Homeopathy is a truly noxious bit of pseudoscience. To metaphorically refer to it as snake oil would be an affront to snake oil salesmen who, after all, at least provide a putatively edible substance in return for their extraordinary fees.
The fact that homeopathic remedies contain absolutely none of the substance that they are supposedly made of has been demonstrated to death. While I am not above doing so again, my purpose here is to consider the way in which homeopaths traditionally weasel out of this: the idea that water has memory. That is, an ordered structure persists in the arrangement of water molecules which had previously surrounded a molecule that has since been removed. The reason we typically talk about the active ingredient being absent instead of talking about these bits of memory is because the idea that these memories last long enough to do anything is fundamentally absurd once you get a step or two chem past 101. Water with memory just does not make sense.
The problem is that we actually have a pretty good idea how long water can ‘remember’ a substance which has been removed from it. One of the ways in which we know this is a cool phenomenon from fluorescence spectroscopy known as solvent relaxation. The way it works is this- a (simplified) fluorescent molecule is surrounded by solvent (in this case, water). For economy of keystrokes, I will call the fluorescent molecule Bob. The dipoles (fancy word, it just means something with two poles- like a north and south end of a magnet or a positive and negative charge on opposite ends of a molecule) of the water line up with the dipoles of Bob, positive to negative like you would expect.
When we shine a very particular light on Bob, Bob will fundamentally change. Bob will absorb energy, instantaneously rearranging Bob’s dipoles. Now Bob is in what is called an excited state. But now Bob’s water does not match Bob. This former configuration contains information about what Bob used to look like, but is no longer stabilized by the Bob’s old dipoles. The water around Bob is now unstable and rearranges itself around the new Bob (or around something else, or just arranges with other water). This rearrangement is solvent relaxation.
Solvent relaxation, it turns out, is pretty fast. Like tens of picoseconds fast, but let’s be generous and call it 100. So the average lifetime of a ‘memory’ in water is 100 ps or 1/10000000000 seconds. There is this handy little formula for relating lifetimes to concentration:
Γ is just 1/ lifetime, [M] is the amount of memories we have left, [M]0 is the amount that we started with and t is time. One more assumption- since these ‘memories’ depend on the relative arrangement of molecules, we should need (at absolute minimum) two water molecules for each memory. Assuming (generously) that 100% of the water in question starts out as memories, that gives us 27.7 moles (or 1.67 x1025 indivisible bits) of memory per liter of water.
So how long would it take until there is less memory left than…?
|The concentration of sodium in your body?||~ Half a nanosecond|
|The median lethal concentration of potassium cyanide?||1.28 nanoseconds|
|One memory in a liter of water?||5.81 nanoseconds|
|One memory in a volume equal to a human?||6.23 nanoseconds|
|One memory in a volume equal to the Great Lakes?||9.58 nanoseconds|
|One memory in a volume equal to the visible universe?||~25,000 nanoseconds|
|The time between individual frames on a television||~42,000,000 nanoseconds|
|The blink of an eye (literal).||~300,000,000 nanoseconds|
|Entire cycle of a single heartbeat during cardiac training exercise.||~450,000,000 nanoseconds|
Water forgets about homeopathy in less time than it takes you to remember it.