path traversed by the beam in the tincture, and measure radiation intensity in the forward direction, I(x)=I0eax, to estimate the number N of scatterers per unit volume, from a = Ag2N/l4.
An assumption in this procedure is that adequate numbers of clathrates are generated and survive long enough to be detected. For this to happen several conditions must be fulfilled, and each defines a variable that becomes relevant for the effectiveness of succussion, if experiments validate our proposal:
Figure 2 Potential energy profile for clathrate formation (schematic). According to Kramers’ theory of chemical reaction rate,l3 this corresponds to a transition from i to f ; with Ub being the energy barrier to be overcome in the process. The rate of clathrate generation is proportional to eUb/kT, where k is Boltzmann’s constant and T the absolute temperature; clathrate stability depends on the depth Ud of their ‘potential well’.
(a) Duration and intensity of succussion: To reach the steady state at each potentisation step, succussion must be of adequate duration and intensity. (b) Clathrate density: This factor appears explicitly in the decay constant of radiation intensity as a function of tincture thickness (a = A(g2N/l4)); it may also be a factor in the tincture’s viscosity u. In the steady state, clathrate density reflects a balance between generation and decay rates. The generation rate depends in turn on the ‘potential barrier’ to be overcome to create clathrates; the decay rate involves both the depth of their ‘potential well’ and the number already present13 (Figure 2). (c) Temperature: This factor affects tincture viscosity and clathrate generation and decay rates.13 If the tincture is at absolute temperature T, thermal Homeopathy
Physical basis of succussion J-L Torres
224
fluctuations have energies of order kT, with k being Boltzmann’s constant, so these rates depend on the interplay between kT and Ub and Ud, the potential energy barrier and depth, respectively (Figure 2). (d) Radiation frequency. If the frequency f of radiation used in the scattering experiment is such that Erad= hf (with h being Planck’s constant) becomes comparable with or larger than Ud in Figure 2, its contribution to the decay rate of clathrates will be significant. This imposes constraints on our choice of wavelength range for the scattering experiment.
Conclusion My argument implies that succussion must be designed subject to two antagonistic constraints: it must be strong enough that the power input allows generation of the relevant structures in a reasonable number of potentisation steps; on the other hand, it must no be so intense that, once created, such structures are disrupted by very small vortices. The availability of machines to perform succussion makes such fine tuning feasible. The obvious empirical way to test the proposal is to compare the effectiveness of tinctures that have undergone the same potentisation procedure, except for the strength of succussion. Unfortunately, a final verdict will have to wait for more precise measurements than are possible at present in homeopathic clinical trials or bioassays. Meanwhile, a judicious practice would be to carefully monitor succussion during each potentisation process, and include its strength on the label of the resulting medicament. Hahnemann14 insisted from the beginning on a systematic succussion procedure: ‘. . .[One] then slams the stoppered (capped) bottle 100 times against a hard, but elastic body (perhaps a leather-bound book) . . .’. His insight seems all the more remarkable in light of our discussion above on the role of the ensuing turbulence as a vehicle of energy transfer from the macroscopic to the molecular realm.
Homeopathy
Acknowledgements The author thanks Coordinacio´n de Investigacio´n Cientı´ fica at Universidad Michoacana in Mexico for support to carry out this work. He is also grateful to an anonymous referee whose comments led to improvements in some aspects of the paper.
