Physical research on ultra-molecular dilutions is one of the main areas of basic research in homeopathy. Until quite recently it was possible to argue that these extreme dilutions had no real effects, and that all the apparent clinical effects of homeopathy must be due to placebo or non-specific effects. However, the growing evidence of their effects from rigorous trials is making such a position increasingly untenable.

Pure water’s structure and properties can be changed. The key lies in the homeopathic succussion process which introduces three vectors: pressure, epitaxy, and nanobubbles. Each of these things are inherent in remedy preparation. All three of them can change structure. And it is structure, not composition, that – largely – controls properties.
[Epitaxy is the transmission of structural information from the surface of one material (usually a solid) to another (usually a liquid)].
[Nanobubbles are inclusions of gaseous O2, N2, CO2, and possibly the active ingredient that have a particle size distribution peak at 100-200 nanometer and exist stably for extremely long periods]

Some experiments using thermoluminescence have shown that dissolved substances modified the intensity of signals related to structure, even when they had been homeopathically diluted beyond Avogadro’s number (Rey; van Wijk, Bosman & van Wijk).

Rey L (2003). Thermoluminescence of ultra-high dilutions of lithium chloride and sodium chloride. Physica (A), 323:67–74 [Abstract]
Van Wijk R, Bosman S, van Wijk PA (2006). Thermoluminescence in ultra-high dilution research. Journal of Alternative and Complementary Medicine,12:437–443 [PubMed]

Modifications of physical parameters of homeopathic dilutions have also been observed by gas discharge visualization (Bell), and by mixing-flow microcalorimetry, electrical conductivity and potentiometry (Elia et al.).

Bell IR, Lewis DA 2nd, Brooks AJ, Lewis SE, Schwartz GE (2003). Gas discharge visualisation evaluation of ultramolecular doses of homeopathic medicines under blinded, controlled conditions. Journal of Alternative and Complementary Medicine, 9:25–38 [PubMed]
Elia V, Niccoli M (1999). Thermodynamics of extremely diluted aqueous solutions. Annals of the New York Academy of Sciences, 879:241–248 [PubMed]
Elia V, Niccoli M (2004). New physico-chemical properties of extremely diluted aqueous solutions. Journal of Thermal Analysis and Calorimetry, 75: 815–836 [Abstract]
Elia V, Napoli E, Niccoli M, Nonatelli L, Ramaglia A, Ventimiglia E (2004). New physico-chemical properties of extremely diluted aqueous solutions: A calorimetric and conductivity study at 25°C. Journal of Thermal Analysis and Calorimetry, 78: 331–342 [Abstract]
Elia V, Marchese M, Montanino M, Napoli E, Niccoli M, Nonatelli L, Ramaglia A (2005). Hydrohysteretic phenomena of “extremely diluted solutions” induced by mechanical treatments. A calorimetric and conductometric study at 25 °C. Journal of Solution Chemistry, 34:947–960[Abstract]
Elia V, Elia L, Cacace P, Napoli E, Niccoli M, Savarese F (2006). Extremely diluted solutions as multi-variable systems. A study of calorimetric and conductometric behaviour as function of the parameter time. Journal of Thermal Analysis and Calorimetry, 84:317–323 [Abstract]
Elia V, Napoli E, Niccoli M, Marchettini N, Tiezzi E(2008). New Physico-Chemical Properties of Extremely Dilute Solutions. A Conductivity Study at 25 °C in Relation to Ageing. Journal of Solution Chemistry, 37:85-96 [Abstract]
Elia V, Napoli E, Niccoli M (2008) On the stability of extremely diluted aqueous solutions at high ionic strength – A calorimetric study at 298 K.Journal of Thermal Analysis and Calorimetry, 92:643-648 [Abstract]
Belon P, Elia V, Elia L, Montanino M, Napoli E (2008) Conductometric and calorimetric studies of the serially diluted and agitated solutions. On the combined anomalous effect of time and volume parameters. Journal of Thermal Analysis and Calorimetry, 93, 459-469 [Abstract]
Elia V, Elia L, Marchettini N, Napoli E, Niccoli M (2008) Physico-chemical properties of aqueous extremely diluted solutions in relation to ageing. Journal of Thermal Analysis and Calorimetry, 93:1003-1011 [Abstract]
Elia V, Napoli E, Niccoli M (2010) Thermodynamic parameters for the binding process of the OH− ion with the dissipative structures. Calorimetric and conductometric titrations. Journal of Thermal Analysis and Calorimetry, Online First™, 11 April 2010 [Abstract]

A possible explanatory hypothesis for the mode of action of serially agitated high dilutions is the Information Medicine Hypothesis, which proposes that the actions of homeopathic medicines should be understood in terms of physically stored information rather than in chemical terms. According to this hypothesis water (and perhaps other polar solvents) under certain circumstances are capable of receiving and storing information about substances with which they have previously been in contact and of transmitting this information to presensitized biosystems (Schulte; Roy; Rao).

Schulte J (1999). Effects of potentization in aqueous solutions. British Homeopathic Journal, 88:155–160 [PubMed]
Roy R, Tiller WA, Bell IR, Hoover MR (2005). The structure of liquid water; novel insights from materials research; potential relevance to homeopathy. Materials Research Innovations, 9-4:577–608 [Abstract]
Rao ML, Roy R, Bell IR, Hoover R (2007).The defining role of structure (including epitaxy) in the plausibility of homeopathy. Homeopathy, 96:175-182 [PubMed]
Rao ML, Roy R, Bell I (2008). Characterization of the structure of ultra dilute sols with remarkable biological properties. Materials Letters, 62: 1487–1490 [PubMed]

In fact, there is strong evidence concerning many ways in which the mechanism of this ‘memory’ may come about (Chaplin). There are also mechanisms by which such solutions may possess effects on biological systems which substantially differ from plain water. The actual mechanism of action may differ between different ‘memory’ occurrences and may be the result of a combination of such phenomena.

Chaplin MF (2007). The Memory of Water: an overview. Homeopathy, 96:143-50 [PubMed]

One of the very best and most comprehensive and most valuable reviews of this topic is a website by Professor Martin Chaplin, of London’s Southbank University, which contains an enormous, complex, and well-organized review of the entire field of water structure and its unique properties.