Homeopathy claims to treat illness with dilute solutions of molecules, very dilute solutions of molecules. A standard dilution is to take a solution of a plant extract and then dilute by a factor of 100, 30 times in succession. This dilutes by a factor of 100³⁰. This is seriously dilute. Consider 1cm³ of a 1% solution of a plant extract molecule in alcohol (ethanol), then as 1cm³ contains around 10²² molecules of alcohol, it will contain 10²⁰ molecules of the plant molecule. Diluting by a factor of 10⁶⁰ reduces the average number of molecules to 10^-40. Roughly speaking, if we could make 10⁴⁰ samples, only one would have a single molecule of the plant extract, the other 10⁴⁰-1 samples would have zero plant molecules in them.

As you might expect, we scientists are typically rather sceptical of the ability of a solution which has zero of the claimed active molecules in it, to cure diseases. Occasionally, attempts are made using scientific methods to show that homeopathy has a rational basis, for example Rao et al. used spectroscopy to study homeopathic solutions.

Spectroscopy can get very complex, but the idea is simple. Molecules interact with light and change it, and each molecule interacts with light in different ways, giving each molecule a unique spectroscopic fingerprint. So, in spectroscopy you shine light through the sample and look at the light that has gone through. This then tells you about the molecules in the sample.

Rao et al. did this, and claimed to see a difference between the alcohol solutions with the homeopathic ingredient, and without it, even at the extreme homeopathic dilutions.

However, as Kerr et al. point out in a comment on their paper, there is something fishy about Rao et al.‘s data for ‘alcohol’. The point is that it is not true that alcohol is alcohol is alcohol. It is just not possible to buy absolutely pure 100% alcohol, that is impossible to make. All you can do is buy pretty pure alcohol, very pure alcohol, which has less than 0.5% impurities, and even purer alcohol with even lower amounts of impurities. But you cannot buy alcohol without any impurities at all – it is not possible to remove all impurities.

For example, see the page on the SigmaAldrich website. The purest alcohol is guaranteed to have less than 0.2% water as an impurity, which is pretty good, but it is not totally pure. And for that you have to pay £46 a litre, which is more expensive than every very classy vodka, although of course it is lot purer and stronger (200 degrees proof) than any vodka.

So, if you dilute a plant extract in low grade, not very pure, alcohol, and compare that to a sample of a higher grade, purer, alcohol, of course you see differences. The homepathic remedy may contain zero molecules from the plant extract, but if it has even 0.5% impurities then that is 5*10¹⁹ molecules of impurities which show up in spectroscopy because it is such a sensitive technique.

I guess the moral is that a homeopathic remedy may contain zero molecules of whatever it is supposed to be made of but will contain many trillions of molecules of various impurities: maybe some salts, a few hydrocarbons, the odd protein molecule, ….