References 1 Endler PC, Schulte J (eds). Ultra High Dilution: Physiology and Physics. Dordrecht: Kluwer Academic Publishers, 1994, especially Parts 2 and 3. 2 Torres J-L, Ruiz MG. Stochastic resonance and the homoeopathic effect. Br Hom J 1996; 85: 134–140. 3 Torres J-L. Homeopathic effect: a network perspective. Br Hom J 2002; 91: 89–94. 4 Anagnostatos GS. Small water clusters (clathrates) in the preparation process of Homoeopathy. In: Endler PC, Schulte J (Eds), Ultra High Dilution: Physiology and Physics. Dordrecht: Kluwer Academic Publishers, 1994, pp 121–128. 5 Del Giudice E. Is the ‘memory of water’ a physical impossibility?. In: Endler PC, Schulte J (Eds). Ultra High Dilution: Physiology and Physics. Dordrecht: Kluwer Academic Publishers, 1994, pp 117–119. 6 Frisch U. Turbulence. Cambridge: Cambridge University Press, 1996. 7 Frisch U, Turbulence. Cambridge: Cambridge University Press, 1996. p 91. 8 Frisch U, Turbulence. Cambridge: Cambridge University Press, 1996., p 2. 9 Del Giudice E, Preparata G, Vitiello G. Water as a free electric dipole laser. Phys Rev Lett 1988; 61: 1085–1088. 10 Preparata G. Quantum Field Theory of Superradiance. In: Cherubini R, Dal Piaz P, Minetti B (Eds). Problems of Fundamental Modern Physics. Singapore: World Scientific, 1990. 11 Jackson JD. Classical Electrodynamics. New York: John Wiley & Sons, 1974, pp 411–427. 12 Born M, Wolf E. Principles of Optics. Cambridge: Cambridge University Press, 1980, pp 633–656. 13 Ha¨nggi P, Talkner P, Borkovec M. Reaction-rate theory. Rev Mod Phys 1990; 62: 251–290. 14 Hahnemann S. Quoted in: Auerbach D. Mass, fluid and wave motion during the preparation of ultra high dilutions. In: Endler PC, Schulte J (Eds.). Ultra High Dilution: Physiology and Physics. Dordrecht: Kluwer Academic Publishers, 1994, p 129.
ORIGINAL PAPER
On the physical basis of succussion J-L Torres1* 1
lnstituto de Fı´sica y Matema´ticas, Universidad Michoacana, Morelia, Michoaca´n, Me´xico
It is argued that succussion drives the homeopathic tincture undergoing potentisation to a turbulent regime, where vortices continually form and disappear, ranging in size from the linear extent of the container to a minimum scale determined by viscosity and the rate of energy dissipation. Input mechanical energy cascades down this population of eddies and becomes available at the microscopic level to perform work (chemical, electrical, etc). A structure generated in the tincture would be rupted by vortices smaller than it, and this sets definite limits on the strength of succussion, so the power input leads to larger vortices than the structures one is trying to create and preserve through potentisation. An experimental procedure to test this proposal is suggested, based on Rayleigh scattering. Homeopathy (2002) 91, 221–224.
Keywords: succussion, turbulence, clathrate
Introduction Full understanding of potentisation and the origin and mechanism of the similitude principle will probably require new physical concepts, given the relative lack of success until now in the quest to understand these phenomena in microscopic terms. A plausible strategy is to look into novel results at the forefront of physical research for potentially useful tools in Homeopathy. However, well-known and even old results from physics are sometimes enough to understand homeopathic features that are described and often ‘explained’ in unnecessarily esoteric terms. In this note, I offer an explanation of succussion in terms of induced turbulence in the tincture undergoing potentisation, that allows transfer of the input mechanical energy all the way down to the molecular level, where it becomes available to perform chemical work. My approach is in the spirit of similar recent attempts to broaden the homeopathic perspective, based on concepts and methods from physics.1–3
Potentisation of homeopathic medicines involves gradual dilution accompanied by succussion at each step. I start from the premise that, whatever the changes brought about by potentisation (generation of stable clathrates or electric dipoles in water, etc.4,5), they occur at the molecular level and require input of energy, macroscopically supplied through mechanical agitation (succussion). A necessary condition to substantiate this assumption is that a mechanism exists to transfer energy from the macroscopic to the molecular scale. In fact, such a mechanism of energy transfer is available: in a turbulent regime, vortices of all sizes within a wide range continually form and disappear, and mechanical energy cascades from the largest all the way down to the microscopic level, where it can either be dissipated as heat due to viscosity, or become available to do work. The role of succussion is then to drive the homeopathic tincture to the turbulent state, by creating and maintaining the corresponding population of vortices.
