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In homeopathic remedies the original substance is often diluted to a point where statistically there should be not a single molecule left of the original substance. The most common explanation by homeopaths, on how it still works although there is no substance left, is that water has a memory. That the "essence" or "imprint" of a molecule can stay in water and continue to have some effect even after the molecule itself is removed.

Is this at all possible from a physical point of view?

Can water molecules (in the liquid phase) form structures that are stable over long periods of time?

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    Short answer: no and no. For added points, ask a homeopath how remedies in sugar pill form keep the memory of the water that they presume had a memory of the original substance. – David Gerard Feb 24 '11 at 23:51
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    if that were true (if homeopathy works), you could cure any disease with tapwater, since it probably will have been in contact with every kind of material in it's existence – oɔɯǝɹ Mar 19 '11 at 23:35
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    At some of the dilutions used, there is more of the active ingredient in tap water than in the actual solution. If water had memory as claimed, then tap water would be more effective than most homeopathic solutions. – Johnny DropTables Mar 29 '11 at 13:49
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    There's less arsenic in a 30C arsenic solution than there is Oliver Cromwell's urine in a glass of London tap water. Do homeopath believers only drink distilled water? Oh, and whenever anyone mentions homeopaths, there must be a link to this: youtube.com/watch?v=HMGIbOGu8q0 – Skizz Mar 29 '11 at 17:18
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    If that were true, I'd wonder whether you could store data in water, homeopathically: "Infinite Capacity Fishbowl USB disk! (Fish not included)" – Piskvor May 7 '12 at 12:36
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No

Water forms strong intermolecular forces between its molecules. This is called hydrogen bonding and is a form of permanent dipole/permanent dipole interaction. Oxygen is more electronegative (its nucleus attracts a bigger share of the electron cloud of the covalent bond) than hydrogen. This causes water to form a permanent dipole where the oxygen has a small negative charge and the hydrogens have small positive charges.

hydrogen bondingFile:Hydrogen-bonding-in-water-2D.png

This causes electrostatic attraction between water molecules and they can form structures for a small amount of time. Other molecules in the water can affect these short lived structures and water does retain some 'memory' of these molecules.

This is how some proponents of homeopathy claim it works. This memory somehow has an opposite effect to the toxin or other chemical that was diluted, although there has not been any mechanism proposed for this.

However, the duration of the water memory has been scientifically tested and shown to be very short (less than one billionth of a second). This means that the memory has gone by the time the patient even takes the dose.

Even if water did have a long term memory, it would not prove homeopathy. There would also need to be evidence that this water memory had the medical effects that have been claimed.

The central argument of this answer is theoretical in nature. We do not allow answers based uniquely on common sense or pure logic. Answers which are wholly based on a theoretical model are generally downvoted and may be deleted. See FAQ: What are theoretical answers?

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    @user unknown - My answer clearly shows I have no belief in homoeopathy and why. Some believers of homoeopathy claim this 'water memory' to be how it works. I have shown with scientific evidence that this can't be the case. This is not a stawman argument because I haven't misrepresented any opinions. The 'wonderful formula' is a simplified diagram that I used to try to explain the underlying science and is not to 'fool the voters'. I don't want to assume everyone has A level Chemisty knowledge so I needed a way to explain hydrogen bonding simply. – david4dev Aug 10 '11 at 6:31
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    Homeopaths use the word 'memory' in a very different sense. They don't claim, that you can deduce which molecules have been in contact some time before, but they claim, that the water overtakes the effect, the liquid would have, if the molecules where still inside. I understand the work, cited by you, in that way, that there is a kind of imprint, a counterpart of the substance in the water. I see that you clearly don't believe in homeopathy, and why, and I appreciate it, but I don't vote on your habitus against homeopathy, but on my impression, whether your answer matches the question. – user unknown Aug 10 '11 at 18:46
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    It's trival to prove this answer wrong. Take a pot of water and put your hand into it and take it out. It will take a lot longer than one billionth of a second till the water reaches it's orginal state. Water is clearly able to retain some information for longer than one billionth of a second. More seriously, if the logic of the answer would be true there wouldn't be any hurricanes. Additional we aren't talking about pure H_2O. – Christian Jan 4 '13 at 18:22
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    @Christian if you have an answer to the question that is contrary to this response and evidenced backed, I would be very interested in seeing you post an answer yourself. – Kaz Dragon Jan 7 '13 at 13:58
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    Also, this answer needs to be updated with references. – Sklivvz Jan 15 '13 at 13:40
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Possible

This was demonstrated by Nobelist Luc Montagnier virologist (discoverer of HIV) in his study and his results were confirmed by his colleges and other scientists. This is well demonstrated and explained in the Water Memory documentary.

Basically in one of their recent experiment (2009) they've recorded EMF reading of water which was containing diluted DNA and exported into the audio file (wav), then sent from France to University of Sannio in Italy (famous for the quality of lab specialised in molecular biology) where tube of purified water was "listening" to the recording for about an hour and "memorizing" it.

The test was successful. The water it-self started to emit reconstituted DNA signals.

So according to Prof Montagnier, the highly diluted DNA in water has retained the memory of the original DNA traces and it returns them under the form of electromagnetic signals.

Currently the classic biology doesn't recognise such phenomenon, but this study can be the turning point for molecular biology, physics, chemistry, medicine and so on. In 2014 UNESCO hosted meeting to discuss this controversial 'memory of water' research.

Currently more independent studies are required to truly confirm Montagnier's findings independently.

References:

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    It must be mentioned that this paper was widely panned by scientists and isn't taken seriously by the scientific community. – Oddthinking Apr 30 '16 at 0:08
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    @kenorb there is no controversy about water memory - it's an absurd theory which has been thoroughly debunked. – Sklivvz Apr 30 '16 at 0:55
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    You didn't show that the UNESCO meeting resolved anything. You just used it (and the Nobel prize) as appeals to authority. – Oddthinking Apr 30 '16 at 0:58
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    @Sklivvz: There's no controversy about water memory in the scientific community. Homeopaths have leapt on this result to promote nonsense ideas, even though Montagnier distanced himself from such conclusions. – Oddthinking Apr 30 '16 at 0:59
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    "This just need to be repeated, as nobody claimed after that it didn't work." This study looked at the device used by Montagnier (developed by developed by Jacques Benveniste). The claimed abilities of the device were unable to be reproduced. – Oddthinking Apr 30 '16 at 1:06

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