Forces of Nature. Andrew Cohen

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СКАЧАТЬ architects, make cells that are initially circular in cross section. The hexagons appear because the bees’ body heat softens the wax until it reaches 45 degrees Celsius, a temperature at which wax begins to flow like a viscous fluid. The circular cells of molten wax then act in a similar way to soap bubbles, joining together at an angle of 120 degrees wherever they meet. If all the bubbles or wax cells are identical in size and spacing, the circular cells spontaneously reform into a sheet of hexagons. Karihaloo and his team demonstrated this by using smoke to interrupt honeybees in the process of making a hive, revealing that the most recently built cells were circular, whilst the older ones had developed into hexagons. This transition from cylindrical to hexagonal structure appears to be what Darwin observed, but the explanation for the transition is different.

      Natural selection is still the basic explanation for the hexagons, but the bees don’t have to go to the trouble of building the most efficient packing shape because physics will do that for them, given a nice sheet of circular cells of similar size and spacing and some body heat. To me, this is even more elegant and efficient; the bees allow physics to finish their work! As the authors of the study write: ‘We cannot … ignore, nor can we not marvel at the role played by the bees in this process by heating, kneading and thinning the wax exactly where needed.’ Is this the solution to a problem that has fired the imagination of so many for so long? The origin of the hexagons continues to be debated, and Karihaloo et al. will probably not be the last word in the literature.

      This is as it should be, and illustrative of something that is often missed in the presentation of science. Scientific results are always preliminary. No good scientist will believe that they have offered the last word on a given subject. A result is published if the authors and a group of their peers consider it to be a valuable contribution to the field. Crucially, this does not mean that it’s correct; it means that it’s not obviously wrong. Rather than closing down a question, publication is intended to be a red flag to bullish colleagues. As one reads in Kepler’s partial, yet evident, delight in not discovering a satisfactory explanation for the structure of a snowflake, there is joy in hearing what you think, my most ingenious colleague.

Knocking on the doors of chemistry

      In the final lines of The Six-Cornered Snowflake, Kepler writes with lovely regret that he is ‘knocking on the doors of chemistry’; the implication being that those doors would be opened by future generations. He asserts, correctly, that the structure of the snowflakes must be due at least in part to some underlying structure or shape, but given that atomic theory didn’t move into the realm of experimentally testable science until the early nineteenth century, and the structure of atoms themselves was a twentieth-century discovery, Kepler had no way of unlocking the doors. We now know that the building blocks of snowflakes are water molecules, and water molecules are capable of extremely complex behaviour when they get together. That may be a surprising statement if we think of water as the colourless, odourless liquid in a glass. Perhaps it shouldn’t be so surprising if we think of water molecules as the objects that come together spontaneously to produce the romantic flourishes of form and exquisite diversity of snowflakes.

      Single water molecules aren’t particularly complicated. They are molecules of hydrogen and oxygen, bonded together. Oxygen was first isolated in 1774 by Joseph Priestley, the son of a Yorkshire woollen cloth maker, and Henry Cavendish first identified hydrogen in 1766. The Nobel Prize in Physics in 1926 was awarded to Jean Baptiste Perrin for the confirmation of the physical reality of molecules, just about within living memory, which demonstrates how difficult it is to study the microscopic world and how quickly cutting-edge science can become common knowledge.

      A water molecule consists of two hydrogen atoms bonded to a single oxygen atom: H₂O (see illustration here). The water molecule isn’t linear – the hydrogen atoms are displaced at an angle of 104.5 degrees. The reason for this is the presence of two extra pairs of electrons that sit on the opposite side of the oxygen atom. To see why that is, let’s have a very brief tutorial on atomic physics and quantum mechanics.

      Atoms are made up of three constituents, as far as chemists are concerned (we’ll dig more deeply into this later on); they consist of a small, dense, atomic nucleus made up of protons and neutrons, with electrons orbiting a long way away. If the nucleus were the size of a tennis ball, the outer electron orbits would be several kilometres across. Hydrogen is the simplest element; its nucleus consists of a single proton. Next is helium, which contains two protons and two neutrons. Oxygen has eight protons and eight neutrons. The nucleus is surrounded by electrons, which are held in place by one of the four fundamental forces of Nature: electromagnetism. Electrons are negatively charged and protons are positively charged, and the negative electric charge of the electron is precisely equal in magnitude but opposite in sign to the positive electric charge of the proton. Nobody knows why these charges are precisely equal in magnitude; it’s one of the great mysteries of fundamental physics. The atoms of each chemical element are electrically neutral, which means that the number of protons in the nucleus is equal to the number of electrons that surround it. Hydrogen atoms have a single electron, therefore, whilst oxygen atoms have eight electrons.

      The structure of a water molecule, showing oxygen’s eight electrons, two of which are shared with the hydrogen atoms.

      The hexagonal crystalline structure of Ice 1_h. Water molecules are attached together by hydrogen bonds, with oxygen atoms from one water molecule lining up with hydrogen atoms from another.

      Now we need a little sprinkle of quantum theory. You can picture the electric charge of the atomic nucleus as creating a kind of box within which the electrons are trapped. Electrons, along with all of the fundamental building blocks of the Universe, obey the laws of quantum theory, which describe how they move. It turns out that the basic rules of quantum theory are counterintuitive and fly in the face of common sense. But that is okay because there is no reason at all to expect the laws that govern the Universe to be in accord with ‘common sense’. The most fundamental rule governing the behaviour of subatomic particles is that they don’t like to stand still. Unfettered, they are very likely to wander off, and the more we try to pin them down, the more they are inclined to wander. The presence of the nucleus tames the anarchic electrons somewhat, by confining them to the ‘nuclear box’.

      Another rule governing the behaviour of electrons is that they don’t much like each other’s company. This is known as the Pauli exclusion principle, also a consequence of the laws of quantum theory. Electrons will arrange themselves around the nucleus such that they stay away from each other, as best they can. There is a caveat, though, which is important for understanding the structure of atoms. Electrons of opposite spin are allowed to get close together (or ‘pair up’). Of course they cannot get too close because they have the same electric charge and ‘like-charges repel’. Spin is a property of subatomic particles that is easy to name but hard to picture. You could think of electrons as little spinning tops, if you like, but that’s a bad analogy on many levels, so you probably shouldn’t. Having said that, spin is a measure of how much an electron is spinning – it is just that the notion of a spinning point is not something we can easily imagine. For particles such as electrons, which are known as ‘spin ½’ particles or fermions, spin can have only two values; these are known as spin-up and spin-down. Spin is a direct, if rather subtle, consequence of the merger between Einstein’s Theory of Special Relativity and quantum theory, achieved by physicist Paul Dirac in his СКАЧАТЬ