Turbulence and Clathrates *Correspondence: Jose`-Leonel Torres, Instituto de Fı´sica y Matema´ticas, Universidad Michoacana, 58060 Morelia, Michoaca´n, Me`xico. E-mail: [email protected] Received 6 March 2002; revised 29 April 2002; accepted 20 May 2002
A turbulent state is one where the velocity at any point in a fluid varies with time both in magnitude and direction, in such a complicated way that it is best described as a random variable, thus allowing treat-
Physical basis of succussion J-L Torres
222
ment of this phenomenon in statistical terms. More pictorially, the fluid develops vortices of many sizes, with large eddies feeding smaller ones with solute or suspended material, energy and angular momentum, until a scale is reached where diffusion becomes dominant, beyond which heat is generated and chemical work may be performed at the molecular level (Figure 1). Persistence of this regime thus requires an external input of energy. More precisely,6 a pure number R LV=n (Reynolds number; ‘B’ denotes proportionality) can be formed with the linear size L of the container where motion takes place, the kinematic viscosity u of the fluid, and its average velocity difference V between two points separated a distance L; turbulence unfolds for large values of R, and fully developed turbulence formally occurs when R ! 1. In a steady state, the energy input at the largest vortices generates and sustains a fluctuating but statistically stable population of smaller ones, that feed in turn a population of yet smaller vortices, and so on; mechanical energy flows through such eddies all the way down to the smallest ones, with linear size, Z ðn3 =eÞ1=4 , where e is the rate of energy dissipation per unit mass and equals the rate of energy input in the steady state. For distances
Figure 1 Two-dimensional rendering of the vortex distribution in a turbulent regime. A fluctuating but statistically stable population of vortices is generated in a steady state, ranging in size from the linear dimension L of the container (in a confined environment) to the dissipation scale Z ðn3 =eÞ1=4 with u being the fluid kinematic viscosity and e the rate of energy dissipation per unit mass; below the scale Z diffusion becomes the dominant mechanism of energy transfer. Arrows show the direction of energy flow. Eddies at each level in the hierarchy are space-filling, and in a steady state, the same average energy flux traverses the system at all scales. Homeopathy
smaller than Z (often called Kolmogorov’s dissipation scale), dissipation effects become dominant over the mechanical ones produced by vortices, and energy diffuses towards the molecular level, generating heat in the process (due to viscosity) and becoming available to do work, subject to the limitations imposed by the laws of thermodynamics. As the energy input e increases, the smallest vortices decrease in size and energy diffusion starts closer to the molecular level; the appearance of stable material features in the tincture with size DoZ thus becomes feasible (ie, structures able to ‘ride’ the existing vortices), as larger ones would be perturbed and possibly torn by the smallest eddies. One would naively expect that after a few dilution steps the viscosity of the tincture would become identical with that of the unperturbed solvent. However, the presence of newly generated clathrates might, in principle, affect the viscosity of the solvent, so u must also be monitored during potentisation, as the limiting scale Z for microscopic structures depends both on energy input and viscosity. Although the detailed relationship between clathrates and viscosity may be complicated, one would expect the effect to grow with clathrate density. Clathrate density in the steady state will depend on a balance condition involving their generation and decay rates; these are in turn related to prominent features of the potential energy profile for clathrates (Figure 2). Succussion thus emerges as an operation whose intensity and duration must be carefully tuned to generate and preserve the appropriate density of microscopic structures in each case. Apart from tincture viscosity, that also needs to be monitored throughout potentisation according to our argument, the relevant parameter turns out to be the rate of energy input e, which is determined by the intensity of succussion. The practical relevance of this constraint can be ascertained with some numerical estimates. We rewrite the above expression for Z more precisely as follows: Z ¼ Aðn3 =eÞ1=4 , with A a numerical coefficient of order unity.7 The condition Z 4 D to preserve structures with size D in the tincture implies e4u3/D4. This dependence of e on the fourth power of D enhances the role of the latter in determining succussion strength. For example, if the relevant clathrates are a few nanometres in diameter (D’ 107 cm), there is practically no upper limit on the input power during succussion (using u’102 cm2/s for the kinematic viscosity of water8). However, if there are clathrates, say, a few micrometres in diameter, e must be lower than about 1 W/g tincture. The presence of stable clathrates several hundred micrometers in size has been suggested in polar solvents like water, through the coherent coupling of its molecules to the quantised electromagnetic field,5,9,10 in the presence of some solute or impurity with an electric dipole moment. For a clathrate 100 mm across, our bound eoV3/D4 implies that succussion
Physical basis of succussion J-L Torres
223
must supply less than 105 W/g tincture, so it must be extremely mild if the desired structures are to survive mechanical perturbation from the smallest vortices. One must add, however, that the existence of such large clathrates was proposed in the static limit, ie, neglecting their possible disruption from thermal effects at finite temperature, so the question of their stability remains open (cf. Figure 2 and observation (c) below).
