Anthropic Water

Water, plain and simple water, is an intriguing substance. Its chemical formula is H₂O. A water molecule is composed of one oxygen atom and two hydrogen atoms. A simple chemical structure indeed. But the spatial structure of water is not as simple as we might imagine. The most ‘straightforward’ structure is the most symmetrical one, with the two hydrogen atoms opposite of each other and the oxygen atom in the middle, the three atoms nicely on a straight line. Like the three atoms in carbon dioxide, CO₂, for example. No, in water the three atoms form a triangle. The angle at the vertex where the oxygen sits is 104.5 degrees. And this is of vital importance. Literally.

It makes water a polar molecule, with the negative charge (the electrons) closer to the oxygen than to the hydrogen. Its bent structure and the charge distribution determine the properties of water as a solvent. They also make water a liquid at standard temperature and pressure, which is quite exceptional for such a light molecule. (Even H₂S, which has a similar structure but a smaller dipole moment, is a gas, even if it is heavier than water.) Without water and its properties, largely determined by its bent shape, there would be no life.

The structure of water can be understood by describing its electron orbits as determined by quantum mechanics. The radii of these orbits (the distance from the relatively heavy and immobile oxygen and hydrogen nuclei) and the velocity of the electrons are such that their product is of the order of one (in so called ‘natural units’). Through the ‘uncertainty relations’ we know that in this case we enter the ‘quantum domain’ and quantum mechanics is the theory we need to describe the physical reality.

It would go too far to call quantum mechanics a straightforward theory. It is quite an amazing theory, but once you have accepted it, its use is straightforward. This does not mean it is easy: water consists of three nuclei and ten electrons and even if you simplify the nuclei to pointlike particles it is impossible, for now and always, to exactly solve the quantum mechanical equation (the Schrödinger equation) for this many body system. It is, however, possible to make acceptable approximations and to resort to the use of computers and the result is that the structure of water, vital for life, follows compellingly from quantum mechanics, a perhaps counter-intuitive but profound construct of the human mind and an accurate description of the physical world.

All this was known when I went to university in 1967 and it was exciting, very exciting, to ‘rediscover’ this during the initial years of university training. There was more to be discovered and personally I was (and I am) attracted by the challenges of elementary particle physics. In recent years a connection between particle physics and another field really catching the imagination, cosmology, has been made. In the beginning there was particle physics... Our understanding of the beginning of the universe, of the very initial phases of the Big Bang, is hampered by our lack of understanding of gravity. It must have played an important role at the quantum level, initially, when the energies involved were very high. A lack of understanding of quantum-gravity does not mean a lack of candidate theories for including gravity in the description of the elementary world. Based on the principles of the theories of relativity and quantum mechanics (a ‘minimal’ condition for candidate theories) and with the notion of ‘elementary particle’ replaced by ‘elementary string’ in fact a practically infinite number of theories can be chosen from. Even if we assume, perhaps somewhat naively, that the right ‘theory of everything’ has been found in principle, no one is capable of singling it out from the huge number of possible theories.

I will now tread on slippery ground. Cosmologists have invoked the ‘anthropic principle’ to explain, or rather to be absolved of explaining why the universe and the laws that govern it are as they are. According to the ‘anthropic principle’, the universe we observe and the laws we find must be consistent with ‘us’, with conscious life – if not, we would not be there to make observations and find explanations in the first place. So only universes compatible with conscious life (is this well-defined?) can ‘exist’. The ‘anthropic principle’ may be interesting philosophically, but, as far as I can see, it is not useful to help us find the right ‘theory of everything’ amidst the huge number of possible theories. Neither is it able to explain the structure of water, but quantum mechanics is, and was so long before anyone felt the need for an anthropic principle!

Jos Engelen

August 17, 2012