Testing the hypothesis How can the proposal that the intensity of succussion determines the size of the largest structures in the tincture be tested in the laboratory? The obvious procedure is through spectroscopic analysis. Briefly, the experiment would consist of detecting clathrates up to a certain size that does not exceed the proposed limit D (u3/e)1/4 for a given power input from succussion, and repeating this test for several values of e. As we are only interested at this stage in the question of the presence of such clathrates, not in individual structural details, Rayleigh scattering should provide the necessary answers. The relevant formulas are those from Rayleigh’s argument for the blue colour of the sky.11 If there are N scatterers with comparable linear size D per unit volume in the tincture, and we irradiate the latter with plane waves of wavelength l D (in practice l\10D leads to a reasonably good approximation), and the radiation traverses a thickness x of the tincture, its intensity will decay as I(x)=I0eax, where I0 is the original intensity of the beam and a, the attenuation coefficient, is given by a = Ag2N/l4 with A a
numerical factor whose precise value is not relevant to our argument, and g the individual polarisability, ie, p=gE, where p is the polarisation induced in a scatterer by the electric field E from the radiation. The experimental procedure would be as follows. Start with a mechanised succussion process that allows precise measurement of the power input e. From this and the tincture viscosity u, calculate the limiting size D ’ (u3/e)1/4 for After reaching a steady-state succussion would be stopped, and the existing vortices allowed to disappear. The tincture is then irradiated with plane electromagnetic waves whose wavelengths fail in the interval lmin l lmax with lmin and lmax such that lmin D lmax, so the condition for Rayleigh scattering (l\10D) is fulfilled. The following measurements would be made:
The intensity I(l) of the beam in the forward
direction after traversing a fixed amount of tincture, for several values of l. If a significant density of structures with (maximum) size D is indeed present, a log–log plot of I(l) vs l will be well fitted by a straight line with slope 4 in the interval 10Dtl lmax, and it will deviate from this line in the interval lmin ltB10D, as Rayleigh scattering is replaced by Mie12 scattering (wavelength comparable with or smaller than linear size of individual scatterers). For a fixed wavelength l, vary the length x of the path traversed by the beam in the tincture, and measure radiation intensity in the forward direction, I(x)=I0eax, to estimate the number N of scatterers per unit volume, from a = Ag2N/l4.
An assumption in this procedure is that adequate numbers of clathrates are generated and survive long enough to be detected. For this to happen several conditions must be fulfilled, and each defines a variable that becomes relevant for the effectiveness of succussion, if experiments validate our proposal:
Figure 2 Potential energy profile for clathrate formation (schematic). According to Kramers’ theory of chemical reaction rate,l3 this corresponds to a transition from i to f ; with Ub being the energy barrier to be overcome in the process. The rate of clathrate generation is proportional to eUb/kT, where k is Boltzmann’s constant and T the absolute temperature; clathrate stability depends on the depth Ud of their ‘potential well’.
(a) Duration and intensity of succussion: To reach the steady state at each potentisation step, succussion must be of adequate duration and intensity. (b) Clathrate density: This factor appears explicitly in the decay constant of radiation intensity as a function of tincture thickness (a = A(g2N/l4)); it may also be a factor in the tincture’s viscosity u. In the steady state, clathrate density reflects a balance between generation and decay rates. The generation rate depends in turn on the ‘potential barrier’ to be overcome to create clathrates; the decay rate involves both the depth of their ‘potential well’ and the number already present13 (Figure 2). (c) Temperature: This factor affects tincture viscosity and clathrate generation and decay rates.13 If the tincture is at absolute temperature T, thermal Homeopathy
Physical basis of succussion J-L Torres
224
fluctuations have energies of order kT, with k being Boltzmann’s constant, so these rates depend on the interplay between kT and Ub and Ud, the potential energy barrier and depth, respectively (Figure 2). (d) Radiation frequency. If the frequency f of radiation used in the scattering experiment is such that Erad= hf (with h being Planck’s constant) becomes comparable with or larger than Ud in Figure 2, its contribution to the decay rate of clathrates will be significant. This imposes constraints on our choice of wavelength range for the scattering experiment.
Conclusion My argument implies that succussion must be designed subject to two antagonistic constraints: it must be strong enough that the power input allows generation of the relevant structures in a reasonable number of potentisation steps; on the other hand, it must no be so intense that, once created, such structures are disrupted by very small vortices. The availability of machines to perform succussion makes such fine tuning feasible. The obvious empirical way to test the proposal is to compare the effectiveness of tinctures that have undergone the same potentisation procedure, except for the strength of succussion. Unfortunately, a final verdict will have to wait for more precise measurements than are possible at present in homeopathic clinical trials or bioassays. Meanwhile, a judicious practice would be to carefully monitor succussion during each potentisation process, and include its strength on the label of the resulting medicament. Hahnemann14 insisted from the beginning on a systematic succussion procedure: ‘. . .[One] then slams the stoppered (capped) bottle 100 times against a hard, but elastic body (perhaps a leather-bound book) . . .’. His insight seems all the more remarkable in light of our discussion above on the role of the ensuing turbulence as a vehicle of energy transfer from the macroscopic to the molecular realm.
Homeopathy
Acknowledgements The author thanks Coordinacio´n de Investigacio´n Cientı´ fica at Universidad Michoacana in Mexico for support to carry out this work. He is also grateful to an anonymous referee whose comments led to improvements in some aspects of the paper.
References 1 Endler PC, Schulte J (eds). Ultra High Dilution: Physiology and Physics. Dordrecht: Kluwer Academic Publishers, 1994, especially Parts 2 and 3. 2 Torres J-L, Ruiz MG. Stochastic resonance and the homoeopathic effect. Br Hom J 1996; 85: 134–140. 3 Torres J-L. Homeopathic effect: a network perspective. Br Hom J 2002; 91: 89–94. 4 Anagnostatos GS. Small water clusters (clathrates) in the preparation process of Homoeopathy. In: Endler PC, Schulte J (Eds), Ultra High Dilution: Physiology and Physics. Dordrecht: Kluwer Academic Publishers, 1994, pp 121–128. 5 Del Giudice E. Is the ‘memory of water’ a physical impossibility?. In: Endler PC, Schulte J (Eds). Ultra High Dilution: Physiology and Physics. Dordrecht: Kluwer Academic Publishers, 1994, pp 117–119. 6 Frisch U. Turbulence. Cambridge: Cambridge University Press, 1996. 7 Frisch U, Turbulence. Cambridge: Cambridge University Press, 1996. p 91. 8 Frisch U, Turbulence. Cambridge: Cambridge University Press, 1996., p 2. 9 Del Giudice E, Preparata G, Vitiello G. Water as a free electric dipole laser. Phys Rev Lett 1988; 61: 1085–1088. 10 Preparata G. Quantum Field Theory of Superradiance. In: Cherubini R, Dal Piaz P, Minetti B (Eds). Problems of Fundamental Modern Physics. Singapore: World Scientific, 1990. 11 Jackson JD. Classical Electrodynamics. New York: John Wiley & Sons, 1974, pp 411–427. 12 Born M, Wolf E. Principles of Optics. Cambridge: Cambridge University Press, 1980, pp 633–656. 13 Ha¨nggi P, Talkner P, Borkovec M. Reaction-rate theory. Rev Mod Phys 1990; 62: 251–290. 14 Hahnemann S. Quoted in: Auerbach D. Mass, fluid and wave motion during the preparation of ultra high dilutions. In: Endler PC, Schulte J (Eds.). Ultra High Dilution: Physiology and Physics. Dordrecht: Kluwer Academic Publishers, 1994, p 129.